    -- (c) The University of Glasgow 2006
    -- (c) The GRASP/AQUA Project, Glasgow University, 1998
    --
    -- Type - public interface

    {-# LANGUAGE FlexibleContexts, PatternSynonyms, ViewPatterns, MultiWayIf, RankNTypes #-}
    {-# OPTIONS_GHC -fno-warn-orphans #-}

    -- | Main functions for manipulating types and type-related things
    module GHC.Core.Type (
            -- Note some of this is just re-exports from TyCon..

            -- * Main data types representing Types
            -- $type_classification

            -- $representation_types
            Type, ForAllTyFlag(..), FunTyFlag(..),
            Specificity(..),
            KindOrType, PredType, ThetaType, FRRType,
            Var, TyVar, isTyVar, TyCoVar, PiTyBinder, ForAllTyBinder, TyVarBinder,
            Mult, Scaled,
            KnotTied, RuntimeRepType,

            -- ** Constructing and deconstructing types
            mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, repGetTyVar_maybe,
            getCastedTyVar_maybe, tyVarKind, varType,

            mkAppTy, mkAppTys, splitAppTy, splitAppTys, splitAppTysNoView,
            splitAppTy_maybe, splitAppTyNoView_maybe, tcSplitAppTyNoView_maybe,

            mkFunTy, mkVisFunTy,
            mkVisFunTyMany, mkVisFunTysMany,
            mkScaledFunTys,
            mkInvisFunTy, mkInvisFunTys,
            tcMkVisFunTy, tcMkScaledFunTys, tcMkInvisFunTy,
            splitFunTy, splitFunTy_maybe,
            splitFunTys, funResultTy, funArgTy,
            funTyConAppTy_maybe, funTyFlagTyCon,
            tyConAppFunTy_maybe, tyConAppFunCo_maybe,
            mkFunctionType, mkScaledFunctionTys, chooseFunTyFlag,

            mkTyConApp, mkTyConTy,
            tyConAppTyCon_maybe, tyConAppTyConPicky_maybe,
            tyConAppArgs_maybe, tyConAppTyCon, tyConAppArgs,

            splitTyConApp_maybe, splitTyConAppNoView_maybe, splitTyConApp,
            tcSplitTyConApp, tcSplitTyConApp_maybe,

            mkForAllTy, mkForAllTys, mkInvisForAllTys, mkTyCoInvForAllTys,
            mkSpecForAllTy, mkSpecForAllTys,
            mkVisForAllTys, mkTyCoForAllTy, mkTyCoForAllTys, mkTyCoInvForAllTy,
            mkInfForAllTy, mkInfForAllTys,
            splitForAllTyCoVars, splitForAllTyVars,
            splitForAllReqTyBinders, splitForAllInvisTyBinders,
            splitForAllForAllTyBinders, splitForAllForAllTyBinder_maybe,
            splitForAllTyCoVar_maybe, splitForAllTyCoVar,
            splitForAllTyVar_maybe, splitForAllCoVar_maybe,
            splitPiTy_maybe, splitPiTy, splitPiTys,
            getRuntimeArgTys,
            mkTyConBindersPreferAnon,
            mkPiTy, mkPiTys,
            piResultTy, piResultTys,
            applyTysX, dropForAlls,
            mkFamilyTyConApp,
            buildSynTyCon,

            mkNumLitTy, isNumLitTy,
            mkStrLitTy, isStrLitTy,
            mkCharLitTy, isCharLitTy,
            isLitTy,

            isPredTy,

            getRuntimeRep, splitRuntimeRep_maybe, kindRep_maybe, kindRep,
            getLevity, levityType_maybe,

            mkCastTy, mkCoercionTy, splitCastTy_maybe,

            ErrorMsgType,
            userTypeError_maybe, deepUserTypeError_maybe, pprUserTypeErrorTy,

            coAxNthLHS,
            stripCoercionTy,

            splitInvisPiTys, splitInvisPiTysN,
            invisibleTyBndrCount,
            filterOutInvisibleTypes, filterOutInferredTypes,
            partitionInvisibleTypes, partitionInvisibles,
            tyConForAllTyFlags, appTyForAllTyFlags,

            -- ** Analyzing types
            TyCoMapper(..), mapTyCo, mapTyCoX,
            TyCoFolder(..), foldTyCo, noView,

            -- (Newtypes)
            newTyConInstRhs,

            -- ** Binders
            mkForAllTyBinder, mkForAllTyBinders,
            mkTyVarBinder, mkTyVarBinders,
            tyVarSpecToBinders,
            isAnonPiTyBinder,
            binderVar, binderVars, binderType, binderFlag, binderFlags,
            piTyBinderType, namedPiTyBinder_maybe,
            anonPiTyBinderType_maybe,
            isVisibleForAllTyFlag, isInvisibleForAllTyFlag, isVisiblePiTyBinder,
            isInvisiblePiTyBinder, isNamedPiTyBinder,
            tyConBindersPiTyBinders,

            -- ** Predicates on types
            isTyVarTy, isFunTy, isCoercionTy,
            isCoercionTy_maybe, isForAllTy,
            isForAllTy_ty, isForAllTy_co,
            isForAllTy_invis_ty,
            isPiTy, isTauTy, isFamFreeTy,
            isCoVarType, isAtomicTy,

            isValidJoinPointType,
            tyConAppNeedsKindSig,

            -- * Space-saving construction
            mkTYPEapp, mkTYPEapp_maybe,
            mkCONSTRAINTapp, mkCONSTRAINTapp_maybe,
            mkBoxedRepApp_maybe, mkTupleRepApp_maybe,
            typeOrConstraintKind,

            -- *** Levity and boxity
            sORTKind_maybe, typeTypeOrConstraint,
            typeLevity, typeLevity_maybe, tyConIsTYPEorCONSTRAINT,
            isLiftedTypeKind, isUnliftedTypeKind, pickyIsLiftedTypeKind,
            isLiftedRuntimeRep, isUnliftedRuntimeRep, runtimeRepLevity_maybe,
            isBoxedRuntimeRep,
            isLiftedLevity, isUnliftedLevity,
            isUnliftedType, isBoxedType, isUnboxedTupleType, isUnboxedSumType,
            kindBoxedRepLevity_maybe,
            mightBeLiftedType, mightBeUnliftedType,
            definitelyLiftedType, definitelyUnliftedType,
            isAlgType, isDataFamilyAppType,
            isPrimitiveType, isStrictType, isTerminatingType,
            isLevityTy, isLevityVar,
            isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy,
            dropRuntimeRepArgs,

            -- * Multiplicity

            isMultiplicityTy, isMultiplicityVar,
            unrestricted, linear, tymult,
            mkScaled, irrelevantMult, scaledSet,
            pattern OneTy, pattern ManyTy,
            isOneTy, isManyTy,
            isLinearType,

            -- * Main data types representing Kinds
            Kind,

            -- ** Finding the kind of a type
            typeKind, typeHasFixedRuntimeRep,
            tcIsLiftedTypeKind,
            isConstraintKind, isConstraintLikeKind, returnsConstraintKind,
            tcIsBoxedTypeKind, isTypeLikeKind,

            -- ** Common Kind
            liftedTypeKind, unliftedTypeKind,

            -- * Type free variables
            tyCoFVsOfType, tyCoFVsBndr, tyCoFVsVarBndr, tyCoFVsVarBndrs,
            tyCoVarsOfType, tyCoVarsOfTypes,
            tyCoVarsOfTypeDSet,
            coVarsOfType,
            coVarsOfTypes,

            anyFreeVarsOfType, anyFreeVarsOfTypes,
            noFreeVarsOfType,
            expandTypeSynonyms,
            typeSize, occCheckExpand,

            -- ** Closing over kinds
            closeOverKindsDSet, closeOverKindsList,
            closeOverKinds,

            -- * Well-scoped lists of variables
            scopedSort, tyCoVarsOfTypeWellScoped,
            tyCoVarsOfTypesWellScoped,

            -- * Forcing evaluation of types
            seqType, seqTypes,

            -- * Other views onto Types
            coreView, coreFullView, rewriterView,

            tyConsOfType,

            -- * Main type substitution data types
            TvSubstEnv,     -- Representation widely visible
            IdSubstEnv,
            Subst(..),    -- Representation visible to a few friends

            -- ** Manipulating type substitutions
            emptyTvSubstEnv, emptySubst, mkEmptySubst,

            mkTCvSubst, zipTvSubst, mkTvSubstPrs,
            zipTCvSubst,
            notElemSubst,
            getTvSubstEnv,
            zapSubst, getSubstInScope, setInScope, getSubstRangeTyCoFVs,
            extendSubstInScope, extendSubstInScopeList, extendSubstInScopeSet,
            extendTCvSubst, extendCvSubst,
            extendTvSubst, extendTvSubstList, extendTvSubstAndInScope,
            extendTCvSubstList,
            extendTvSubstWithClone,
            extendTCvSubstWithClone,
            isInScope, composeTCvSubst, zipTyEnv, zipCoEnv,
            isEmptySubst, unionSubst, isEmptyTCvSubst,

            -- ** Performing substitution on types and kinds
            substTy, substTys, substScaledTy, substScaledTys, substTyWith, substTysWith, substTheta,
            substTyAddInScope,
            substTyUnchecked, substTysUnchecked, substScaledTyUnchecked, substScaledTysUnchecked,
            substThetaUnchecked, substTyWithUnchecked,
            substCo, substCoUnchecked, substCoWithUnchecked,
            substTyVarBndr, substTyVarBndrs, substTyVar, substTyVars,
            substVarBndr, substVarBndrs,
            substTyCoBndr, substTyVarToTyVar,
            cloneTyVarBndr, cloneTyVarBndrs, lookupTyVar,

            -- * Tidying type related things up for printing
            tidyType,      tidyTypes,
            tidyOpenType,  tidyOpenTypes,
            tidyVarBndr, tidyVarBndrs, tidyFreeTyCoVars,
            tidyOpenTyCoVar, tidyOpenTyCoVars,
            tidyTyCoVarOcc,
            tidyTopType,
            tidyForAllTyBinder, tidyForAllTyBinders,

            -- * Kinds
            isTYPEorCONSTRAINT,
            isConcreteType, isFixedRuntimeRepKind,
        ) where

    import GHC.Prelude

    import GHC.Types.Basic

    -- We import the representation and primitive functions from GHC.Core.TyCo.Rep.
    -- Many things are reexported, but not the representation!

    import GHC.Core.TyCo.Rep
    import GHC.Core.TyCo.Subst
    import GHC.Core.TyCo.Tidy
    import GHC.Core.TyCo.FVs

    -- friends:
    import GHC.Types.Var
    import GHC.Types.Var.Env
    import GHC.Types.Var.Set
    import GHC.Types.Unique.Set

    import GHC.Core.TyCon
    import GHC.Builtin.Types.Prim

    import {-# SOURCE #-} GHC.Builtin.Types
       ( charTy, naturalTy
       , typeSymbolKind, liftedTypeKind, unliftedTypeKind
       , constraintKind, zeroBitTypeKind
       , manyDataConTy, oneDataConTy
       , liftedRepTy, unliftedRepTy, zeroBitRepTy )

    import GHC.Types.Name( Name )
    import GHC.Builtin.Names
    import GHC.Core.Coercion.Axiom

    import {-# SOURCE #-} GHC.Core.Coercion
       ( mkNomReflCo, mkGReflCo, mkReflCo
       , mkTyConAppCo, mkAppCo
       , mkForAllCo, mkFunCo2, mkAxiomInstCo, mkUnivCo
       , mkSymCo, mkTransCo, mkSelCo, mkLRCo, mkInstCo
       , mkKindCo, mkSubCo, mkFunCo, funRole
       , decomposePiCos, coercionKind
       , coercionRKind, coercionType
       , isReflexiveCo, seqCo
       , topNormaliseNewType_maybe
       )
    import {-# SOURCE #-} GHC.Tc.Utils.TcType ( isConcreteTyVar )

    -- others
    import GHC.Utils.Misc
    import GHC.Utils.FV
    import GHC.Utils.Outputable
    import GHC.Utils.Panic
    import GHC.Data.FastString

    import GHC.Data.Maybe   ( orElse, isJust, firstJust )

    -- $type_classification
    -- #type_classification#
    --
    -- Types are any, but at least one, of:
    --
    -- [Boxed]              Iff its representation is a pointer to an object on the
    --                      GC'd heap. Operationally, heap objects can be entered as
    --                      a means of evaluation.
    --
    -- [Lifted]             Iff it has bottom as an element: An instance of a
    --                      lifted type might diverge when evaluated.
    --                      GHC Haskell's unboxed types are unlifted.
    --                      An unboxed, but lifted type is not very useful.
    --                      (Example: A byte-represented type, where evaluating 0xff
    --                      computes the 12345678th collatz number modulo 0xff.)
    --                      Only lifted types may be unified with a type variable.
    --
    -- [Algebraic]          Iff it is a type with one or more constructors, whether
    --                      declared with @data@ or @newtype@.
    --                      An algebraic type is one that can be deconstructed
    --                      with a case expression. There are algebraic types that
    --                      are not lifted types, like unlifted data types or
    --                      unboxed tuples.
    --
    -- [Data]               Iff it is a type declared with @data@, or a boxed tuple.
    --                      There are also /unlifted/ data types.
    --
    -- [Primitive]          Iff it is a built-in type that can't be expressed in Haskell.
    --
    -- [Unlifted]           Anything that isn't lifted is considered unlifted.
    --
    -- Currently, all primitive types are unlifted, but that's not necessarily
    -- the case: for example, @Int@ could be primitive.
    --
    -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
    -- but unlifted (such as @ByteArray#@).  The only primitive types that we
    -- classify as algebraic are the unboxed tuples.
    --
    -- Some examples of type classifications that may make this a bit clearer are:
    --
    -- @
    -- Type          primitive       boxed           lifted          algebraic
    -- -----------------------------------------------------------------------------
    -- Int#          Yes             No              No              No
    -- ByteArray#    Yes             Yes             No              No
    -- (\# a, b \#)  Yes             No              No              Yes
    -- (\# a | b \#) Yes             No              No              Yes
    -- (  a, b  )    No              Yes             Yes             Yes
    -- [a]           No              Yes             Yes             Yes
    -- @

    -- $representation_types
    -- A /source type/ is a type that is a separate type as far as the type checker is
    -- concerned, but which has a more low-level representation as far as Core-to-Core
    -- passes and the rest of the back end is concerned.
    --
    -- You don't normally have to worry about this, as the utility functions in
    -- this module will automatically convert a source into a representation type
    -- if they are spotted, to the best of its abilities. If you don't want this
    -- to happen, use the equivalent functions from the "TcType" module.

    {-
    ************************************************************************
    *                                                                      *
                    Type representation
    *                                                                      *
    ************************************************************************
    -}

    rewriterView :: Type -> Maybe Type
    -- Unwrap a type synonym only when either:
    --   The type synonym is forgetful, or
    --   the type synonym mentions a type family in its expansion
    -- See Note [Rewriting synonyms]
    {-# INLINE rewriterView #-}
    rewriterView :: Type -> Maybe Type
    rewriterView (TyConApp TyCon
    tc [Type]
    tys)
      | TyCon -> Bool
    isTypeSynonymTyCon TyCon
    tc
      , TyCon -> Bool
    isForgetfulSynTyCon TyCon
    tc Bool -> Bool -> Bool
    || Bool -> Bool
    not (TyCon -> Bool
    isFamFreeTyCon TyCon
    tc)
      = TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
    rewriterView Type
    _other
      = Maybe Type
    forall a. Maybe a
    Nothing

    coreView :: Type -> Maybe Type
    -- ^ This function strips off the /top layer only/ of a type synonym
    -- application (if any) its underlying representation type.
    -- Returns 'Nothing' if there is nothing to look through.
    --
    -- This function does not look through type family applications.
    --
    -- By being non-recursive and inlined, this case analysis gets efficiently
    -- joined onto the case analysis that the caller is already doing
    coreView :: Type -> Maybe Type
    coreView (TyConApp TyCon
    tc [Type]
    tys) = TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
    coreView Type
    _                 = Maybe Type
    forall a. Maybe a
    Nothing
    -- See Note [Inlining coreView].
    {-# INLINE coreView #-}

    coreFullView, core_full_view :: Type -> Type
    -- ^ Iterates 'coreView' until there is no more to synonym to expand.
    -- NB: coreFullView is non-recursive and can be inlined;
    --     core_full_view is the recursive one
    -- See Note [Inlining coreView].
    coreFullView :: Type -> Type
    coreFullView ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    _)
      | TyCon -> Bool
    isTypeSynonymTyCon TyCon
    tc = Type -> Type
    core_full_view Type
    ty
    coreFullView Type
    ty = Type
    ty
    {-# INLINE coreFullView #-}

    core_full_view :: Type -> Type
    core_full_view Type
    ty
      | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type
    core_full_view Type
    ty'
      | Bool
    otherwise               = Type
    ty

    -----------------------------------------------
    -- | @expandSynTyConApp_maybe tc tys@ expands the RHS of type synonym @tc@
    -- instantiated at arguments @tys@, or returns 'Nothing' if @tc@ is not a
    -- synonym.
    expandSynTyConApp_maybe :: TyCon -> [Type] -> Maybe Type
    {-# INLINE expandSynTyConApp_maybe #-}
    -- This INLINE will inline the call to expandSynTyConApp_maybe in coreView,
    -- which will eliminate the allocation Just/Nothing in the result
    -- Don't be tempted to make `expand_syn` (which is NOINLINE) return the
    -- Just/Nothing, else you'll increase allocation
    expandSynTyConApp_maybe :: TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    arg_tys
      | Just ([TyVar]
    tvs, Type
    rhs) <- TyCon -> Maybe ([TyVar], Type)
    synTyConDefn_maybe TyCon
    tc
      , [Type]
    arg_tys [Type] -> Arity -> Bool
    `saturates` TyCon -> Arity
    tyConArity TyCon
    tc
      = Type -> Maybe Type
    forall a. a -> Maybe a
    Just (Type -> Maybe Type) -> Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $! ([TyVar] -> Type -> [Type] -> Type
    expand_syn [TyVar]
    tvs Type
    rhs [Type]
    arg_tys)
        -- Why strict application? Because every client of this function will evaluat
        -- that (expand_syn ...) thunk, so it's more efficient not to build a thunk.
        -- Mind you, this function is always INLINEd, so the client context is probably
        -- enough to avoid thunk construction and so the $! is just belt-and-braces.
      | Bool
    otherwise
      = Maybe Type
    forall a. Maybe a
    Nothing

    saturates :: [Type] -> Arity -> Bool
    saturates :: [Type] -> Arity -> Bool
    saturates [Type]
    _       Arity
    0 = Bool
    True
    saturates []      Arity
    _ = Bool
    False
    saturates (Type
    _:[Type]
    tys) Arity
    n = Bool -> Bool -> Bool
    forall a. HasCallStack => Bool -> a -> a
    assert( Arity
    n Arity -> Arity -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Arity
    0 ) (Bool -> Bool) -> Bool -> Bool
    forall a b. (a -> b) -> a -> b
    $ [Type] -> Arity -> Bool
    saturates [Type]
    tys (Arity
    nArity -> Arity -> Arity
    forall a. Num a => a -> a -> a
    -Arity
    1)
                           -- Arities are always positive; the assertion just checks
                           -- that, to avoid an infinite loop in the bad case

    -- | A helper for 'expandSynTyConApp_maybe' to avoid inlining this cold path
    -- into call-sites.
    --
    -- Precondition: the call is saturated or over-saturated;
    --               i.e. length tvs <= length arg_tys
    expand_syn :: [TyVar]  -- ^ the variables bound by the synonym
               -> Type     -- ^ the RHS of the synonym
               -> [Type]   -- ^ the type arguments the synonym is instantiated at.
               -> Type
    {-# NOINLINE expand_syn #-} -- We never want to inline this cold-path.

    expand_syn :: [TyVar] -> Type -> [Type] -> Type
    expand_syn [TyVar]
    tvs Type
    rhs [Type]
    arg_tys
      -- No substitution necessary if either tvs or tys is empty
      -- This is both more efficient, and steers clear of an infinite
      -- loop; see Note [Care using synonyms to compress types]
      | [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    arg_tys  = Bool -> Type -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([TyVar] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [TyVar]
    tvs) Type
    rhs
      | [TyVar] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [TyVar]
    tvs      = Type -> [Type] -> Type
    mkAppTys Type
    rhs [Type]
    arg_tys
      | Bool
    otherwise     = Subst -> [TyVar] -> [Type] -> Type
    go Subst
    empty_subst [TyVar]
    tvs [Type]
    arg_tys
      where
        empty_subst :: Subst
    empty_subst = InScopeSet -> Subst
    mkEmptySubst InScopeSet
    in_scope
        in_scope :: InScopeSet
    in_scope = VarSet -> InScopeSet
    mkInScopeSet (VarSet -> InScopeSet) -> VarSet -> InScopeSet
    forall a b. (a -> b) -> a -> b
    $ [Type] -> VarSet
    shallowTyCoVarsOfTypes ([Type] -> VarSet) -> [Type] -> VarSet
    forall a b. (a -> b) -> a -> b
    $ [Type]
    arg_tys
          -- The free vars of 'rhs' should all be bound by 'tenv',
          -- so we only need the free vars of tys
          -- See also Note [The substitution invariant] in GHC.Core.TyCo.Subst.

        go :: Subst -> [TyVar] -> [Type] -> Type
    go Subst
    subst [] [Type]
    tys
          | [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys  = Type
    rhs'  -- Exactly Saturated
          | Bool
    otherwise = Type -> [Type] -> Type
    mkAppTys Type
    rhs' [Type]
    tys
              -- Its important to use mkAppTys, rather than (foldl AppTy),
              -- because the function part might well return a
              -- partially-applied type constructor; indeed, usually will!
          where
            rhs' :: Type
    rhs' = HasDebugCallStack => Subst -> Type -> Type
    Subst -> Type -> Type
    substTy Subst
    subst Type
    rhs

        go Subst
    subst (TyVar
    tv:[TyVar]
    tvs) (Type
    ty:[Type]
    tys) = Subst -> [TyVar] -> [Type] -> Type
    go (Subst -> TyVar -> Type -> Subst
    extendTvSubst Subst
    subst TyVar
    tv Type
    ty) [TyVar]
    tvs [Type]
    tys

        go Subst
    _ (TyVar
    _:[TyVar]
    _) [] = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "expand_syn" ([TyVar] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    rhs SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    arg_tys)
                       -- Under-saturated, precondition failed

    {- Note [Inlining coreView]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It is very common to have a function

      f :: Type -> ...
      f ty | Just ty' <- coreView ty = f ty'
      f (TyVarTy ...) = ...
      f ...           = ...

    If f is not otherwise recursive, the initial call to coreView
    causes f to become recursive, which kills the possibility of
    inlining. Instead, for non-recursive functions, we prefer to
    use coreFullView, which guarantees to unwrap top-level type
    synonyms. It can be inlined and is efficient and non-allocating
    in its fast path. For this to really be fast, all calls made
    on its fast path must also be inlined, linked back to this Note.
    -}

    {- *********************************************************************
    *                                                                      *
                    expandTypeSynonyms
    *                                                                      *
    ********************************************************************* -}

    expandTypeSynonyms :: Type -> Type
    -- ^ Expand out all type synonyms.  Actually, it'd suffice to expand out
    -- just the ones that discard type variables (e.g.  type Funny a = Int)
    -- But we don't know which those are currently, so we just expand all.
    --
    -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type,
    -- not in the kinds of any TyCon or TyVar mentioned in the type.
    --
    -- Keep this synchronized with 'synonymTyConsOfType'
    expandTypeSynonyms :: Type -> Type
    expandTypeSynonyms Type
    ty
      = Subst -> Type -> Type
    go (InScopeSet -> Subst
    mkEmptySubst InScopeSet
    in_scope) Type
    ty
      where
        in_scope :: InScopeSet
    in_scope = VarSet -> InScopeSet
    mkInScopeSet (Type -> VarSet
    tyCoVarsOfType Type
    ty)

        go :: Subst -> Type -> Type
    go Subst
    subst (TyConApp TyCon
    tc [Type]
    tys)
          | ExpandsSyn [(TyVar, Type)]
    tenv Type
    rhs [Type]
    tys' <- TyCon -> [Type] -> ExpandSynResult Type
    forall tyco. TyCon -> [tyco] -> ExpandSynResult tyco
    expandSynTyCon_maybe TyCon
    tc [Type]
    expanded_tys
          = let subst' :: Subst
    subst' = InScopeSet -> TvSubstEnv -> Subst
    mkTvSubst InScopeSet
    in_scope ([(TyVar, Type)] -> TvSubstEnv
    forall a. [(TyVar, a)] -> VarEnv a
    mkVarEnv [(TyVar, Type)]
    tenv)
                -- Make a fresh substitution; rhs has nothing to
                -- do with anything that has happened so far
                -- NB: if you make changes here, be sure to build an
                --     /idempotent/ substitution, even in the nested case
                --        type T a b = a -> b
                --        type S x y = T y x
                -- (#11665)
            in  Type -> [Type] -> Type
    mkAppTys (Subst -> Type -> Type
    go Subst
    subst' Type
    rhs) [Type]
    tys'
          | Bool
    otherwise
          = TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    expanded_tys
          where
            expanded_tys :: [Type]
    expanded_tys = ((Type -> Type) -> [Type] -> [Type]
    forall a b. (a -> b) -> [a] -> [b]
    map (Subst -> Type -> Type
    go Subst
    subst) [Type]
    tys)

        go Subst
    _     (LitTy TyLit
    l)     = TyLit -> Type
    LitTy TyLit
    l
        go Subst
    subst (TyVarTy TyVar
    tv)  = Subst -> TyVar -> Type
    substTyVar Subst
    subst TyVar
    tv
        go Subst
    subst (AppTy Type
    t1 Type
    t2) = Type -> Type -> Type
    mkAppTy (Subst -> Type -> Type
    go Subst
    subst Type
    t1) (Subst -> Type -> Type
    go Subst
    subst Type
    t2)
        go Subst
    subst ty :: Type
    ty@(FunTy FunTyFlag
    _ Type
    mult Type
    arg Type
    res)
          = Type
    ty { ft_mult = go subst mult, ft_arg = go subst arg, ft_res = go subst res }
        go Subst
    subst (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    vis) Type
    t)
          = let (Subst
    subst', TyVar
    tv') = (Subst -> Type -> Type) -> Subst -> TyVar -> (Subst, TyVar)
    substVarBndrUsing Subst -> Type -> Type
    go Subst
    subst TyVar
    tv in
            VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv' ForAllTyFlag
    vis) (Subst -> Type -> Type
    go Subst
    subst' Type
    t)
        go Subst
    subst (CastTy Type
    ty KindCoercion
    co)  = Type -> KindCoercion -> Type
    mkCastTy (Subst -> Type -> Type
    go Subst
    subst Type
    ty) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go Subst
    subst (CoercionTy KindCoercion
    co) = KindCoercion -> Type
    mkCoercionTy (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)

        go_mco :: Subst -> MCoercionN -> MCoercionN
    go_mco Subst
    _     MCoercionN
    MRefl    = MCoercionN
    MRefl
        go_mco Subst
    subst (MCo KindCoercion
    co) = KindCoercion -> MCoercionN
    MCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)

        go_co :: Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst (Refl Type
    ty)
          = Type -> KindCoercion
    mkNomReflCo (Subst -> Type -> Type
    go Subst
    subst Type
    ty)
        go_co Subst
    subst (GRefl Role
    r Type
    ty MCoercionN
    mco)
          = Role -> Type -> MCoercionN -> KindCoercion
    mkGReflCo Role
    r (Subst -> Type -> Type
    go Subst
    subst Type
    ty) (Subst -> MCoercionN -> MCoercionN
    go_mco Subst
    subst MCoercionN
    mco)
           -- NB: coercions are always expanded upon creation
        go_co Subst
    subst (TyConAppCo Role
    r TyCon
    tc [KindCoercion]
    args)
          = HasDebugCallStack =>
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    mkTyConAppCo Role
    r TyCon
    tc ((KindCoercion -> KindCoercion) -> [KindCoercion] -> [KindCoercion]
    forall a b. (a -> b) -> [a] -> [b]
    map (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst) [KindCoercion]
    args)
        go_co Subst
    subst (AppCo KindCoercion
    co KindCoercion
    arg)
          = KindCoercion -> KindCoercion -> KindCoercion
    mkAppCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    arg)
        go_co Subst
    subst (ForAllCo { fco_tcv :: KindCoercion -> TyVar
    fco_tcv = TyVar
    tv, fco_visL :: KindCoercion -> ForAllTyFlag
    fco_visL = ForAllTyFlag
    visL, fco_visR :: KindCoercion -> ForAllTyFlag
    fco_visR = ForAllTyFlag
    visR
                              , fco_kind :: KindCoercion -> KindCoercion
    fco_kind = KindCoercion
    kind_co, fco_body :: KindCoercion -> KindCoercion
    fco_body = KindCoercion
    co })
          = let (Subst
    subst', TyVar
    tv', KindCoercion
    kind_co') = Subst -> TyVar -> KindCoercion -> (Subst, TyVar, KindCoercion)
    go_cobndr Subst
    subst TyVar
    tv KindCoercion
    kind_co in
            HasDebugCallStack =>
    TyVar
    -> ForAllTyFlag
    -> ForAllTyFlag
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    TyVar
    -> ForAllTyFlag
    -> ForAllTyFlag
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    mkForAllCo TyVar
    tv' ForAllTyFlag
    visL ForAllTyFlag
    visR KindCoercion
    kind_co' (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst' KindCoercion
    co)
        go_co Subst
    subst (FunCo Role
    r FunTyFlag
    afl FunTyFlag
    afr KindCoercion
    w KindCoercion
    co1 KindCoercion
    co2)
          = Role
    -> FunTyFlag
    -> FunTyFlag
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    mkFunCo2 Role
    r FunTyFlag
    afl FunTyFlag
    afr (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    w) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co1) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co2)
        go_co Subst
    subst (CoVarCo TyVar
    cv)
          = Subst -> TyVar -> KindCoercion
    substCoVar Subst
    subst TyVar
    cv
        go_co Subst
    subst (AxiomInstCo CoAxiom Branched
    ax Arity
    ind [KindCoercion]
    args)
          = CoAxiom Branched -> Arity -> [KindCoercion] -> KindCoercion
    mkAxiomInstCo CoAxiom Branched
    ax Arity
    ind ((KindCoercion -> KindCoercion) -> [KindCoercion] -> [KindCoercion]
    forall a b. (a -> b) -> [a] -> [b]
    map (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst) [KindCoercion]
    args)
        go_co Subst
    subst (UnivCo UnivCoProvenance
    p Role
    r Type
    t1 Type
    t2)
          = UnivCoProvenance -> Role -> Type -> Type -> KindCoercion
    mkUnivCo (Subst -> UnivCoProvenance -> UnivCoProvenance
    go_prov Subst
    subst UnivCoProvenance
    p) Role
    r (Subst -> Type -> Type
    go Subst
    subst Type
    t1) (Subst -> Type -> Type
    go Subst
    subst Type
    t2)
        go_co Subst
    subst (SymCo KindCoercion
    co)
          = KindCoercion -> KindCoercion
    mkSymCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_co Subst
    subst (TransCo KindCoercion
    co1 KindCoercion
    co2)
          = KindCoercion -> KindCoercion -> KindCoercion
    mkTransCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co1) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co2)
        go_co Subst
    subst (SelCo CoSel
    n KindCoercion
    co)
          = HasDebugCallStack => CoSel -> KindCoercion -> KindCoercion
    CoSel -> KindCoercion -> KindCoercion
    mkSelCo CoSel
    n (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_co Subst
    subst (LRCo LeftOrRight
    lr KindCoercion
    co)
          = LeftOrRight -> KindCoercion -> KindCoercion
    mkLRCo LeftOrRight
    lr (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_co Subst
    subst (InstCo KindCoercion
    co KindCoercion
    arg)
          = KindCoercion -> KindCoercion -> KindCoercion
    mkInstCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co) (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    arg)
        go_co Subst
    subst (KindCo KindCoercion
    co)
          = KindCoercion -> KindCoercion
    mkKindCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_co Subst
    subst (SubCo KindCoercion
    co)
          = HasDebugCallStack => KindCoercion -> KindCoercion
    KindCoercion -> KindCoercion
    mkSubCo (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_co Subst
    subst (AxiomRuleCo CoAxiomRule
    ax [KindCoercion]
    cs)
          = CoAxiomRule -> [KindCoercion] -> KindCoercion
    AxiomRuleCo CoAxiomRule
    ax ((KindCoercion -> KindCoercion) -> [KindCoercion] -> [KindCoercion]
    forall a b. (a -> b) -> [a] -> [b]
    map (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst) [KindCoercion]
    cs)
        go_co Subst
    _ (HoleCo CoercionHole
    h)
          = String -> SDoc -> KindCoercion
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "expandTypeSynonyms hit a hole" (CoercionHole -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr CoercionHole
    h)

        go_prov :: Subst -> UnivCoProvenance -> UnivCoProvenance
    go_prov Subst
    subst (PhantomProv KindCoercion
    co)    = KindCoercion -> UnivCoProvenance
    PhantomProv (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_prov Subst
    subst (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UnivCoProvenance
    ProofIrrelProv (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst KindCoercion
    co)
        go_prov Subst
    _     p :: UnivCoProvenance
    p@(PluginProv String
    _)    = UnivCoProvenance
    p

          -- the "False" and "const" are to accommodate the type of
          -- substForAllCoBndrUsing, which is general enough to
          -- handle coercion optimization (which sometimes swaps the
          -- order of a coercion)
        go_cobndr :: Subst -> TyVar -> KindCoercion -> (Subst, TyVar, KindCoercion)
    go_cobndr Subst
    subst = Bool
    -> (KindCoercion -> KindCoercion)
    -> Subst
    -> TyVar
    -> KindCoercion
    -> (Subst, TyVar, KindCoercion)
    substForAllCoBndrUsing Bool
    False (Subst -> KindCoercion -> KindCoercion
    go_co Subst
    subst) Subst
    subst

    {- Notes on type synonyms
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
    to return type synonyms wherever possible. Thus

            type Foo a = a -> a

    we want
            splitFunTys (a -> Foo a) = ([a], Foo a)
    not                                ([a], a -> a)

    The reason is that we then get better (shorter) type signatures in
    interfaces.  Notably this plays a role in tcTySigs in GHC.Tc.Gen.Bind.
    -}

    {- *********************************************************************
    *                                                                      *
                    Random functions (todo: organise)
    *                                                                      *
    ********************************************************************* -}

    -- | An INLINE helper for function such as 'kindRep_maybe' below.
    --
    -- @isTyConKeyApp_maybe key ty@ returns @Just tys@ iff
    -- the type @ty = T tys@, where T's unique = key
    -- key must not be `fUNTyConKey`; to test for functions, use `splitFunTy_maybe`.
    -- Thanks to this fact, we don't have to pattern match on `FunTy` here.
    isTyConKeyApp_maybe :: Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe :: Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    key Type
    ty
      | TyConApp TyCon
    tc [Type]
    args <- Type -> Type
    coreFullView Type
    ty
      , TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    key
      = [Type] -> Maybe [Type]
    forall a. a -> Maybe a
    Just [Type]
    args
      | Bool
    otherwise
      = Maybe [Type]
    forall a. Maybe a
    Nothing
    {-# INLINE isTyConKeyApp_maybe #-}

    -- | Extract the RuntimeRep classifier of a type from its kind. For example,
    -- @kindRep * = LiftedRep@; Panics if this is not possible.
    -- Treats * and Constraint as the same
    kindRep :: HasDebugCallStack => Kind -> RuntimeRepType
    kindRep :: HasDebugCallStack => Type -> Type
    kindRep Type
    k = case HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    kindRep_maybe Type
    k of
                  Just Type
    r  -> Type
    r
                  Maybe Type
    Nothing -> String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "kindRep" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    k)

    -- | Given a kind (TYPE rr) or (CONSTRAINT rr), extract its RuntimeRep classifier rr.
    -- For example, @kindRep_maybe * = Just LiftedRep@
    -- Returns 'Nothing' if the kind is not of form (TYPE rr)
    kindRep_maybe :: HasDebugCallStack => Kind -> Maybe RuntimeRepType
    kindRep_maybe :: HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    kind
      | Just (TypeOrConstraint
    _, Type
    rep) <- Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind = Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    rep
      | Bool
    otherwise                            = Maybe Type
    forall a. Maybe a
    Nothing

    -- | Returns True if the argument is (lifted) Type or Constraint
    -- See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim
    isLiftedTypeKind :: Kind -> Bool
    isLiftedTypeKind :: Type -> Bool
    isLiftedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    kindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isLiftedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    -- | Returns True if the kind classifies unlifted types (like 'Int#') and False
    -- otherwise. Note that this returns False for representation-polymorphic
    -- kinds, which may be specialized to a kind that classifies unlifted types.
    isUnliftedTypeKind :: Kind -> Bool
    isUnliftedTypeKind :: Type -> Bool
    isUnliftedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    kindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isUnliftedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    pickyIsLiftedTypeKind :: Kind -> Bool
    -- Checks whether the kind is literally
    --      TYPE LiftedRep
    -- or   TYPE ('BoxedRep 'Lifted)
    -- or   Type
    -- without expanding type synonyms or anything
    -- Used only when deciding whether to suppress the ":: *" in
    -- (a :: *) when printing kinded type variables
    -- See Note [Suppressing * kinds] in GHC.Core.TyCo.Ppr
    pickyIsLiftedTypeKind :: Type -> Bool
    pickyIsLiftedTypeKind Type
    kind
      | TyConApp TyCon
    tc [Type
    arg] <- Type
    kind
      , TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    tYPETyConKey
      , TyConApp TyCon
    rr_tc [Type]
    rr_args <- Type
    arg = case [Type]
    rr_args of
          [] -> TyCon
    rr_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedRepTyConKey
          [Type
    rr_arg]
            | TyCon
    rr_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey
            , TyConApp TyCon
    lev [] <- Type
    rr_arg
            , TyCon
    lev TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedDataConKey -> Bool
    True
          [Type]
    _ -> Bool
    False
      | TyConApp TyCon
    tc [] <- Type
    kind
      , TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedTypeKindTyConKey = Bool
    True
      | Bool
    otherwise                          = Bool
    False

    -- | Check whether a kind is of the form `TYPE (BoxedRep Lifted)`
    -- or `TYPE (BoxedRep Unlifted)`.
    --
    -- Returns:
    --
    --  - `Just Lifted` for `TYPE (BoxedRep Lifted)` and `Type`,
    --  - `Just Unlifted` for `TYPE (BoxedRep Unlifted)` and `UnliftedType`,
    --  - `Nothing` for anything else, e.g. `TYPE IntRep`, `TYPE (BoxedRep l)`, etc.
    kindBoxedRepLevity_maybe :: Type -> Maybe Levity
    kindBoxedRepLevity_maybe :: Type -> Maybe Levity
    kindBoxedRepLevity_maybe Type
    ty
      | Just Type
    rep <- HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    kindRep_maybe Type
    ty
      , Type -> Bool
    isBoxedRuntimeRep Type
    rep
      = Type -> Maybe Levity
    runtimeRepLevity_maybe Type
    rep
      | Bool
    otherwise
      = Maybe Levity
    forall a. Maybe a
    Nothing

    -- | Check whether a type of kind 'RuntimeRep' is lifted.
    --
    -- 'isLiftedRuntimeRep' is:
    --
    --  * True of @LiftedRep :: RuntimeRep@
    --  * False of type variables, type family applications,
    --    and of other reps such as @IntRep :: RuntimeRep@.
    isLiftedRuntimeRep :: RuntimeRepType -> Bool
    isLiftedRuntimeRep :: Type -> Bool
    isLiftedRuntimeRep Type
    rep
      = Type -> Maybe Levity
    runtimeRepLevity_maybe Type
    rep Maybe Levity -> Maybe Levity -> Bool
    forall a. Eq a => a -> a -> Bool
    == Levity -> Maybe Levity
    forall a. a -> Maybe a
    Just Levity
    Lifted

    -- | Check whether a type of kind 'RuntimeRep' is unlifted.
    --
    --  * True of definitely unlifted 'RuntimeRep's such as
    --    'UnliftedRep', 'IntRep', 'FloatRep', ...
    --  * False of 'LiftedRep',
    --  * False for type variables and type family applications.
    isUnliftedRuntimeRep :: RuntimeRepType -> Bool
    isUnliftedRuntimeRep :: Type -> Bool
    isUnliftedRuntimeRep Type
    rep =
      Type -> Maybe Levity
    runtimeRepLevity_maybe Type
    rep Maybe Levity -> Maybe Levity -> Bool
    forall a. Eq a => a -> a -> Bool
    == Levity -> Maybe Levity
    forall a. a -> Maybe a
    Just Levity
    Unlifted

    -- | An INLINE helper for functions such as 'isLiftedLevity' and 'isUnliftedLevity'.
    --
    -- Checks whether the type is a nullary 'TyCon' application,
    -- for a 'TyCon' with the given 'Unique'.
    isNullaryTyConKeyApp :: Unique -> Type -> Bool
    isNullaryTyConKeyApp :: Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    key Type
    ty
      | Just [Type]
    args <- Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    key Type
    ty
      = Bool -> Bool -> Bool
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) Bool
    True
      | Bool
    otherwise
      = Bool
    False
    {-# INLINE isNullaryTyConKeyApp #-}

    isLiftedLevity :: Type -> Bool
    isLiftedLevity :: Type -> Bool
    isLiftedLevity = Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    liftedDataConKey

    isUnliftedLevity :: Type -> Bool
    isUnliftedLevity :: Type -> Bool
    isUnliftedLevity = Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    unliftedDataConKey

    -- | Is this the type 'Levity'?
    isLevityTy :: Type -> Bool
    isLevityTy :: Type -> Bool
    isLevityTy = Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    levityTyConKey

    -- | Is this the type 'RuntimeRep'?
    isRuntimeRepTy :: Type -> Bool
    isRuntimeRepTy :: Type -> Bool
    isRuntimeRepTy = Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    runtimeRepTyConKey

    -- | Is a tyvar of type 'RuntimeRep'?
    isRuntimeRepVar :: TyVar -> Bool
    isRuntimeRepVar :: TyVar -> Bool
    isRuntimeRepVar = Type -> Bool
    isRuntimeRepTy (Type -> Bool) -> (TyVar -> Type) -> TyVar -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . TyVar -> Type
    tyVarKind

    -- | Is a tyvar of type 'Levity'?
    isLevityVar :: TyVar -> Bool
    isLevityVar :: TyVar -> Bool
    isLevityVar = Type -> Bool
    isLevityTy (Type -> Bool) -> (TyVar -> Type) -> TyVar -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . TyVar -> Type
    tyVarKind

    -- | Is this the type 'Multiplicity'?
    isMultiplicityTy :: Type -> Bool
    isMultiplicityTy :: Type -> Bool
    isMultiplicityTy  = Unique -> Type -> Bool
    isNullaryTyConKeyApp Unique
    multiplicityTyConKey

    -- | Is a tyvar of type 'Multiplicity'?
    isMultiplicityVar :: TyVar -> Bool
    isMultiplicityVar :: TyVar -> Bool
    isMultiplicityVar = Type -> Bool
    isMultiplicityTy (Type -> Bool) -> (TyVar -> Type) -> TyVar -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . TyVar -> Type
    tyVarKind

    --------------------------------------------
    --  Splitting RuntimeRep
    --------------------------------------------

    -- | (splitRuntimeRep_maybe rr) takes a Type rr :: RuntimeRep, and
    --   returns the (TyCon,[Type]) for the RuntimeRep, if possible, where
    --   the TyCon is one of the promoted DataCons of RuntimeRep.
    -- Remember: the unique on TyCon that is a a promoted DataCon is the
    --           same as the unique on the DataCon
    --           See Note [Promoted data constructors] in GHC.Core.TyCon
    -- May not be possible if `rr` is a type variable or type
    --   family application
    splitRuntimeRep_maybe :: RuntimeRepType -> Maybe (TyCon, [Type])
    splitRuntimeRep_maybe :: Type -> Maybe (TyCon, [Type])
    splitRuntimeRep_maybe Type
    rep
      | TyConApp TyCon
    rr_tc [Type]
    args <- Type -> Type
    coreFullView Type
    rep
      , TyCon -> Bool
    isPromotedDataCon TyCon
    rr_tc
        -- isPromotedDataCon: be careful of type families (F tys) :: RuntimeRep,
      = (TyCon, [Type]) -> Maybe (TyCon, [Type])
    forall a. a -> Maybe a
    Just (TyCon
    rr_tc, [Type]
    args)
      | Bool
    otherwise
      = Maybe (TyCon, [Type])
    forall a. Maybe a
    Nothing

    -- | See 'isBoxedRuntimeRep_maybe'.
    isBoxedRuntimeRep :: RuntimeRepType -> Bool
    isBoxedRuntimeRep :: Type -> Bool
    isBoxedRuntimeRep Type
    rep = Maybe Type -> Bool
    forall a. Maybe a -> Bool
    isJust (Type -> Maybe Type
    isBoxedRuntimeRep_maybe Type
    rep)

    -- | `isBoxedRuntimeRep_maybe (rep :: RuntimeRep)` returns `Just lev` if `rep`
    -- expands to `Boxed lev` and returns `Nothing` otherwise.
    --
    -- Types with this runtime rep are represented by pointers on the GC'd heap.
    isBoxedRuntimeRep_maybe :: RuntimeRepType -> Maybe LevityType
    isBoxedRuntimeRep_maybe :: Type -> Maybe Type
    isBoxedRuntimeRep_maybe Type
    rep
      | Just (TyCon
    rr_tc, [Type]
    args) <- Type -> Maybe (TyCon, [Type])
    splitRuntimeRep_maybe Type
    rep
      , TyCon
    rr_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey
      , [Type
    lev] <- [Type]
    args
      = Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    lev
      | Bool
    otherwise
      = Maybe Type
    forall a. Maybe a
    Nothing

    -- | Check whether a type (usually of kind 'RuntimeRep') is lifted, unlifted,
    --   or unknown.  Returns Nothing if the type isn't of kind 'RuntimeRep'.
    --
    -- `runtimeRepLevity_maybe rr` returns:
    --
    --   * `Just Lifted` if `rr` is `LiftedRep :: RuntimeRep`
    --   * `Just Unlifted` if `rr` is definitely unlifted, e.g. `IntRep`
    --   * `Nothing` if not known (e.g. it's a type variable or a type family application).
    runtimeRepLevity_maybe :: RuntimeRepType -> Maybe Levity
    runtimeRepLevity_maybe :: Type -> Maybe Levity
    runtimeRepLevity_maybe Type
    rep
      | Just (TyCon
    rr_tc, [Type]
    args) <- Type -> Maybe (TyCon, [Type])
    splitRuntimeRep_maybe Type
    rep
      =       -- NB: args might be non-empty e.g. TupleRep [r1, .., rn]
        if (TyCon
    rr_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey)
        then case [Type]
    args of
                [Type
    lev] -> Type -> Maybe Levity
    levityType_maybe Type
    lev
                [Type]
    _     -> Maybe Levity
    forall a. Maybe a
    Nothing  -- Type isn't of kind RuntimeRep
                         -- The latter case happens via the call to isLiftedRuntimeRep
                         -- in GHC.Tc.Errors.Ppr.pprMismatchMsg (#22742)
        else Levity -> Maybe Levity
    forall a. a -> Maybe a
    Just Levity
    Unlifted
            -- Avoid searching all the unlifted RuntimeRep type cons
            -- In the RuntimeRep data type, only LiftedRep is lifted
      | Bool
    otherwise
      = Maybe Levity
    forall a. Maybe a
    Nothing

    --------------------------------------------
    --  Splitting Levity
    --------------------------------------------

    -- | `levityType_maybe` takes a Type of kind Levity, and returns its levity
    -- May not be possible for a type variable or type family application
    levityType_maybe :: LevityType -> Maybe Levity
    levityType_maybe :: Type -> Maybe Levity
    levityType_maybe Type
    lev
      | TyConApp TyCon
    lev_tc [Type]
    args <- Type -> Type
    coreFullView Type
    lev
      = if | TyCon
    lev_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedDataConKey   -> Bool -> Maybe Levity -> Maybe Levity
    forall a. HasCallStack => Bool -> a -> a
    assert( [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Levity -> Maybe Levity) -> Maybe Levity -> Maybe Levity
    forall a b. (a -> b) -> a -> b
    $ Levity -> Maybe Levity
    forall a. a -> Maybe a
    Just Levity
    Lifted
           | TyCon
    lev_tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    unliftedDataConKey -> Bool -> Maybe Levity -> Maybe Levity
    forall a. HasCallStack => Bool -> a -> a
    assert( [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Levity -> Maybe Levity) -> Maybe Levity -> Maybe Levity
    forall a b. (a -> b) -> a -> b
    $ Levity -> Maybe Levity
    forall a. a -> Maybe a
    Just Levity
    Unlifted
           | Bool
    otherwise                          -> Maybe Levity
    forall a. Maybe a
    Nothing
      | Bool
    otherwise
      = Maybe Levity
    forall a. Maybe a
    Nothing

    {- *********************************************************************
    *                                                                      *
                   mapType
    *                                                                      *
    ************************************************************************

    These functions do a map-like operation over types, performing some operation
    on all variables and binding sites. Primarily used for zonking.

    Note [Efficiency for ForAllCo case of mapTyCoX]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    As noted in Note [ForAllCo] in GHC.Core.TyCo.Rep, a ForAllCo is a bit redundant.
    It stores a TyCoVar and a Coercion, where the kind of the TyCoVar always matches
    the left-hand kind of the coercion. This is convenient lots of the time, but
    not when mapping a function over a coercion.

    The problem is that tcm_tybinder will affect the TyCoVar's kind and
    mapCoercion will affect the Coercion, and we hope that the results will be
    the same. Even if they are the same (which should generally happen with
    correct algorithms), then there is an efficiency issue. In particular,
    this problem seems to make what should be a linear algorithm into a potentially
    exponential one. But it's only going to be bad in the case where there's
    lots of foralls in the kinds of other foralls. Like this:

      forall a : (forall b : (forall c : ...). ...). ...

    This construction seems unlikely. So we'll do the inefficient, easy way
    for now.

    Note [Specialising mappers]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    These INLINE pragmas are indispensable. mapTyCo and mapTyCoX are used
    to implement zonking, and it's vital that they get specialised to the TcM
    monad and the particular mapper in use.

    Even specialising to the monad alone made a 20% allocation difference
    in perf/compiler/T5030.

    See Note [Specialising foldType] in "GHC.Core.TyCo.Rep" for more details of this
    idiom.
    -}

    -- | This describes how a "map" operation over a type/coercion should behave
    data TyCoMapper env m
      = TyCoMapper
          { forall env (m :: * -> *).
    TyCoMapper env m -> env -> TyVar -> m Type
    tcm_tyvar :: env -> TyVar -> m Type
          , forall env (m :: * -> *).
    TyCoMapper env m -> env -> TyVar -> m KindCoercion
    tcm_covar :: env -> CoVar -> m Coercion
          , forall env (m :: * -> *).
    TyCoMapper env m -> env -> CoercionHole -> m KindCoercion
    tcm_hole  :: env -> CoercionHole -> m Coercion
              -- ^ What to do with coercion holes.
              -- See Note [Coercion holes] in "GHC.Core.TyCo.Rep".

          , forall env (m :: * -> *).
    TyCoMapper env m
    -> forall r.
       env -> TyVar -> ForAllTyFlag -> (env -> TyVar -> m r) -> m r
    tcm_tycobinder :: forall r. env -> TyCoVar -> ForAllTyFlag
                           -> (env -> TyCoVar -> m r) -> m r
              -- ^ The returned env is used in the extended scope

          , forall env (m :: * -> *). TyCoMapper env m -> TyCon -> m TyCon
    tcm_tycon :: TyCon -> m TyCon
              -- ^ This is used only for TcTyCons
              -- a) To zonk TcTyCons
              -- b) To turn TcTyCons into TyCons.
              --    See Note [Type checking recursive type and class declarations]
              --    in "GHC.Tc.TyCl"
          }

    {-# INLINE mapTyCo #-}  -- See Note [Specialising mappers]
    mapTyCo :: Monad m => TyCoMapper () m
            -> ( Type       -> m  Type
               , [Type]     -> m  [Type]
               , Coercion   -> m  Coercion
               , [Coercion] -> m [Coercion] )
    mapTyCo :: forall (m :: * -> *).
    Monad m =>
    TyCoMapper () m
    -> (Type -> m Type, [Type] -> m [Type],
        KindCoercion -> m KindCoercion, [KindCoercion] -> m [KindCoercion])
    mapTyCo TyCoMapper () m
    mapper
      = case TyCoMapper () m
    -> (() -> Type -> m Type, () -> [Type] -> m [Type],
        () -> KindCoercion -> m KindCoercion,
        () -> [KindCoercion] -> m [KindCoercion])
    forall (m :: * -> *) env.
    Monad m =>
    TyCoMapper env m
    -> (env -> Type -> m Type, env -> [Type] -> m [Type],
        env -> KindCoercion -> m KindCoercion,
        env -> [KindCoercion] -> m [KindCoercion])
    mapTyCoX TyCoMapper () m
    mapper of
         (() -> Type -> m Type
    go_ty, () -> [Type] -> m [Type]
    go_tys, () -> KindCoercion -> m KindCoercion
    go_co, () -> [KindCoercion] -> m [KindCoercion]
    go_cos)
            -> (() -> Type -> m Type
    go_ty (), () -> [Type] -> m [Type]
    go_tys (), () -> KindCoercion -> m KindCoercion
    go_co (), () -> [KindCoercion] -> m [KindCoercion]
    go_cos ())

    {-# INLINE mapTyCoX #-}  -- See Note [Specialising mappers]
    mapTyCoX :: Monad m => TyCoMapper env m
             -> ( env -> Type       -> m Type
                , env -> [Type]     -> m [Type]
                , env -> Coercion   -> m Coercion
                , env -> [Coercion] -> m [Coercion] )
    mapTyCoX :: forall (m :: * -> *) env.
    Monad m =>
    TyCoMapper env m
    -> (env -> Type -> m Type, env -> [Type] -> m [Type],
        env -> KindCoercion -> m KindCoercion,
        env -> [KindCoercion] -> m [KindCoercion])
    mapTyCoX (TyCoMapper { tcm_tyvar :: forall env (m :: * -> *).
    TyCoMapper env m -> env -> TyVar -> m Type
    tcm_tyvar = env -> TyVar -> m Type
    tyvar
                         , tcm_tycobinder :: forall env (m :: * -> *).
    TyCoMapper env m
    -> forall r.
       env -> TyVar -> ForAllTyFlag -> (env -> TyVar -> m r) -> m r
    tcm_tycobinder = forall r.
    env -> TyVar -> ForAllTyFlag -> (env -> TyVar -> m r) -> m r
    tycobinder
                         , tcm_tycon :: forall env (m :: * -> *). TyCoMapper env m -> TyCon -> m TyCon
    tcm_tycon = TyCon -> m TyCon
    tycon
                         , tcm_covar :: forall env (m :: * -> *).
    TyCoMapper env m -> env -> TyVar -> m KindCoercion
    tcm_covar = env -> TyVar -> m KindCoercion
    covar
                         , tcm_hole :: forall env (m :: * -> *).
    TyCoMapper env m -> env -> CoercionHole -> m KindCoercion
    tcm_hole = env -> CoercionHole -> m KindCoercion
    cohole })
      = (env -> Type -> m Type
    go_ty, env -> [Type] -> m [Type]
    go_tys, env -> KindCoercion -> m KindCoercion
    go_co, env -> [KindCoercion] -> m [KindCoercion]
    go_cos)
      where
        go_tys :: env -> [Type] -> m [Type]
    go_tys !env
    _   []       = [Type] -> m [Type]
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return []
        go_tys !env
    env (Type
    ty:[Type]
    tys) = (:) (Type -> [Type] -> [Type]) -> m Type -> m ([Type] -> [Type])
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty m ([Type] -> [Type]) -> m [Type] -> m [Type]
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> [Type] -> m [Type]
    go_tys env
    env [Type]
    tys

        go_ty :: env -> Type -> m Type
    go_ty !env
    env (TyVarTy TyVar
    tv)    = env -> TyVar -> m Type
    tyvar env
    env TyVar
    tv
        go_ty !env
    env (AppTy Type
    t1 Type
    t2)   = Type -> Type -> Type
    mkAppTy (Type -> Type -> Type) -> m Type -> m (Type -> Type)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    t1 m (Type -> Type) -> m Type -> m Type
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t2
        go_ty !env
    _   ty :: Type
    ty@(LitTy {})   = Type -> m Type
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    ty
        go_ty !env
    env (CastTy Type
    ty KindCoercion
    co)  = Type -> KindCoercion -> Type
    mkCastTy (Type -> KindCoercion -> Type)
    -> m Type -> m (KindCoercion -> Type)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty m (KindCoercion -> Type) -> m KindCoercion -> m Type
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_ty !env
    env (CoercionTy KindCoercion
    co) = KindCoercion -> Type
    CoercionTy (KindCoercion -> Type) -> m KindCoercion -> m Type
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co

        go_ty !env
    env ty :: Type
    ty@(FunTy FunTyFlag
    _ Type
    w Type
    arg Type
    res)
          = do { w' <- env -> Type -> m Type
    go_ty env
    env Type
    w; arg' <- go_ty env arg; res' <- go_ty env res
               ; return (ty { ft_mult = w', ft_arg = arg', ft_res = res' }) }

        go_ty !env
    env ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    tys)
          | TyCon -> Bool
    isTcTyCon TyCon
    tc
          = do { tc' <- TyCon -> m TyCon
    tycon TyCon
    tc
               ; mkTyConApp tc' <$> go_tys env tys }

          -- Not a TcTyCon
          | [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys    -- Avoid allocation in this very
          = Type -> m Type
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    ty   -- common case (E.g. Int, LiftedRep etc)

          | Bool
    otherwise
          = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc ([Type] -> Type) -> m [Type] -> m Type
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [Type] -> m [Type]
    go_tys env
    env [Type]
    tys

        go_ty !env
    env (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    vis) Type
    inner)
          = do { env -> TyVar -> ForAllTyFlag -> (env -> TyVar -> m Type) -> m Type
    forall r.
    env -> TyVar -> ForAllTyFlag -> (env -> TyVar -> m r) -> m r
    tycobinder env
    env TyVar
    tv ForAllTyFlag
    vis ((env -> TyVar -> m Type) -> m Type)
    -> (env -> TyVar -> m Type) -> m Type
    forall a b. (a -> b) -> a -> b
    $ \env
    env' TyVar
    tv' -> do
               ; inner' <- env -> Type -> m Type
    go_ty env
    env' Type
    inner
               ; return $ ForAllTy (Bndr tv' vis) inner' }

        go_cos :: env -> [KindCoercion] -> m [KindCoercion]
    go_cos !env
    _   []       = [KindCoercion] -> m [KindCoercion]
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return []
        go_cos !env
    env (KindCoercion
    co:[KindCoercion]
    cos) = (:) (KindCoercion -> [KindCoercion] -> [KindCoercion])
    -> m KindCoercion -> m ([KindCoercion] -> [KindCoercion])
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co m ([KindCoercion] -> [KindCoercion])
    -> m [KindCoercion] -> m [KindCoercion]
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos

        go_mco :: env -> MCoercionN -> m MCoercionN
    go_mco !env
    _   MCoercionN
    MRefl    = MCoercionN -> m MCoercionN
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return MCoercionN
    MRefl
        go_mco !env
    env (MCo KindCoercion
    co) = KindCoercion -> MCoercionN
    MCo (KindCoercion -> MCoercionN) -> m KindCoercion -> m MCoercionN
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co)

        go_co :: env -> KindCoercion -> m KindCoercion
    go_co !env
    env (Refl Type
    ty)                  = Type -> KindCoercion
    Refl (Type -> KindCoercion) -> m Type -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty
        go_co !env
    env (GRefl Role
    r Type
    ty MCoercionN
    mco)           = Role -> Type -> MCoercionN -> KindCoercion
    mkGReflCo Role
    r (Type -> MCoercionN -> KindCoercion)
    -> m Type -> m (MCoercionN -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty m (MCoercionN -> KindCoercion) -> m MCoercionN -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> MCoercionN -> m MCoercionN
    go_mco env
    env MCoercionN
    mco
        go_co !env
    env (AppCo KindCoercion
    c1 KindCoercion
    c2)              = KindCoercion -> KindCoercion -> KindCoercion
    mkAppCo (KindCoercion -> KindCoercion -> KindCoercion)
    -> m KindCoercion -> m (KindCoercion -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 m (KindCoercion -> KindCoercion)
    -> m KindCoercion -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c2
        go_co !env
    env (FunCo Role
    r FunTyFlag
    afl FunTyFlag
    afr KindCoercion
    cw KindCoercion
    c1 KindCoercion
    c2) = Role
    -> FunTyFlag
    -> FunTyFlag
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    mkFunCo2 Role
    r FunTyFlag
    afl FunTyFlag
    afr (KindCoercion -> KindCoercion -> KindCoercion -> KindCoercion)
    -> m KindCoercion
    -> m (KindCoercion -> KindCoercion -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    cw
                                               m (KindCoercion -> KindCoercion -> KindCoercion)
    -> m KindCoercion -> m (KindCoercion -> KindCoercion)
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 m (KindCoercion -> KindCoercion)
    -> m KindCoercion -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c2
        go_co !env
    env (CoVarCo TyVar
    cv)               = env -> TyVar -> m KindCoercion
    covar env
    env TyVar
    cv
        go_co !env
    env (HoleCo CoercionHole
    hole)              = env -> CoercionHole -> m KindCoercion
    cohole env
    env CoercionHole
    hole
        go_co !env
    env (UnivCo UnivCoProvenance
    p Role
    r Type
    t1 Type
    t2)         = UnivCoProvenance -> Role -> Type -> Type -> KindCoercion
    mkUnivCo (UnivCoProvenance -> Role -> Type -> Type -> KindCoercion)
    -> m UnivCoProvenance -> m (Role -> Type -> Type -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> UnivCoProvenance -> m UnivCoProvenance
    go_prov env
    env UnivCoProvenance
    p m (Role -> Type -> Type -> KindCoercion)
    -> m Role -> m (Type -> Type -> KindCoercion)
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> Role -> m Role
    forall a. a -> m a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Role
    r
                                               m (Type -> Type -> KindCoercion)
    -> m Type -> m (Type -> KindCoercion)
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t1 m (Type -> KindCoercion) -> m Type -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t2
        go_co !env
    env (SymCo KindCoercion
    co)                 = KindCoercion -> KindCoercion
    mkSymCo (KindCoercion -> KindCoercion) -> m KindCoercion -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co !env
    env (TransCo KindCoercion
    c1 KindCoercion
    c2)            = KindCoercion -> KindCoercion -> KindCoercion
    mkTransCo (KindCoercion -> KindCoercion -> KindCoercion)
    -> m KindCoercion -> m (KindCoercion -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 m (KindCoercion -> KindCoercion)
    -> m KindCoercion -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c2
        go_co !env
    env (AxiomRuleCo CoAxiomRule
    r [KindCoercion]
    cos)        = CoAxiomRule -> [KindCoercion] -> KindCoercion
    AxiomRuleCo CoAxiomRule
    r ([KindCoercion] -> KindCoercion)
    -> m [KindCoercion] -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos
        go_co !env
    env (SelCo CoSel
    i KindCoercion
    co)               = HasDebugCallStack => CoSel -> KindCoercion -> KindCoercion
    CoSel -> KindCoercion -> KindCoercion
    mkSelCo CoSel
    i (KindCoercion -> KindCoercion) -> m KindCoercion -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co !env
    env (LRCo LeftOrRight
    lr KindCoercion
    co)               = LeftOrRight -> KindCoercion -> KindCoercion
    mkLRCo LeftOrRight
    lr (KindCoercion -> KindCoercion) -> m KindCoercion -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co !env
    env (InstCo KindCoercion
    co KindCoercion
    arg)            = KindCoercion -> KindCoercion -> KindCoercion
    mkInstCo (KindCoercion -> KindCoercion -> KindCoercion)
    -> m KindCoercion -> m (KindCoercion -> KindCoercion)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co m (KindCoercion -> KindCoercion)
    -> m KindCoercion -> m KindCoercion
    forall a b. m (a -> b) -> m a -> m b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    arg
        go_co !env
    env (KindCo KindCoercion
    co)                = KindCoercion -> KindCoercion
    mkKindCo (KindCoercion -> KindCoercion) -> m KindCoercion -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co !env
    env (SubCo KindCoercion
    co)                 = HasDebugCallStack => KindCoercion -> KindCoercion
    KindCoercion -> KindCoercion
    mkSubCo (KindCoercion -> KindCoercion) -> m KindCoercion -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co !env
    env (AxiomInstCo CoAxiom Branched
    ax Arity
    i [KindCoercion]
    cos)     = CoAxiom Branched -> Arity -> [KindCoercion] -> KindCoercion
    mkAxiomInstCo CoAxiom Branched
    ax Arity
    i ([KindCoercion] -> KindCoercion)
    -> m [KindCoercion] -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos
        go_co !env
    env co :: KindCoercion
    co@(TyConAppCo Role
    r TyCon
    tc [KindCoercion]
    cos)
          | TyCon -> Bool
    isTcTyCon TyCon
    tc
          = do { tc' <- TyCon -> m TyCon
    tycon TyCon
    tc
               ; mkTyConAppCo r tc' <$> go_cos env cos }

          -- Not a TcTyCon
          | [KindCoercion] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [KindCoercion]
    cos    -- Avoid allocation in this very
          = KindCoercion -> m KindCoercion
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return KindCoercion
    co   -- common case (E.g. Int, LiftedRep etc)

          | Bool
    otherwise
          = HasDebugCallStack =>
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    mkTyConAppCo Role
    r TyCon
    tc ([KindCoercion] -> KindCoercion)
    -> m [KindCoercion] -> m KindCoercion
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos
        go_co !env
    env (ForAllCo { fco_tcv :: KindCoercion -> TyVar
    fco_tcv = TyVar
    tv, fco_visL :: KindCoercion -> ForAllTyFlag
    fco_visL = ForAllTyFlag
    visL, fco_visR :: KindCoercion -> ForAllTyFlag
    fco_visR = ForAllTyFlag
    visR
                             , fco_kind :: KindCoercion -> KindCoercion
    fco_kind = KindCoercion
    kind_co, fco_body :: KindCoercion -> KindCoercion
    fco_body = KindCoercion
    co })
          = do { kind_co' <- env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    kind_co
               ; tycobinder env tv visL $ \env
    env' TyVar
    tv' ->  do
               ; co' <- env -> KindCoercion -> m KindCoercion
    go_co env
    env' KindCoercion
    co
               ; return $ mkForAllCo tv' visL visR kind_co' co' }
            -- See Note [Efficiency for ForAllCo case of mapTyCoX]

        go_prov :: env -> UnivCoProvenance -> m UnivCoProvenance
    go_prov !env
    env (PhantomProv KindCoercion
    co)    = KindCoercion -> UnivCoProvenance
    PhantomProv (KindCoercion -> UnivCoProvenance)
    -> m KindCoercion -> m UnivCoProvenance
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_prov !env
    env (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UnivCoProvenance
    ProofIrrelProv (KindCoercion -> UnivCoProvenance)
    -> m KindCoercion -> m UnivCoProvenance
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_prov !env
    _   p :: UnivCoProvenance
    p@(PluginProv String
    _)    = UnivCoProvenance -> m UnivCoProvenance
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    p

    {- *********************************************************************
    *                                                                      *
                          TyVarTy
    *                                                                      *
    ********************************************************************* -}

    -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
    -- given message if this is not a type variable type. See also 'getTyVar_maybe'
    getTyVar :: HasDebugCallStack => Type -> TyVar
    getTyVar :: HasDebugCallStack => Type -> TyVar
    getTyVar Type
    ty = case Type -> Maybe TyVar
    getTyVar_maybe Type
    ty of
                        Just TyVar
    tv -> TyVar
    tv
                        Maybe TyVar
    Nothing -> String -> SDoc -> TyVar
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "getTyVar" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Attempts to obtain the type variable underlying a 'Type'
    getTyVar_maybe :: Type -> Maybe TyVar
    getTyVar_maybe :: Type -> Maybe TyVar
    getTyVar_maybe = Type -> Maybe TyVar
    repGetTyVar_maybe (Type -> Maybe TyVar) -> (Type -> Type) -> Type -> Maybe TyVar
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Type
    coreFullView

    -- | Attempts to obtain the type variable underlying a 'Type', without
    -- any expansion
    repGetTyVar_maybe :: Type -> Maybe TyVar
    repGetTyVar_maybe :: Type -> Maybe TyVar
    repGetTyVar_maybe (TyVarTy TyVar
    tv) = TyVar -> Maybe TyVar
    forall a. a -> Maybe a
    Just TyVar
    tv
    repGetTyVar_maybe Type
    _            = Maybe TyVar
    forall a. Maybe a
    Nothing

    isTyVarTy :: Type -> Bool
    isTyVarTy :: Type -> Bool
    isTyVarTy Type
    ty = Maybe TyVar -> Bool
    forall a. Maybe a -> Bool
    isJust (Type -> Maybe TyVar
    getTyVar_maybe Type
    ty)

    -- | If the type is a tyvar, possibly under a cast, returns it, along
    -- with the coercion. Thus, the co is :: kind tv ~N kind ty
    getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN)
    getCastedTyVar_maybe :: Type -> Maybe (TyVar, KindCoercion)
    getCastedTyVar_maybe Type
    ty = case Type -> Type
    coreFullView Type
    ty of
      CastTy (TyVarTy TyVar
    tv) KindCoercion
    co -> (TyVar, KindCoercion) -> Maybe (TyVar, KindCoercion)
    forall a. a -> Maybe a
    Just (TyVar
    tv, KindCoercion
    co)
      TyVarTy TyVar
    tv             -> (TyVar, KindCoercion) -> Maybe (TyVar, KindCoercion)
    forall a. a -> Maybe a
    Just (TyVar
    tv, Role -> Type -> KindCoercion
    mkReflCo Role
    Nominal (TyVar -> Type
    tyVarKind TyVar
    tv))
      Type
    _                      -> Maybe (TyVar, KindCoercion)
    forall a. Maybe a
    Nothing

    {- *********************************************************************
    *                                                                      *
                          AppTy
    *                                                                      *
    ********************************************************************* -}

    {- We need to be pretty careful with AppTy to make sure we obey the
    invariant that a TyConApp is always visibly so.  mkAppTy maintains the
    invariant: use it.

    Note [Decomposing fat arrow c=>t]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Can we unify (a b) with (Eq a => ty)?   If we do so, we end up with
    a partial application like ((=>) (Eq a)) which doesn't make sense in
    source Haskell.  In contrast, we *can* unify (a b) with (t1 -> t2).
    Here's an example (#9858) of how you might do it:
       i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep
       i p = typeRep p

       j = i (Proxy :: Proxy (Eq Int => Int))
    The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes,
    but suppose we want that.  But then in the call to 'i', we end
    up decomposing (Eq Int => Int), and we definitely don't want that.

    We are willing to split (t1 -=> t2) because the argument is still of
    kind Type, not Constraint.  So the criterion is isVisibleFunArg.

    In Core there is no real reason to avoid such decomposition.  But for now I've
    put the test in splitAppTyNoView_maybe, which applies throughout, because the
    other calls to splitAppTy are in GHC.Core.Unify, which is also used by the
    type checker (e.g. when matching type-function equations).
    -}

    -- | Applies a type to another, as in e.g. @k a@
    mkAppTy :: Type -> Type -> Type
      -- See Note [Respecting definitional equality], invariant (EQ1).
    mkAppTy :: Type -> Type -> Type
    mkAppTy (CastTy Type
    fun_ty KindCoercion
    co) Type
    arg_ty
      | ([KindCoercion
    arg_co], KindCoercion
    res_co) <- HasDebugCallStack =>
    KindCoercion
    -> Pair Type -> [Type] -> ([KindCoercion], KindCoercion)
    KindCoercion
    -> Pair Type -> [Type] -> ([KindCoercion], KindCoercion)
    decomposePiCos KindCoercion
    co (KindCoercion -> Pair Type
    coercionKind KindCoercion
    co) [Type
    arg_ty]
      = (Type
    fun_ty Type -> Type -> Type
    `mkAppTy` (Type
    arg_ty Type -> KindCoercion -> Type
    `mkCastTy` KindCoercion
    arg_co)) Type -> KindCoercion -> Type
    `mkCastTy` KindCoercion
    res_co

    mkAppTy (TyConApp TyCon
    tc [Type]
    tys) Type
    ty2 = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc ([Type]
    tys [Type] -> [Type] -> [Type]
    forall a. [a] -> [a] -> [a]
    ++ [Type
    ty2])
    mkAppTy Type
    ty1               Type
    ty2 = Type -> Type -> Type
    AppTy Type
    ty1 Type
    ty2
            -- Note that the TyConApp could be an
            -- under-saturated type synonym.  GHC allows that; e.g.
            --      type Foo k = k a -> k a
            --      type Id x = x
            --      foo :: Foo Id -> Foo Id
            --
            -- Here Id is partially applied in the type sig for Foo,
            -- but once the type synonyms are expanded all is well
            --
            -- Moreover in GHC.Tc.Types.tcInferTyApps we build up a type
            --   (T t1 t2 t3) one argument at a type, thus forming
            --   (T t1), (T t1 t2), etc

    mkAppTys :: Type -> [Type] -> Type
    mkAppTys :: Type -> [Type] -> Type
    mkAppTys Type
    ty1                []   = Type
    ty1
    mkAppTys (CastTy Type
    fun_ty KindCoercion
    co) [Type]
    arg_tys  -- much more efficient then nested mkAppTy
                                         -- Why do this? See (EQ1) of
                                         -- Note [Respecting definitional equality]
                                         -- in GHC.Core.TyCo.Rep
      = (Type -> Type -> Type) -> Type -> [Type] -> Type
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    foldl' Type -> Type -> Type
    AppTy ((Type -> [Type] -> Type
    mkAppTys Type
    fun_ty [Type]
    casted_arg_tys) Type -> KindCoercion -> Type
    `mkCastTy` KindCoercion
    res_co) [Type]
    leftovers
      where
        ([KindCoercion]
    arg_cos, KindCoercion
    res_co) = HasDebugCallStack =>
    KindCoercion
    -> Pair Type -> [Type] -> ([KindCoercion], KindCoercion)
    KindCoercion
    -> Pair Type -> [Type] -> ([KindCoercion], KindCoercion)
    decomposePiCos KindCoercion
    co (KindCoercion -> Pair Type
    coercionKind KindCoercion
    co) [Type]
    arg_tys
        ([Type]
    args_to_cast, [Type]
    leftovers) = [KindCoercion] -> [Type] -> ([Type], [Type])
    forall b a. [b] -> [a] -> ([a], [a])
    splitAtList [KindCoercion]
    arg_cos [Type]
    arg_tys
        casted_arg_tys :: [Type]
    casted_arg_tys = (Type -> KindCoercion -> Type)
    -> [Type] -> [KindCoercion] -> [Type]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith Type -> KindCoercion -> Type
    mkCastTy [Type]
    args_to_cast [KindCoercion]
    arg_cos
    mkAppTys (TyConApp TyCon
    tc [Type]
    tys1) [Type]
    tys2 = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc ([Type]
    tys1 [Type] -> [Type] -> [Type]
    forall a. [a] -> [a] -> [a]
    ++ [Type]
    tys2)
    mkAppTys Type
    ty1                [Type]
    tys2 = (Type -> Type -> Type) -> Type -> [Type] -> Type
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    foldl' Type -> Type -> Type
    AppTy Type
    ty1 [Type]
    tys2

    -------------
    splitAppTy_maybe :: Type -> Maybe (Type, Type)
    -- ^ Attempt to take a type application apart, whether it is a
    -- function, type constructor, or plain type application. Note
    -- that type family applications are NEVER unsaturated by this!
    splitAppTy_maybe :: Type -> Maybe (Type, Type)
    splitAppTy_maybe = HasDebugCallStack => Type -> Maybe (Type, Type)
    Type -> Maybe (Type, Type)
    splitAppTyNoView_maybe (Type -> Maybe (Type, Type))
    -> (Type -> Type) -> Type -> Maybe (Type, Type)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Type
    coreFullView

    splitAppTy :: Type -> (Type, Type)
    -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
    -- and panics if this is not possible
    splitAppTy :: Type -> (Type, Type)
    splitAppTy Type
    ty = Type -> Maybe (Type, Type)
    splitAppTy_maybe Type
    ty Maybe (Type, Type) -> (Type, Type) -> (Type, Type)
    forall a. Maybe a -> a -> a
    `orElse` String -> SDoc -> (Type, Type)
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitAppTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -------------
    splitAppTyNoView_maybe :: HasDebugCallStack => Type -> Maybe (Type,Type)
    -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
    -- any coreView stuff is already done
    splitAppTyNoView_maybe :: HasDebugCallStack => Type -> Maybe (Type, Type)
    splitAppTyNoView_maybe (AppTy Type
    ty1 Type
    ty2)
      = (Type, Type) -> Maybe (Type, Type)
    forall a. a -> Maybe a
    Just (Type
    ty1, Type
    ty2)

    splitAppTyNoView_maybe (FunTy FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2)
      | Just (TyCon
    tc, [Type]
    tys)   <- FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2
      , Just ([Type]
    tys', Type
    ty') <- [Type] -> Maybe ([Type], Type)
    forall a. [a] -> Maybe ([a], a)
    snocView [Type]
    tys
      = (Type, Type) -> Maybe (Type, Type)
    forall a. a -> Maybe a
    Just (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tys', Type
    ty')

    splitAppTyNoView_maybe (TyConApp TyCon
    tc [Type]
    tys)
      | Bool -> Bool
    not (TyCon -> Bool
    tyConMustBeSaturated TyCon
    tc) Bool -> Bool -> Bool
    || [Type]
    tys [Type] -> Arity -> Bool
    forall a. [a] -> Arity -> Bool
    `lengthExceeds` TyCon -> Arity
    tyConArity TyCon
    tc
      , Just ([Type]
    tys', Type
    ty') <- [Type] -> Maybe ([Type], Type)
    forall a. [a] -> Maybe ([a], a)
    snocView [Type]
    tys
      = (Type, Type) -> Maybe (Type, Type)
    forall a. a -> Maybe a
    Just (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tys', Type
    ty')    -- Never create unsaturated type family apps!

    splitAppTyNoView_maybe Type
    _other = Maybe (Type, Type)
    forall a. Maybe a
    Nothing

    tcSplitAppTyNoView_maybe :: Type -> Maybe (Type,Type)
    -- ^ Just like splitAppTyNoView_maybe, but does not split (c => t)
    -- See Note [Decomposing fat arrow c=>t]
    tcSplitAppTyNoView_maybe :: Type -> Maybe (Type, Type)
    tcSplitAppTyNoView_maybe Type
    ty
      | FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af } <- Type
    ty
      , Bool -> Bool
    not (FunTyFlag -> Bool
    isVisibleFunArg FunTyFlag
    af)  -- See Note [Decomposing fat arrow c=>t]
      = Maybe (Type, Type)
    forall a. Maybe a
    Nothing
      | Bool
    otherwise
      = HasDebugCallStack => Type -> Maybe (Type, Type)
    Type -> Maybe (Type, Type)
    splitAppTyNoView_maybe Type
    ty

    -------------
    splitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
    -- ^ Recursively splits a type as far as is possible, leaving a residual
    -- type being applied to and the type arguments applied to it. Never fails,
    -- even if that means returning an empty list of type applications.
    splitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
    splitAppTys Type
    ty = Type -> Type -> [Type] -> (Type, [Type])
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [Type] -> (Type, [Type])
    split Type
    orig_ty Type
    ty [Type]
    args | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type -> [Type] -> (Type, [Type])
    split Type
    orig_ty Type
    ty' [Type]
    args
        split Type
    _       (AppTy Type
    ty Type
    arg)        [Type]
    args = Type -> Type -> [Type] -> (Type, [Type])
    split Type
    ty Type
    ty (Type
    argType -> [Type] -> [Type]
    forall a. a -> [a] -> [a]
    :[Type]
    args)
        split Type
    _       (TyConApp TyCon
    tc [Type]
    tc_args) [Type]
    args
          = let -- keep type families saturated
                n :: Arity
    n | TyCon -> Bool
    tyConMustBeSaturated TyCon
    tc = TyCon -> Arity
    tyConArity TyCon
    tc
                  | Bool
    otherwise               = Arity
    0
                ([Type]
    tc_args1, [Type]
    tc_args2) = Arity -> [Type] -> ([Type], [Type])
    forall a. Arity -> [a] -> ([a], [a])
    splitAt Arity
    n [Type]
    tc_args
            in
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tc_args1, [Type]
    tc_args2 [Type] -> [Type] -> [Type]
    forall a. [a] -> [a] -> [a]
    ++ [Type]
    args)
        split Type
    _   (FunTy FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2) [Type]
    args
          | Just (TyCon
    tc,[Type]
    tys) <- FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2
          = Bool -> (Type, [Type]) -> (Type, [Type])
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args )
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [], [Type]
    tys)

        split Type
    orig_ty Type
    _ [Type]
    args  = (Type
    orig_ty, [Type]
    args)

    -- | Like 'splitAppTys', but doesn't look through type synonyms
    splitAppTysNoView :: HasDebugCallStack => Type -> (Type, [Type])
    splitAppTysNoView :: HasDebugCallStack => Type -> (Type, [Type])
    splitAppTysNoView Type
    ty = Type -> [Type] -> (Type, [Type])
    split Type
    ty []
      where
        split :: Type -> [Type] -> (Type, [Type])
    split (AppTy Type
    ty Type
    arg) [Type]
    args = Type -> [Type] -> (Type, [Type])
    split Type
    ty (Type
    argType -> [Type] -> [Type]
    forall a. a -> [a] -> [a]
    :[Type]
    args)
        split (TyConApp TyCon
    tc [Type]
    tc_args) [Type]
    args
          = let n :: Arity
    n | TyCon -> Bool
    tyConMustBeSaturated TyCon
    tc = TyCon -> Arity
    tyConArity TyCon
    tc
                  | Bool
    otherwise               = Arity
    0
                ([Type]
    tc_args1, [Type]
    tc_args2) = Arity -> [Type] -> ([Type], [Type])
    forall a. Arity -> [a] -> ([a], [a])
    splitAt Arity
    n [Type]
    tc_args
            in
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tc_args1, [Type]
    tc_args2 [Type] -> [Type] -> [Type]
    forall a. [a] -> [a] -> [a]
    ++ [Type]
    args)
        split (FunTy FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2) [Type]
    args
          | Just (TyCon
    tc, [Type]
    tys) <- FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    w Type
    ty1 Type
    ty2
          = Bool -> (Type, [Type]) -> (Type, [Type])
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args )
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [], [Type]
    tys)

        split Type
    ty [Type]
    args = (Type
    ty, [Type]
    args)

    {- *********************************************************************
    *                                                                      *
                          LitTy
    *                                                                      *
    ********************************************************************* -}

    mkNumLitTy :: Integer -> Type
    mkNumLitTy :: Integer -> Type
    mkNumLitTy Integer
    n = TyLit -> Type
    LitTy (Integer -> TyLit
    NumTyLit Integer
    n)

    -- | Is this a numeric literal. We also look through type synonyms.
    isNumLitTy :: Type -> Maybe Integer
    isNumLitTy :: Type -> Maybe Integer
    isNumLitTy Type
    ty
      | LitTy (NumTyLit Integer
    n) <- Type -> Type
    coreFullView Type
    ty = Integer -> Maybe Integer
    forall a. a -> Maybe a
    Just Integer
    n
      | Bool
    otherwise                             = Maybe Integer
    forall a. Maybe a
    Nothing

    mkStrLitTy :: FastString -> Type
    mkStrLitTy :: FastString -> Type
    mkStrLitTy FastString
    s = TyLit -> Type
    LitTy (FastString -> TyLit
    StrTyLit FastString
    s)

    -- | Is this a symbol literal. We also look through type synonyms.
    isStrLitTy :: Type -> Maybe FastString
    isStrLitTy :: Type -> Maybe FastString
    isStrLitTy Type
    ty
      | LitTy (StrTyLit FastString
    s) <- Type -> Type
    coreFullView Type
    ty = FastString -> Maybe FastString
    forall a. a -> Maybe a
    Just FastString
    s
      | Bool
    otherwise                             = Maybe FastString
    forall a. Maybe a
    Nothing

    mkCharLitTy :: Char -> Type
    mkCharLitTy :: Char -> Type
    mkCharLitTy Char
    c = TyLit -> Type
    LitTy (Char -> TyLit
    CharTyLit Char
    c)

    -- | Is this a char literal? We also look through type synonyms.
    isCharLitTy :: Type -> Maybe Char
    isCharLitTy :: Type -> Maybe Char
    isCharLitTy Type
    ty
      | LitTy (CharTyLit Char
    s) <- Type -> Type
    coreFullView Type
    ty = Char -> Maybe Char
    forall a. a -> Maybe a
    Just Char
    s
      | Bool
    otherwise                              = Maybe Char
    forall a. Maybe a
    Nothing

    -- | Is this a type literal (symbol, numeric, or char)?
    isLitTy :: Type -> Maybe TyLit
    isLitTy :: Type -> Maybe TyLit
    isLitTy Type
    ty
      | LitTy TyLit
    l <- Type -> Type
    coreFullView Type
    ty = TyLit -> Maybe TyLit
    forall a. a -> Maybe a
    Just TyLit
    l
      | Bool
    otherwise                  = Maybe TyLit
    forall a. Maybe a
    Nothing

    -- | A type of kind 'ErrorMessage' (from the 'GHC.TypeError' module).
    type ErrorMsgType = Type

    -- | Is this type a custom user error?
    -- If so, give us the error message.
    userTypeError_maybe :: Type -> Maybe ErrorMsgType
    userTypeError_maybe :: Type -> Maybe Type
    userTypeError_maybe Type
    ty
      | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Maybe Type
    userTypeError_maybe Type
    ty'
    userTypeError_maybe (TyConApp TyCon
    tc (Type
    _kind : Type
    msg : [Type]
    _))
      | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    errorMessageTypeErrorFamName
              -- There may be more than 2 arguments, if the type error is
              -- used as a type constructor (e.g. at kind `Type -> Type`).
      = Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    msg
    userTypeError_maybe Type
    _
      = Maybe Type
    forall a. Maybe a
    Nothing

    deepUserTypeError_maybe :: Type -> Maybe ErrorMsgType
    -- Look for custom user error, deeply inside the type
    deepUserTypeError_maybe :: Type -> Maybe Type
    deepUserTypeError_maybe Type
    ty
      | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Maybe Type
    userTypeError_maybe Type
    ty'
    deepUserTypeError_maybe (TyConApp TyCon
    tc [Type]
    tys)
      | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    errorMessageTypeErrorFamName
      , Type
    _kind : Type
    msg : [Type]
    _ <- [Type]
    tys
              -- There may be more than 2 arguments, if the type error is
              -- used as a type constructor (e.g. at kind `Type -> Type`).
      = Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    msg

      | TyCon -> Bool
    tyConMustBeSaturated TyCon
    tc  -- Don't go looking for user type errors
                                 -- inside type family arguments (see #20241).
      = (Type -> Maybe Type -> Maybe Type)
    -> Maybe Type -> [Type] -> Maybe Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (Maybe Type -> Maybe Type -> Maybe Type
    forall a. Maybe a -> Maybe a -> Maybe a
    firstJust (Maybe Type -> Maybe Type -> Maybe Type)
    -> (Type -> Maybe Type) -> Type -> Maybe Type -> Maybe Type
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Maybe Type
    deepUserTypeError_maybe) Maybe Type
    forall a. Maybe a
    Nothing (Arity -> [Type] -> [Type]
    forall a. Arity -> [a] -> [a]
    drop (TyCon -> Arity
    tyConArity TyCon
    tc) [Type]
    tys)
      | Bool
    otherwise
      = (Type -> Maybe Type -> Maybe Type)
    -> Maybe Type -> [Type] -> Maybe Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (Maybe Type -> Maybe Type -> Maybe Type
    forall a. Maybe a -> Maybe a -> Maybe a
    firstJust (Maybe Type -> Maybe Type -> Maybe Type)
    -> (Type -> Maybe Type) -> Type -> Maybe Type -> Maybe Type
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Maybe Type
    deepUserTypeError_maybe) Maybe Type
    forall a. Maybe a
    Nothing [Type]
    tys
    deepUserTypeError_maybe (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    ty) = Type -> Maybe Type
    deepUserTypeError_maybe Type
    ty
    deepUserTypeError_maybe (FunTy { ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res })
      = Type -> Maybe Type
    deepUserTypeError_maybe Type
    arg Maybe Type -> Maybe Type -> Maybe Type
    forall a. Maybe a -> Maybe a -> Maybe a
    `firstJust` Type -> Maybe Type
    deepUserTypeError_maybe Type
    res
    deepUserTypeError_maybe (AppTy Type
    t1 Type
    t2)
      = Type -> Maybe Type
    deepUserTypeError_maybe Type
    t1 Maybe Type -> Maybe Type -> Maybe Type
    forall a. Maybe a -> Maybe a -> Maybe a
    `firstJust` Type -> Maybe Type
    deepUserTypeError_maybe Type
    t2
    deepUserTypeError_maybe (CastTy Type
    ty KindCoercion
    _)
      = Type -> Maybe Type
    deepUserTypeError_maybe Type
    ty
    deepUserTypeError_maybe Type
    _   -- TyVarTy, CoercionTy, LitTy
      = Maybe Type
    forall a. Maybe a
    Nothing

    -- | Render a type corresponding to a user type error into a SDoc.
    pprUserTypeErrorTy :: ErrorMsgType -> SDoc
    pprUserTypeErrorTy :: Type -> SDoc
    pprUserTypeErrorTy Type
    ty =
      case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of

        -- Text "Something"
        Just (TyCon
    tc,[Type
    txt])
          | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    typeErrorTextDataConName
          , Just FastString
    str <- Type -> Maybe FastString
    isStrLitTy Type
    txt -> FastString -> SDoc
    forall doc. IsLine doc => FastString -> doc
    ftext FastString
    str

        -- ShowType t
        Just (TyCon
    tc,[Type
    _k,Type
    t])
          | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    typeErrorShowTypeDataConName -> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    t

        -- t1 :<>: t2
        Just (TyCon
    tc,[Type
    t1,Type
    t2])
          | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    typeErrorAppendDataConName ->
            Type -> SDoc
    pprUserTypeErrorTy Type
    t1 SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> Type -> SDoc
    pprUserTypeErrorTy Type
    t2

        -- t1 :$$: t2
        Just (TyCon
    tc,[Type
    t1,Type
    t2])
          | TyCon -> Name
    tyConName TyCon
    tc Name -> Name -> Bool
    forall a. Eq a => a -> a -> Bool
    == Name
    typeErrorVAppendDataConName ->
            Type -> SDoc
    pprUserTypeErrorTy Type
    t1 SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ Type -> SDoc
    pprUserTypeErrorTy Type
    t2

        -- An unevaluated type function
        Maybe (TyCon, [Type])
    _ -> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty

    {- *********************************************************************
    *                                                                      *
                          FunTy
    *                                                                      *
    ********************************************************************* -}

    {- Note [Representation of function types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Functions (e.g. Int -> Char) can be thought of as being applications
    of funTyCon (known in Haskell surface syntax as (->)), (note that
    `RuntimeRep' quantifiers are left inferred)

        (->) :: forall {r1 :: RuntimeRep} {r2 :: RuntimeRep}
                       (a :: TYPE r1) (b :: TYPE r2).
                a -> b -> Type

    However, for efficiency's sake we represent saturated applications of (->)
    with FunTy. For instance, the type,

        (->) r1 r2 a b

    is equivalent to,

        FunTy (Anon a) b

    Note how the RuntimeReps are implied in the FunTy representation. For this
    reason we must be careful when reconstructing the TyConApp representation (see,
    for instance, splitTyConApp_maybe).

    In the compiler we maintain the invariant that all saturated applications of
    (->) are represented with FunTy.

    See #11714.
    -}

    -----------------------------------------------
    funTyConAppTy_maybe :: FunTyFlag -> Type -> Type -> Type
                        -> Maybe (TyCon, [Type])
    -- ^ Given the components of a FunTy
    -- figure out the corresponding TyConApp.
    funTyConAppTy_maybe :: FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    mult Type
    arg Type
    res
      | Just Type
    arg_rep <- HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    getRuntimeRep_maybe Type
    arg
      , Just Type
    res_rep <- HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    getRuntimeRep_maybe Type
    res
      , let args :: [Type]
    args | FunTyFlag -> Bool
    isFUNArg FunTyFlag
    af = [Type
    mult, Type
    arg_rep, Type
    res_rep, Type
    arg, Type
    res]
                 | Bool
    otherwise   = [      Type
    arg_rep, Type
    res_rep, Type
    arg, Type
    res]
      = (TyCon, [Type]) -> Maybe (TyCon, [Type])
    forall a. a -> Maybe a
    Just ((TyCon, [Type]) -> Maybe (TyCon, [Type]))
    -> (TyCon, [Type]) -> Maybe (TyCon, [Type])
    forall a b. (a -> b) -> a -> b
    $ (FunTyFlag -> TyCon
    funTyFlagTyCon FunTyFlag
    af, [Type]
    args)
      | Bool
    otherwise
      = Maybe (TyCon, [Type])
    forall a. Maybe a
    Nothing

    tyConAppFunTy_maybe :: HasDebugCallStack => TyCon -> [Type] -> Maybe Type
    -- ^ Return Just if this TyConApp should be represented as a FunTy
    tyConAppFunTy_maybe :: HasDebugCallStack => TyCon -> [Type] -> Maybe Type
    tyConAppFunTy_maybe TyCon
    tc [Type]
    tys
      | Just (FunTyFlag
    af, Type
    mult, Type
    arg, Type
    res) <- Type -> TyCon -> [Type] -> Maybe (FunTyFlag, Type, Type, Type)
    forall a.
    (HasDebugCallStack, Outputable a) =>
    a -> TyCon -> [a] -> Maybe (FunTyFlag, a, a, a)
    ty_con_app_fun_maybe Type
    manyDataConTy TyCon
    tc [Type]
    tys
                = Type -> Maybe Type
    forall a. a -> Maybe a
    Just (FunTy { ft_af :: FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type
    ft_mult = Type
    mult, ft_arg :: Type
    ft_arg = Type
    arg, ft_res :: Type
    ft_res = Type
    res })
      | Bool
    otherwise = Maybe Type
    forall a. Maybe a
    Nothing

    tyConAppFunCo_maybe :: HasDebugCallStack => Role -> TyCon -> [Coercion]
                        -> Maybe Coercion
    -- ^ Return Just if this TyConAppCo should be represented as a FunCo
    tyConAppFunCo_maybe :: HasDebugCallStack =>
    Role -> TyCon -> [KindCoercion] -> Maybe KindCoercion
    tyConAppFunCo_maybe Role
    r TyCon
    tc [KindCoercion]
    cos
      | Just (FunTyFlag
    af, KindCoercion
    mult, KindCoercion
    arg, KindCoercion
    res) <- KindCoercion
    -> TyCon
    -> [KindCoercion]
    -> Maybe (FunTyFlag, KindCoercion, KindCoercion, KindCoercion)
    forall a.
    (HasDebugCallStack, Outputable a) =>
    a -> TyCon -> [a] -> Maybe (FunTyFlag, a, a, a)
    ty_con_app_fun_maybe KindCoercion
    mult_refl TyCon
    tc [KindCoercion]
    cos
      = KindCoercion -> Maybe KindCoercion
    forall a. a -> Maybe a
    Just (Role
    -> FunTyFlag
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    -> KindCoercion
    mkFunCo Role
    r FunTyFlag
    af KindCoercion
    mult KindCoercion
    arg KindCoercion
    res)
      | Bool
    otherwise
      = Maybe KindCoercion
    forall a. Maybe a
    Nothing
      where
        mult_refl :: KindCoercion
    mult_refl = Role -> Type -> KindCoercion
    mkReflCo (Role -> FunSel -> Role
    funRole Role
    r FunSel
    SelMult) Type
    manyDataConTy

    ty_con_app_fun_maybe :: (HasDebugCallStack, Outputable a) => a -> TyCon -> [a]
                         -> Maybe (FunTyFlag, a, a, a)
    {-# INLINE ty_con_app_fun_maybe #-}
    -- Specialise this function for its two call sites
    ty_con_app_fun_maybe :: forall a.
    (HasDebugCallStack, Outputable a) =>
    a -> TyCon -> [a] -> Maybe (FunTyFlag, a, a, a)
    ty_con_app_fun_maybe a
    many_ty_co TyCon
    tc [a]
    args
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    fUNTyConKey     = Maybe (FunTyFlag, a, a, a)
    fUN_case
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    tcArrowTyConKey = FunTyFlag -> Maybe (FunTyFlag, a, a, a)
    non_FUN_case FunTyFlag
    FTF_T_C
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    ctArrowTyConKey = FunTyFlag -> Maybe (FunTyFlag, a, a, a)
    non_FUN_case FunTyFlag
    FTF_C_T
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    ccArrowTyConKey = FunTyFlag -> Maybe (FunTyFlag, a, a, a)
    non_FUN_case FunTyFlag
    FTF_C_C
      | Bool
    otherwise                  = Maybe (FunTyFlag, a, a, a)
    forall a. Maybe a
    Nothing
      where
        tc_uniq :: Unique
    tc_uniq = TyCon -> Unique
    tyConUnique TyCon
    tc

        fUN_case :: Maybe (FunTyFlag, a, a, a)
    fUN_case
          | (a
    w:a
    _r1:a
    _r2:a
    a1:a
    a2:[a]
    rest) <- [a]
    args
          = Bool
    -> SDoc -> Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr ([a] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [a]
    rest) (TyCon -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyCon
    tc SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [a] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [a]
    args) (Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a))
    -> Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a b. (a -> b) -> a -> b
    $
            (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a. a -> Maybe a
    Just (FunTyFlag
    FTF_T_T, a
    w, a
    a1, a
    a2)
          | Bool
    otherwise = Maybe (FunTyFlag, a, a, a)
    forall a. Maybe a
    Nothing

        non_FUN_case :: FunTyFlag -> Maybe (FunTyFlag, a, a, a)
    non_FUN_case FunTyFlag
    ftf
          | (a
    _r1:a
    _r2:a
    a1:a
    a2:[a]
    rest) <- [a]
    args
          = Bool
    -> SDoc -> Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr ([a] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [a]
    rest) (TyCon -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyCon
    tc SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [a] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [a]
    args) (Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a))
    -> Maybe (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a b. (a -> b) -> a -> b
    $
            (FunTyFlag, a, a, a) -> Maybe (FunTyFlag, a, a, a)
    forall a. a -> Maybe a
    Just (FunTyFlag
    ftf, a
    many_ty_co, a
    a1, a
    a2)
          | Bool
    otherwise
          = Maybe (FunTyFlag, a, a, a)
    forall a. Maybe a
    Nothing

    mkFunctionType :: HasDebugCallStack => Mult -> Type -> Type -> Type
    -- ^ This one works out the FunTyFlag from the argument type
    -- See GHC.Types.Var Note [FunTyFlag]
    mkFunctionType :: HasDebugCallStack => Type -> Type -> Type -> Type
    mkFunctionType Type
    mult Type
    arg_ty Type
    res_ty
     = FunTy { ft_af :: FunTyFlag
    ft_af = FunTyFlag
    af, ft_arg :: Type
    ft_arg = Type
    arg_ty, ft_res :: Type
    ft_res = Type
    res_ty
             , ft_mult :: Type
    ft_mult = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr Bool
    mult_ok ([Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type
    mult, Type
    arg_ty, Type
    res_ty]) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
                         Type
    mult }
      where
        af :: FunTyFlag
    af = HasDebugCallStack => Type -> Type -> FunTyFlag
    Type -> Type -> FunTyFlag
    chooseFunTyFlag Type
    arg_ty Type
    res_ty
        mult_ok :: Bool
    mult_ok = FunTyFlag -> Bool
    isVisibleFunArg FunTyFlag
    af Bool -> Bool -> Bool
    || Type -> Bool
    isManyTy Type
    mult

    mkScaledFunctionTys :: [Scaled Type] -> Type -> Type
    -- ^ Like mkFunctionType, compute the FunTyFlag from the arguments
    mkScaledFunctionTys :: [Scaled Type] -> Type -> Type
    mkScaledFunctionTys [Scaled Type]
    arg_tys Type
    res_ty
      = (Scaled Type -> Type -> Type) -> Type -> [Scaled Type] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr Scaled Type -> Type -> Type
    mk Type
    res_ty [Scaled Type]
    arg_tys
      where
        mk :: Scaled Type -> Type -> Type
    mk (Scaled Type
    mult Type
    arg_ty) Type
    res_ty
          = HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
    FunTyFlag -> Type -> Type -> Type -> Type
    mkFunTy (HasDebugCallStack => Type -> Type -> FunTyFlag
    Type -> Type -> FunTyFlag
    chooseFunTyFlag Type
    arg_ty Type
    res_ty)
                    Type
    mult Type
    arg_ty Type
    res_ty

    chooseFunTyFlag :: HasDebugCallStack => Type -> Type -> FunTyFlag
    -- ^ See GHC.Types.Var Note [FunTyFlag]
    chooseFunTyFlag :: HasDebugCallStack => Type -> Type -> FunTyFlag
    chooseFunTyFlag Type
    arg_ty Type
    res_ty
      = TypeOrConstraint -> TypeOrConstraint -> FunTyFlag
    mkFunTyFlag (HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    arg_ty) (HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    res_ty)

    splitFunTy :: Type -> (Mult, Type, Type)
    -- ^ Attempts to extract the multiplicity, argument and result types from a type,
    -- and panics if that is not possible. See also 'splitFunTy_maybe'
    splitFunTy :: Type -> (Type, Type, Type)
    splitFunTy Type
    ty = case Type -> Maybe (FunTyFlag, Type, Type, Type)
    splitFunTy_maybe Type
    ty of
                       Just (FunTyFlag
    _af, Type
    mult, Type
    arg, Type
    res) -> (Type
    mult,Type
    arg,Type
    res)
                       Maybe (FunTyFlag, Type, Type, Type)
    Nothing                    -> String -> SDoc -> (Type, Type, Type)
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitFunTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    {-# INLINE splitFunTy_maybe #-}
    splitFunTy_maybe :: Type -> Maybe (FunTyFlag, Mult, Type, Type)
    -- ^ Attempts to extract the multiplicity, argument and result types from a type
    splitFunTy_maybe :: Type -> Maybe (FunTyFlag, Type, Type, Type)
    splitFunTy_maybe Type
    ty
      | FunTy FunTyFlag
    af Type
    w Type
    arg Type
    res <- Type -> Type
    coreFullView Type
    ty = (FunTyFlag, Type, Type, Type)
    -> Maybe (FunTyFlag, Type, Type, Type)
    forall a. a -> Maybe a
    Just (FunTyFlag
    af, Type
    w, Type
    arg, Type
    res)
      | Bool
    otherwise                             = Maybe (FunTyFlag, Type, Type, Type)
    forall a. Maybe a
    Nothing

    splitFunTys :: Type -> ([Scaled Type], Type)
    splitFunTys :: Type -> ([Scaled Type], Type)
    splitFunTys Type
    ty = [Scaled Type] -> Type -> Type -> ([Scaled Type], Type)
    split [] Type
    ty Type
    ty
      where
          -- common case first
        split :: [Scaled Type] -> Type -> Type -> ([Scaled Type], Type)
    split [Scaled Type]
    args Type
    _       (FunTy FunTyFlag
    _ Type
    w Type
    arg Type
    res) = [Scaled Type] -> Type -> Type -> ([Scaled Type], Type)
    split (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    Scaled Type
    w Type
    arg Scaled Type -> [Scaled Type] -> [Scaled Type]
    forall a. a -> [a] -> [a]
    : [Scaled Type]
    args) Type
    res Type
    res
        split [Scaled Type]
    args Type
    orig_ty Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = [Scaled Type] -> Type -> Type -> ([Scaled Type], Type)
    split [Scaled Type]
    args Type
    orig_ty Type
    ty'
        split [Scaled Type]
    args Type
    orig_ty Type
    _                   = ([Scaled Type] -> [Scaled Type]
    forall a. [a] -> [a]
    reverse [Scaled Type]
    args, Type
    orig_ty)

    funResultTy :: HasDebugCallStack => Type -> Type
    -- ^ Extract the function result type and panic if that is not possible
    funResultTy :: HasDebugCallStack => Type -> Type
    funResultTy Type
    ty
      | FunTy { ft_res :: Type -> Type
    ft_res = Type
    res } <- Type -> Type
    coreFullView Type
    ty = Type
    res
      | Bool
    otherwise                                 = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "funResultTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    funArgTy :: HasDebugCallStack => Type -> Type
    -- ^ Extract the function argument type and panic if that is not possible
    funArgTy :: HasDebugCallStack => Type -> Type
    funArgTy Type
    ty
      | FunTy { ft_arg :: Type -> Type
    ft_arg = Type
    arg } <- Type -> Type
    coreFullView Type
    ty = Type
    arg
      | Bool
    otherwise                                 = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "funArgTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- ^ Just like 'piResultTys' but for a single argument
    -- Try not to iterate 'piResultTy', because it's inefficient to substitute
    -- one variable at a time; instead use 'piResultTys"
    piResultTy :: HasDebugCallStack => Type -> Type ->  Type
    piResultTy :: HasDebugCallStack => Type -> Type -> Type
    piResultTy Type
    ty Type
    arg = case Type -> Type -> Maybe Type
    piResultTy_maybe Type
    ty Type
    arg of
                          Just Type
    res -> Type
    res
                          Maybe Type
    Nothing  -> String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "piResultTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    arg)

    piResultTy_maybe :: Type -> Type -> Maybe Type
    -- We don't need a 'tc' version, because
    -- this function behaves the same for Type and Constraint
    piResultTy_maybe :: Type -> Type -> Maybe Type
    piResultTy_maybe Type
    ty Type
    arg = case Type -> Type
    coreFullView Type
    ty of
      FunTy { ft_res :: Type -> Type
    ft_res = Type
    res } -> Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    res

      ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    res
        -> let empty_subst :: Subst
    empty_subst = InScopeSet -> Subst
    mkEmptySubst (InScopeSet -> Subst) -> InScopeSet -> Subst
    forall a b. (a -> b) -> a -> b
    $ VarSet -> InScopeSet
    mkInScopeSet (VarSet -> InScopeSet) -> VarSet -> InScopeSet
    forall a b. (a -> b) -> a -> b
    $
                             [Type] -> VarSet
    tyCoVarsOfTypes [Type
    arg,Type
    res]
           in Type -> Maybe Type
    forall a. a -> Maybe a
    Just (HasDebugCallStack => Subst -> Type -> Type
    Subst -> Type -> Type
    substTy (Subst -> TyVar -> Type -> Subst
    extendTCvSubst Subst
    empty_subst TyVar
    tv Type
    arg) Type
    res)

      Type
    _ -> Maybe Type
    forall a. Maybe a
    Nothing

    -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn)
    --   where f :: f_ty
    -- 'piResultTys' is interesting because:
    --      1. 'f_ty' may have more for-alls than there are args
    --      2. Less obviously, it may have fewer for-alls
    -- For case 2. think of:
    --   piResultTys (forall a.a) [forall b.b, Int]
    -- This really can happen, but only (I think) in situations involving
    -- undefined.  For example:
    --       undefined :: forall a. a
    -- Term: undefined @(forall b. b->b) @Int
    -- This term should have type (Int -> Int), but notice that
    -- there are more type args than foralls in 'undefined's type.

    -- If you edit this function, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in GHC.Core.Lint

    -- This is a heavily used function (e.g. from typeKind),
    -- so we pay attention to efficiency, especially in the special case
    -- where there are no for-alls so we are just dropping arrows from
    -- a function type/kind.
    piResultTys :: HasDebugCallStack => Type -> [Type] -> Type
    piResultTys :: HasDebugCallStack => Type -> [Type] -> Type
    piResultTys Type
    ty [] = Type
    ty
    piResultTys Type
    ty orig_args :: [Type]
    orig_args@(Type
    arg:[Type]
    args)
      | FunTy { ft_res :: Type -> Type
    ft_res = Type
    res } <- Type
    ty
      = HasDebugCallStack => Type -> [Type] -> Type
    Type -> [Type] -> Type
    piResultTys Type
    res [Type]
    args

      | ForAllTy (Bndr TyVar
    tcv ForAllTyFlag
    _) Type
    res <- Type
    ty
      = -- Both type and coercion variables
        Subst -> Type -> [Type] -> Type
    go (Subst -> TyVar -> Type -> Subst
    extendTCvSubst Subst
    init_subst TyVar
    tcv Type
    arg) Type
    res [Type]
    args

      | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty
      = HasDebugCallStack => Type -> [Type] -> Type
    Type -> [Type] -> Type
    piResultTys Type
    ty' [Type]
    orig_args

      | Bool
    otherwise
      = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "piResultTys1" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    orig_args)
      where
        init_subst :: Subst
    init_subst = InScopeSet -> Subst
    mkEmptySubst (InScopeSet -> Subst) -> InScopeSet -> Subst
    forall a b. (a -> b) -> a -> b
    $ VarSet -> InScopeSet
    mkInScopeSet ([Type] -> VarSet
    tyCoVarsOfTypes (Type
    tyType -> [Type] -> [Type]
    forall a. a -> [a] -> [a]
    :[Type]
    orig_args))

        go :: Subst -> Type -> [Type] -> Type
        go :: Subst -> Type -> [Type] -> Type
    go Subst
    subst Type
    ty [] = Subst -> Type -> Type
    substTyUnchecked Subst
    subst Type
    ty

        go Subst
    subst Type
    ty all_args :: [Type]
    all_args@(Type
    arg:[Type]
    args)
          | FunTy { ft_res :: Type -> Type
    ft_res = Type
    res } <- Type
    ty
          = Subst -> Type -> [Type] -> Type
    go Subst
    subst Type
    res [Type]
    args

          | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    res <- Type
    ty
          = Subst -> Type -> [Type] -> Type
    go (Subst -> TyVar -> Type -> Subst
    extendTCvSubst Subst
    subst TyVar
    tv Type
    arg) Type
    res [Type]
    args

          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty
          = Subst -> Type -> [Type] -> Type
    go Subst
    subst Type
    ty' [Type]
    all_args

          | Bool -> Bool
    not (Subst -> Bool
    isEmptyTCvSubst Subst
    subst)  -- See Note [Care with kind instantiation]
          = Subst -> Type -> [Type] -> Type
    go Subst
    init_subst
              (HasDebugCallStack => Subst -> Type -> Type
    Subst -> Type -> Type
    substTy Subst
    subst Type
    ty)
              [Type]
    all_args

          | Bool
    otherwise
          = -- We have not run out of arguments, but the function doesn't
            -- have the right kind to apply to them; so panic.
            -- Without the explicit isEmptyVarEnv test, an ill-kinded type
            -- would give an infinite loop, which is very unhelpful
            -- c.f. #15473
            String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "piResultTys2" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    orig_args SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    all_args)

    applyTysX :: HasDebugCallStack => [TyVar] -> Type -> [Type] -> Type
    -- applyTysX beta-reduces (/\tvs. body_ty) arg_tys
    -- Assumes that (/\tvs. body_ty) is closed
    applyTysX :: HasDebugCallStack => [TyVar] -> Type -> [Type] -> Type
    applyTysX [TyVar]
    tvs Type
    body_ty [Type]
    arg_tys
      = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr ([TyVar]
    tvs [TyVar] -> [Type] -> Bool
    forall a b. [a] -> [b] -> Bool
    `leLength` [Type]
    arg_tys) SDoc
    pp_stuff (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
        Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Type -> VarSet
    tyCoVarsOfType Type
    body_ty VarSet -> VarSet -> Bool
    `subVarSet` [TyVar] -> VarSet
    mkVarSet [TyVar]
    tvs) SDoc
    pp_stuff (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
        Type -> [Type] -> Type
    mkAppTys ([TyVar] -> [Type] -> Type -> Type
    HasDebugCallStack => [TyVar] -> [Type] -> Type -> Type
    substTyWith [TyVar]
    tvs [Type]
    arg_tys_prefix Type
    body_ty)
                 [Type]
    arg_tys_rest
      where
        pp_stuff :: SDoc
    pp_stuff = [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat [[TyVar] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs, Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    body_ty, [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    arg_tys]
        ([Type]
    arg_tys_prefix, [Type]
    arg_tys_rest) = [TyVar] -> [Type] -> ([Type], [Type])
    forall b a. [b] -> [a] -> ([a], [a])
    splitAtList [TyVar]
    tvs [Type]
    arg_tys

    {- Note [Care with kind instantiation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have
      T :: forall k. k
    and we are finding the kind of
      T (forall b. b -> b) * Int
    Then
      T (forall b. b->b) :: k[ k :-> forall b. b->b]
                         :: forall b. b -> b
    So
      T (forall b. b->b) * :: (b -> b)[ b :-> *]
                           :: * -> *

    In other words we must instantiate the forall!

    Similarly (#15428)
       S :: forall k f. k -> f k
    and we are finding the kind of
       S * (* ->) Int Bool
    We have
       S * (* ->) :: (k -> f k)[ k :-> *, f :-> (* ->)]
                  :: * -> * -> *
    So again we must instantiate.

    The same thing happens in GHC.CoreToIface.toIfaceAppArgsX.
    -}

    {- *********************************************************************
    *                                                                      *
                          TyConApp
    *                                                                      *
    ********************************************************************* -}

    -- splitTyConApp "looks through" synonyms, because they don't
    -- mean a distinct type, but all other type-constructor applications
    -- including functions are returned as Just ..

    -- | Retrieve the tycon heading this type, if there is one. Does /not/
    -- look through synonyms.
    tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
    tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
    tyConAppTyConPicky_maybe (TyConApp TyCon
    tc [Type]
    _)        = TyCon -> Maybe TyCon
    forall a. a -> Maybe a
    Just TyCon
    tc
    tyConAppTyConPicky_maybe (FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af }) = TyCon -> Maybe TyCon
    forall a. a -> Maybe a
    Just (FunTyFlag -> TyCon
    funTyFlagTyCon FunTyFlag
    af)
    tyConAppTyConPicky_maybe Type
    _                      = Maybe TyCon
    forall a. Maybe a
    Nothing

    -- | The same as @fst . splitTyConApp@
    -- We can short-cut the FunTy case
    {-# INLINE tyConAppTyCon_maybe #-}
    tyConAppTyCon_maybe :: Type -> Maybe TyCon
    tyConAppTyCon_maybe :: Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty = case Type -> Type
    coreFullView Type
    ty of
      TyConApp TyCon
    tc [Type]
    _        -> TyCon -> Maybe TyCon
    forall a. a -> Maybe a
    Just TyCon
    tc
      FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af } -> TyCon -> Maybe TyCon
    forall a. a -> Maybe a
    Just (FunTyFlag -> TyCon
    funTyFlagTyCon FunTyFlag
    af)
      Type
    _                    -> Maybe TyCon
    forall a. Maybe a
    Nothing

    tyConAppTyCon :: HasDebugCallStack => Type -> TyCon
    tyConAppTyCon :: HasDebugCallStack => Type -> TyCon
    tyConAppTyCon Type
    ty = Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty Maybe TyCon -> TyCon -> TyCon
    forall a. Maybe a -> a -> a
    `orElse` String -> SDoc -> TyCon
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tyConAppTyCon" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | The same as @snd . splitTyConApp@
    tyConAppArgs_maybe :: Type -> Maybe [Type]
    tyConAppArgs_maybe :: Type -> Maybe [Type]
    tyConAppArgs_maybe Type
    ty = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
                              Just (TyCon
    _, [Type]
    tys) -> [Type] -> Maybe [Type]
    forall a. a -> Maybe a
    Just [Type]
    tys
                              Maybe (TyCon, [Type])
    Nothing       -> Maybe [Type]
    forall a. Maybe a
    Nothing

    tyConAppArgs :: HasCallStack => Type -> [Type]
    tyConAppArgs :: HasCallStack => Type -> [Type]
    tyConAppArgs Type
    ty = Type -> Maybe [Type]
    tyConAppArgs_maybe Type
    ty Maybe [Type] -> [Type] -> [Type]
    forall a. Maybe a -> a -> a
    `orElse` String -> SDoc -> [Type]
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tyConAppArgs" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Attempts to tease a type apart into a type constructor and the application
    -- of a number of arguments to that constructor. Panics if that is not possible.
    -- See also 'splitTyConApp_maybe'
    splitTyConApp :: Type -> (TyCon, [Type])
    splitTyConApp :: Type -> (TyCon, [Type])
    splitTyConApp Type
    ty = HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty Maybe (TyCon, [Type]) -> (TyCon, [Type]) -> (TyCon, [Type])
    forall a. Maybe a -> a -> a
    `orElse` String -> SDoc -> (TyCon, [Type])
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitTyConApp" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Attempts to tease a type apart into a type constructor and the application
    -- of a number of arguments to that constructor
    splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty = HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConAppNoView_maybe (Type -> Type
    coreFullView Type
    ty)

    splitTyConAppNoView_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    -- Same as splitTyConApp_maybe but without looking through synonyms
    splitTyConAppNoView_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConAppNoView_maybe Type
    ty
      = case Type
    ty of
          FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res}
                          -> FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    w Type
    arg Type
    res
          TyConApp TyCon
    tc [Type]
    tys -> (TyCon, [Type]) -> Maybe (TyCon, [Type])
    forall a. a -> Maybe a
    Just (TyCon
    tc, [Type]
    tys)
          Type
    _               -> Maybe (TyCon, [Type])
    forall a. Maybe a
    Nothing

    -- | tcSplitTyConApp_maybe splits a type constructor application into
    -- its type constructor and applied types.
    --
    -- Differs from splitTyConApp_maybe in that it does *not* split types
    -- headed with (=>), as that's not a TyCon in the type-checker.
    --
    -- Note that this may fail (in funTyConAppTy_maybe) in the case
    -- of a 'FunTy' with an argument of unknown kind 'FunTy'
    -- (e.g. `FunTy (a :: k) Int`, since the kind of @a@ isn't of
    -- the form `TYPE rep`.  This isn't usually a problem but may
    -- be temporarily the case during canonicalization:
    --     see Note [Decomposing FunTy] in GHC.Tc.Solver.Equality
    --     and Note [The Purely Kinded Type Invariant (PKTI)] in GHC.Tc.Gen.HsType,
    --         Wrinkle around FunTy
    --
    -- Consequently, you may need to zonk your type before
    -- using this function.
    tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
    -- Defined here to avoid module loops between Unify and TcType.
    tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    ty
      = case Type -> Type
    coreFullView Type
    ty of
          FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res}
                          | FunTyFlag -> Bool
    isVisibleFunArg FunTyFlag
    af    -- Visible args only
                            -- See Note [Decomposing fat arrow c=>t]
                          -> FunTyFlag -> Type -> Type -> Type -> Maybe (TyCon, [Type])
    funTyConAppTy_maybe FunTyFlag
    af Type
    w Type
    arg Type
    res
          TyConApp TyCon
    tc [Type]
    tys -> (TyCon, [Type]) -> Maybe (TyCon, [Type])
    forall a. a -> Maybe a
    Just (TyCon
    tc, [Type]
    tys)
          Type
    _               -> Maybe (TyCon, [Type])
    forall a. Maybe a
    Nothing

    tcSplitTyConApp :: Type -> (TyCon, [Type])
    tcSplitTyConApp :: Type -> (TyCon, [Type])
    tcSplitTyConApp Type
    ty
      = HasCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    ty Maybe (TyCon, [Type]) -> (TyCon, [Type]) -> (TyCon, [Type])
    forall a. Maybe a -> a -> a
    `orElse` String -> SDoc -> (TyCon, [Type])
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tcSplitTyConApp" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    ---------------------------
    newTyConInstRhs :: TyCon -> [Type] -> Type
    -- ^ Unwrap one 'layer' of newtype on a type constructor and its
    -- arguments, using an eta-reduced version of the @newtype@ if possible.
    -- This requires tys to have at least @newTyConInstArity tycon@ elements.
    newTyConInstRhs :: TyCon -> [Type] -> Type
    newTyConInstRhs TyCon
    tycon [Type]
    tys
        = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr ([TyVar]
    tvs [TyVar] -> [Type] -> Bool
    forall a b. [a] -> [b] -> Bool
    `leLength` [Type]
    tys) (TyCon -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyCon
    tycon SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    tys SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [TyVar] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
          [TyVar] -> Type -> [Type] -> Type
    HasDebugCallStack => [TyVar] -> Type -> [Type] -> Type
    applyTysX [TyVar]
    tvs Type
    rhs [Type]
    tys
      where
        ([TyVar]
    tvs, Type
    rhs) = TyCon -> ([TyVar], Type)
    newTyConEtadRhs TyCon
    tycon

    {- *********************************************************************
    *                                                                      *
                          CastTy
    *                                                                      *
    ********************************************************************* -}

    splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
    splitCastTy_maybe :: Type -> Maybe (Type, KindCoercion)
    splitCastTy_maybe Type
    ty
      | CastTy Type
    ty' KindCoercion
    co <- Type -> Type
    coreFullView Type
    ty = (Type, KindCoercion) -> Maybe (Type, KindCoercion)
    forall a. a -> Maybe a
    Just (Type
    ty', KindCoercion
    co)
      | Bool
    otherwise                        = Maybe (Type, KindCoercion)
    forall a. Maybe a
    Nothing

    -- | Make a 'CastTy'. The Coercion must be nominal. Checks the
    -- Coercion for reflexivity, dropping it if it's reflexive.
    -- See @Note [Respecting definitional equality]@ in "GHC.Core.TyCo.Rep"
    mkCastTy :: Type -> Coercion -> Type
    mkCastTy :: Type -> KindCoercion -> Type
    mkCastTy Type
    orig_ty KindCoercion
    co | KindCoercion -> Bool
    isReflexiveCo KindCoercion
    co = Type
    orig_ty  -- (EQ2) from the Note
    -- NB: Do the slow check here. This is important to keep the splitXXX
    -- functions working properly. Otherwise, we may end up with something
    -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz)
    -- fails under splitFunTy_maybe. This happened with the cheaper check
    -- in test dependent/should_compile/dynamic-paper.
    mkCastTy Type
    orig_ty KindCoercion
    co = Type -> KindCoercion -> Type
    mk_cast_ty Type
    orig_ty KindCoercion
    co

    -- | Like 'mkCastTy', but avoids checking the coercion for reflexivity,
    -- as that can be expensive.
    mk_cast_ty :: Type -> Coercion -> Type
    mk_cast_ty :: Type -> KindCoercion -> Type
    mk_cast_ty Type
    orig_ty KindCoercion
    co = Type -> Type
    go Type
    orig_ty
      where
        go :: Type -> Type
        -- See Note [Using coreView in mk_cast_ty]
        go :: Type -> Type
    go Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type
    go Type
    ty'

        go (CastTy Type
    ty KindCoercion
    co1)
          -- (EQ3) from the Note
          = Type -> KindCoercion -> Type
    mkCastTy Type
    ty (KindCoercion
    co1 KindCoercion -> KindCoercion -> KindCoercion
    `mkTransCo` KindCoercion
    co)
              -- call mkCastTy again for the reflexivity check

        go (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    vis) Type
    inner_ty)
          -- (EQ4) from the Note
          -- See Note [Weird typing rule for ForAllTy] in GHC.Core.TyCo.Rep.
          | TyVar -> Bool
    isTyVar TyVar
    tv
          , let fvs :: VarSet
    fvs = KindCoercion -> VarSet
    tyCoVarsOfCo KindCoercion
    co
          = -- have to make sure that pushing the co in doesn't capture the bound var!
            if TyVar
    tv TyVar -> VarSet -> Bool
    `elemVarSet` VarSet
    fvs
            then let empty_subst :: Subst
    empty_subst = InScopeSet -> Subst
    mkEmptySubst (VarSet -> InScopeSet
    mkInScopeSet VarSet
    fvs)
                     (Subst
    subst, TyVar
    tv') = HasDebugCallStack => Subst -> TyVar -> (Subst, TyVar)
    Subst -> TyVar -> (Subst, TyVar)
    substVarBndr Subst
    empty_subst TyVar
    tv
                 in VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv' ForAllTyFlag
    vis) (HasDebugCallStack => Subst -> Type -> Type
    Subst -> Type -> Type
    substTy Subst
    subst Type
    inner_ty Type -> KindCoercion -> Type
    `mk_cast_ty` KindCoercion
    co)
            else VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ForAllTyFlag
    vis) (Type
    inner_ty Type -> KindCoercion -> Type
    `mk_cast_ty` KindCoercion
    co)

        go Type
    _ = Type -> KindCoercion -> Type
    CastTy Type
    orig_ty KindCoercion
    co -- NB: orig_ty: preserve synonyms if possible

    {-
    Note [Using coreView in mk_cast_ty]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Invariants (EQ3) and (EQ4) of Note [Respecting definitional equality] in
    GHC.Core.TyCo.Rep must apply regardless of type synonyms. For instance,
    consider this example (#19742):

       type EqSameNat = () |> co
       useNatEq :: EqSameNat |> sym co

    (Those casts aren't visible in the user-source code, of course; see #19742 for
    what the user might write.)

    The type `EqSameNat |> sym co` looks as if it satisfies (EQ3), as it has no
    nested casts, but if we expand EqSameNat, we see that it doesn't.
    And then Bad Things happen.

    The solution is easy: just use `coreView` when establishing (EQ3) and (EQ4) in
    `mk_cast_ty`.
    -}

    {- *********************************************************************
    *                                                                      *
                         CoercionTy
      CoercionTy allows us to inject coercions into types. A CoercionTy
      should appear only in the right-hand side of an application.
    *                                                                      *
    ********************************************************************* -}

    mkCoercionTy :: Coercion -> Type
    mkCoercionTy :: KindCoercion -> Type
    mkCoercionTy = KindCoercion -> Type
    CoercionTy

    isCoercionTy :: Type -> Bool
    isCoercionTy :: Type -> Bool
    isCoercionTy (CoercionTy KindCoercion
    _) = Bool
    True
    isCoercionTy Type
    _              = Bool
    False

    isCoercionTy_maybe :: Type -> Maybe Coercion
    isCoercionTy_maybe :: Type -> Maybe KindCoercion
    isCoercionTy_maybe (CoercionTy KindCoercion
    co) = KindCoercion -> Maybe KindCoercion
    forall a. a -> Maybe a
    Just KindCoercion
    co
    isCoercionTy_maybe Type
    _               = Maybe KindCoercion
    forall a. Maybe a
    Nothing

    stripCoercionTy :: Type -> Coercion
    stripCoercionTy :: Type -> KindCoercion
    stripCoercionTy (CoercionTy KindCoercion
    co) = KindCoercion
    co
    stripCoercionTy Type
    ty              = String -> SDoc -> KindCoercion
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "stripCoercionTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    {- *********************************************************************
    *                                                                      *
                          ForAllTy
    *                                                                      *
    ********************************************************************* -}

    tyConBindersPiTyBinders :: [TyConBinder] -> [PiTyBinder]
    -- Return the tyConBinders in PiTyBinder form
    tyConBindersPiTyBinders :: [TyConBinder] -> [PiTyBinder]
    tyConBindersPiTyBinders = (TyConBinder -> PiTyBinder) -> [TyConBinder] -> [PiTyBinder]
    forall a b. (a -> b) -> [a] -> [b]
    map TyConBinder -> PiTyBinder
    to_tyb
      where
        to_tyb :: TyConBinder -> PiTyBinder
    to_tyb (Bndr TyVar
    tv (NamedTCB ForAllTyFlag
    vis)) = VarBndr TyVar ForAllTyFlag -> PiTyBinder
    Named (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ForAllTyFlag
    vis)
        to_tyb (Bndr TyVar
    tv TyConBndrVis
    AnonTCB)        = Scaled Type -> FunTyFlag -> PiTyBinder
    Anon (Type -> Scaled Type
    forall a. a -> Scaled a
    tymult (TyVar -> Type
    varType TyVar
    tv)) FunTyFlag
    FTF_T_T

    -- | Make a dependent forall over a TyCoVar
    mkTyCoForAllTy :: TyCoVar -> ForAllTyFlag -> Type -> Type
    mkTyCoForAllTy :: TyVar -> ForAllTyFlag -> Type -> Type
    mkTyCoForAllTy TyVar
    tv ForAllTyFlag
    vis Type
    ty
      | TyVar -> Bool
    isCoVar TyVar
    tv
      , Bool -> Bool
    not (TyVar
    tv TyVar -> VarSet -> Bool
    `elemVarSet` Type -> VarSet
    tyCoVarsOfType Type
    ty)
       -- Maintain ForAllTy's invariants
        -- See Note [Unused coercion variable in ForAllTy] in GHC.Core.TyCo.Rep
      = HasDebugCallStack => Type -> Type -> Type
    Type -> Type -> Type
    mkVisFunTyMany (TyVar -> Type
    varType TyVar
    tv) Type
    ty
      | Bool
    otherwise
      = VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (ForAllTyFlag -> TyVar -> VarBndr TyVar ForAllTyFlag
    forall vis. vis -> TyVar -> VarBndr TyVar vis
    mkForAllTyBinder ForAllTyFlag
    vis TyVar
    tv) Type
    ty

    -- | Make a dependent forall over a TyCoVar
    mkTyCoForAllTys :: [ForAllTyBinder] -> Type -> Type
    mkTyCoForAllTys :: [VarBndr TyVar ForAllTyFlag] -> Type -> Type
    mkTyCoForAllTys [VarBndr TyVar ForAllTyFlag]
    bndrs Type
    ty
      = (VarBndr TyVar ForAllTyFlag -> Type -> Type)
    -> Type -> [VarBndr TyVar ForAllTyFlag] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (\(Bndr TyVar
    var ForAllTyFlag
    vis) -> TyVar -> ForAllTyFlag -> Type -> Type
    mkTyCoForAllTy TyVar
    var ForAllTyFlag
    vis) Type
    ty [VarBndr TyVar ForAllTyFlag]
    bndrs

    -- | Make a dependent forall over an 'Inferred' variable
    mkTyCoInvForAllTy :: TyCoVar -> Type -> Type
    mkTyCoInvForAllTy :: TyVar -> Type -> Type
    mkTyCoInvForAllTy TyVar
    tv Type
    ty = TyVar -> ForAllTyFlag -> Type -> Type
    mkTyCoForAllTy TyVar
    tv ForAllTyFlag
    Inferred Type
    ty

    -- | Like 'mkTyCoInvForAllTy', but tv should be a tyvar
    mkInfForAllTy :: TyVar -> Type -> Type
    mkInfForAllTy :: TyVar -> Type -> Type
    mkInfForAllTy TyVar
    tv Type
    ty = Bool
    -> (VarBndr TyVar ForAllTyFlag -> Type -> Type)
    -> VarBndr TyVar ForAllTyFlag
    -> Type
    -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert (TyVar -> Bool
    isTyVar TyVar
    tv )
                          VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ForAllTyFlag
    Inferred) Type
    ty

    -- | Like 'mkForAllTys', but assumes all variables are dependent and
    -- 'Inferred', a common case
    mkTyCoInvForAllTys :: [TyCoVar] -> Type -> Type
    mkTyCoInvForAllTys :: [TyVar] -> Type -> Type
    mkTyCoInvForAllTys [TyVar]
    tvs Type
    ty = (TyVar -> Type -> Type) -> Type -> [TyVar] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr TyVar -> Type -> Type
    mkTyCoInvForAllTy Type
    ty [TyVar]
    tvs

    -- | Like 'mkTyCoInvForAllTys', but tvs should be a list of tyvar
    mkInfForAllTys :: [TyVar] -> Type -> Type
    mkInfForAllTys :: [TyVar] -> Type -> Type
    mkInfForAllTys [TyVar]
    tvs Type
    ty = (TyVar -> Type -> Type) -> Type -> [TyVar] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr TyVar -> Type -> Type
    mkInfForAllTy Type
    ty [TyVar]
    tvs

    -- | Like 'mkForAllTy', but assumes the variable is dependent and 'Specified',
    -- a common case
    mkSpecForAllTy :: TyVar -> Type -> Type
    mkSpecForAllTy :: TyVar -> Type -> Type
    mkSpecForAllTy TyVar
    tv Type
    ty = Bool
    -> (VarBndr TyVar ForAllTyFlag -> Type -> Type)
    -> VarBndr TyVar ForAllTyFlag
    -> Type
    -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert (TyVar -> Bool
    isTyVar TyVar
    tv )
                           -- covar is always Inferred, so input should be tyvar
                           VarBndr TyVar ForAllTyFlag -> Type -> Type
    ForAllTy (TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ForAllTyFlag
    Specified) Type
    ty

    -- | Like 'mkForAllTys', but assumes all variables are dependent and
    -- 'Specified', a common case
    mkSpecForAllTys :: [TyVar] -> Type -> Type
    mkSpecForAllTys :: [TyVar] -> Type -> Type
    mkSpecForAllTys [TyVar]
    tvs Type
    ty = (TyVar -> Type -> Type) -> Type -> [TyVar] -> Type
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr TyVar -> Type -> Type
    mkSpecForAllTy Type
    ty [TyVar]
    tvs

    -- | Like mkForAllTys, but assumes all variables are dependent and visible
    mkVisForAllTys :: [TyVar] -> Type -> Type
    mkVisForAllTys :: [TyVar] -> Type -> Type
    mkVisForAllTys [TyVar]
    tvs = Bool
    -> ([VarBndr TyVar ForAllTyFlag] -> Type -> Type)
    -> [VarBndr TyVar ForAllTyFlag]
    -> Type
    -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ((TyVar -> Bool) -> [TyVar] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all TyVar -> Bool
    isTyVar [TyVar]
    tvs )
                         -- covar is always Inferred, so all inputs should be tyvar
                         [VarBndr TyVar ForAllTyFlag] -> Type -> Type
    mkForAllTys [ TyVar -> ForAllTyFlag -> VarBndr TyVar ForAllTyFlag
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ForAllTyFlag
    Required | TyVar
    tv <- [TyVar]
    tvs ]

    -- | Given a list of type-level vars and the free vars of a result kind,
    -- makes PiTyBinders, preferring anonymous binders
    -- if the variable is, in fact, not dependent.
    -- e.g.    mkTyConBindersPreferAnon [(k:*),(b:k),(c:k)] (k->k)
    -- We want (k:*) Named, (b:k) Anon, (c:k) Anon
    --
    -- All non-coercion binders are /visible/.
    mkTyConBindersPreferAnon :: [TyVar]      -- ^ binders
                             -> TyCoVarSet   -- ^ free variables of result
                             -> [TyConBinder]
    mkTyConBindersPreferAnon :: [TyVar] -> VarSet -> [TyConBinder]
    mkTyConBindersPreferAnon [TyVar]
    vars VarSet
    inner_tkvs = Bool
    -> (([TyConBinder], VarSet) -> [TyConBinder])
    -> ([TyConBinder], VarSet)
    -> [TyConBinder]
    forall a. HasCallStack => Bool -> a -> a
    assert ((TyVar -> Bool) -> [TyVar] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all TyVar -> Bool
    isTyVar [TyVar]
    vars)
                                               ([TyConBinder], VarSet) -> [TyConBinder]
    forall a b. (a, b) -> a
    fst ([TyVar] -> ([TyConBinder], VarSet)
    go [TyVar]
    vars)
      where
        go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
        go :: [TyVar] -> ([TyConBinder], VarSet)
    go [] = ([], VarSet
    inner_tkvs)
        go (TyVar
    v:[TyVar]
    vs) | TyVar
    v TyVar -> VarSet -> Bool
    `elemVarSet` VarSet
    fvs
                  = ( TyVar -> TyConBndrVis -> TyConBinder
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    v (ForAllTyFlag -> TyConBndrVis
    NamedTCB ForAllTyFlag
    Required) TyConBinder -> [TyConBinder] -> [TyConBinder]
    forall a. a -> [a] -> [a]
    : [TyConBinder]
    binders
                    , VarSet
    fvs VarSet -> TyVar -> VarSet
    `delVarSet` TyVar
    v VarSet -> VarSet -> VarSet
    `unionVarSet` VarSet
    kind_vars )
                  | Bool
    otherwise
                  = ( TyVar -> TyConBndrVis -> TyConBinder
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    v TyConBndrVis
    AnonTCB TyConBinder -> [TyConBinder] -> [TyConBinder]
    forall a. a -> [a] -> [a]
    : [TyConBinder]
    binders
                    , VarSet
    fvs VarSet -> VarSet -> VarSet
    `unionVarSet` VarSet
    kind_vars )
          where
            ([TyConBinder]
    binders, VarSet
    fvs) = [TyVar] -> ([TyConBinder], VarSet)
    go [TyVar]
    vs
            kind_vars :: VarSet
    kind_vars      = Type -> VarSet
    tyCoVarsOfType (Type -> VarSet) -> Type -> VarSet
    forall a b. (a -> b) -> a -> b
    $ TyVar -> Type
    tyVarKind TyVar
    v

    -- | Take a ForAllTy apart, returning the binders and result type
    splitForAllForAllTyBinders :: Type -> ([ForAllTyBinder], Type)
    splitForAllForAllTyBinders :: Type -> ([VarBndr TyVar ForAllTyFlag], Type)
    splitForAllForAllTyBinders Type
    ty = Type
    -> Type
    -> [VarBndr TyVar ForAllTyFlag]
    -> ([VarBndr TyVar ForAllTyFlag], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type
    -> Type
    -> [VarBndr TyVar ForAllTyFlag]
    -> ([VarBndr TyVar ForAllTyFlag], Type)
    split Type
    _ (ForAllTy VarBndr TyVar ForAllTyFlag
    b Type
    res) [VarBndr TyVar ForAllTyFlag]
    bs                   = Type
    -> Type
    -> [VarBndr TyVar ForAllTyFlag]
    -> ([VarBndr TyVar ForAllTyFlag], Type)
    split Type
    res Type
    res (VarBndr TyVar ForAllTyFlag
    bVarBndr TyVar ForAllTyFlag
    -> [VarBndr TyVar ForAllTyFlag] -> [VarBndr TyVar ForAllTyFlag]
    forall a. a -> [a] -> [a]
    :[VarBndr TyVar ForAllTyFlag]
    bs)
        split Type
    orig_ty Type
    ty [VarBndr TyVar ForAllTyFlag]
    bs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type
    -> Type
    -> [VarBndr TyVar ForAllTyFlag]
    -> ([VarBndr TyVar ForAllTyFlag], Type)
    split Type
    orig_ty Type
    ty' [VarBndr TyVar ForAllTyFlag]
    bs
        split Type
    orig_ty Type
    _                [VarBndr TyVar ForAllTyFlag]
    bs             = ([VarBndr TyVar ForAllTyFlag] -> [VarBndr TyVar ForAllTyFlag]
    forall a. [a] -> [a]
    reverse [VarBndr TyVar ForAllTyFlag]
    bs, Type
    orig_ty)
    {-# INLINE splitForAllForAllTyBinders #-}

    -- | Take a ForAllTy apart, returning the list of tycovars and the result type.
    -- This always succeeds, even if it returns only an empty list. Note that the
    -- result type returned may have free variables that were bound by a forall.
    splitForAllTyCoVars :: Type -> ([TyCoVar], Type)
    splitForAllTyCoVars :: Type -> ([TyVar], Type)
    splitForAllTyCoVars Type
    ty = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    _       (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    ty)    [TyVar]
    tvs = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty (TyVar
    tvTyVar -> [TyVar] -> [TyVar]
    forall a. a -> [a] -> [a]
    :[TyVar]
    tvs)
        split Type
    orig_ty Type
    ty [TyVar]
    tvs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    orig_ty Type
    ty' [TyVar]
    tvs
        split Type
    orig_ty Type
    _                            [TyVar]
    tvs = ([TyVar] -> [TyVar]
    forall a. [a] -> [a]
    reverse [TyVar]
    tvs, Type
    orig_ty)

    -- | Like 'splitForAllTyCoVars', but split only for tyvars.
    -- This always succeeds, even if it returns only an empty list. Note that the
    -- result type returned may have free variables that were bound by a forall.
    splitForAllTyVars :: Type -> ([TyVar], Type)
    splitForAllTyVars :: Type -> ([TyVar], Type)
    splitForAllTyVars Type
    ty = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    _ (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    ty) [TyVar]
    tvs | TyVar -> Bool
    isTyVar TyVar
    tv = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty (TyVar
    tvTyVar -> [TyVar] -> [TyVar]
    forall a. a -> [a] -> [a]
    :[TyVar]
    tvs)
        split Type
    orig_ty Type
    ty [TyVar]
    tvs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty     = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    orig_ty Type
    ty' [TyVar]
    tvs
        split Type
    orig_ty Type
    _                   [TyVar]
    tvs              = ([TyVar] -> [TyVar]
    forall a. [a] -> [a]
    reverse [TyVar]
    tvs, Type
    orig_ty)

    -- | Like 'splitForAllTyCoVars', but only splits 'ForAllTy's with 'Required' type
    -- variable binders. Furthermore, each returned tyvar is annotated with '()'.
    splitForAllReqTyBinders :: Type -> ([ReqTyBinder], Type)
    splitForAllReqTyBinders :: Type -> ([ReqTyBinder], Type)
    splitForAllReqTyBinders Type
    ty = Type -> Type -> [ReqTyBinder] -> ([ReqTyBinder], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [ReqTyBinder] -> ([ReqTyBinder], Type)
    split Type
    _ (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    Required) Type
    ty) [ReqTyBinder]
    tvs   = Type -> Type -> [ReqTyBinder] -> ([ReqTyBinder], Type)
    split Type
    ty Type
    ty (TyVar -> () -> ReqTyBinder
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ()ReqTyBinder -> [ReqTyBinder] -> [ReqTyBinder]
    forall a. a -> [a] -> [a]
    :[ReqTyBinder]
    tvs)
        split Type
    orig_ty Type
    ty [ReqTyBinder]
    tvs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type -> [ReqTyBinder] -> ([ReqTyBinder], Type)
    split Type
    orig_ty Type
    ty' [ReqTyBinder]
    tvs
        split Type
    orig_ty Type
    _                   [ReqTyBinder]
    tvs          = ([ReqTyBinder] -> [ReqTyBinder]
    forall a. [a] -> [a]
    reverse [ReqTyBinder]
    tvs, Type
    orig_ty)

    -- | Like 'splitForAllTyCoVars', but only splits 'ForAllTy's with 'Invisible' type
    -- variable binders. Furthermore, each returned tyvar is annotated with its
    -- 'Specificity'.
    splitForAllInvisTyBinders :: Type -> ([InvisTyBinder], Type)
    splitForAllInvisTyBinders :: Type -> ([InvisTyBinder], Type)
    splitForAllInvisTyBinders Type
    ty = Type -> Type -> [InvisTyBinder] -> ([InvisTyBinder], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [InvisTyBinder] -> ([InvisTyBinder], Type)
    split Type
    _ (ForAllTy (Bndr TyVar
    tv (Invisible Specificity
    spec)) Type
    ty) [InvisTyBinder]
    tvs = Type -> Type -> [InvisTyBinder] -> ([InvisTyBinder], Type)
    split Type
    ty Type
    ty (TyVar -> Specificity -> InvisTyBinder
    forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv Specificity
    specInvisTyBinder -> [InvisTyBinder] -> [InvisTyBinder]
    forall a. a -> [a] -> [a]
    :[InvisTyBinder]
    tvs)
        split Type
    orig_ty Type
    ty [InvisTyBinder]
    tvs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty       = Type -> Type -> [InvisTyBinder] -> ([InvisTyBinder], Type)
    split Type
    orig_ty Type
    ty' [InvisTyBinder]
    tvs
        split Type
    orig_ty Type
    _                   [InvisTyBinder]
    tvs                = ([InvisTyBinder] -> [InvisTyBinder]
    forall a. [a] -> [a]
    reverse [InvisTyBinder]
    tvs, Type
    orig_ty)

    -- | Checks whether this is a proper forall (with a named binder)
    isForAllTy :: Type -> Bool
    isForAllTy :: Type -> Bool
    isForAllTy Type
    ty
      | ForAllTy {} <- Type -> Type
    coreFullView Type
    ty = Bool
    True
      | Bool
    otherwise                      = Bool
    False

    -- | Like `isForAllTy`, but returns True only if it is a tyvar binder
    isForAllTy_ty :: Type -> Bool
    isForAllTy_ty :: Type -> Bool
    isForAllTy_ty Type
    ty
      | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    _ <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isTyVar TyVar
    tv
      = Bool
    True

      | Bool
    otherwise = Bool
    False

    -- | Like `isForAllTy`, but returns True only if it is an inferred tyvar binder
    isForAllTy_invis_ty :: Type -> Bool
    isForAllTy_invis_ty :: Type -> Bool
    isForAllTy_invis_ty  Type
    ty
      | ForAllTy (Bndr TyVar
    tv (Invisible Specificity
    InferredSpec)) Type
    _ <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isTyVar TyVar
    tv
      = Bool
    True

      | Bool
    otherwise = Bool
    False

    -- | Like `isForAllTy`, but returns True only if it is a covar binder
    isForAllTy_co :: Type -> Bool
    isForAllTy_co :: Type -> Bool
    isForAllTy_co Type
    ty
      | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    _ <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isCoVar TyVar
    tv
      = Bool
    True

      | Bool
    otherwise = Bool
    False

    -- | Is this a function or forall?
    isPiTy :: Type -> Bool
    isPiTy :: Type -> Bool
    isPiTy Type
    ty = case Type -> Type
    coreFullView Type
    ty of
      ForAllTy {} -> Bool
    True
      FunTy {}    -> Bool
    True
      Type
    _           -> Bool
    False

    -- | Is this a function?
    isFunTy :: Type -> Bool
    isFunTy :: Type -> Bool
    isFunTy Type
    ty
      | FunTy {} <- Type -> Type
    coreFullView Type
    ty = Bool
    True
      | Bool
    otherwise                   = Bool
    False

    -- | Take a forall type apart, or panics if that is not possible.
    splitForAllTyCoVar :: Type -> (TyCoVar, Type)
    splitForAllTyCoVar :: Type -> (TyVar, Type)
    splitForAllTyCoVar Type
    ty
      | Just (TyVar, Type)
    answer <- Type -> Maybe (TyVar, Type)
    splitForAllTyCoVar_maybe Type
    ty = (TyVar, Type)
    answer
      | Bool
    otherwise                                  = String -> SDoc -> (TyVar, Type)
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitForAllTyCoVar" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Drops all ForAllTys
    dropForAlls :: Type -> Type
    dropForAlls :: Type -> Type
    dropForAlls Type
    ty = Type -> Type
    go Type
    ty
      where
        go :: Type -> Type
    go (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    res)            = Type -> Type
    go Type
    res
        go Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type
    go Type
    ty'
        go Type
    res                         = Type
    res

    -- | Attempts to take a ForAllTy apart, returning the full ForAllTyBinder
    splitForAllForAllTyBinder_maybe :: Type -> Maybe (ForAllTyBinder, Type)
    splitForAllForAllTyBinder_maybe :: Type -> Maybe (VarBndr TyVar ForAllTyFlag, Type)
    splitForAllForAllTyBinder_maybe Type
    ty
      | ForAllTy VarBndr TyVar ForAllTyFlag
    bndr Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty = (VarBndr TyVar ForAllTyFlag, Type)
    -> Maybe (VarBndr TyVar ForAllTyFlag, Type)
    forall a. a -> Maybe a
    Just (VarBndr TyVar ForAllTyFlag
    bndr, Type
    inner_ty)
      | Bool
    otherwise                                 = Maybe (VarBndr TyVar ForAllTyFlag, Type)
    forall a. Maybe a
    Nothing

    -- | Attempts to take a ForAllTy apart, returning the Var
    splitForAllTyCoVar_maybe :: Type -> Maybe (TyCoVar, Type)
    splitForAllTyCoVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllTyCoVar_maybe Type
    ty
      | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty = (TyVar, Type) -> Maybe (TyVar, Type)
    forall a. a -> Maybe a
    Just (TyVar
    tv, Type
    inner_ty)
      | Bool
    otherwise                                        = Maybe (TyVar, Type)
    forall a. Maybe a
    Nothing

    -- | Attempts to take a ForAllTy apart, but only if the binder is a TyVar
    splitForAllTyVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllTyVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllTyVar_maybe Type
    ty
      | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isTyVar TyVar
    tv
      = (TyVar, Type) -> Maybe (TyVar, Type)
    forall a. a -> Maybe a
    Just (TyVar
    tv, Type
    inner_ty)

      | Bool
    otherwise = Maybe (TyVar, Type)
    forall a. Maybe a
    Nothing

    -- | Like 'splitForAllTyCoVar_maybe', but only returns Just if it is a covar binder.
    splitForAllCoVar_maybe :: Type -> Maybe (CoVar, Type)
    splitForAllCoVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllCoVar_maybe Type
    ty
      | ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isCoVar TyVar
    tv
      = (TyVar, Type) -> Maybe (TyVar, Type)
    forall a. a -> Maybe a
    Just (TyVar
    tv, Type
    inner_ty)

      | Bool
    otherwise = Maybe (TyVar, Type)
    forall a. Maybe a
    Nothing

    -- | Attempts to take a forall type apart; works with proper foralls and
    -- functions
    {-# INLINE splitPiTy_maybe #-}  -- callers will immediately deconstruct
    splitPiTy_maybe :: Type -> Maybe (PiTyBinder, Type)
    splitPiTy_maybe :: Type -> Maybe (PiTyBinder, Type)
    splitPiTy_maybe Type
    ty = case Type -> Type
    coreFullView Type
    ty of
      ForAllTy VarBndr TyVar ForAllTyFlag
    bndr Type
    ty -> (PiTyBinder, Type) -> Maybe (PiTyBinder, Type)
    forall a. a -> Maybe a
    Just (VarBndr TyVar ForAllTyFlag -> PiTyBinder
    Named VarBndr TyVar ForAllTyFlag
    bndr, Type
    ty)
      FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res}
                       -> (PiTyBinder, Type) -> Maybe (PiTyBinder, Type)
    forall a. a -> Maybe a
    Just (Scaled Type -> FunTyFlag -> PiTyBinder
    Anon (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    mkScaled Type
    w Type
    arg) FunTyFlag
    af, Type
    res)
      Type
    _                -> Maybe (PiTyBinder, Type)
    forall a. Maybe a
    Nothing

    -- | Takes a forall type apart, or panics
    splitPiTy :: Type -> (PiTyBinder, Type)
    splitPiTy :: Type -> (PiTyBinder, Type)
    splitPiTy Type
    ty
      | Just (PiTyBinder, Type)
    answer <- Type -> Maybe (PiTyBinder, Type)
    splitPiTy_maybe Type
    ty = (PiTyBinder, Type)
    answer
      | Bool
    otherwise                         = String -> SDoc -> (PiTyBinder, Type)
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitPiTy" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Split off all PiTyBinders to a type, splitting both proper foralls
    -- and functions
    splitPiTys :: Type -> ([PiTyBinder], Type)
    splitPiTys :: Type -> ([PiTyBinder], Type)
    splitPiTys Type
    ty = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    _       (ForAllTy VarBndr TyVar ForAllTyFlag
    b Type
    res) [PiTyBinder]
    bs = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    res Type
    res (VarBndr TyVar ForAllTyFlag -> PiTyBinder
    Named VarBndr TyVar ForAllTyFlag
    b  PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
        split Type
    _       (FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res }) [PiTyBinder]
    bs
                                          = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    res Type
    res (Scaled Type -> FunTyFlag -> PiTyBinder
    Anon (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    Scaled Type
    w Type
    arg) FunTyFlag
    af PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
        split Type
    orig_ty Type
    ty [PiTyBinder]
    bs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    orig_ty Type
    ty' [PiTyBinder]
    bs
        split Type
    orig_ty Type
    _                [PiTyBinder]
    bs = ([PiTyBinder] -> [PiTyBinder]
    forall a. [a] -> [a]
    reverse [PiTyBinder]
    bs, Type
    orig_ty)

    -- | Extracts a list of run-time arguments from a function type,
    -- looking through newtypes to the right of arrows.
    --
    -- Examples:
    --
    -- @
    --    newtype Identity a = I a
    --
    --    getRuntimeArgTys (Int -> Bool -> Double) == [(Int, FTF_T_T), (Bool, FTF_T_T)]
    --    getRuntimeArgTys (Identity Int -> Bool -> Double) == [(Identity Int, FTF_T_T), (Bool, FTF_T_T)]
    --    getRuntimeArgTys (Int -> Identity (Bool -> Identity Double)) == [(Int, FTF_T_T), (Bool, FTF_T_T)]
    --    getRuntimeArgTys (forall a. Show a => Identity a -> a -> Int -> Bool)
    --             == [(Show a, FTF_C_T), (Identity a, FTF_T_T),(a, FTF_T_T),(Int, FTF_T_T)]
    -- @
    --
    -- Note that, in the last case, the returned types might mention an out-of-scope
    -- type variable. This function is used only when we really care about the /kinds/
    -- of the returned types, so this is OK.
    --
    -- **Warning**: this function can return an infinite list. For example:
    --
    -- @
    --   newtype N a = MkN (a -> N a)
    --   getRuntimeArgTys (N a) == repeat (a, FTF_T_T)
    -- @
    getRuntimeArgTys :: Type -> [(Scaled Type, FunTyFlag)]
    getRuntimeArgTys :: Type -> [(Scaled Type, FunTyFlag)]
    getRuntimeArgTys = Type -> [(Scaled Type, FunTyFlag)]
    go
      where
        go :: Type -> [(Scaled Type, FunTyFlag)]
        go :: Type -> [(Scaled Type, FunTyFlag)]
    go (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    res)
          = Type -> [(Scaled Type, FunTyFlag)]
    go Type
    res
        go (FunTy { ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res, ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af })
          = (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    Scaled Type
    w Type
    arg, FunTyFlag
    af) (Scaled Type, FunTyFlag)
    -> [(Scaled Type, FunTyFlag)] -> [(Scaled Type, FunTyFlag)]
    forall a. a -> [a] -> [a]
    : Type -> [(Scaled Type, FunTyFlag)]
    go Type
    res
        go Type
    ty
          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty
          = Type -> [(Scaled Type, FunTyFlag)]
    go Type
    ty'
          | Just (KindCoercion
    _,Type
    ty') <- Type -> Maybe (KindCoercion, Type)
    topNormaliseNewType_maybe Type
    ty
          = Type -> [(Scaled Type, FunTyFlag)]
    go Type
    ty'
          | Bool
    otherwise
          = []

    invisibleTyBndrCount :: Type -> Int
    -- Returns the number of leading invisible forall'd binders in the type
    -- Includes invisible predicate arguments; e.g. for
    --    e.g.  forall {k}. (k ~ *) => k -> k
    -- returns 2 not 1
    invisibleTyBndrCount :: Type -> Arity
    invisibleTyBndrCount Type
    ty = [PiTyBinder] -> Arity
    forall a. [a] -> Arity
    forall (t :: * -> *) a. Foldable t => t a -> Arity
    length (([PiTyBinder], Type) -> [PiTyBinder]
    forall a b. (a, b) -> a
    fst (Type -> ([PiTyBinder], Type)
    splitInvisPiTys Type
    ty))

    -- | Like 'splitPiTys', but returns only *invisible* binders, including constraints.
    -- Stops at the first visible binder.
    splitInvisPiTys :: Type -> ([PiTyBinder], Type)
    splitInvisPiTys :: Type -> ([PiTyBinder], Type)
    splitInvisPiTys Type
    ty = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    ty Type
    ty []
       where
        split :: Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    _ (ForAllTy VarBndr TyVar ForAllTyFlag
    b Type
    res) [PiTyBinder]
    bs
          | Bndr TyVar
    _ ForAllTyFlag
    vis <- VarBndr TyVar ForAllTyFlag
    b
          , ForAllTyFlag -> Bool
    isInvisibleForAllTyFlag ForAllTyFlag
    vis   = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    res Type
    res (VarBndr TyVar ForAllTyFlag -> PiTyBinder
    Named VarBndr TyVar ForAllTyFlag
    b  PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
        split Type
    _ (FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    mult, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res })  [PiTyBinder]
    bs
          | FunTyFlag -> Bool
    isInvisibleFunArg FunTyFlag
    af     = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    res Type
    res (Scaled Type -> FunTyFlag -> PiTyBinder
    Anon (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    mkScaled Type
    mult Type
    arg) FunTyFlag
    af PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
        split Type
    orig_ty Type
    ty [PiTyBinder]
    bs
          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty  = Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Type
    orig_ty Type
    ty' [PiTyBinder]
    bs
        split Type
    orig_ty Type
    _          [PiTyBinder]
    bs  = ([PiTyBinder] -> [PiTyBinder]
    forall a. [a] -> [a]
    reverse [PiTyBinder]
    bs, Type
    orig_ty)

    splitInvisPiTysN :: Int -> Type -> ([PiTyBinder], Type)
    -- ^ Same as 'splitInvisPiTys', but stop when
    --   - you have found @n@ 'PiTyBinder's,
    --   - or you run out of invisible binders
    splitInvisPiTysN :: Arity -> Type -> ([PiTyBinder], Type)
    splitInvisPiTysN Arity
    n Type
    ty = Arity -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    forall {t}.
    (Eq t, Num t) =>
    t -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split Arity
    n Type
    ty Type
    ty []
       where
        split :: t -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split t
    n Type
    orig_ty Type
    ty [PiTyBinder]
    bs
          | t
    n t -> t -> Bool
    forall a. Eq a => a -> a -> Bool
    == t
    0                  = ([PiTyBinder] -> [PiTyBinder]
    forall a. [a] -> [a]
    reverse [PiTyBinder]
    bs, Type
    orig_ty)
          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = t -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split t
    n Type
    orig_ty Type
    ty' [PiTyBinder]
    bs
          | ForAllTy VarBndr TyVar ForAllTyFlag
    b Type
    res <- Type
    ty
          , Bndr TyVar
    _ ForAllTyFlag
    vis <- VarBndr TyVar ForAllTyFlag
    b
          , ForAllTyFlag -> Bool
    isInvisibleForAllTyFlag ForAllTyFlag
    vis  = t -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split (t
    nt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1) Type
    res Type
    res (VarBndr TyVar ForAllTyFlag -> PiTyBinder
    Named VarBndr TyVar ForAllTyFlag
    b  PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
          | FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    mult, ft_arg :: Type -> Type
    ft_arg = Type
    arg, ft_res :: Type -> Type
    ft_res = Type
    res } <- Type
    ty
          , FunTyFlag -> Bool
    isInvisibleFunArg FunTyFlag
    af   = t -> Type -> Type -> [PiTyBinder] -> ([PiTyBinder], Type)
    split (t
    nt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1) Type
    res Type
    res (Scaled Type -> FunTyFlag -> PiTyBinder
    Anon (Type -> Type -> Scaled Type
    forall a. Type -> a -> Scaled a
    Scaled Type
    mult Type
    arg) FunTyFlag
    af PiTyBinder -> [PiTyBinder] -> [PiTyBinder]
    forall a. a -> [a] -> [a]
    : [PiTyBinder]
    bs)
          | Bool
    otherwise              = ([PiTyBinder] -> [PiTyBinder]
    forall a. [a] -> [a]
    reverse [PiTyBinder]
    bs, Type
    orig_ty)

    -- | Given a 'TyCon' and a list of argument types, filter out any invisible
    -- (i.e., 'Inferred' or 'Specified') arguments.
    filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
    filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
    filterOutInvisibleTypes TyCon
    tc [Type]
    tys = ([Type], [Type]) -> [Type]
    forall a b. (a, b) -> b
    snd (([Type], [Type]) -> [Type]) -> ([Type], [Type]) -> [Type]
    forall a b. (a -> b) -> a -> b
    $ TyCon -> [Type] -> ([Type], [Type])
    partitionInvisibleTypes TyCon
    tc [Type]
    tys

    -- | Given a 'TyCon' and a list of argument types, filter out any 'Inferred'
    -- arguments.
    filterOutInferredTypes :: TyCon -> [Type] -> [Type]
    filterOutInferredTypes :: TyCon -> [Type] -> [Type]
    filterOutInferredTypes TyCon
    tc [Type]
    tys =
      [Bool] -> [Type] -> [Type]
    forall a. [Bool] -> [a] -> [a]
    filterByList ((ForAllTyFlag -> Bool) -> [ForAllTyFlag] -> [Bool]
    forall a b. (a -> b) -> [a] -> [b]
    map (ForAllTyFlag -> ForAllTyFlag -> Bool
    forall a. Eq a => a -> a -> Bool
    /= ForAllTyFlag
    Inferred) ([ForAllTyFlag] -> [Bool]) -> [ForAllTyFlag] -> [Bool]
    forall a b. (a -> b) -> a -> b
    $ TyCon -> [Type] -> [ForAllTyFlag]
    tyConForAllTyFlags TyCon
    tc [Type]
    tys) [Type]
    tys

    -- | Given a 'TyCon' and a list of argument types, partition the arguments
    -- into:
    --
    -- 1. 'Inferred' or 'Specified' (i.e., invisible) arguments and
    --
    -- 2. 'Required' (i.e., visible) arguments
    partitionInvisibleTypes :: TyCon -> [Type] -> ([Type], [Type])
    partitionInvisibleTypes :: TyCon -> [Type] -> ([Type], [Type])
    partitionInvisibleTypes TyCon
    tc [Type]
    tys =
      [Bool] -> [Type] -> ([Type], [Type])
    forall a. [Bool] -> [a] -> ([a], [a])
    partitionByList ((ForAllTyFlag -> Bool) -> [ForAllTyFlag] -> [Bool]
    forall a b. (a -> b) -> [a] -> [b]
    map ForAllTyFlag -> Bool
    isInvisibleForAllTyFlag ([ForAllTyFlag] -> [Bool]) -> [ForAllTyFlag] -> [Bool]
    forall a b. (a -> b) -> a -> b
    $ TyCon -> [Type] -> [ForAllTyFlag]
    tyConForAllTyFlags TyCon
    tc [Type]
    tys) [Type]
    tys

    -- | Given a list of things paired with their visibilities, partition the
    -- things into (invisible things, visible things).
    partitionInvisibles :: [(a, ForAllTyFlag)] -> ([a], [a])
    partitionInvisibles :: forall a. [(a, ForAllTyFlag)] -> ([a], [a])
    partitionInvisibles = ((a, ForAllTyFlag) -> Either a a)
    -> [(a, ForAllTyFlag)] -> ([a], [a])
    forall a b c. (a -> Either b c) -> [a] -> ([b], [c])
    partitionWith (a, ForAllTyFlag) -> Either a a
    forall a. (a, ForAllTyFlag) -> Either a a
    pick_invis
      where
        pick_invis :: (a, ForAllTyFlag) -> Either a a
        pick_invis :: forall a. (a, ForAllTyFlag) -> Either a a
    pick_invis (a
    thing, ForAllTyFlag
    vis) | ForAllTyFlag -> Bool
    isInvisibleForAllTyFlag ForAllTyFlag
    vis = a -> Either a a
    forall a b. a -> Either a b
    Left a
    thing
                                | Bool
    otherwise              = a -> Either a a
    forall a b. b -> Either a b
    Right a
    thing

    -- | Given a 'TyCon' and a list of argument types to which the 'TyCon' is
    -- applied, determine each argument's visibility
    -- ('Inferred', 'Specified', or 'Required').
    --
    -- Wrinkle: consider the following scenario:
    --
    -- > T :: forall k. k -> k
    -- > tyConForAllTyFlags T [forall m. m -> m -> m, S, R, Q]
    --
    -- After substituting, we get
    --
    -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n
    --
    -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again,
    -- and @Q@ is visible.
    tyConForAllTyFlags :: TyCon -> [Type] -> [ForAllTyFlag]
    tyConForAllTyFlags :: TyCon -> [Type] -> [ForAllTyFlag]
    tyConForAllTyFlags TyCon
    tc = Type -> [Type] -> [ForAllTyFlag]
    fun_kind_arg_flags (TyCon -> Type
    tyConKind TyCon
    tc)

    -- | Given a 'Type' and a list of argument types to which the 'Type' is
    -- applied, determine each argument's visibility
    -- ('Inferred', 'Specified', or 'Required').
    --
    -- Most of the time, the arguments will be 'Required', but not always. Consider
    -- @f :: forall a. a -> Type@. In @f Type Bool@, the first argument (@Type@) is
    -- 'Specified' and the second argument (@Bool@) is 'Required'. It is precisely
    -- this sort of higher-rank situation in which 'appTyForAllTyFlags' comes in handy,
    -- since @f Type Bool@ would be represented in Core using 'AppTy's.
    -- (See also #15792).
    appTyForAllTyFlags :: Type -> [Type] -> [ForAllTyFlag]
    appTyForAllTyFlags :: Type -> [Type] -> [ForAllTyFlag]
    appTyForAllTyFlags Type
    ty = Type -> [Type] -> [ForAllTyFlag]
    fun_kind_arg_flags (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty)

    -- | Given a function kind and a list of argument types (where each argument's
    -- kind aligns with the corresponding position in the argument kind), determine
    -- each argument's visibility ('Inferred', 'Specified', or 'Required').
    fun_kind_arg_flags :: Kind -> [Type] -> [ForAllTyFlag]
    fun_kind_arg_flags :: Type -> [Type] -> [ForAllTyFlag]
    fun_kind_arg_flags = Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    emptySubst
      where
        go :: Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    subst Type
    ki [Type]
    arg_tys
          | Just Type
    ki' <- Type -> Maybe Type
    coreView Type
    ki = Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    subst Type
    ki' [Type]
    arg_tys
        go Subst
    _ Type
    _ [] = []
        go Subst
    subst (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    argf) Type
    res_ki) (Type
    arg_ty:[Type]
    arg_tys)
          = ForAllTyFlag
    argf ForAllTyFlag -> [ForAllTyFlag] -> [ForAllTyFlag]
    forall a. a -> [a] -> [a]
    : Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    subst' Type
    res_ki [Type]
    arg_tys
          where
            subst' :: Subst
    subst' = Subst -> TyVar -> Type -> Subst
    extendTvSubst Subst
    subst TyVar
    tv Type
    arg_ty
        go Subst
    subst (TyVarTy TyVar
    tv) [Type]
    arg_tys
          | Just Type
    ki <- Subst -> TyVar -> Maybe Type
    lookupTyVar Subst
    subst TyVar
    tv = Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    subst Type
    ki [Type]
    arg_tys
        -- This FunTy case is important to handle kinds with nested foralls, such
        -- as this kind (inspired by #16518):
        --
        --   forall {k1} k2. k1 -> k2 -> forall k3. k3 -> Type
        --
        -- Here, we want to get the following ForAllTyFlags:
        --
        -- [Inferred,   Specified, Required, Required, Specified, Required]
        -- forall {k1}. forall k2. k1 ->     k2 ->     forall k3. k3 ->     Type
        go Subst
    subst (FunTy{ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_res :: Type -> Type
    ft_res = Type
    res_ki}) (Type
    _:[Type]
    arg_tys)
          = ForAllTyFlag
    argf ForAllTyFlag -> [ForAllTyFlag] -> [ForAllTyFlag]
    forall a. a -> [a] -> [a]
    : Subst -> Type -> [Type] -> [ForAllTyFlag]
    go Subst
    subst Type
    res_ki [Type]
    arg_tys
          where
            argf :: ForAllTyFlag
    argf | FunTyFlag -> Bool
    isVisibleFunArg FunTyFlag
    af = ForAllTyFlag
    Required
                 | Bool
    otherwise          = ForAllTyFlag
    Inferred
        go Subst
    _ Type
    _ [Type]
    arg_tys = (Type -> ForAllTyFlag) -> [Type] -> [ForAllTyFlag]
    forall a b. (a -> b) -> [a] -> [b]
    map (ForAllTyFlag -> Type -> ForAllTyFlag
    forall a b. a -> b -> a
    const ForAllTyFlag
    Required) [Type]
    arg_tys
                            -- something is ill-kinded. But this can happen
                            -- when printing errors. Assume everything is Required.

    -- @isTauTy@ tests if a type has no foralls or (=>)
    isTauTy :: Type -> Bool
    isTauTy :: Type -> Bool
    isTauTy Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Bool
    isTauTy Type
    ty'
    isTauTy (TyVarTy TyVar
    _)       = Bool
    True
    isTauTy (LitTy {})        = Bool
    True
    isTauTy (TyConApp TyCon
    tc [Type]
    tys) = (Type -> Bool) -> [Type] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Type -> Bool
    isTauTy [Type]
    tys Bool -> Bool -> Bool
    && TyCon -> Bool
    isTauTyCon TyCon
    tc
    isTauTy (AppTy Type
    a Type
    b)       = Type -> Bool
    isTauTy Type
    a Bool -> Bool -> Bool
    && Type -> Bool
    isTauTy Type
    b
    isTauTy (FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    a, ft_res :: Type -> Type
    ft_res = Type
    b })
     | FunTyFlag -> Bool
    isInvisibleFunArg FunTyFlag
    af   = Bool
    False                               -- e.g., Eq a => b
     | Bool
    otherwise              = Type -> Bool
    isTauTy Type
    w Bool -> Bool -> Bool
    && Type -> Bool
    isTauTy Type
    a Bool -> Bool -> Bool
    && Type -> Bool
    isTauTy Type
    b -- e.g., a -> b
    isTauTy (ForAllTy {})     = Bool
    False
    isTauTy (CastTy Type
    ty KindCoercion
    _)     = Type -> Bool
    isTauTy Type
    ty
    isTauTy (CoercionTy KindCoercion
    _)    = Bool
    False  -- Not sure about this

    isAtomicTy :: Type -> Bool
    -- True if the type is just a single token, and can be printed compactly
    -- Used when deciding how to lay out type error messages; see the
    -- call in GHC.Tc.Errors
    isAtomicTy :: Type -> Bool
    isAtomicTy (TyVarTy {})    = Bool
    True
    isAtomicTy (LitTy {})      = Bool
    True
    isAtomicTy (TyConApp TyCon
    _ []) = Bool
    True

    isAtomicTy Type
    ty | Type -> Bool
    isLiftedTypeKind Type
    ty = Bool
    True
       -- 'Type' prints compactly as *
       -- See GHC.Iface.Type.ppr_kind_type

    isAtomicTy Type
    _ = Bool
    False

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Type families}
    *                                                                      *
    ************************************************************************
    -}

    mkFamilyTyConApp :: TyCon -> [Type] -> Type
    -- ^ Given a family instance TyCon and its arg types, return the
    -- corresponding family type.  E.g:
    --
    -- > data family T a
    -- > data instance T (Maybe b) = MkT b
    --
    -- Where the instance tycon is :RTL, so:
    --
    -- > mkFamilyTyConApp :RTL Int  =  T (Maybe Int)
    mkFamilyTyConApp :: TyCon -> [Type] -> Type
    mkFamilyTyConApp TyCon
    tc [Type]
    tys
      | Just (TyCon
    fam_tc, [Type]
    fam_tys) <- TyCon -> Maybe (TyCon, [Type])
    tyConFamInst_maybe TyCon
    tc
      , let tvs :: [TyVar]
    tvs = TyCon -> [TyVar]
    tyConTyVars TyCon
    tc
            fam_subst :: Subst
    fam_subst = Bool -> SDoc -> Subst -> Subst
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr ([TyVar]
    tvs [TyVar] -> [Type] -> Bool
    forall a b. [a] -> [b] -> Bool
    `equalLength` [Type]
    tys) (TyCon -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TyCon
    tc SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [Type] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Type]
    tys) (Subst -> Subst) -> Subst -> Subst
    forall a b. (a -> b) -> a -> b
    $
                        [TyVar] -> [Type] -> Subst
    HasDebugCallStack => [TyVar] -> [Type] -> Subst
    zipTvSubst [TyVar]
    tvs [Type]
    tys
      = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    fam_tc (HasDebugCallStack => Subst -> [Type] -> [Type]
    Subst -> [Type] -> [Type]
    substTys Subst
    fam_subst [Type]
    fam_tys)
      | Bool
    otherwise
      = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc [Type]
    tys

    -- | Get the type on the LHS of a coercion induced by a type/data
    -- family instance.
    coAxNthLHS :: CoAxiom br -> Int -> Type
    coAxNthLHS :: forall (br :: BranchFlag). CoAxiom br -> Arity -> Type
    coAxNthLHS CoAxiom br
    ax Arity
    ind =
      TyCon -> [Type] -> Type
    mkTyConApp (CoAxiom br -> TyCon
    forall (br :: BranchFlag). CoAxiom br -> TyCon
    coAxiomTyCon CoAxiom br
    ax) (CoAxBranch -> [Type]
    coAxBranchLHS (CoAxiom br -> Arity -> CoAxBranch
    forall (br :: BranchFlag). CoAxiom br -> Arity -> CoAxBranch
    coAxiomNthBranch CoAxiom br
    ax Arity
    ind))

    isFamFreeTy :: Type -> Bool
    isFamFreeTy :: Type -> Bool
    isFamFreeTy Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Bool
    isFamFreeTy Type
    ty'
    isFamFreeTy (TyVarTy TyVar
    _)       = Bool
    True
    isFamFreeTy (LitTy {})        = Bool
    True
    isFamFreeTy (TyConApp TyCon
    tc [Type]
    tys) = (Type -> Bool) -> [Type] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Type -> Bool
    isFamFreeTy [Type]
    tys Bool -> Bool -> Bool
    && TyCon -> Bool
    isFamFreeTyCon TyCon
    tc
    isFamFreeTy (AppTy Type
    a Type
    b)       = Type -> Bool
    isFamFreeTy Type
    a Bool -> Bool -> Bool
    && Type -> Bool
    isFamFreeTy Type
    b
    isFamFreeTy (FunTy FunTyFlag
    _ Type
    w Type
    a Type
    b)   = Type -> Bool
    isFamFreeTy Type
    w Bool -> Bool -> Bool
    && Type -> Bool
    isFamFreeTy Type
    a Bool -> Bool -> Bool
    && Type -> Bool
    isFamFreeTy Type
    b
    isFamFreeTy (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    ty)   = Type -> Bool
    isFamFreeTy Type
    ty
    isFamFreeTy (CastTy Type
    ty KindCoercion
    _)     = Type -> Bool
    isFamFreeTy Type
    ty
    isFamFreeTy (CoercionTy KindCoercion
    _)    = Bool
    False  -- Not sure about this

    buildSynTyCon :: Name -> [KnotTied TyConBinder] -> Kind   -- ^ /result/ kind
                  -> [Role] -> KnotTied Type -> TyCon
    -- This function is here because here is where we have
    --   isFamFree and isTauTy
    buildSynTyCon :: Name -> [TyConBinder] -> Type -> [Role] -> Type -> TyCon
    buildSynTyCon Name
    name [TyConBinder]
    binders Type
    res_kind [Role]
    roles Type
    rhs
      = Name
    -> [TyConBinder]
    -> Type
    -> [Role]
    -> Type
    -> Bool
    -> Bool
    -> Bool
    -> Bool
    -> TyCon
    mkSynonymTyCon Name
    name [TyConBinder]
    binders Type
    res_kind [Role]
    roles Type
    rhs
                       Bool
    is_tau Bool
    is_fam_free Bool
    is_forgetful Bool
    is_concrete
      where
        is_tau :: Bool
    is_tau       = Type -> Bool
    isTauTy Type
    rhs
        is_fam_free :: Bool
    is_fam_free  = Type -> Bool
    isFamFreeTy Type
    rhs
        is_concrete :: Bool
    is_concrete  = (TyCon -> Bool) -> UniqSet TyCon -> Bool
    forall a. (a -> Bool) -> UniqSet a -> Bool
    uniqSetAll TyCon -> Bool
    isConcreteTyCon UniqSet TyCon
    rhs_tycons
             -- NB: is_concrete is allowed to be conservative, returning False
             --     more often than it could.  e.g.
             --       type S a b = b
             --       type family F a
             --       type T a = S (F a) a
             -- We will mark T as not-concrete, even though (since S ignore its first
             -- argument, it could be marked concrete.

        is_forgetful :: Bool
    is_forgetful = Bool -> Bool
    not ((TyConBinder -> Bool) -> [TyConBinder] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all ((TyVar -> VarSet -> Bool
    `elemVarSet` VarSet
    rhs_tyvars) (TyVar -> Bool) -> (TyConBinder -> TyVar) -> TyConBinder -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . TyConBinder -> TyVar
    forall tv argf. VarBndr tv argf -> tv
    binderVar) [TyConBinder]
    binders) Bool -> Bool -> Bool
    ||
                       (TyCon -> Bool) -> UniqSet TyCon -> Bool
    forall a. (a -> Bool) -> UniqSet a -> Bool
    uniqSetAny TyCon -> Bool
    isForgetfulSynTyCon UniqSet TyCon
    rhs_tycons
             -- NB: is_forgetful is allowed to be conservative, returning True more often
             -- than it should. See comments on GHC.Core.TyCon.isForgetfulSynTyCon

        rhs_tycons :: UniqSet TyCon
    rhs_tycons = Type -> UniqSet TyCon
    tyConsOfType   Type
    rhs
        rhs_tyvars :: VarSet
    rhs_tyvars = Type -> VarSet
    tyCoVarsOfType Type
    rhs

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Liftedness}
    *                                                                      *
    ************************************************************************
    -}

    -- | Tries to compute the 'Levity' of the given type. Returns either
    -- a definite 'Levity', or 'Nothing' if we aren't sure (e.g. the
    -- type is representation-polymorphic).
    --
    -- Panics if the kind does not have the shape @TYPE r@.
    typeLevity_maybe :: HasDebugCallStack => Type -> Maybe Levity
    typeLevity_maybe :: HasDebugCallStack => Type -> Maybe Levity
    typeLevity_maybe Type
    ty = Type -> Maybe Levity
    runtimeRepLevity_maybe (HasDebugCallStack => Type -> Type
    Type -> Type
    getRuntimeRep Type
    ty)

    typeLevity :: HasDebugCallStack => Type -> Levity
    typeLevity :: HasDebugCallStack => Type -> Levity
    typeLevity Type
    ty = case HasDebugCallStack => Type -> Maybe Levity
    Type -> Maybe Levity
    typeLevity_maybe Type
    ty of
                       Just Levity
    lev -> Levity
    lev
                       Maybe Levity
    Nothing  -> String -> SDoc -> Levity
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "typeLevity" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

    -- | Is the given type definitely unlifted?
    -- See "Type#type_classification" for what an unlifted type is.
    --
    -- Panics on representation-polymorphic types; See 'mightBeUnliftedType' for
    -- a more approximate predicate that behaves better in the presence of
    -- representation polymorphism.
    isUnliftedType :: HasDebugCallStack => Type -> Bool
            -- isUnliftedType returns True for forall'd unlifted types:
            --      x :: forall a. Int#
            -- I found bindings like these were getting floated to the top level.
    isUnliftedType :: HasDebugCallStack => Type -> Bool
    isUnliftedType Type
    ty =
      case HasDebugCallStack => Type -> Maybe Levity
    Type -> Maybe Levity
    typeLevity_maybe Type
    ty of
        Just Levity
    Lifted   -> Bool
    False
        Just Levity
    Unlifted -> Bool
    True
        Maybe Levity
    Nothing       -> String -> SDoc -> Bool
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "isUnliftedType" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty))

    -- | Returns:
    --
    -- * 'False' if the type is /guaranteed/ unlifted or
    -- * 'True' if it lifted, OR we aren't sure
    --    (e.g. in a representation-polymorphic case)
    mightBeLiftedType :: Type -> Bool
    mightBeLiftedType :: Type -> Bool
    mightBeLiftedType = Maybe Levity -> Bool
    mightBeLifted (Maybe Levity -> Bool) -> (Type -> Maybe Levity) -> Type -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . HasDebugCallStack => Type -> Maybe Levity
    Type -> Maybe Levity
    typeLevity_maybe

    definitelyLiftedType :: Type -> Bool
    definitelyLiftedType :: Type -> Bool
    definitelyLiftedType = Bool -> Bool
    not (Bool -> Bool) -> (Type -> Bool) -> Type -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Bool
    mightBeUnliftedType

    -- | Returns:
    --
    -- * 'False' if the type is /guaranteed/ lifted or
    -- * 'True' if it is unlifted, OR we aren't sure
    --    (e.g. in a representation-polymorphic case)
    mightBeUnliftedType :: Type -> Bool
    mightBeUnliftedType :: Type -> Bool
    mightBeUnliftedType = Maybe Levity -> Bool
    mightBeUnlifted (Maybe Levity -> Bool) -> (Type -> Maybe Levity) -> Type -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . HasDebugCallStack => Type -> Maybe Levity
    Type -> Maybe Levity
    typeLevity_maybe

    definitelyUnliftedType :: Type -> Bool
    definitelyUnliftedType :: Type -> Bool
    definitelyUnliftedType = Bool -> Bool
    not (Bool -> Bool) -> (Type -> Bool) -> Type -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Bool
    mightBeLiftedType

    -- | See "Type#type_classification" for what a boxed type is.
    -- Panics on representation-polymorphic types; See 'mightBeUnliftedType' for
    -- a more approximate predicate that behaves better in the presence of
    -- representation polymorphism.
    isBoxedType :: Type -> Bool
    isBoxedType :: Type -> Bool
    isBoxedType Type
    ty = Type -> Bool
    isBoxedRuntimeRep (HasDebugCallStack => Type -> Type
    Type -> Type
    getRuntimeRep Type
    ty)

    -- | Is this a type of kind RuntimeRep? (e.g. LiftedRep)
    isRuntimeRepKindedTy :: Type -> Bool
    isRuntimeRepKindedTy :: Type -> Bool
    isRuntimeRepKindedTy = Type -> Bool
    isRuntimeRepTy (Type -> Bool) -> (Type -> Type) -> Type -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind

    -- | Drops prefix of RuntimeRep constructors in 'TyConApp's. Useful for e.g.
    -- dropping 'LiftedRep arguments of unboxed tuple TyCon applications:
    --
    --   dropRuntimeRepArgs [ 'LiftedRep, 'IntRep
    --                      , String, Int# ] == [String, Int#]
    --
    dropRuntimeRepArgs :: [Type] -> [Type]
    dropRuntimeRepArgs :: [Type] -> [Type]
    dropRuntimeRepArgs = (Type -> Bool) -> [Type] -> [Type]
    forall a. (a -> Bool) -> [a] -> [a]
    dropWhile Type -> Bool
    isRuntimeRepKindedTy

    -- | Extract the RuntimeRep classifier of a type. For instance,
    -- @getRuntimeRep_maybe Int = Just LiftedRep@. Returns 'Nothing' if this is not
    -- possible.
    getRuntimeRep_maybe :: HasDebugCallStack
                        => Type -> Maybe RuntimeRepType
    getRuntimeRep_maybe :: HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe = HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    kindRep_maybe (Type -> Maybe Type) -> (Type -> Type) -> Type -> Maybe Type
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind

    -- | Extract the RuntimeRep classifier of a type. For instance,
    -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible.
    getRuntimeRep :: HasDebugCallStack => Type -> RuntimeRepType
    getRuntimeRep :: HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty
      = case HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    getRuntimeRep_maybe Type
    ty of
          Just Type
    r  -> Type
    r
          Maybe Type
    Nothing -> String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "getRuntimeRep" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty))

    -- | Extract the 'Levity' of a type. For example, @getLevity_maybe Int = Just Lifted@,
    -- @getLevity (Array# Int) = Just Unlifted@, @getLevity Float# = Nothing@.
    --
    -- Returns 'Nothing' if this is not possible. Does not look through type family applications.
    getLevity_maybe :: HasDebugCallStack => Type -> Maybe Type
    getLevity_maybe :: HasDebugCallStack => Type -> Maybe Type
    getLevity_maybe Type
    ty
      | Just Type
    rep <- HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    getRuntimeRep_maybe Type
    ty
      -- Directly matching on TyConApp after expanding type synonyms
      -- saves allocations compared to `splitTyConApp_maybe`. See #22254.
      -- Given that this is a pretty hot function we make use of the fact
      -- and use isTyConKeyApp_maybe instead.
      , Just [Type
    lev] <- Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    boxedRepDataConKey Type
    rep
      = Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    lev
      | Bool
    otherwise
      = Maybe Type
    forall a. Maybe a
    Nothing

    -- | Extract the 'Levity' of a type. For example, @getLevity Int = Lifted@,
    -- or @getLevity (Array# Int) = Unlifted@.
    --
    -- Panics if this is not possible. Does not look through type family applications.
    getLevity :: HasDebugCallStack => Type -> Type
    getLevity :: HasDebugCallStack => Type -> Type
    getLevity Type
    ty
      | Just Type
    lev <- HasDebugCallStack => Type -> Maybe Type
    Type -> Maybe Type
    getLevity_maybe Type
    ty
      = Type
    lev
      | Bool
    otherwise
      = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "getLevity" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty))

    isUnboxedTupleType :: Type -> Bool
    isUnboxedTupleType :: Type -> Bool
    isUnboxedTupleType Type
    ty
      = HasDebugCallStack => Type -> TyCon
    Type -> TyCon
    tyConAppTyCon (HasDebugCallStack => Type -> Type
    Type -> Type
    getRuntimeRep Type
    ty) TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    tupleRepDataConKey
      -- NB: Do not use typePrimRep, as that can't tell the difference between
      -- unboxed tuples and unboxed sums

    isUnboxedSumType :: Type -> Bool
    isUnboxedSumType :: Type -> Bool
    isUnboxedSumType Type
    ty
      = HasDebugCallStack => Type -> TyCon
    Type -> TyCon
    tyConAppTyCon (HasDebugCallStack => Type -> Type
    Type -> Type
    getRuntimeRep Type
    ty) TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    sumRepDataConKey

    -- | See "Type#type_classification" for what an algebraic type is.
    -- Should only be applied to /types/, as opposed to e.g. partially
    -- saturated type constructors
    isAlgType :: Type -> Bool
    isAlgType :: Type -> Bool
    isAlgType Type
    ty
      = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
          Just (TyCon
    tc, [Type]
    ty_args) -> Bool -> (TyCon -> Bool) -> TyCon -> Bool
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type]
    ty_args [Type] -> Arity -> Bool
    forall a. [a] -> Arity -> Bool
    `lengthIs` TyCon -> Arity
    tyConArity TyCon
    tc )
                                TyCon -> Bool
    isAlgTyCon TyCon
    tc
          Maybe (TyCon, [Type])
    _other             -> Bool
    False

    -- | Check whether a type is a data family type
    isDataFamilyAppType :: Type -> Bool
    isDataFamilyAppType :: Type -> Bool
    isDataFamilyAppType Type
    ty = case Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty of
                               Just TyCon
    tc -> TyCon -> Bool
    isDataFamilyTyCon TyCon
    tc
                               Maybe TyCon
    _       -> Bool
    False

    -- | Computes whether an argument (or let right hand side) should
    -- be computed strictly or lazily, based only on its type.
    -- Currently, it's just 'isUnliftedType'.
    -- Panics on representation-polymorphic types.
    isStrictType :: HasDebugCallStack => Type -> Bool
    isStrictType :: HasDebugCallStack => Type -> Bool
    isStrictType = HasDebugCallStack => Type -> Bool
    Type -> Bool
    isUnliftedType

    isTerminatingType :: HasDebugCallStack => Type -> Bool
    -- ^ True <=> a term of this type cannot be bottom
    -- This identifies the types described by
    --    Note [NON-BOTTOM-DICTS invariant] in GHC.Core
    -- NB: unlifted types are not terminating types!
    --     e.g. you can write a term (loop 1)::Int# that diverges.
    isTerminatingType :: HasDebugCallStack => Type -> Bool
    isTerminatingType Type
    ty = case Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty of
        Just TyCon
    tc -> TyCon -> Bool
    isClassTyCon TyCon
    tc Bool -> Bool -> Bool
    && Bool -> Bool
    not (TyCon -> Bool
    isNewTyCon TyCon
    tc)
        Maybe TyCon
    _       -> Bool
    False

    -- | Does this type classify a core (unlifted) Coercion?
    -- At either role nominal or representational
    --    (t1 ~# t2) or (t1 ~R# t2)
    -- See Note [Types for coercions, predicates, and evidence] in "GHC.Core.TyCo.Rep"
    isCoVarType :: Type -> Bool
      -- ToDo: should we check saturation?
    isCoVarType :: Type -> Bool
    isCoVarType Type
    ty
      | Just TyCon
    tc <- Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty
      = TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    eqPrimTyConKey Bool -> Bool -> Bool
    || TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    eqReprPrimTyConKey
      | Bool
    otherwise
      = Bool
    False

    isPrimitiveType :: Type -> Bool
    -- ^ Returns true of types that are opaque to Haskell.
    isPrimitiveType :: Type -> Bool
    isPrimitiveType Type
    ty = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
                            Just (TyCon
    tc, [Type]
    ty_args) -> Bool -> (TyCon -> Bool) -> TyCon -> Bool
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type]
    ty_args [Type] -> Arity -> Bool
    forall a. [a] -> Arity -> Bool
    `lengthIs` TyCon -> Arity
    tyConArity TyCon
    tc )
                                                  TyCon -> Bool
    isPrimTyCon TyCon
    tc
                            Maybe (TyCon, [Type])
    _                  -> Bool
    False

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Join points}
    *                                                                      *
    ************************************************************************
    -}

    -- | Determine whether a type could be the type of a join point of given total
    -- arity, according to the polymorphism rule. A join point cannot be polymorphic
    -- in its return type, since given
    --   join j @a @b x y z = e1 in e2,
    -- the types of e1 and e2 must be the same, and a and b are not in scope for e2.
    -- (See Note [The polymorphism rule of join points] in "GHC.Core".) Returns False
    -- also if the type simply doesn't have enough arguments.
    --
    -- Note that we need to know how many arguments (type *and* value) the putative
    -- join point takes; for instance, if
    --   j :: forall a. a -> Int
    -- then j could be a binary join point returning an Int, but it could *not* be a
    -- unary join point returning a -> Int.
    --
    -- TODO: See Note [Excess polymorphism and join points]
    isValidJoinPointType :: JoinArity -> Type -> Bool
    isValidJoinPointType :: Arity -> Type -> Bool
    isValidJoinPointType Arity
    arity Type
    ty
      = VarSet -> Arity -> Type -> Bool
    forall {t}. (Eq t, Num t) => VarSet -> t -> Type -> Bool
    valid_under VarSet
    emptyVarSet Arity
    arity Type
    ty
      where
        valid_under :: VarSet -> t -> Type -> Bool
    valid_under VarSet
    tvs t
    arity Type
    ty
          | t
    arity t -> t -> Bool
    forall a. Eq a => a -> a -> Bool
    == t
    0
          = VarSet
    tvs VarSet -> VarSet -> Bool
    `disjointVarSet` Type -> VarSet
    tyCoVarsOfType Type
    ty
          | Just (TyVar
    t, Type
    ty') <- Type -> Maybe (TyVar, Type)
    splitForAllTyCoVar_maybe Type
    ty
          = VarSet -> t -> Type -> Bool
    valid_under (VarSet
    tvs VarSet -> TyVar -> VarSet
    `extendVarSet` TyVar
    t) (t
    arityt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1) Type
    ty'
          | Just (FunTyFlag
    _, Type
    _, Type
    _, Type
    res_ty) <- Type -> Maybe (FunTyFlag, Type, Type, Type)
    splitFunTy_maybe Type
    ty
          = VarSet -> t -> Type -> Bool
    valid_under VarSet
    tvs (t
    arityt -> t -> t
    forall a. Num a => a -> a -> a
    -t
    1) Type
    res_ty
          | Bool
    otherwise
          = Bool
    False

    {- Note [Excess polymorphism and join points]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In principle, if a function would be a join point except that it fails
    the polymorphism rule (see Note [The polymorphism rule of join points] in
    GHC.Core), it can still be made a join point with some effort. This is because
    all tail calls must return the same type (they return to the same context!), and
    thus if the return type depends on an argument, that argument must always be the
    same.

    For instance, consider:

      let f :: forall a. a -> Char -> [a]
          f @a x c = ... f @a y 'a' ...
      in ... f @Int 1 'b' ... f @Int 2 'c' ...

    (where the calls are tail calls). `f` fails the polymorphism rule because its
    return type is [a], where [a] is bound. But since the type argument is always
    'Int', we can rewrite it as:

      let f' :: Int -> Char -> [Int]
          f' x c = ... f' y 'a' ...
      in ... f' 1 'b' ... f 2 'c' ...

    and now we can make f' a join point:

      join f' :: Int -> Char -> [Int]
           f' x c = ... jump f' y 'a' ...
      in ... jump f' 1 'b' ... jump f' 2 'c' ...

    It's not clear that this comes up often, however. TODO: Measure how often and
    add this analysis if necessary.  See #14620.

    ************************************************************************
    *                                                                      *
    \subsection{Sequencing on types}
    *                                                                      *
    ************************************************************************
    -}

    seqType :: Type -> ()
    seqType :: Type -> ()
    seqType (LitTy TyLit
    n)                   = TyLit
    n TyLit -> () -> ()
    forall a b. a -> b -> b
    `seq` ()
    seqType (TyVarTy TyVar
    tv)                = TyVar
    tv TyVar -> () -> ()
    forall a b. a -> b -> b
    `seq` ()
    seqType (AppTy Type
    t1 Type
    t2)               = Type -> ()
    seqType Type
    t1 () -> () -> ()
    forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t2
    seqType (FunTy FunTyFlag
    _ Type
    w Type
    t1 Type
    t2)           = Type -> ()
    seqType Type
    w () -> () -> ()
    forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t1 () -> () -> ()
    forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t2
    seqType (TyConApp TyCon
    tc [Type]
    tys)           = TyCon
    tc TyCon -> () -> ()
    forall a b. a -> b -> b
    `seq` [Type] -> ()
    seqTypes [Type]
    tys
    seqType (ForAllTy (Bndr TyVar
    tv ForAllTyFlag
    _) Type
    ty)   = Type -> ()
    seqType (TyVar -> Type
    varType TyVar
    tv) () -> () -> ()
    forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    ty
    seqType (CastTy Type
    ty KindCoercion
    co)              = Type -> ()
    seqType Type
    ty () -> () -> ()
    forall a b. a -> b -> b
    `seq` KindCoercion -> ()
    seqCo KindCoercion
    co
    seqType (CoercionTy KindCoercion
    co)             = KindCoercion -> ()
    seqCo KindCoercion
    co

    seqTypes :: [Type] -> ()
    seqTypes :: [Type] -> ()
    seqTypes []       = ()
    seqTypes (Type
    ty:[Type]
    tys) = Type -> ()
    seqType Type
    ty () -> () -> ()
    forall a b. a -> b -> b
    `seq` [Type] -> ()
    seqTypes [Type]
    tys

    {-
    ************************************************************************
    *                                                                      *
            The kind of a type
    *                                                                      *
    ************************************************************************

    Note [Kinding rules for types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Here are the key kinding rules for types

              torc1 is TYPE or CONSTRAINT
              torc2 is TYPE or CONSTRAINT
              t1 : torc1 rep1
              t2 : torc2 rep2
       (FUN)  ----------------
              t1 -> t2 : torc2 LiftedRep
              -- In fact the arrow varies with torc1/torc2
              -- See Note [Function type constructors and FunTy]
              -- in GHC.Builtin.Types.Prim

              torc is TYPE or CONSTRAINT
              ty : body_torc rep
              ki : Type
              `a` is a type variable
              `a` is not free in rep
    (FORALL1) -----------------------
              forall (a::ki). ty : body_torc rep

              torc is TYPE or CONSTRAINT
              ty : body_torc rep
              `c` is a coercion variable
              `c` is not free in rep
              `c` is free in ty       -- Surprise 1!
    (FORALL2) -------------------------
              forall (cv::k1 ~#{N,R} k2). ty : body_torc LiftedRep
                                               -- Surprise 2!

    Note that:
    * (FORALL1) rejects (forall (a::Maybe). blah)

    * (FORALL2) Surprise 1:
      See GHC.Core.TyCo.Rep Note [Unused coercion variable in ForAllTy]

    * (FORALL2) Surprise 2: coercion abstractions are not erased, so
      this must be LiftedRep, just like (FUN).  (FORALL2) is just a
      dependent form of (FUN).

    Note [Phantom type variables in kinds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider

      type K (r :: RuntimeRep) = Type   -- Note 'r' is unused
      data T r :: K r                   -- T :: forall r -> K r
      foo :: forall r. T r

    The body of the forall in foo's type has kind (K r), and
    normally it would make no sense to have
       forall r. (ty :: K r)
    because the kind of the forall would escape the binding
    of 'r'.  But in this case it's fine because (K r) expands
    to Type, so we explicitly /permit/ the type
       forall r. T r

    To accommodate such a type, in typeKind (forall a.ty) we use
    occCheckExpand to expand any type synonyms in the kind of 'ty'
    to eliminate 'a'.  See kinding rule (FORALL) in
    Note [Kinding rules for types]

    See also
     * GHC.Core.Type.occCheckExpand
     * GHC.Core.Utils.coreAltsType
     * GHC.Tc.Validity.checkEscapingKind
    all of which grapple with the same problem.

    See #14939.
    -}

    -----------------------------
    typeKind :: HasDebugCallStack => Type -> Kind
    -- No need to expand synonyms
    typeKind :: HasDebugCallStack => Type -> Type
    typeKind (TyConApp TyCon
    tc [Type]
    tys)      = HasDebugCallStack => Type -> [Type] -> Type
    Type -> [Type] -> Type
    piResultTys (TyCon -> Type
    tyConKind TyCon
    tc) [Type]
    tys
    typeKind (LitTy TyLit
    l)              = TyLit -> Type
    typeLiteralKind TyLit
    l
    typeKind (FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af }) = case FunTyFlag -> TypeOrConstraint
    funTyFlagResultTypeOrConstraint FunTyFlag
    af of
                                         TypeOrConstraint
    TypeLike       -> Type
    liftedTypeKind
                                         TypeOrConstraint
    ConstraintLike -> Type
    constraintKind
    typeKind (TyVarTy TyVar
    tyvar)        = TyVar -> Type
    tyVarKind TyVar
    tyvar
    typeKind (CastTy Type
    _ty KindCoercion
    co)        = KindCoercion -> Type
    coercionRKind KindCoercion
    co
    typeKind (CoercionTy KindCoercion
    co)        = KindCoercion -> Type
    coercionType KindCoercion
    co

    typeKind (AppTy Type
    fun Type
    arg)
      = Type -> [Type] -> Type
    go Type
    fun [Type
    arg]
      where
        -- Accumulate the type arguments, so we can call piResultTys,
        -- rather than a succession of calls to piResultTy (which is
        -- asymptotically costly as the number of arguments increases)
        go :: Type -> [Type] -> Type
    go (AppTy Type
    fun Type
    arg) [Type]
    args = Type -> [Type] -> Type
    go Type
    fun (Type
    argType -> [Type] -> [Type]
    forall a. a -> [a] -> [a]
    :[Type]
    args)
        go Type
    fun             [Type]
    args = HasDebugCallStack => Type -> [Type] -> Type
    Type -> [Type] -> Type
    piResultTys (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    fun) [Type]
    args

    typeKind ty :: Type
    ty@(ForAllTy {})
      = Bool -> SDoc -> Type -> Type
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Bool -> Bool
    not ([TyVar] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [TyVar]
    tcvs)) (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty) (Type -> Type) -> Type -> Type
    forall a b. (a -> b) -> a -> b
    $
           -- If tcvs is empty somehow we'll get an infinite loop!
        case [TyVar] -> Type -> Maybe Type
    occCheckExpand [TyVar]
    tcvs Type
    body_kind of
          -- We must make sure tvs do not occur in kind,
          -- as they would be out of scope!
          -- See Note [Phantom type variables in kinds]
          Maybe Type
    Nothing -> String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "typeKind"
                      (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ [TyVar] -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tcvs SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    body SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    body_kind)

          Just Type
    k' | (TyVar -> Bool) -> [TyVar] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all TyVar -> Bool
    isTyVar [TyVar]
    tcvs -> Type
    k'                     -- Rule (FORALL1)
                  | Bool
    otherwise        -> Type
    lifted_kind_from_body  -- Rule (FORALL2)
      where
        ([TyVar]
    tcvs, Type
    body) = Type -> ([TyVar], Type)
    splitForAllTyCoVars Type
    ty  -- Important: splits both TyVar and CoVar binders
        body_kind :: Type
    body_kind    = HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    body

        lifted_kind_from_body :: Type
    lifted_kind_from_body  -- Implements (FORALL2)
          = case Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    body_kind of
              Just (TypeOrConstraint
    ConstraintLike, Type
    _) -> Type
    constraintKind
              Just (TypeOrConstraint
    TypeLike,       Type
    _) -> Type
    liftedTypeKind
              Maybe (TypeOrConstraint, Type)
    Nothing -> String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "typeKind" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    body_kind)

    ---------------------------------------------

    sORTKind_maybe :: Kind -> Maybe (TypeOrConstraint, Type)
    -- Sees if the argument is of form (TYPE rep) or (CONSTRAINT rep)
    -- and if so returns which, and the runtime rep
    --
    -- This is a "hot" function.  Do not call splitTyConApp_maybe here,
    -- to avoid the faff with FunTy
    sORTKind_maybe :: Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe (TyConApp TyCon
    tc [Type]
    tys)
      -- First, short-cuts for Type and Constraint that do no allocation
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    liftedTypeKindTyConKey = Bool
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. HasCallStack => Bool -> a -> a
    assert( [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys ) (Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type))
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a b. (a -> b) -> a -> b
    $ (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. a -> Maybe a
    Just (TypeOrConstraint
    TypeLike,       Type
    liftedRepTy)
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    constraintKindTyConKey = Bool
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. HasCallStack => Bool -> a -> a
    assert( [Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys ) (Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type))
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a b. (a -> b) -> a -> b
    $ (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. a -> Maybe a
    Just (TypeOrConstraint
    ConstraintLike, Type
    liftedRepTy)
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    tYPETyConKey           = TypeOrConstraint -> Maybe (TypeOrConstraint, Type)
    get_rep TypeOrConstraint
    TypeLike
      | Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    cONSTRAINTTyConKey     = TypeOrConstraint -> Maybe (TypeOrConstraint, Type)
    get_rep TypeOrConstraint
    ConstraintLike
      | Just Type
    ty' <- TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys = Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    ty'
      where
        !tc_uniq :: Unique
    tc_uniq = TyCon -> Unique
    tyConUnique TyCon
    tc
         -- This bang on tc_uniq is important.  It means that sORTKind_maybe starts
         -- by evaluating tc_uniq, and then ends up with a single case with a 4-way branch

        get_rep :: TypeOrConstraint -> Maybe (TypeOrConstraint, Type)
    get_rep TypeOrConstraint
    torc = case [Type]
    tys of
                         (Type
    rep:[Type]
    _reps) -> Bool
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    _reps) (Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type))
    -> Maybe (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a b. (a -> b) -> a -> b
    $ (TypeOrConstraint, Type) -> Maybe (TypeOrConstraint, Type)
    forall a. a -> Maybe a
    Just (TypeOrConstraint
    torc, Type
    rep)
                         []          -> Maybe (TypeOrConstraint, Type)
    forall a. Maybe a
    Nothing

    sORTKind_maybe Type
    _ = Maybe (TypeOrConstraint, Type)
    forall a. Maybe a
    Nothing

    typeTypeOrConstraint :: HasDebugCallStack => Type -> TypeOrConstraint
    -- Precondition: expects a type that classifies values.
    -- Returns whether it is TypeLike or ConstraintLike.
    -- Equivalent to calling sORTKind_maybe, but faster in the FunTy case
    typeTypeOrConstraint :: HasDebugCallStack => Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    ty
       = case Type -> Type
    coreFullView Type
    ty of
           FunTy { ft_af :: Type -> FunTyFlag
    ft_af = FunTyFlag
    af } -> FunTyFlag -> TypeOrConstraint
    funTyFlagResultTypeOrConstraint FunTyFlag
    af
           Type
    ty' | Just (TypeOrConstraint
    torc, Type
    _) <- Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty')
              -> TypeOrConstraint
    torc
              | Bool
    otherwise
              -> String -> SDoc -> TypeOrConstraint
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "typeOrConstraint" (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty))

    isPredTy :: HasDebugCallStack => Type -> Bool
    -- Precondition: expects a type that classifies values
    -- See Note [Types for coercions, predicates, and evidence] in GHC.Core.TyCo.Rep
    -- Returns True for types of kind (CONSTRAINT _), False for ones of kind (TYPE _)
    isPredTy :: HasDebugCallStack => Type -> Bool
    isPredTy Type
    ty = case HasDebugCallStack => Type -> TypeOrConstraint
    Type -> TypeOrConstraint
    typeTypeOrConstraint Type
    ty of
                      TypeOrConstraint
    TypeLike       -> Bool
    False
                      TypeOrConstraint
    ConstraintLike -> Bool
    True

    -- | Does this classify a type allowed to have values? Responds True to things
    -- like *, TYPE Lifted, TYPE IntRep, TYPE v, Constraint.
    isTYPEorCONSTRAINT :: Kind -> Bool
    -- ^ True of a kind `TYPE _` or `CONSTRAINT _`
    isTYPEorCONSTRAINT :: Type -> Bool
    isTYPEorCONSTRAINT Type
    k = Maybe (TypeOrConstraint, Type) -> Bool
    forall a. Maybe a -> Bool
    isJust (Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    k)

    tyConIsTYPEorCONSTRAINT :: TyCon -> Bool
    tyConIsTYPEorCONSTRAINT :: TyCon -> Bool
    tyConIsTYPEorCONSTRAINT TyCon
    tc
      = Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    tYPETyConKey Bool -> Bool -> Bool
    || Unique
    tc_uniq Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    cONSTRAINTTyConKey
      where
        !tc_uniq :: Unique
    tc_uniq = TyCon -> Unique
    tyConUnique TyCon
    tc

    isConstraintLikeKind :: Kind -> Bool
    -- True of (CONSTRAINT _)
    isConstraintLikeKind :: Type -> Bool
    isConstraintLikeKind Type
    kind
      = case Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind of
          Just (TypeOrConstraint
    ConstraintLike, Type
    _) -> Bool
    True
          Maybe (TypeOrConstraint, Type)
    _                        -> Bool
    False

    isConstraintKind :: Kind -> Bool
    -- True of (CONSTRAINT LiftedRep)
    isConstraintKind :: Type -> Bool
    isConstraintKind Type
    kind
      = case Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind of
          Just (TypeOrConstraint
    ConstraintLike, Type
    rep) -> Type -> Bool
    isLiftedRuntimeRep Type
    rep
          Maybe (TypeOrConstraint, Type)
    _                          -> Bool
    False

    tcIsLiftedTypeKind :: Kind -> Bool
    -- ^ Is this kind equivalent to 'Type' i.e. TYPE LiftedRep?
    tcIsLiftedTypeKind :: Type -> Bool
    tcIsLiftedTypeKind Type
    kind
      | Just (TypeOrConstraint
    TypeLike, Type
    rep) <- Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind
      = Type -> Bool
    isLiftedRuntimeRep Type
    rep
      | Bool
    otherwise
      = Bool
    False

    tcIsBoxedTypeKind :: Kind -> Bool
    -- ^ Is this kind equivalent to @TYPE (BoxedRep l)@ for some @l :: Levity@?
    tcIsBoxedTypeKind :: Type -> Bool
    tcIsBoxedTypeKind Type
    kind
      | Just (TypeOrConstraint
    TypeLike, Type
    rep) <- Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind
      = Type -> Bool
    isBoxedRuntimeRep Type
    rep
      | Bool
    otherwise
      = Bool
    False

    -- | Is this kind equivalent to @TYPE r@ (for some unknown r)?
    --
    -- This considers 'Constraint' to be distinct from @*@.
    isTypeLikeKind :: Kind -> Bool
    isTypeLikeKind :: Type -> Bool
    isTypeLikeKind Type
    kind
      = case Type -> Maybe (TypeOrConstraint, Type)
    sORTKind_maybe Type
    kind of
          Just (TypeOrConstraint
    TypeLike, Type
    _) -> Bool
    True
          Maybe (TypeOrConstraint, Type)
    _                  -> Bool
    False

    returnsConstraintKind :: Kind -> Bool
    -- True <=> the Kind ultimately returns a Constraint
    --   E.g.  * -> Constraint
    --         forall k. k -> Constraint
    returnsConstraintKind :: Type -> Bool
    returnsConstraintKind Type
    kind
      | Just Type
    kind' <- Type -> Maybe Type
    coreView Type
    kind = Type -> Bool
    returnsConstraintKind Type
    kind'
    returnsConstraintKind (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    ty)         = Type -> Bool
    returnsConstraintKind Type
    ty
    returnsConstraintKind (FunTy { ft_res :: Type -> Type
    ft_res = Type
    ty }) = Type -> Bool
    returnsConstraintKind Type
    ty
    returnsConstraintKind Type
    kind                    = Type -> Bool
    isConstraintLikeKind Type
    kind

    --------------------------
    typeLiteralKind :: TyLit -> Kind
    typeLiteralKind :: TyLit -> Type
    typeLiteralKind (NumTyLit {}) = Type
    naturalTy
    typeLiteralKind (StrTyLit {}) = Type
    typeSymbolKind
    typeLiteralKind (CharTyLit {}) = Type
    charTy

    -- | Returns True if a type has a syntactically fixed runtime rep,
    -- as per Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.
    --
    -- This function is equivalent to `isFixedRuntimeRepKind . typeKind`
    -- but much faster.
    --
    -- __Precondition:__ The type has kind @('TYPE' blah)@
    typeHasFixedRuntimeRep :: HasDebugCallStack => Type -> Bool
    typeHasFixedRuntimeRep :: HasDebugCallStack => Type -> Bool
    typeHasFixedRuntimeRep = Type -> Bool
    go
      where
        go :: Type -> Bool
    go (TyConApp TyCon
    tc [Type]
    _)
          | TyCon -> Bool
    tcHasFixedRuntimeRep TyCon
    tc = Bool
    True
        go (FunTy {})               = Bool
    True
        go (LitTy {})               = Bool
    True
        go (ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    ty)          = Type -> Bool
    go Type
    ty
        go Type
    ty                       = HasDebugCallStack => Type -> Bool
    Type -> Bool
    isFixedRuntimeRepKind (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    ty)

    -- | Checks that a kind of the form 'Type', 'Constraint'
    -- or @'TYPE r@ is concrete. See 'isConcreteType'.
    --
    -- __Precondition:__ The type has kind `TYPE blah` or `CONSTRAINT blah`
    isFixedRuntimeRepKind :: HasDebugCallStack => Kind -> Bool
    isFixedRuntimeRepKind :: HasDebugCallStack => Type -> Bool
    isFixedRuntimeRepKind Type
    k
      = Bool -> SDoc -> Bool -> Bool
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Type -> Bool
    isTYPEorCONSTRAINT Type
    k) (Type -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Type
    k) (Bool -> Bool) -> Bool -> Bool
    forall a b. (a -> b) -> a -> b
    $
        -- the isLiftedTypeKind check is necessary b/c of Constraint
        Type -> Bool
    isConcreteType Type
    k

    -- | Tests whether the given type is concrete, i.e. it
    -- whether it consists only of concrete type constructors,
    -- concrete type variables, and applications.
    --
    -- See Note [Concrete types] in GHC.Tc.Utils.Concrete.
    isConcreteType :: Type -> Bool
    isConcreteType :: Type -> Bool
    isConcreteType = Type -> Bool
    go
      where
        go :: Type -> Bool
    go (TyVarTy TyVar
    tv)        = TyVar -> Bool
    isConcreteTyVar TyVar
    tv
        go (AppTy Type
    ty1 Type
    ty2)     = Type -> Bool
    go Type
    ty1 Bool -> Bool -> Bool
    && Type -> Bool
    go Type
    ty2
        go (TyConApp TyCon
    tc [Type]
    tys)   = TyCon -> [Type] -> Bool
    go_tc TyCon
    tc [Type]
    tys
        go ForAllTy{}          = Bool
    False
        go (FunTy FunTyFlag
    _ Type
    w Type
    t1 Type
    t2)   =  Type -> Bool
    go Type
    w
                               Bool -> Bool -> Bool
    && Type -> Bool
    go (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    t1) Bool -> Bool -> Bool
    && Type -> Bool
    go Type
    t1
                               Bool -> Bool -> Bool
    && Type -> Bool
    go (HasDebugCallStack => Type -> Type
    Type -> Type
    typeKind Type
    t2) Bool -> Bool -> Bool
    && Type -> Bool
    go Type
    t2
        go LitTy{}             = Bool
    True
        go CastTy{}            = Bool
    False
        go CoercionTy{}        = Bool
    False

        go_tc :: TyCon -> [Type] -> Bool
    go_tc TyCon
    tc [Type]
    tys
          | TyCon -> Bool
    isForgetfulSynTyCon TyCon
    tc  -- E.g. type S a = Int
                                    -- Then (S x) is concrete even if x isn't
          , Just Type
    ty' <- TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
          = Type -> Bool
    go Type
    ty'

          -- Apart from forgetful synonyms, isConcreteTyCon
          -- is enough; no need to expand.  This is good for e.g
          --      type LiftedRep = BoxedRep Lifted
          | TyCon -> Bool
    isConcreteTyCon TyCon
    tc
          = (Type -> Bool) -> [Type] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all Type -> Bool
    go [Type]
    tys

          | Bool
    otherwise  -- E.g. type families
          = Bool
    False

    {-
    %************************************************************************
    %*                                                                      *
             Pretty-printing
    %*                                                                      *
    %************************************************************************

    Most pretty-printing is either in GHC.Core.TyCo.Rep or GHC.Iface.Type.

    -}

    -- | Does a 'TyCon' (that is applied to some number of arguments) need to be
    -- ascribed with an explicit kind signature to resolve ambiguity if rendered as
    -- a source-syntax type?
    -- (See @Note [When does a tycon application need an explicit kind signature?]@
    -- for a full explanation of what this function checks for.)
    tyConAppNeedsKindSig
      :: Bool  -- ^ Should specified binders count towards injective positions in
               --   the kind of the TyCon? (If you're using visible kind
               --   applications, then you want True here.
      -> TyCon
      -> Int   -- ^ The number of args the 'TyCon' is applied to.
      -> Bool  -- ^ Does @T t_1 ... t_n@ need a kind signature? (Where @n@ is the
               --   number of arguments)
    tyConAppNeedsKindSig :: Bool -> TyCon -> Arity -> Bool
    tyConAppNeedsKindSig Bool
    spec_inj_pos TyCon
    tc Arity
    n_args
      | Ordering
    LT <- [TyConBinder] -> Arity -> Ordering
    forall a. [a] -> Arity -> Ordering
    listLengthCmp [TyConBinder]
    tc_binders Arity
    n_args
      = Bool
    False
      | Bool
    otherwise
      = let ([TyConBinder]
    dropped_binders, [TyConBinder]
    remaining_binders)
              = Arity -> [TyConBinder] -> ([TyConBinder], [TyConBinder])
    forall a. Arity -> [a] -> ([a], [a])
    splitAt Arity
    n_args [TyConBinder]
    tc_binders
            result_kind :: Type
    result_kind  = [TyConBinder] -> Type -> Type
    mkTyConKind [TyConBinder]
    remaining_binders Type
    tc_res_kind
            result_vars :: VarSet
    result_vars  = Type -> VarSet
    tyCoVarsOfType Type
    result_kind
            dropped_vars :: VarSet
    dropped_vars = FV -> VarSet
    fvVarSet (FV -> VarSet) -> FV -> VarSet
    forall a b. (a -> b) -> a -> b
    $
                           (TyConBinder -> FV) -> [TyConBinder] -> FV
    forall a. (a -> FV) -> [a] -> FV
    mapUnionFV TyConBinder -> FV
    injective_vars_of_binder [TyConBinder]
    dropped_binders

        in Bool -> Bool
    not (VarSet -> VarSet -> Bool
    subVarSet VarSet
    result_vars VarSet
    dropped_vars)
      where
        tc_binders :: [TyConBinder]
    tc_binders  = TyCon -> [TyConBinder]
    tyConBinders TyCon
    tc
        tc_res_kind :: Type
    tc_res_kind = TyCon -> Type
    tyConResKind TyCon
    tc

        -- Returns the variables that would be fixed by knowing a TyConBinder. See
        -- Note [When does a tycon application need an explicit kind signature?]
        -- for a more detailed explanation of what this function does.
        injective_vars_of_binder :: TyConBinder -> FV
        injective_vars_of_binder :: TyConBinder -> FV
    injective_vars_of_binder (Bndr TyVar
    tv TyConBndrVis
    vis) =
          case TyConBndrVis
    vis of
            TyConBndrVis
    AnonTCB        -> Bool -> Type -> FV
    injectiveVarsOfType Bool
    False -- conservative choice
                                                  (TyVar -> Type
    varType TyVar
    tv)
            NamedTCB ForAllTyFlag
    argf  | ForAllTyFlag -> Bool
    source_of_injectivity ForAllTyFlag
    argf
                           -> TyVar -> FV
    unitFV TyVar
    tv FV -> FV -> FV
    `unionFV`
                              Bool -> Type -> FV
    injectiveVarsOfType Bool
    False (TyVar -> Type
    varType TyVar
    tv)
            TyConBndrVis
    _              -> FV
    emptyFV

        source_of_injectivity :: ForAllTyFlag -> Bool
    source_of_injectivity ForAllTyFlag
    Required  = Bool
    True
        source_of_injectivity ForAllTyFlag
    Specified = Bool
    spec_inj_pos
        source_of_injectivity ForAllTyFlag
    Inferred  = Bool
    False

    {-
    Note [When does a tycon application need an explicit kind signature?]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    There are a couple of places in GHC where we convert Core Types into forms that
    more closely resemble user-written syntax. These include:

    1. Template Haskell Type reification (see, for instance, GHC.Tc.Gen.Splice.reify_tc_app)
    2. Converting Types to LHsTypes (such as in Haddock.Convert in haddock)

    This conversion presents a challenge: how do we ensure that the resulting type
    has enough kind information so as not to be ambiguous? To better motivate this
    question, consider the following Core type:

      -- Foo :: Type -> Type
      type Foo = Proxy Type

    There is nothing ambiguous about the RHS of Foo in Core. But if we were to,
    say, reify it into a TH Type, then it's tempting to just drop the invisible
    Type argument and simply return `Proxy`. But now we've lost crucial kind
    information: we don't know if we're dealing with `Proxy Type` or `Proxy Bool`
    or `Proxy Int` or something else! We've inadvertently introduced ambiguity.

    Unlike in other situations in GHC, we can't just turn on
    -fprint-explicit-kinds, as we need to produce something which has the same
    structure as a source-syntax type. Moreover, we can't rely on visible kind
    application, since the first kind argument to Proxy is inferred, not specified.
    Our solution is to annotate certain tycons with their kinds whenever they
    appear in applied form in order to resolve the ambiguity. For instance, we
    would reify the RHS of Foo like so:

      type Foo = (Proxy :: Type -> Type)

    We need to devise an algorithm that determines precisely which tycons need
    these explicit kind signatures. We certainly don't want to annotate _every_
    tycon with a kind signature, or else we might end up with horribly bloated
    types like the following:

      (Either :: Type -> Type -> Type) (Int :: Type) (Char :: Type)

    We only want to annotate tycons that absolutely require kind signatures in
    order to resolve some sort of ambiguity, and nothing more.

    Suppose we have a tycon application (T ty_1 ... ty_n). Why might this type
    require a kind signature? It might require it when we need to fill in any of
    T's omitted arguments. By "omitted argument", we mean one that is dropped when
    reifying ty_1 ... ty_n. Sometimes, the omitted arguments are inferred and
    specified arguments (e.g., TH reification in GHC.Tc.Gen.Splice), and sometimes the
    omitted arguments are only the inferred ones (e.g., in situations where
    specified arguments are reified through visible kind application).
    Regardless, the key idea is that _some_ arguments are going to be omitted after
    reification, and the only mechanism we have at our disposal for filling them in
    is through explicit kind signatures.

    What do we mean by "fill in"? Let's consider this small example:

      T :: forall {k}. Type -> (k -> Type) -> k

    Moreover, we have this application of T:

      T @{j} Int aty

    When we reify this type, we omit the inferred argument @{j}. Is it fixed by the
    other (non-inferred) arguments? Yes! If we know the kind of (aty :: blah), then
    we'll generate an equality constraint (kappa -> Type) and, assuming we can
    solve it, that will fix `kappa`. (Here, `kappa` is the unification variable
    that we instantiate `k` with.)

    Therefore, for any application of a tycon T to some arguments, the Question We
    Must Answer is:

    * Given the first n arguments of T, do the kinds of the non-omitted arguments
      fill in the omitted arguments?

    (This is still a bit hand-wavy, but we'll refine this question incrementally
    as we explain more of the machinery underlying this process.)

    Answering this question is precisely the role that the `injectiveVarsOfType`
    and `injective_vars_of_binder` functions exist to serve. If an omitted argument
    `a` appears in the set returned by `injectiveVarsOfType ty`, then knowing
    `ty` determines (i.e., fills in) `a`. (More on `injective_vars_of_binder` in a
    bit.)

    More formally, if
    `a` is in `injectiveVarsOfType ty`
    and  S1(ty) ~ S2(ty),
    then S1(a)  ~ S2(a),
    where S1 and S2 are arbitrary substitutions.

    For example, is `F` is a non-injective type family, then

      injectiveVarsOfType(Either c (Maybe (a, F b c))) = {a, c}

    Now that we know what this function does, here is a second attempt at the
    Question We Must Answer:

    * Given the first n arguments of T (ty_1 ... ty_n), consider the binders
      of T that are instantiated by non-omitted arguments. Do the injective
      variables of these binders fill in the remainder of T's kind?

    Alright, we're getting closer. Next, we need to clarify what the injective
    variables of a tycon binder are. This the role that the
    `injective_vars_of_binder` function serves. Here is what this function does for
    each form of tycon binder:

    * Anonymous binders are injective positions. For example, in the promoted data
      constructor '(:):

        '(:) :: forall a. a -> [a] -> [a]

      The second and third tyvar binders (of kinds `a` and `[a]`) are both
      anonymous, so if we had '(:) 'True '[], then the kinds of 'True and
      '[] would contribute to the kind of '(:) 'True '[]. Therefore,
      injective_vars_of_binder(_ :: a) = injectiveVarsOfType(a) = {a}.
      (Similarly, injective_vars_of_binder(_ :: [a]) = {a}.)
    * Named binders:
      - Inferred binders are never injective positions. For example, in this data
        type:

          data Proxy a
          Proxy :: forall {k}. k -> Type

        If we had Proxy 'True, then the kind of 'True would not contribute to the
        kind of Proxy 'True. Therefore,
        injective_vars_of_binder(forall {k}. ...) = {}.
      - Required binders are injective positions. For example, in this data type:

          data Wurble k (a :: k) :: k
          Wurble :: forall k -> k -> k

      The first tyvar binder (of kind `forall k`) has required visibility, so if
      we had Wurble (Maybe a) Nothing, then the kind of Maybe a would
      contribute to the kind of Wurble (Maybe a) Nothing. Hence,
      injective_vars_of_binder(forall a -> ...) = {a}.
      - Specified binders /might/ be injective positions, depending on how you
        approach things. Continuing the '(:) example:

          '(:) :: forall a. a -> [a] -> [a]

        Normally, the (forall a. ...) tyvar binder wouldn't contribute to the kind
        of '(:) 'True '[], since it's not explicitly instantiated by the user. But
        if visible kind application is enabled, then this is possible, since the
        user can write '(:) @Bool 'True '[]. (In that case,
        injective_vars_of_binder(forall a. ...) = {a}.)

        There are some situations where using visible kind application is appropriate
        and others where it is not (e.g., TH
        reification), so the `injective_vars_of_binder` function is parameterized by
        a Bool which decides if specified binders should be counted towards
        injective positions or not.

    Now that we've defined injective_vars_of_binder, we can refine the Question We
    Must Answer once more:

    * Given the first n arguments of T (ty_1 ... ty_n), consider the binders
      of T that are instantiated by non-omitted arguments. For each such binder
      b_i, take the union of all injective_vars_of_binder(b_i). Is this set a
      superset of the free variables of the remainder of T's kind?

    If the answer to this question is "no", then (T ty_1 ... ty_n) needs an
    explicit kind signature, since T's kind has kind variables leftover that
    aren't fixed by the non-omitted arguments.

    One last sticking point: what does "the remainder of T's kind" mean? You might
    be tempted to think that it corresponds to all of the arguments in the kind of
    T that would normally be instantiated by omitted arguments. But this isn't
    quite right, strictly speaking. Consider the following (silly) example:

      S :: forall {k}. Type -> Type

    And suppose we have this application of S:

      S Int Bool

    The Int argument would be omitted, and
    injective_vars_of_binder(_ :: Type) = {}. This is not a superset of {k}, which
    might suggest that (S Bool) needs an explicit kind signature. But
    (S Bool :: Type) doesn't actually fix `k`! This is because the kind signature
    only affects the /result/ of the application, not all of the individual
    arguments. So adding a kind signature here won't make a difference. Therefore,
    the fourth (and final) iteration of the Question We Must Answer is:

    * Given the first n arguments of T (ty_1 ... ty_n), consider the binders
      of T that are instantiated by non-omitted arguments. For each such binder
      b_i, take the union of all injective_vars_of_binder(b_i). Is this set a
      superset of the free variables of the kind of (T ty_1 ... ty_n)?

    Phew, that was a lot of work!

    How can be sure that this is correct? That is, how can we be sure that in the
    event that we leave off a kind annotation, that one could infer the kind of the
    tycon application from its arguments? It's essentially a proof by induction: if
    we can infer the kinds of every subtree of a type, then the whole tycon
    application will have an inferrable kind--unless, of course, the remainder of
    the tycon application's kind has uninstantiated kind variables.

    What happens if T is oversaturated? That is, if T's kind has fewer than n
    arguments, in the case that the concrete application instantiates a result
    kind variable with an arrow kind? If we run out of arguments, we do not attach
    a kind annotation. This should be a rare case, indeed. Here is an example:

       data T1 :: k1 -> k2 -> *
       data T2 :: k1 -> k2 -> *

       type family G (a :: k) :: k
       type instance G T1 = T2

       type instance F Char = (G T1 Bool :: (* -> *) -> *)   -- F from above

    Here G's kind is (forall k. k -> k), and the desugared RHS of that last
    instance of F is (G (* -> (* -> *) -> *) (T1 * (* -> *)) Bool). According to
    the algorithm above, there are 3 arguments to G so we should peel off 3
    arguments in G's kind. But G's kind has only two arguments. This is the
    rare special case, and we choose not to annotate the application of G with
    a kind signature. After all, we needn't do this, since that instance would
    be reified as:

       type instance F Char = G (T1 :: * -> (* -> *) -> *) Bool

    So the kind of G isn't ambiguous anymore due to the explicit kind annotation
    on its argument. See #8953 and test th/T8953.
    -}

    {-
    ************************************************************************
    *                                                                      *
            Multiplicities
    *                                                                      *
    ************************************************************************

    These functions would prefer to be in GHC.Core.Multiplicity, but
    they some are used elsewhere in this module, and wanted to bring
    their friends here with them.
    -}

    unrestricted, linear, tymult :: a -> Scaled a

    -- | Scale a payload by Many
    unrestricted :: forall a. a -> Scaled a
    unrestricted = Type -> a -> Scaled a
    forall a. Type -> a -> Scaled a
    Scaled Type
    ManyTy

    -- | Scale a payload by One
    linear :: forall a. a -> Scaled a
    linear = Type -> a -> Scaled a
    forall a. Type -> a -> Scaled a
    Scaled Type
    OneTy

    -- | Scale a payload by Many; used for type arguments in core
    tymult :: forall a. a -> Scaled a
    tymult = Type -> a -> Scaled a
    forall a. Type -> a -> Scaled a
    Scaled Type
    ManyTy

    irrelevantMult :: Scaled a -> a
    irrelevantMult :: forall a. Scaled a -> a
    irrelevantMult = Scaled a -> a
    forall a. Scaled a -> a
    scaledThing

    mkScaled :: Mult -> a -> Scaled a
    mkScaled :: forall a. Type -> a -> Scaled a
    mkScaled = Type -> a -> Scaled a
    forall a. Type -> a -> Scaled a
    Scaled

    scaledSet :: Scaled a -> b -> Scaled b
    scaledSet :: forall a b. Scaled a -> b -> Scaled b
    scaledSet (Scaled Type
    m a
    _) b
    b = Type -> b -> Scaled b
    forall a. Type -> a -> Scaled a
    Scaled Type
    m b
    b

    pattern OneTy :: Mult
    pattern $mOneTy :: forall {r}. Type -> ((# #) -> r) -> ((# #) -> r) -> r
    $bOneTy :: Type
    OneTy <- (isOneTy -> True)
      where OneTy = Type
    oneDataConTy

    pattern ManyTy :: Mult
    pattern $mManyTy :: forall {r}. Type -> ((# #) -> r) -> ((# #) -> r) -> r
    $bManyTy :: Type
    ManyTy <- (isManyTy -> True)
      where ManyTy = Type
    manyDataConTy

    isManyTy :: Mult -> Bool
    isManyTy :: Type -> Bool
    isManyTy Type
    ty
      | Just TyCon
    tc <- Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty
      = TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    manyDataConKey
    isManyTy Type
    _ = Bool
    False

    isOneTy :: Mult -> Bool
    isOneTy :: Type -> Bool
    isOneTy Type
    ty
      | Just TyCon
    tc <- Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty
      = TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    oneDataConKey
    isOneTy Type
    _ = Bool
    False

    isLinearType :: Type -> Bool
    -- ^ @isLinear t@ returns @True@ of a if @t@ is a type of (curried) function
    -- where at least one argument is linear (or otherwise non-unrestricted). We use
    -- this function to check whether it is safe to eta reduce an Id in CorePrep. It
    -- is always safe to return 'True', because 'True' deactivates the optimisation.
    isLinearType :: Type -> Bool
    isLinearType Type
    ty = case Type
    ty of
                          FunTy FunTyFlag
    _ Type
    ManyTy Type
    _ Type
    res -> Type -> Bool
    isLinearType Type
    res
                          FunTy FunTyFlag
    _ Type
    _ Type
    _ Type
    _        -> Bool
    True
                          ForAllTy VarBndr TyVar ForAllTyFlag
    _ Type
    res       -> Type -> Bool
    isLinearType Type
    res
                          Type
    _ -> Bool
    False

    {- *********************************************************************
    *                                                                      *
                        Space-saving construction
    *                                                                      *
    ********************************************************************* -}

    {- Note [Using synonyms to compress types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Was: [Prefer Type over TYPE (BoxedRep Lifted)]

    The Core of nearly any program will have numerous occurrences of the Types

       TyConApp BoxedRep [TyConApp Lifted []]    -- Synonym LiftedRep
       TyConApp BoxedRep [TyConApp Unlifted []]  -- Synonym UnliftedREp
       TyConApp TYPE [TyConApp LiftedRep []]     -- Synonym Type
       TyConApp TYPE [TyConApp UnliftedRep []]   -- Synonym UnliftedType

    While investigating #17292 we found that these constituted a majority
    of all TyConApp constructors on the heap:

        (From a sample of 100000 TyConApp closures)
        0x45f3523    - 28732 - `Type`
        0x420b840702 - 9629  - generic type constructors
        0x42055b7e46 - 9596
        0x420559b582 - 9511
        0x420bb15a1e - 9509
        0x420b86c6ba - 9501
        0x42055bac1e - 9496
        0x45e68fd    - 538   - `TYPE ...`

    Consequently, we try hard to ensure that operations on such types are
    efficient. Specifically, we strive to

     a. Avoid heap allocation of such types; use a single static TyConApp
     b. Use a small (shallow in the tree-depth sense) representation
        for such types

    Goal (b) is particularly useful as it makes traversals (e.g. free variable
    traversal, substitution, and comparison) more efficient.
    Comparison in particular takes special advantage of nullary type synonym
    applications (e.g. things like @TyConApp typeTyCon []@), Note [Comparing
    nullary type synonyms] in "GHC.Core.Type".

    To accomplish these we use a number of tricks, implemented by mkTyConApp.

     1. Instead of (TyConApp BoxedRep [TyConApp Lifted []]),
        we prefer a statically-allocated (TyConApp LiftedRep [])
        where `LiftedRep` is a type synonym:
           type LiftedRep = BoxedRep Lifted
        Similarly for UnliftedRep

     2. Instead of (TyConApp TYPE [TyConApp LiftedRep []])
        we prefer the statically-allocated (TyConApp Type [])
        where `Type` is a type synonym
           type Type = TYPE LiftedRep
        Similarly for UnliftedType

    These serve goal (b) since there are no applied type arguments to traverse,
    e.g., during comparison.

     3. We have a single, statically allocated top-level binding to
        represent `TyConApp GHC.Types.Type []` (namely
        'GHC.Builtin.Types.Prim.liftedTypeKind'), ensuring that we don't
        need to allocate such types (goal (a)).  See functions
        mkTYPEapp and mkBoxedRepApp

     4. We use the sharing mechanism described in Note [Sharing nullary TyConApps]
        in GHC.Core.TyCon to ensure that we never need to allocate such
        nullary applications (goal (a)).

    See #17958, #20541
    -}

    -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to
    -- its arguments.  Applies its arguments to the constructor from left to right.
    mkTyConApp :: TyCon -> [Type] -> Type
    mkTyConApp :: TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tycon []
      = -- See Note [Sharing nullary TyConApps] in GHC.Core.TyCon
        TyCon -> Type
    mkTyConTy TyCon
    tycon

    mkTyConApp TyCon
    tycon tys :: [Type]
    tys@(Type
    ty1:[Type]
    rest)
      | Just Type
    fun_ty <- HasDebugCallStack => TyCon -> [Type] -> Maybe Type
    TyCon -> [Type] -> Maybe Type
    tyConAppFunTy_maybe TyCon
    tycon [Type]
    tys
      = Type
    fun_ty

      -- See Note [Using synonyms to compress types]
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    tYPETyConKey
      , Just Type
    ty <- Type -> Maybe Type
    mkTYPEapp_maybe Type
    ty1
      = Bool -> Type -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    rest) Type
    ty

      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    cONSTRAINTTyConKey
      , Just Type
    ty <- Type -> Maybe Type
    mkCONSTRAINTapp_maybe Type
    ty1
      = Bool -> Type -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    rest) Type
    ty

      -- See Note [Using synonyms to compress types]
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    boxedRepDataConTyConKey
      , Just Type
    ty <- Type -> Maybe Type
    mkBoxedRepApp_maybe Type
    ty1
      = Bool -> Type -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    rest) Type
    ty

      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    tupleRepDataConTyConKey
      , Just Type
    ty <- Type -> Maybe Type
    mkTupleRepApp_maybe Type
    ty1
      = Bool -> Type -> Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    rest) Type
    ty

      -- The catch-all case
      | Bool
    otherwise
      = TyCon -> [Type] -> Type
    TyConApp TyCon
    tycon [Type]
    tys
      where
        key :: Unique
    key = TyCon -> Unique
    tyConUnique TyCon
    tycon

    {- Note [Care using synonyms to compress types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Using a synonym to compress a types has a tricky wrinkle. Consider
    coreView applied to (TyConApp LiftedRep [])

    * coreView expands the LiftedRep synonym:
         type LiftedRep = BoxedRep Lifted

    * Danger: we might apply the empty substitution to the RHS of the
      synonym.  And substTy calls mkTyConApp BoxedRep [Lifted]. And
      mkTyConApp compresses that back to LiftedRep.  Loop!

    * Solution: in expandSynTyConApp_maybe, don't call substTy for nullary
      type synonyms.  That's more efficient anyway.
    -}

    mkTYPEapp :: RuntimeRepType -> Type
    mkTYPEapp :: Type -> Type
    mkTYPEapp Type
    rr
      = case Type -> Maybe Type
    mkTYPEapp_maybe Type
    rr of
           Just Type
    ty -> Type
    ty
           Maybe Type
    Nothing -> TyCon -> [Type] -> Type
    TyConApp TyCon
    tYPETyCon [Type
    rr]

    mkTYPEapp_maybe :: RuntimeRepType -> Maybe Type
    -- ^ Given a @RuntimeRep@, applies @TYPE@ to it.
    -- On the fly it rewrites
    --      TYPE LiftedRep      -->   liftedTypeKind    (a synonym)
    --      TYPE UnliftedRep    -->   unliftedTypeKind  (ditto)
    --      TYPE ZeroBitRep     -->   zeroBitTypeKind   (ditto)
    -- NB: no need to check for TYPE (BoxedRep Lifted), TYPE (BoxedRep Unlifted)
    --     because those inner types should already have been rewritten
    --     to LiftedRep and UnliftedRep respectively, by mkTyConApp
    --
    -- see Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim.
    -- See Note [Using synonyms to compress types] in GHC.Core.Type
    {-# NOINLINE mkTYPEapp_maybe #-}
    mkTYPEapp_maybe :: Type -> Maybe Type
    mkTYPEapp_maybe (TyConApp TyCon
    tc [Type]
    args)
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    liftedRepTyConKey    = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    liftedTypeKind   -- TYPE LiftedRep
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    unliftedRepTyConKey  = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    unliftedTypeKind -- TYPE UnliftedRep
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    zeroBitRepTyConKey   = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    zeroBitTypeKind  -- TYPE ZeroBitRep
      where
        key :: Unique
    key = TyCon -> Unique
    tyConUnique TyCon
    tc
    mkTYPEapp_maybe Type
    _ = Maybe Type
    forall a. Maybe a
    Nothing

    ------------------
    mkCONSTRAINTapp :: RuntimeRepType -> Type
    -- ^ Just like mkTYPEapp
    mkCONSTRAINTapp :: Type -> Type
    mkCONSTRAINTapp Type
    rr
      = case Type -> Maybe Type
    mkCONSTRAINTapp_maybe Type
    rr of
           Just Type
    ty -> Type
    ty
           Maybe Type
    Nothing -> TyCon -> [Type] -> Type
    TyConApp TyCon
    cONSTRAINTTyCon [Type
    rr]

    mkCONSTRAINTapp_maybe :: RuntimeRepType -> Maybe Type
    -- ^ Just like mkTYPEapp_maybe
    {-# NOINLINE mkCONSTRAINTapp_maybe #-}
    mkCONSTRAINTapp_maybe :: Type -> Maybe Type
    mkCONSTRAINTapp_maybe (TyConApp TyCon
    tc [Type]
    args)
      | TyCon
    tc TyCon -> Unique -> Bool
    forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedRepTyConKey = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $
                                        Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    constraintKind   -- CONSTRAINT LiftedRep
    mkCONSTRAINTapp_maybe Type
    _ = Maybe Type
    forall a. Maybe a
    Nothing

    ------------------
    mkBoxedRepApp_maybe :: LevityType -> Maybe Type
    -- ^ Given a `Levity`, apply `BoxedRep` to it
    -- On the fly, rewrite
    --      BoxedRep Lifted     -->   liftedRepTy    (a synonym)
    --      BoxedRep Unlifted   -->   unliftedRepTy  (ditto)
    -- See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim.
    -- See Note [Using synonyms to compress types] in GHC.Core.Type
    {-# NOINLINE mkBoxedRepApp_maybe #-}
    mkBoxedRepApp_maybe :: Type -> Maybe Type
    mkBoxedRepApp_maybe (TyConApp TyCon
    tc [Type]
    args)
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    liftedDataConKey   = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    liftedRepTy    -- BoxedRep Lifted
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    unliftedDataConKey = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    unliftedRepTy  -- BoxedRep Unlifted
      where
        key :: Unique
    key = TyCon -> Unique
    tyConUnique TyCon
    tc
    mkBoxedRepApp_maybe Type
    _ = Maybe Type
    forall a. Maybe a
    Nothing

    mkTupleRepApp_maybe :: Type -> Maybe Type
    -- ^ Given a `[RuntimeRep]`, apply `TupleRep` to it
    -- On the fly, rewrite
    --      TupleRep [] -> zeroBitRepTy   (a synonym)
    -- See Note [TYPE and CONSTRAINT] in GHC.Builtin.Types.Prim.
    -- See Note [Using synonyms to compress types] in GHC.Core.Type
    {-# NOINLINE mkTupleRepApp_maybe #-}
    mkTupleRepApp_maybe :: Type -> Maybe Type
    mkTupleRepApp_maybe (TyConApp TyCon
    tc [Type]
    args)
      | Unique
    key Unique -> Unique -> Bool
    forall a. Eq a => a -> a -> Bool
    == Unique
    nilDataConKey = Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert ([Type] -> Bool
    forall a. [a] -> Bool
    isSingleton [Type]
    args) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $ Type -> Maybe Type
    forall a. a -> Maybe a
    Just Type
    zeroBitRepTy  -- ZeroBitRep
      where
        key :: Unique
    key = TyCon -> Unique
    tyConUnique TyCon
    tc
    mkTupleRepApp_maybe Type
    _ = Maybe Type
    forall a. Maybe a
    Nothing

    typeOrConstraintKind :: TypeOrConstraint -> RuntimeRepType -> Kind
    typeOrConstraintKind :: TypeOrConstraint -> Type -> Type
    typeOrConstraintKind TypeOrConstraint
    TypeLike       Type
    rep = Type -> Type
    mkTYPEapp       Type
    rep
    typeOrConstraintKind TypeOrConstraint
    ConstraintLike Type
    rep = Type -> Type
    mkCONSTRAINTapp Type
    rep