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

    {-# LANGUAGE CPP, FlexibleContexts, PatternSynonyms, ViewPatterns, MultiWayIf #-}
    {-# OPTIONS_GHC -fno-warn-orphans #-}
    {-# OPTIONS_GHC -Wno-incomplete-record-updates #-}

    -- | 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, ArgFlag(..), AnonArgFlag(..),
            Specificity(..),
            KindOrType, PredType, ThetaType,
            Var, TyVar, isTyVar, TyCoVar, TyCoBinder, TyCoVarBinder, TyVarBinder,
            Mult, Scaled,
            KnotTied,

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

            mkAppTy, mkAppTys, splitAppTy, splitAppTys, repSplitAppTys,
            splitAppTy_maybe, repSplitAppTy_maybe, tcRepSplitAppTy_maybe,

            mkFunTy, mkVisFunTy, mkInvisFunTy,
            mkVisFunTys,
            mkVisFunTyMany, mkInvisFunTyMany,
            mkVisFunTysMany, mkInvisFunTysMany,
            splitFunTy, splitFunTy_maybe,
            splitFunTys, funResultTy, funArgTy,

            mkTyConApp, mkTyConTy, tYPE,
            tyConAppTyCon_maybe, tyConAppTyConPicky_maybe,
            tyConAppArgs_maybe, tyConAppTyCon, tyConAppArgs,
            splitTyConApp_maybe, splitTyConApp, tyConAppArgN,
            tcSplitTyConApp_maybe,
            splitListTyConApp_maybe,
            repSplitTyConApp_maybe,
            tcRepSplitTyConApp_maybe,

            mkForAllTy, mkForAllTys, mkInvisForAllTys, mkTyCoInvForAllTys,
            mkSpecForAllTy, mkSpecForAllTys,
            mkVisForAllTys, mkTyCoInvForAllTy,
            mkInfForAllTy, mkInfForAllTys,
            splitForAllTyCoVars,
            splitForAllReqTVBinders, splitForAllInvisTVBinders,
            splitForAllTyCoVarBinders,
            splitForAllTyCoVar_maybe, splitForAllTyCoVar,
            splitForAllTyVar_maybe, splitForAllCoVar_maybe,
            splitPiTy_maybe, splitPiTy, splitPiTys,
            mkTyConBindersPreferAnon,
            mkPiTy, mkPiTys,
            piResultTy, piResultTys,
            applyTysX, dropForAlls,
            mkFamilyTyConApp,
            buildSynTyCon,

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

            isPredTy,

            getRuntimeRep_maybe, kindRep_maybe, kindRep,

            mkCastTy, mkCoercionTy, splitCastTy_maybe,

            userTypeError_maybe, pprUserTypeErrorTy,

            coAxNthLHS,
            stripCoercionTy,

            splitInvisPiTys, splitInvisPiTysN,
            invisibleTyBndrCount,
            filterOutInvisibleTypes, filterOutInferredTypes,
            partitionInvisibleTypes, partitionInvisibles,
            tyConArgFlags, appTyArgFlags,

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

            -- (Newtypes)
            newTyConInstRhs,

            -- ** Binders
            sameVis,
            mkTyCoVarBinder, mkTyCoVarBinders,
            mkTyVarBinder, mkTyVarBinders,
            tyVarSpecToBinders,
            mkAnonBinder,
            isAnonTyCoBinder,
            binderVar, binderVars, binderType, binderArgFlag,
            tyCoBinderType, tyCoBinderVar_maybe,
            tyBinderType,
            binderRelevantType_maybe,
            isVisibleArgFlag, isInvisibleArgFlag, isVisibleBinder,
            isInvisibleBinder, isNamedBinder,
            tyConBindersTyCoBinders,

            -- ** Common type constructors
            funTyCon, unrestrictedFunTyCon,

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

            isValidJoinPointType,
            tyConAppNeedsKindSig,

            -- *** Levity and boxity
            isLiftedType_maybe,
            isLiftedTypeKind, isUnliftedTypeKind, isBoxedTypeKind, pickyIsLiftedTypeKind,
            isLiftedRuntimeRep, isUnliftedRuntimeRep, isBoxedRuntimeRep,
            isLiftedLevity, isUnliftedLevity,
            isUnliftedType, isBoxedType, mightBeUnliftedType, isUnboxedTupleType, isUnboxedSumType,
            isAlgType, isDataFamilyAppType,
            isPrimitiveType, isStrictType,
            isLevityTy, isLevityVar,
            isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy,
            dropRuntimeRepArgs,
            getRuntimeRep,

            -- * Multiplicity

            isMultiplicityTy, isMultiplicityVar,
            unrestricted, linear, tymult,
            mkScaled, irrelevantMult, scaledSet,
            pattern One, pattern Many,
            isOneDataConTy, isManyDataConTy,
            isLinearType,

            -- * Main data types representing Kinds
            Kind,

            -- ** Finding the kind of a type
            typeKind, tcTypeKind, isTypeLevPoly, resultIsLevPoly,
            tcIsLiftedTypeKind, tcIsConstraintKind, tcReturnsConstraintKind,
            tcIsBoxedTypeKind, tcIsRuntimeTypeKind,

            -- ** Common Kind
            liftedTypeKind, unliftedTypeKind,

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

            anyFreeVarsOfType, anyFreeVarsOfTypes,
            noFreeVarsOfType,
            splitVisVarsOfType, splitVisVarsOfTypes,
            expandTypeSynonyms,
            typeSize, occCheckExpand,

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

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

            -- * Type comparison
            eqType, eqTypeX, eqTypes, nonDetCmpType, nonDetCmpTypes, nonDetCmpTypeX,
            nonDetCmpTypesX, nonDetCmpTc,
            eqVarBndrs,

            -- * Forcing evaluation of types
            seqType, seqTypes,

            -- * Other views onto Types
            coreView, tcView,

            tyConsOfType,

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

            -- ** Manipulating type substitutions
            emptyTvSubstEnv, emptyTCvSubst, mkEmptyTCvSubst,

            mkTCvSubst, zipTvSubst, mkTvSubstPrs,
            zipTCvSubst,
            notElemTCvSubst,
            getTvSubstEnv, setTvSubstEnv,
            zapTCvSubst, getTCvInScope, getTCvSubstRangeFVs,
            extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet,
            extendTCvSubst, extendCvSubst,
            extendTvSubst, extendTvSubstBinderAndInScope,
            extendTvSubstList, extendTvSubstAndInScope,
            extendTCvSubstList,
            extendTvSubstWithClone,
            extendTCvSubstWithClone,
            isInScope, composeTCvSubstEnv, composeTCvSubst, zipTyEnv, zipCoEnv,
            isEmptyTCvSubst, unionTCvSubst,

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

            -- * Tidying type related things up for printing
            tidyType,      tidyTypes,
            tidyOpenType,  tidyOpenTypes,
            tidyOpenKind,
            tidyVarBndr, tidyVarBndrs, tidyFreeTyCoVars,
            tidyOpenTyCoVar, tidyOpenTyCoVars,
            tidyTyCoVarOcc,
            tidyTopType,
            tidyKind,
            tidyTyCoVarBinder, tidyTyCoVarBinders,

            -- * Kinds
            isConstraintKindCon,
            classifiesTypeWithValues,
            isKindLevPoly
        ) where

    #include "HsVersions.h"

    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, listTyCon
                                     , typeSymbolKind, liftedTypeKind, unliftedTypeKind
                                     , liftedRepTyCon, unliftedRepTyCon
                                     , constraintKind
                                     , unrestrictedFunTyCon
                                     , manyDataConTy, oneDataConTy )
    import GHC.Types.Name( Name )
    import GHC.Builtin.Names
    import GHC.Core.Coercion.Axiom
    import {-# SOURCE #-} GHC.Core.Coercion
       ( mkNomReflCo, mkGReflCo, mkReflCo
       , mkTyConAppCo, mkAppCo, mkCoVarCo, mkAxiomRuleCo
       , mkForAllCo, mkFunCo, mkAxiomInstCo, mkUnivCo
       , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo
       , mkKindCo, mkSubCo
       , decomposePiCos, coercionKind, coercionLKind
       , coercionRKind, coercionType
       , isReflexiveCo, seqCo )

    -- others
    import GHC.Utils.Misc
    import GHC.Utils.FV
    import GHC.Utils.Outputable
    import GHC.Utils.Panic
    import GHC.Data.FastString
    import GHC.Data.Pair
    import GHC.Data.List.SetOps
    import GHC.Types.Unique ( nonDetCmpUnique )

    import GHC.Data.Maybe   ( orElse, expectJust )
    import Data.Maybe       ( isJust )
    import Control.Monad    ( guard )

    -- $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.
    --
    -- 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
    *                                                                      *
    ************************************************************************

    Note [coreView vs tcView]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    So far as the typechecker is concerned, 'Constraint' and 'TYPE
    LiftedRep' are distinct kinds.

    But in Core these two are treated as identical.

    We implement this by making 'coreView' convert 'Constraint' to 'TYPE
    LiftedRep' on the fly.  The function tcView (used in the type checker)
    does not do this. Accordingly, tcView is used in type-checker-oriented
    functions (including the pure unifier, used in instance resolution),
    while coreView is used during e.g. optimisation passes.

    See also #11715, which tracks removing this inconsistency.

    The inconsistency actually leads to a potential soundness bug, in that
    Constraint and Type are considered *apart* by the type family engine.
    To wit, we can write

      type family F a
      type instance F Type = Bool
      type instance F Constraint = Int

    and (because Type ~# Constraint in Core), thus build a coercion between
    Int and Bool. I (Richard E) conjecture that this never happens in practice,
    but it's very uncomfortable. This, essentially, is the root problem
    underneath #11715, which is quite resistant to an easy fix. The best
    idea is to have roles in kind coercions, but that has yet to be implemented.
    See also "A Role for Dependent Types in Haskell", ICFP 2019, which describes
    how roles in kinds might work out.

    -}

    -- | Gives the typechecker view of a type. This unwraps synonyms but
    -- leaves 'Constraint' alone. c.f. 'coreView', which turns 'Constraint' into
    -- 'Type'. Returns 'Nothing' if no unwrapping happens.
    -- See also Note [coreView vs tcView]
    tcView :: Type -> Maybe Type
    tcView :: Type -> Maybe Type
    tcView (TyConApp TyCon
    tc [Type]
    tys)
      | res :: Maybe Type
    res@(Just Type
    _) <- TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
      = Maybe Type
    res
    tcView Type
    _ = forall a. Maybe a
    Nothing
    -- See Note [Inlining coreView].
    {-# INLINE tcView #-}

    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 considers 'Constraint' to be a synonym of @Type@.
    --
    -- 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 ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    tys)
      | res :: Maybe Type
    res@(Just Type
    _) <- TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
      = Maybe Type
    res

      -- At the Core level, Constraint = Type
      -- See Note [coreView vs tcView]
      | TyCon -> Bool
    isConstraintKindCon TyCon
    tc
      = ASSERT2( null tys, ppr ty )
        forall a. a -> Maybe a
    Just Type
    liftedTypeKind

    coreView Type
    _ = forall a. Maybe a
    Nothing
    -- See Note [Inlining coreView].
    {-# INLINE coreView #-}

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

    -- | @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
    expandSynTyConApp_maybe :: TyCon -> [Type] -> Maybe Type
    expandSynTyConApp_maybe TyCon
    tc [Type]
    tys
      | Just ([TyVar]
    tvs, Type
    rhs) <- TyCon -> Maybe ([TyVar], Type)
    synTyConDefn_maybe TyCon
    tc
      , [Type]
    tys forall a. [a] -> Int -> Bool
    `lengthAtLeast` Int
    arity
      = forall a. a -> Maybe a
    Just (Int -> [TyVar] -> Type -> [Type] -> Type
    expand_syn Int
    arity [TyVar]
    tvs Type
    rhs [Type]
    tys)
      | Bool
    otherwise
      = forall a. Maybe a
    Nothing
      where
        arity :: Int
    arity = TyCon -> Int
    tyConArity TyCon
    tc
    -- Without this INLINE the call to expandSynTyConApp_maybe in coreView
    -- will result in an avoidable allocation.
    {-# INLINE expandSynTyConApp_maybe #-}

    -- | A helper for 'expandSynTyConApp_maybe' to avoid inlining this cold path
    -- into call-sites.
    expand_syn :: Int      -- ^ the arity of the synonym
               -> [TyVar]  -- ^ the variables bound by the synonym
               -> Type     -- ^ the RHS of the synonym
               -> [Type]   -- ^ the type arguments the synonym is instantiated at.
               -> Type
    expand_syn :: Int -> [TyVar] -> Type -> [Type] -> Type
    expand_syn Int
    arity [TyVar]
    tvs Type
    rhs [Type]
    tys
      | [Type]
    tys forall a. [a] -> Int -> Bool
    `lengthExceeds` Int
    arity = Type -> [Type] -> Type
    mkAppTys Type
    rhs' (forall a. Int -> [a] -> [a]
    drop Int
    arity [Type]
    tys)
      | Bool
    otherwise                 = Type
    rhs'
      where
        rhs' :: Type
    rhs' = HasCallStack => TCvSubst -> Type -> Type
    substTy ([(TyVar, Type)] -> TCvSubst
    mkTvSubstPrs ([TyVar]
    tvs forall a b. [a] -> [b] -> [(a, b)]
    `zip` [Type]
    tys)) Type
    rhs
                   -- The free vars of 'rhs' should all be bound by 'tenv', so it's
                   -- ok to use 'substTy' here (which is what expandSynTyConApp_maybe does).
                   -- See also Note [The substitution invariant] in GHC.Core.TyCo.Subst.
                   -- Its important to use mkAppTys, rather than (foldl AppTy),
                   -- because the function part might well return a
                   -- partially-applied type constructor; indeed, usually will!
    -- We never want to inline this cold-path.
    {-# INLINE expand_syn #-}

    coreFullView :: Type -> Type
    -- ^ Iterates 'coreView' until there is no more to synonym to expand.
    -- See Note [Inlining coreView].
    coreFullView :: Type -> Type
    coreFullView ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    _)
      | TyCon -> Bool
    isTypeSynonymTyCon TyCon
    tc Bool -> Bool -> Bool
    || TyCon -> Bool
    isConstraintKindCon TyCon
    tc = Type -> Type
    go Type
    ty
      where
        go :: Type -> Type
    go Type
    ty
          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type
    go Type
    ty'
          | Bool
    otherwise = Type
    ty

    coreFullView Type
    ty = Type
    ty
    {-# INLINE coreFullView #-}

    {- 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 :: 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
      = TCvSubst -> Type -> Type
    go (InScopeSet -> TCvSubst
    mkEmptyTCvSubst InScopeSet
    in_scope) Type
    ty
      where
        in_scope :: InScopeSet
    in_scope = TyCoVarSet -> InScopeSet
    mkInScopeSet (Type -> TyCoVarSet
    tyCoVarsOfType Type
    ty)

        go :: TCvSubst -> Type -> Type
    go TCvSubst
    subst (TyConApp TyCon
    tc [Type]
    tys)
          | Just ([(TyVar, Type)]
    tenv, Type
    rhs, [Type]
    tys') <- forall tyco.
    TyCon -> [tyco] -> Maybe ([(TyVar, tyco)], Type, [tyco])
    expandSynTyCon_maybe TyCon
    tc [Type]
    expanded_tys
          = let subst' :: TCvSubst
    subst' = InScopeSet -> TvSubstEnv -> TCvSubst
    mkTvSubst InScopeSet
    in_scope (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 (TCvSubst -> Type -> Type
    go TCvSubst
    subst' Type
    rhs) [Type]
    tys'
          | Bool
    otherwise
          = TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    expanded_tys
          where
            expanded_tys :: [Type]
    expanded_tys = (forall a b. (a -> b) -> [a] -> [b]
    map (TCvSubst -> Type -> Type
    go TCvSubst
    subst) [Type]
    tys)

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

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

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

        go_prov :: TCvSubst -> UnivCoProvenance -> UnivCoProvenance
    go_prov TCvSubst
    subst (PhantomProv KindCoercion
    co)    = KindCoercion -> UnivCoProvenance
    PhantomProv (TCvSubst -> KindCoercion -> KindCoercion
    go_co TCvSubst
    subst KindCoercion
    co)
        go_prov TCvSubst
    subst (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UnivCoProvenance
    ProofIrrelProv (TCvSubst -> KindCoercion -> KindCoercion
    go_co TCvSubst
    subst KindCoercion
    co)
        go_prov TCvSubst
    _     p :: UnivCoProvenance
    p@(PluginProv String
    _)    = UnivCoProvenance
    p
        go_prov TCvSubst
    _     p :: UnivCoProvenance
    p@(CorePrepProv Bool
    _)  = 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 :: TCvSubst
    -> TyVar -> KindCoercion -> (TCvSubst, TyVar, KindCoercion)
    go_cobndr TCvSubst
    subst = Bool
    -> (KindCoercion -> KindCoercion)
    -> TCvSubst
    -> TyVar
    -> KindCoercion
    -> (TCvSubst, TyVar, KindCoercion)
    substForAllCoBndrUsing Bool
    False (TCvSubst -> KindCoercion -> KindCoercion
    go_co TCvSubst
    subst) TCvSubst
    subst

    -- | 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
    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 forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    key
      = forall a. a -> Maybe a
    Just [Type]
    args
      | Bool
    otherwise
      = 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 -> Type
    kindRep :: HasDebugCallStack => Type -> Type
    kindRep Type
    k = case HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    k of
                  Just Type
    r  -> Type
    r
                  Maybe Type
    Nothing -> forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "kindRep" (forall a. Outputable a => a -> SDoc
    ppr Type
    k)

    -- | Given a kind (TYPE rr), extract its RuntimeRep classifier rr.
    -- For example, @kindRep_maybe * = Just LiftedRep@
    -- Returns 'Nothing' if the kind is not of form (TYPE rr)
    -- Treats * and Constraint as the same
    kindRep_maybe :: HasDebugCallStack => Kind -> Maybe Type
    kindRep_maybe :: HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    kind
      | Just [Type
    arg] <- Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    tYPETyConKey Type
    kind = forall a. a -> Maybe a
    Just Type
    arg
      | Bool
    otherwise                                           = forall a. Maybe a
    Nothing

    -- | Returns True if the kind classifies types which are allocated on
    -- the GC'd heap and False otherwise. Note that this returns False for
    -- levity-polymorphic kinds, which may be specialized to a kind that
    -- classifies AddrRep or even unboxed kinds.
    isBoxedTypeKind :: Kind -> Bool
    isBoxedTypeKind :: Type -> Bool
    isBoxedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isBoxedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    -- | This version considers Constraint to be the same as *. Returns True
    -- if the argument is equivalent to Type/Constraint and False otherwise.
    -- See Note [Kind Constraint and kind Type]
    isLiftedTypeKind :: Kind -> Bool
    isLiftedTypeKind :: Type -> Bool
    isLiftedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isLiftedRuntimeRep 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 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 forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedRepTyConKey
          [Type
    rr_arg]
            | TyCon
    rr_tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey
            , TyConApp TyCon
    lev [] <- Type
    rr_arg
            , TyCon
    lev forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedDataConKey -> Bool
    True
          [Type]
    _ -> Bool
    False
      | TyConApp TyCon
    tc [] <- Type
    kind
      , TyCon
    tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedTypeKindTyConKey = Bool
    True
      | Bool
    otherwise                          = Bool
    False

    -- | Returns True if the kind classifies unlifted types (like 'Int#') and False
    -- otherwise. Note that this returns False for levity-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
    kindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isUnliftedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    -- | See 'isBoxedRuntimeRep_maybe'.
    isBoxedRuntimeRep :: Type -> Bool
    isBoxedRuntimeRep :: Type -> Bool
    isBoxedRuntimeRep Type
    rep = 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 :: Type -> Maybe Type
    isBoxedRuntimeRep_maybe :: Type -> Maybe Type
    isBoxedRuntimeRep_maybe Type
    rep
      | Just [Type
    lev] <- Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    boxedRepDataConKey Type
    rep
      = forall a. a -> Maybe a
    Just Type
    lev
      | Bool
    otherwise
      = forall a. Maybe a
    Nothing

    isLiftedRuntimeRep :: Type -> Bool
    -- isLiftedRuntimeRep is true of LiftedRep :: RuntimeRep
    -- False of type variables (a :: RuntimeRep)
    --   and of other reps e.g. (IntRep :: RuntimeRep)
    isLiftedRuntimeRep :: Type -> Bool
    isLiftedRuntimeRep Type
    rep
      | Just [Type
    lev] <- Unique -> Type -> Maybe [Type]
    isTyConKeyApp_maybe Unique
    boxedRepDataConKey Type
    rep
      = Type -> Bool
    isLiftedLevity Type
    lev
      | Bool
    otherwise
      = Bool
    False

    isUnliftedRuntimeRep :: Type -> Bool
    -- PRECONDITION: The type has kind RuntimeRep
    -- True of definitely-unlifted RuntimeReps
    -- False of           (LiftedRep :: RuntimeRep)
    --   and of variables (a :: RuntimeRep)
    isUnliftedRuntimeRep :: Type -> Bool
    isUnliftedRuntimeRep Type
    rep
      | TyConApp TyCon
    rr_tc [Type]
    args <- Type -> Type
    coreFullView Type
    rep -- NB: args might be non-empty
                                                --     e.g. TupleRep [r1, .., rn]
      , TyCon -> Bool
    isPromotedDataCon TyCon
    rr_tc =
          -- NB: args might be non-empty e.g. TupleRep [r1, .., rn]
          if (TyCon
    rr_tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey)
            then case [Type]
    args of
              [Type
    lev] -> Type -> Bool
    isUnliftedLevity Type
    lev
              [Type]
    _     -> Bool
    False
            else Bool
    True
            -- Avoid searching all the unlifted RuntimeRep type cons
            -- In the RuntimeRep data type, only LiftedRep is lifted
            -- But be careful of type families (F tys) :: RuntimeRep,
            -- hence the isPromotedDataCon rr_tc
    isUnliftedRuntimeRep Type
    _ = Bool
    False

    -- | An INLINE helper for function such as 'isLiftedRuntimeRep' below.
    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
      = ASSERT( null args ) 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 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 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 forall b c a. (b -> c) -> (a -> b) -> a -> c
    . TyVar -> Type
    tyVarKind

    {- *********************************************************************
    *                                                                      *
                   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 [Forall coercions] 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 -> env -> TyVar -> ArgFlag -> m (env, TyVar)
    tcm_tycobinder :: env -> TyCoVar -> ArgFlag -> m (env, TyCoVar)
              -- ^ 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 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 -> env -> TyVar -> ArgFlag -> m (env, TyVar)
    tcm_tycobinder = env -> TyVar -> ArgFlag -> m (env, TyVar)
    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
    _   []       = forall (m :: * -> *) a. Monad m => a -> m a
    return []
        go_tys env
    env (Type
    ty:[Type]
    tys) = (:) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty 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 forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    t1 forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t2
        go_ty env
    _   ty :: Type
    ty@(LitTy {})   = forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    ty
        go_ty env
    env (CastTy Type
    ty KindCoercion
    co)  = Type -> KindCoercion -> Type
    mkCastTy forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty 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 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 AnonArgFlag
    _ Type
    w Type
    arg Type
    res)
          = do { Type
    w' <- env -> Type -> m Type
    go_ty env
    env Type
    w; Type
    arg' <- env -> Type -> m Type
    go_ty env
    env Type
    arg; Type
    res' <- env -> Type -> m Type
    go_ty env
    env Type
    res
               ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Type
    ty { ft_mult :: Type
    ft_mult = Type
    w', ft_arg :: Type
    ft_arg = Type
    arg', ft_res :: Type
    ft_res = Type
    res' }) }

        go_ty env
    env ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    tys)
          | TyCon -> Bool
    isTcTyCon TyCon
    tc
          = do { TyCon
    tc' <- TyCon -> m TyCon
    tycon TyCon
    tc
               ; TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc' forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [Type] -> m [Type]
    go_tys env
    env [Type]
    tys }

          -- Not a TcTyCon
          | forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys    -- Avoid allocation in this very
          = 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 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 ArgFlag
    vis) Type
    inner)
          = do { (env
    env', TyVar
    tv') <- env -> TyVar -> ArgFlag -> m (env, TyVar)
    tycobinder env
    env TyVar
    tv ArgFlag
    vis
               ; Type
    inner' <- env -> Type -> m Type
    go_ty env
    env' Type
    inner
               ; forall (m :: * -> *) a. Monad m => a -> m a
    return forall a b. (a -> b) -> a -> b
    $ VarBndr TyVar ArgFlag -> Type -> Type
    ForAllTy (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv' ArgFlag
    vis) Type
    inner' }

        go_cos :: env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    _   []       = forall (m :: * -> *) a. Monad m => a -> m a
    return []
        go_cos env
    env (KindCoercion
    co:[KindCoercion]
    cos) = (:) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co 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    = forall (m :: * -> *) a. Monad m => a -> m a
    return MCoercionN
    MRefl
        go_mco env
    env (MCo KindCoercion
    co) = KindCoercion -> MCoercionN
    MCo 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 forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty
        go_co env
    env (GRefl Role
    r Type
    ty MCoercionN
    mco)    = Role -> Type -> MCoercionN -> KindCoercion
    mkGReflCo Role
    r forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> Type -> m Type
    go_ty env
    env Type
    ty 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 forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c2
        go_co env
    env (FunCo Role
    r KindCoercion
    cw KindCoercion
    c1 KindCoercion
    c2)   = Role
    -> KindCoercion -> KindCoercion -> KindCoercion -> KindCoercion
    mkFunCo Role
    r forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    cw forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 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 forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> UnivCoProvenance -> m UnivCoProvenance
    go_prov env
    env UnivCoProvenance
    p forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> forall (f :: * -> *) a. Applicative f => a -> f a
    pure Role
    r
                                        forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t1 forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> Type -> m Type
    go_ty env
    env Type
    t2
        go_co env
    env (SymCo KindCoercion
    co)          = KindCoercion -> KindCoercion
    mkSymCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co env
    env (TransCo KindCoercion
    c1 KindCoercion
    c2)     = KindCoercion -> KindCoercion -> KindCoercion
    mkTransCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c1 forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    c2
        go_co env
    env (AxiomRuleCo CoAxiomRule
    r [KindCoercion]
    cos) = CoAxiomRule -> [KindCoercion] -> KindCoercion
    AxiomRuleCo CoAxiomRule
    r forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos
        go_co env
    env (NthCo Role
    r Int
    i KindCoercion
    co)      = HasDebugCallStack => Role -> Int -> KindCoercion -> KindCoercion
    mkNthCo Role
    r Int
    i forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co env
    env (LRCo LeftOrRight
    lr KindCoercion
    co)        = LeftOrRight -> KindCoercion -> KindCoercion
    mkLRCo LeftOrRight
    lr forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co env
    env (InstCo KindCoercion
    co KindCoercion
    arg)     = KindCoercion -> KindCoercion -> KindCoercion
    mkInstCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    arg
        go_co env
    env (KindCo KindCoercion
    co)         = KindCoercion -> KindCoercion
    mkKindCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co env
    env (SubCo KindCoercion
    co)          = HasDebugCallStack => KindCoercion -> KindCoercion
    mkSubCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_co env
    env (AxiomInstCo CoAxiom Branched
    ax Int
    i [KindCoercion]
    cos) = CoAxiom Branched -> Int -> [KindCoercion] -> KindCoercion
    mkAxiomInstCo CoAxiom Branched
    ax Int
    i forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> 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 { TyCon
    tc' <- TyCon -> m TyCon
    tycon TyCon
    tc
               ; HasDebugCallStack =>
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    mkTyConAppCo Role
    r TyCon
    tc' forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> [KindCoercion] -> m [KindCoercion]
    go_cos env
    env [KindCoercion]
    cos }

          -- Not a TcTyCon
          | forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [KindCoercion]
    cos    -- Avoid allocation in this very
          = 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
    mkTyConAppCo Role
    r TyCon
    tc 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 TyVar
    tv KindCoercion
    kind_co KindCoercion
    co)
          = do { KindCoercion
    kind_co' <- env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    kind_co
               ; (env
    env', TyVar
    tv') <- env -> TyVar -> ArgFlag -> m (env, TyVar)
    tycobinder env
    env TyVar
    tv ArgFlag
    Inferred
               ; KindCoercion
    co' <- env -> KindCoercion -> m KindCoercion
    go_co env
    env' KindCoercion
    co
               ; forall (m :: * -> *) a. Monad m => a -> m a
    return forall a b. (a -> b) -> a -> b
    $ TyVar -> KindCoercion -> KindCoercion -> KindCoercion
    mkForAllCo TyVar
    tv' KindCoercion
    kind_co' KindCoercion
    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 forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_prov env
    env (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UnivCoProvenance
    ProofIrrelProv forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> env -> KindCoercion -> m KindCoercion
    go_co env
    env KindCoercion
    co
        go_prov env
    _   p :: UnivCoProvenance
    p@(PluginProv String
    _)    = forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    p
        go_prov env
    _   p :: UnivCoProvenance
    p@(CorePrepProv Bool
    _)  = forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    p

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Constructor-specific functions}
    *                                                                      *
    ************************************************************************

    ---------------------------------------------------------------------
                                    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 :: String -> Type -> TyVar
    getTyVar :: String -> Type -> TyVar
    getTyVar String
    msg Type
    ty = case Type -> Maybe TyVar
    getTyVar_maybe Type
    ty of
                        Just TyVar
    tv -> TyVar
    tv
                        Maybe TyVar
    Nothing -> forall a. String -> a
    panic (String
    "getTyVar: " forall a. [a] -> [a] -> [a]
    ++ String
    msg)

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

    -- | 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 -> forall a. a -> Maybe a
    Just (TyVar
    tv, KindCoercion
    co)
      TyVarTy TyVar
    tv             -> forall a. a -> Maybe a
    Just (TyVar
    tv, Role -> Type -> KindCoercion
    mkReflCo Role
    Nominal (TyVar -> Type
    tyVarKind TyVar
    tv))
      Type
    _                      -> forall a. Maybe a
    Nothing

    -- | 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) = forall a. a -> Maybe a
    Just TyVar
    tv
    repGetTyVar_maybe Type
    _            = 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.

    This really only applies to the type checker; in Core, '=>' and '->'
    are the same, as are 'Constraint' and '*'.  But for now I've put
    the test in repSplitAppTy_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)
    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 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
      = 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)
    decomposePiCos KindCoercion
    co (KindCoercion -> Pair Type
    coercionKind KindCoercion
    co) [Type]
    arg_tys
        ([Type]
    args_to_cast, [Type]
    leftovers) = forall b a. [b] -> [a] -> ([a], [a])
    splitAtList [KindCoercion]
    arg_cos [Type]
    arg_tys
        casted_arg_tys :: [Type]
    casted_arg_tys = 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 forall a. [a] -> [a] -> [a]
    ++ [Type]
    tys2)
    mkAppTys Type
    ty1                [Type]
    tys2 = 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)
    repSplitAppTy_maybe forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Type
    coreFullView

    -------------
    repSplitAppTy_maybe :: HasDebugCallStack => Type -> Maybe (Type,Type)
    -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
    -- any Core view stuff is already done
    repSplitAppTy_maybe :: HasDebugCallStack => Type -> Maybe (Type, Type)
    repSplitAppTy_maybe (FunTy AnonArgFlag
    _ Type
    w Type
    ty1 Type
    ty2)
      = forall a. a -> Maybe a
    Just (TyCon -> [Type] -> Type
    TyConApp TyCon
    funTyCon [Type
    w, Type
    rep1, Type
    rep2, Type
    ty1], Type
    ty2)
      where
        rep1 :: Type
    rep1 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty1
        rep2 :: Type
    rep2 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty2

    repSplitAppTy_maybe (AppTy Type
    ty1 Type
    ty2)
      = forall a. a -> Maybe a
    Just (Type
    ty1, Type
    ty2)

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

    repSplitAppTy_maybe Type
    _other = forall a. Maybe a
    Nothing

    -- This one doesn't break apart (c => t).
    -- See Note [Decomposing fat arrow c=>t]
    -- Defined here to avoid module loops between Unify and TcType.
    tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type)
    -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that
    -- any coreView stuff is already done. Refuses to look through (c => t)
    tcRepSplitAppTy_maybe :: Type -> Maybe (Type, Type)
    tcRepSplitAppTy_maybe (FunTy { ft_af :: Type -> AnonArgFlag
    ft_af = AnonArgFlag
    af, ft_mult :: Type -> Type
    ft_mult = Type
    w, ft_arg :: Type -> Type
    ft_arg = Type
    ty1, ft_res :: Type -> Type
    ft_res = Type
    ty2 })
      | AnonArgFlag
    VisArg <- AnonArgFlag
    af   -- See Note [Decomposing fat arrow c=>t]

      -- See Note [The Purely Kinded Type Invariant (PKTI)] in GHC.Tc.Gen.HsType,
      -- Wrinkle around FunTy
      , Just Type
    rep1 <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    ty1
      , Just Type
    rep2 <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    ty2
      = forall a. a -> Maybe a
    Just (TyCon -> [Type] -> Type
    TyConApp TyCon
    funTyCon [Type
    w, Type
    rep1, Type
    rep2, Type
    ty1], Type
    ty2)

      | Bool
    otherwise
      = forall a. Maybe a
    Nothing

    tcRepSplitAppTy_maybe (AppTy Type
    ty1 Type
    ty2)    = forall a. a -> Maybe a
    Just (Type
    ty1, Type
    ty2)
    tcRepSplitAppTy_maybe (TyConApp TyCon
    tc [Type]
    tys)
      | Bool -> Bool
    not (TyCon -> Bool
    mustBeSaturated TyCon
    tc) Bool -> Bool -> Bool
    || [Type]
    tys forall a. [a] -> Int -> Bool
    `lengthExceeds` TyCon -> Int
    tyConArity TyCon
    tc
      , Just ([Type]
    tys', Type
    ty') <- forall a. [a] -> Maybe ([a], a)
    snocView [Type]
    tys
      = forall a. a -> Maybe a
    Just (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tys', Type
    ty')    -- Never create unsaturated type family apps!
    tcRepSplitAppTy_maybe Type
    _other = forall a. Maybe a
    Nothing

    -------------
    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 = case Type -> Maybe (Type, Type)
    splitAppTy_maybe Type
    ty of
                    Just (Type, Type)
    pr -> (Type, Type)
    pr
                    Maybe (Type, Type)
    Nothing -> forall a. String -> a
    panic String
    "splitAppTy"

    -------------
    splitAppTys :: 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 :: 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
    argforall a. a -> [a] -> [a]
    :[Type]
    args)
        split Type
    _       (TyConApp TyCon
    tc [Type]
    tc_args) [Type]
    args
          = let -- keep type families saturated
                n :: Int
    n | TyCon -> Bool
    mustBeSaturated TyCon
    tc = TyCon -> Int
    tyConArity TyCon
    tc
                  | Bool
    otherwise          = Int
    0
                ([Type]
    tc_args1, [Type]
    tc_args2) = forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    n [Type]
    tc_args
            in
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tc_args1, [Type]
    tc_args2 forall a. [a] -> [a] -> [a]
    ++ [Type]
    args)
        split Type
    _   (FunTy AnonArgFlag
    _ Type
    w Type
    ty1 Type
    ty2) [Type]
    args
          = ASSERT( null args )
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    funTyCon [], [Type
    w, Type
    rep1, Type
    rep2, Type
    ty1, Type
    ty2])
          where
            rep1 :: Type
    rep1 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty1
            rep2 :: Type
    rep2 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty2

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

    -- | Like 'splitAppTys', but doesn't look through type synonyms
    repSplitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
    repSplitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
    repSplitAppTys 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
    argforall a. a -> [a] -> [a]
    :[Type]
    args)
        split (TyConApp TyCon
    tc [Type]
    tc_args) [Type]
    args
          = let n :: Int
    n | TyCon -> Bool
    mustBeSaturated TyCon
    tc = TyCon -> Int
    tyConArity TyCon
    tc
                  | Bool
    otherwise          = Int
    0
                ([Type]
    tc_args1, [Type]
    tc_args2) = forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    n [Type]
    tc_args
            in
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    tc [Type]
    tc_args1, [Type]
    tc_args2 forall a. [a] -> [a] -> [a]
    ++ [Type]
    args)
        split (FunTy AnonArgFlag
    _ Type
    w Type
    ty1 Type
    ty2) [Type]
    args
          = ASSERT( null args )
            (TyCon -> [Type] -> Type
    TyConApp TyCon
    funTyCon [], [Type
    w, Type
    rep1, Type
    rep2, Type
    ty1, Type
    ty2])
          where
            rep1 :: Type
    rep1 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty1
            rep2 :: Type
    rep2 = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty2

        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 = forall a. a -> Maybe a
    Just Integer
    n
      | Bool
    otherwise                             = 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 = forall a. a -> Maybe a
    Just FastString
    s
      | Bool
    otherwise                             = 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 = forall a. a -> Maybe a
    Just Char
    s
      | Bool
    otherwise                              = 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 = forall a. a -> Maybe a
    Just TyLit
    l
      | Bool
    otherwise                  = forall a. Maybe a
    Nothing

    -- | Is this type a custom user error?
    -- If so, give us the kind and the error message.
    userTypeError_maybe :: Type -> Maybe Type
    userTypeError_maybe :: Type -> Maybe Type
    userTypeError_maybe Type
    t
      = do { (TyCon
    tc, Type
    _kind : Type
    msg : [Type]
    _) <- HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    t
              -- There may be more than 2 arguments, if the type error is
              -- used as a type constructor (e.g. at kind `Type -> Type`).

           ; forall (f :: * -> *). Alternative f => Bool -> f ()
    guard (TyCon -> Name
    tyConName TyCon
    tc forall a. Eq a => a -> a -> Bool
    == Name
    errorMessageTypeErrorFamName)
           ; forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    msg }

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

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

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

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

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

        -- An unevaluated type function
        Maybe (TyCon, [Type])
    _ -> 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.
    -}

    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 = forall a. HasCallStack => String -> Maybe a -> a
    expectJust String
    "splitFunTy" forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Maybe (Type, Type, Type)
    splitFunTy_maybe

    {-# INLINE splitFunTy_maybe #-}
    splitFunTy_maybe :: Type -> Maybe (Mult, Type, Type)
    -- ^ Attempts to extract the multiplicity, argument and result types from a type
    splitFunTy_maybe :: Type -> Maybe (Type, Type, Type)
    splitFunTy_maybe Type
    ty
      | FunTy AnonArgFlag
    _ Type
    w Type
    arg Type
    res <- Type -> Type
    coreFullView Type
    ty = forall a. a -> Maybe a
    Just (Type
    w, Type
    arg, Type
    res)
      | Bool
    otherwise                            = 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 AnonArgFlag
    _ Type
    w Type
    arg Type
    res) = [Scaled Type] -> Type -> Type -> ([Scaled Type], Type)
    split ((forall a. Type -> a -> Scaled a
    Scaled Type
    w Type
    arg)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
    _                   = (forall a. [a] -> [a]
    reverse [Scaled Type]
    args, Type
    orig_ty)

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

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

      ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    res
        -> let empty_subst :: TCvSubst
    empty_subst = InScopeSet -> TCvSubst
    mkEmptyTCvSubst forall a b. (a -> b) -> a -> b
    $ TyCoVarSet -> InScopeSet
    mkInScopeSet forall a b. (a -> b) -> a -> b
    $
                             [Type] -> TyCoVarSet
    tyCoVarsOfTypes [Type
    arg,Type
    res]
           in forall a. a -> Maybe a
    Just (HasCallStack => TCvSubst -> Type -> Type
    substTy (TCvSubst -> TyVar -> Type -> TCvSubst
    extendTCvSubst TCvSubst
    empty_subst TyVar
    tv Type
    arg) Type
    res)

      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
    piResultTys Type
    res [Type]
    args

      | ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    res <- Type
    ty
      = TCvSubst -> Type -> [Type] -> Type
    go (TCvSubst -> TyVar -> Type -> TCvSubst
    extendTCvSubst TCvSubst
    init_subst TyVar
    tv Type
    arg) Type
    res [Type]
    args

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

      | Bool
    otherwise
      = forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "piResultTys1" (forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr [Type]
    orig_args)
      where
        init_subst :: TCvSubst
    init_subst = InScopeSet -> TCvSubst
    mkEmptyTCvSubst forall a b. (a -> b) -> a -> b
    $ TyCoVarSet -> InScopeSet
    mkInScopeSet ([Type] -> TyCoVarSet
    tyCoVarsOfTypes (Type
    tyforall a. a -> [a] -> [a]
    :[Type]
    orig_args))

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

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

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

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

          | Bool -> Bool
    not (TCvSubst -> Bool
    isEmptyTCvSubst TCvSubst
    subst)  -- See Note [Care with kind instantiation]
          = TCvSubst -> Type -> [Type] -> Type
    go TCvSubst
    init_subst
              (HasCallStack => TCvSubst -> Type -> Type
    substTy TCvSubst
    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
            forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "piResultTys2" (forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr [Type]
    orig_args SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr [Type]
    all_args)

    applyTysX :: [TyVar] -> Type -> [Type] -> Type
    -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys
    -- Assumes that (/\tvs. body_ty) is closed
    applyTysX :: [TyVar] -> Type -> [Type] -> Type
    applyTysX [TyVar]
    tvs Type
    body_ty [Type]
    arg_tys
      = ASSERT2( arg_tys `lengthAtLeast` n_tvs, pp_stuff )
        ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff )
        Type -> [Type] -> Type
    mkAppTys (HasCallStack => [TyVar] -> [Type] -> Type -> Type
    substTyWith [TyVar]
    tvs (forall a. Int -> [a] -> [a]
    take Int
    n_tvs [Type]
    arg_tys) Type
    body_ty)
                 (forall a. Int -> [a] -> [a]
    drop Int
    n_tvs [Type]
    arg_tys)
      where
        pp_stuff :: SDoc
    pp_stuff = [SDoc] -> SDoc
    vcat [forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs, forall a. Outputable a => a -> SDoc
    ppr Type
    body_ty, forall a. Outputable a => a -> SDoc
    ppr [Type]
    arg_tys]
        n_tvs :: Int
    n_tvs = forall (t :: * -> *) a. Foldable t => t a -> Int
    length [TyVar]
    tvs

    {- 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]
    _) = forall a. a -> Maybe a
    Just TyCon
    tc
    tyConAppTyConPicky_maybe (FunTy {})      = forall a. a -> Maybe a
    Just TyCon
    funTyCon
    tyConAppTyConPicky_maybe Type
    _               = forall a. Maybe a
    Nothing

    -- | The same as @fst . splitTyConApp@
    {-# 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]
    _ -> forall a. a -> Maybe a
    Just TyCon
    tc
      FunTy {}      -> forall a. a -> Maybe a
    Just TyCon
    funTyCon
      Type
    _             -> forall a. Maybe a
    Nothing

    tyConAppTyCon :: Type -> TyCon
    tyConAppTyCon :: Type -> TyCon
    tyConAppTyCon Type
    ty = Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty forall a. Maybe a -> a -> a
    `orElse` forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tyConAppTyCon" (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 Type -> Type
    coreFullView Type
    ty of
      TyConApp TyCon
    _ [Type]
    tys -> forall a. a -> Maybe a
    Just [Type]
    tys
      FunTy AnonArgFlag
    _ Type
    w Type
    arg Type
    res
        | Just Type
    rep1 <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    arg
        , Just Type
    rep2 <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    res
        -> forall a. a -> Maybe a
    Just [Type
    w, Type
    rep1, Type
    rep2, Type
    arg, Type
    res]
      Type
    _ -> forall a. Maybe a
    Nothing

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

    tyConAppArgN :: Int -> Type -> Type
    -- Executing Nth
    tyConAppArgN :: Int -> Type -> Type
    tyConAppArgN Int
    n Type
    ty
      = case Type -> Maybe [Type]
    tyConAppArgs_maybe Type
    ty of
          Just [Type]
    tys -> [Type]
    tys forall a. Outputable a => [a] -> Int -> a
    `getNth` Int
    n
          Maybe [Type]
    Nothing  -> forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tyConAppArgN" (forall a. Outputable a => a -> SDoc
    ppr Int
    n SDoc -> SDoc -> 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 = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
                       Just (TyCon, [Type])
    stuff -> (TyCon, [Type])
    stuff
                       Maybe (TyCon, [Type])
    Nothing    -> forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitTyConApp" (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 = HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    repSplitTyConApp_maybe forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> Type
    coreFullView

    -- | Split a type constructor application into its type constructor and
    -- applied types. Note that this may fail 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@). Consequently, you may need to zonk your
    -- type before using this function.
    --
    -- This does *not* split types headed with (=>), as that's not a TyCon in the
    -- type-checker.
    --
    -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'.
    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 | Just Type
    ty' <- Type -> Maybe Type
    tcView Type
    ty = HasCallStack => Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    ty'
                             | Bool
    otherwise             = HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    tcRepSplitTyConApp_maybe Type
    ty

    -------------------
    repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    -- ^ Like 'splitTyConApp_maybe', but doesn't look through synonyms. This
    -- assumes the synonyms have already been dealt with.
    repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    repSplitTyConApp_maybe (TyConApp TyCon
    tc [Type]
    tys) = forall a. a -> Maybe a
    Just (TyCon
    tc, [Type]
    tys)
    repSplitTyConApp_maybe (FunTy AnonArgFlag
    _ Type
    w Type
    arg Type
    res)
      -- NB: we're in Core, so no check for VisArg
      = forall a. a -> Maybe a
    Just (TyCon
    funTyCon, [Type
    w, Type
    arg_rep, Type
    res_rep, Type
    arg, Type
    res])
      where
        arg_rep :: Type
    arg_rep = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    arg
        res_rep :: Type
    res_rep = HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    res
    repSplitTyConApp_maybe Type
    _ = forall a. Maybe a
    Nothing

    tcRepSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    -- ^ Like 'tcSplitTyConApp_maybe', but doesn't look through synonyms. This
    -- assumes the synonyms have already been dealt with.
    --
    -- Moreover, for a FunTy, it only succeeds if the argument types
    -- have enough info to extract the runtime-rep arguments that
    -- the funTyCon requires.  This will usually be true;
    -- but may be temporarily false during canonicalization:
    --     see Note [Decomposing FunTy] in GHC.Tc.Solver.Canonical
    --     and Note [The Purely Kinded Type Invariant (PKTI)] in GHC.Tc.Gen.HsType,
    --         Wrinkle around FunTy
    tcRepSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    tcRepSplitTyConApp_maybe (TyConApp TyCon
    tc [Type]
    tys) = forall a. a -> Maybe a
    Just (TyCon
    tc, [Type]
    tys)
    tcRepSplitTyConApp_maybe (FunTy AnonArgFlag
    VisArg Type
    w Type
    arg Type
    res)
      -- NB: VisArg. See Note [Decomposing fat arrow c=>t]
      | Just Type
    arg_rep <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    arg
      , Just Type
    res_rep <- HasDebugCallStack => Type -> Maybe Type
    getRuntimeRep_maybe Type
    res
      = forall a. a -> Maybe a
    Just (TyCon
    funTyCon, [Type
    w, Type
    arg_rep, Type
    res_rep, Type
    arg, Type
    res])
    tcRepSplitTyConApp_maybe Type
    _ = forall a. Maybe a
    Nothing

    -------------------
    -- | Attempts to tease a list type apart and gives the type of the elements if
    -- successful (looks through type synonyms)
    splitListTyConApp_maybe :: Type -> Maybe Type
    splitListTyConApp_maybe :: Type -> Maybe Type
    splitListTyConApp_maybe Type
    ty = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
      Just (TyCon
    tc,[Type
    e]) | TyCon
    tc forall a. Eq a => a -> a -> Bool
    == TyCon
    listTyCon -> forall a. a -> Maybe a
    Just Type
    e
      Maybe (TyCon, [Type])
    _other                          -> forall a. Maybe a
    Nothing

    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
        = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs )
          [TyVar] -> Type -> [Type] -> Type
    applyTysX [TyVar]
    tvs Type
    rhs [Type]
    tys
      where
        ([TyVar]
    tvs, Type
    rhs) = TyCon -> ([TyVar], Type)
    newTyConEtadRhs TyCon
    tycon

    {-
    ---------------------------------------------------------------------
                               CastTy
                               ~~~~~~
    A casted type has its *kind* casted into something new.
    -}

    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 = forall a. a -> Maybe a
    Just (Type
    ty', KindCoercion
    co)
      | Bool
    otherwise                        = 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
    ty KindCoercion
    co | KindCoercion -> Bool
    isReflexiveCo KindCoercion
    co = Type
    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 (CastTy Type
    ty KindCoercion
    co1) KindCoercion
    co2
      -- (EQ3) from the Note
      = Type -> KindCoercion -> Type
    mkCastTy Type
    ty (KindCoercion
    co1 KindCoercion -> KindCoercion -> KindCoercion
    `mkTransCo` KindCoercion
    co2)
          -- call mkCastTy again for the reflexivity check

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

    mkCastTy Type
    ty KindCoercion
    co = Type -> KindCoercion -> Type
    CastTy Type
    ty KindCoercion
    co

    tyConBindersTyCoBinders :: [TyConBinder] -> [TyCoBinder]
    -- Return the tyConBinders in TyCoBinder form
    tyConBindersTyCoBinders :: [TyConBinder] -> [TyCoBinder]
    tyConBindersTyCoBinders = forall a b. (a -> b) -> [a] -> [b]
    map TyConBinder -> TyCoBinder
    to_tyb
      where
        to_tyb :: TyConBinder -> TyCoBinder
    to_tyb (Bndr TyVar
    tv (NamedTCB ArgFlag
    vis)) = VarBndr TyVar ArgFlag -> TyCoBinder
    Named (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ArgFlag
    vis)
        to_tyb (Bndr TyVar
    tv (AnonTCB AnonArgFlag
    af))   = AnonArgFlag -> Scaled Type -> TyCoBinder
    Anon AnonArgFlag
    af (forall a. a -> Scaled a
    tymult (TyVar -> Type
    varType TyVar
    tv))

    -- | Create the plain type constructor type which has been applied to no type arguments at all.
    mkTyConTy :: TyCon -> Type
    mkTyConTy :: TyCon -> Type
    mkTyConTy TyCon
    tycon = TyCon -> Type
    tyConNullaryTy TyCon
    tycon
      -- see Note [Sharing nullary TyConApps] in GHC.Core.TyCon

    -- | 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 [Type]
    tys
      | forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Type]
    tys
      = TyCon -> Type
    mkTyConTy TyCon
    tycon

      | TyCon -> Bool
    isFunTyCon TyCon
    tycon
      , [Type
    w, Type
    _rep1,Type
    _rep2,Type
    ty1,Type
    ty2] <- [Type]
    tys
      -- The FunTyCon (->) is always a visible one
      = FunTy { ft_af :: AnonArgFlag
    ft_af = AnonArgFlag
    VisArg, ft_mult :: Type
    ft_mult = Type
    w, ft_arg :: Type
    ft_arg = Type
    ty1, ft_res :: Type
    ft_res = Type
    ty2 }

      -- See Note [Prefer Type over TYPE 'LiftedRep].
      | TyCon
    tycon forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    tYPETyConKey
      , [Type
    rep] <- [Type]
    tys
      = Type -> Type
    tYPE Type
    rep
      -- The catch-all case
      | Bool
    otherwise
      = TyCon -> [Type] -> Type
    TyConApp TyCon
    tycon [Type]
    tys

    {-
    Note [Prefer Type over TYPE 'LiftedRep]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The Core of nearly any program will have numerous occurrences of
    @TYPE 'LiftedRep@ (and, equivalently, 'Type') floating about. Concretely, while
    investigating #17292 we found that these constituting a majority of 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
     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:

     1. Instead of representing the lifted kind as
        @TyConApp tYPETyCon [liftedRepDataCon]@ we rather prefer to
        use the 'GHC.Types.Type' type synonym (represented as a nullary TyConApp).
        This serves goal (b) since there are no applied type arguments to traverse,
        e.g., during comparison.

     2. We have a 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)).

     3. 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.
    -}

    -- | Given a @RuntimeRep@, applies @TYPE@ to it.
    -- See Note [TYPE and RuntimeRep] in GHC.Builtin.Types.Prim.
    tYPE :: Type -> Type
    tYPE :: Type -> Type
    tYPE rr :: Type
    rr@(TyConApp TyCon
    tc [Type
    arg])
      -- See Note [Prefer Type of TYPE 'LiftedRep]
      | TyCon
    tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    boxedRepDataConKey
      , TyConApp TyCon
    tc' [] <- Type
    arg
      = if | TyCon
    tc' forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    liftedDataConKey   -> Type
    liftedTypeKind   -- TYPE (BoxedRep 'Lifted)
           | TyCon
    tc' forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    unliftedDataConKey -> Type
    unliftedTypeKind -- TYPE (BoxedRep 'Unlifted)
           | Bool
    otherwise                       -> TyCon -> [Type] -> Type
    TyConApp TyCon
    tYPETyCon [Type
    rr]
      | TyCon
    tc forall a. Eq a => a -> a -> Bool
    == TyCon
    liftedRepTyCon                               -- TYPE LiftedRep
      = Type
    liftedTypeKind
      | TyCon
    tc forall a. Eq a => a -> a -> Bool
    == TyCon
    unliftedRepTyCon                             -- TYPE UnliftedRep
      = Type
    unliftedTypeKind
    tYPE Type
    rr = TyCon -> [Type] -> Type
    TyConApp TyCon
    tYPETyCon [Type
    rr]

    {-
    --------------------------------------------------------------------
                                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) = forall a. a -> Maybe a
    Just KindCoercion
    co
    isCoercionTy_maybe Type
    _               = forall a. Maybe a
    Nothing

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

    {-
    ---------------------------------------------------------------------
                                    SynTy
                                    ~~~~~

    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.

    ---------------------------------------------------------------------
                                    ForAllTy
                                    ~~~~~~~~
    -}

    -- | Make a dependent forall over an 'Inferred' variable
    mkTyCoInvForAllTy :: TyCoVar -> Type -> Type
    mkTyCoInvForAllTy :: TyVar -> Type -> Type
    mkTyCoInvForAllTy TyVar
    tv Type
    ty
      | TyVar -> Bool
    isCoVar TyVar
    tv
      , Bool -> Bool
    not (TyVar
    tv TyVar -> TyCoVarSet -> Bool
    `elemVarSet` Type -> TyCoVarSet
    tyCoVarsOfType Type
    ty)
      = Type -> Type -> Type
    mkVisFunTyMany (TyVar -> Type
    varType TyVar
    tv) Type
    ty
      | Bool
    otherwise
      = VarBndr TyVar ArgFlag -> Type -> Type
    ForAllTy (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ArgFlag
    Inferred) Type
    ty

    -- | Like 'mkTyCoInvForAllTy', but tv should be a tyvar
    mkInfForAllTy :: TyVar -> Type -> Type
    mkInfForAllTy :: TyVar -> Type -> Type
    mkInfForAllTy TyVar
    tv Type
    ty = ASSERT( isTyVar tv )
                          VarBndr TyVar ArgFlag -> Type -> Type
    ForAllTy (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ArgFlag
    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 = 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 = 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 = ASSERT( isTyVar tv )
                           -- covar is always Inferred, so input should be tyvar
                           VarBndr TyVar ArgFlag -> Type -> Type
    ForAllTy (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ArgFlag
    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 = 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 = ASSERT( all isTyVar tvs )
                         -- covar is always Inferred, so all inputs should be tyvar
                         [VarBndr TyVar ArgFlag] -> Type -> Type
    mkForAllTys [ forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv ArgFlag
    Required | TyVar
    tv <- [TyVar]
    tvs ]

    -- | Given a list of type-level vars and the free vars of a result kind,
    -- makes TyCoBinders, 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] -> TyCoVarSet -> [TyConBinder]
    mkTyConBindersPreferAnon [TyVar]
    vars TyCoVarSet
    inner_tkvs = ASSERT( all isTyVar vars)
                                               forall a b. (a, b) -> a
    fst ([TyVar] -> ([TyConBinder], TyCoVarSet)
    go [TyVar]
    vars)
      where
        go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
        go :: [TyVar] -> ([TyConBinder], TyCoVarSet)
    go [] = ([], TyCoVarSet
    inner_tkvs)
        go (TyVar
    v:[TyVar]
    vs) | TyVar
    v TyVar -> TyCoVarSet -> Bool
    `elemVarSet` TyCoVarSet
    fvs
                  = ( forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    v (ArgFlag -> TyConBndrVis
    NamedTCB ArgFlag
    Required) forall a. a -> [a] -> [a]
    : [TyConBinder]
    binders
                    , TyCoVarSet
    fvs TyCoVarSet -> TyVar -> TyCoVarSet
    `delVarSet` TyVar
    v TyCoVarSet -> TyCoVarSet -> TyCoVarSet
    `unionVarSet` TyCoVarSet
    kind_vars )
                  | Bool
    otherwise
                  = ( forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    v (AnonArgFlag -> TyConBndrVis
    AnonTCB AnonArgFlag
    VisArg) forall a. a -> [a] -> [a]
    : [TyConBinder]
    binders
                    , TyCoVarSet
    fvs TyCoVarSet -> TyCoVarSet -> TyCoVarSet
    `unionVarSet` TyCoVarSet
    kind_vars )
          where
            ([TyConBinder]
    binders, TyCoVarSet
    fvs) = [TyVar] -> ([TyConBinder], TyCoVarSet)
    go [TyVar]
    vs
            kind_vars :: TyCoVarSet
    kind_vars      = Type -> TyCoVarSet
    tyCoVarsOfType forall a b. (a -> b) -> a -> b
    $ TyVar -> Type
    tyVarKind TyVar
    v

    -- | 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 ArgFlag
    _) Type
    ty)    [TyVar]
    tvs = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty (TyVar
    tvforall 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 = (forall a. [a] -> [a]
    reverse [TyVar]
    tvs, Type
    orig_ty)

    -- | Splits the longest initial sequence of 'ForAllTy's that satisfy
    -- @argf_pred@, returning the binders transformed by @argf_pred@
    splitSomeForAllTyCoVarBndrs :: (ArgFlag -> Maybe af) -> Type -> ([VarBndr TyCoVar af], Type)
    splitSomeForAllTyCoVarBndrs :: forall af.
    (ArgFlag -> Maybe af) -> Type -> ([VarBndr TyVar af], Type)
    splitSomeForAllTyCoVarBndrs ArgFlag -> Maybe af
    argf_pred Type
    ty = Type -> Type -> [VarBndr TyVar af] -> ([VarBndr TyVar af], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type -> Type -> [VarBndr TyVar af] -> ([VarBndr TyVar af], Type)
    split Type
    _ (ForAllTy (Bndr TyVar
    tcv ArgFlag
    argf) Type
    ty) [VarBndr TyVar af]
    tvs
          | Just af
    argf' <- ArgFlag -> Maybe af
    argf_pred ArgFlag
    argf               = Type -> Type -> [VarBndr TyVar af] -> ([VarBndr TyVar af], Type)
    split Type
    ty Type
    ty (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tcv af
    argf' forall a. a -> [a] -> [a]
    : [VarBndr TyVar af]
    tvs)
        split Type
    orig_ty Type
    ty [VarBndr TyVar af]
    tvs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Type -> [VarBndr TyVar af] -> ([VarBndr TyVar af], Type)
    split Type
    orig_ty Type
    ty' [VarBndr TyVar af]
    tvs
        split Type
    orig_ty Type
    _                            [VarBndr TyVar af]
    tvs = (forall a. [a] -> [a]
    reverse [VarBndr TyVar af]
    tvs, Type
    orig_ty)

    -- | Like 'splitForAllTyCoVars', but only splits 'ForAllTy's with 'Required' type
    -- variable binders. Furthermore, each returned tyvar is annotated with '()'.
    splitForAllReqTVBinders :: Type -> ([ReqTVBinder], Type)
    splitForAllReqTVBinders :: Type -> ([ReqTVBinder], Type)
    splitForAllReqTVBinders Type
    ty = forall af.
    (ArgFlag -> Maybe af) -> Type -> ([VarBndr TyVar af], Type)
    splitSomeForAllTyCoVarBndrs ArgFlag -> Maybe ()
    argf_pred Type
    ty
      where
        argf_pred :: ArgFlag -> Maybe ()
        argf_pred :: ArgFlag -> Maybe ()
    argf_pred ArgFlag
    Required       = forall a. a -> Maybe a
    Just ()
        argf_pred (Invisible {}) = forall a. Maybe a
    Nothing

    -- | Like 'splitForAllTyCoVars', but only splits 'ForAllTy's with 'Invisible' type
    -- variable binders. Furthermore, each returned tyvar is annotated with its
    -- 'Specificity'.
    splitForAllInvisTVBinders :: Type -> ([InvisTVBinder], Type)
    splitForAllInvisTVBinders :: Type -> ([InvisTVBinder], Type)
    splitForAllInvisTVBinders Type
    ty = forall af.
    (ArgFlag -> Maybe af) -> Type -> ([VarBndr TyVar af], Type)
    splitSomeForAllTyCoVarBndrs ArgFlag -> Maybe Specificity
    argf_pred Type
    ty
      where
        argf_pred :: ArgFlag -> Maybe Specificity
        argf_pred :: ArgFlag -> Maybe Specificity
    argf_pred ArgFlag
    Required         = forall a. Maybe a
    Nothing
        argf_pred (Invisible Specificity
    spec) = forall a. a -> Maybe a
    Just Specificity
    spec

    -- | 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 ArgFlag
    _) Type
    ty) [TyVar]
    tvs | TyVar -> Bool
    isTyVar TyVar
    tv = Type -> Type -> [TyVar] -> ([TyVar], Type)
    split Type
    ty Type
    ty (TyVar
    tvforall 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              = (forall a. [a] -> [a]
    reverse [TyVar]
    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 ArgFlag
    _) 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 ArgFlag
    _) 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                                  = forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "splitForAllTyCoVar" (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 ArgFlag
    _ 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 forall type apart, but only if it's a proper forall,
    -- with a named binder
    splitForAllTyCoVar_maybe :: Type -> Maybe (TyCoVar, Type)
    splitForAllTyCoVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllTyCoVar_maybe Type
    ty
      | ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty = forall a. a -> Maybe a
    Just (TyVar
    tv, Type
    inner_ty)
      | Bool
    otherwise                                        = forall a. Maybe a
    Nothing

    -- | Like 'splitForAllTyCoVar_maybe', but only returns Just if it is a tyvar binder.
    splitForAllTyVar_maybe :: Type -> Maybe (TyCoVar, Type)
    splitForAllTyVar_maybe :: Type -> Maybe (TyVar, Type)
    splitForAllTyVar_maybe Type
    ty
      | ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    inner_ty <- Type -> Type
    coreFullView Type
    ty
      , TyVar -> Bool
    isTyVar TyVar
    tv
      = forall a. a -> Maybe a
    Just (TyVar
    tv, Type
    inner_ty)

      | Bool
    otherwise = forall a. Maybe a
    Nothing

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

      | Bool
    otherwise = 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 (TyCoBinder, Type)
    splitPiTy_maybe :: Type -> Maybe (TyCoBinder, Type)
    splitPiTy_maybe Type
    ty = case Type -> Type
    coreFullView Type
    ty of
      ForAllTy VarBndr TyVar ArgFlag
    bndr Type
    ty -> forall a. a -> Maybe a
    Just (VarBndr TyVar ArgFlag -> TyCoBinder
    Named VarBndr TyVar ArgFlag
    bndr, Type
    ty)
      FunTy { ft_af :: Type -> AnonArgFlag
    ft_af = AnonArgFlag
    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}
                       -> forall a. a -> Maybe a
    Just (AnonArgFlag -> Scaled Type -> TyCoBinder
    Anon AnonArgFlag
    af (forall a. Type -> a -> Scaled a
    mkScaled Type
    w Type
    arg), Type
    res)
      Type
    _                -> forall a. Maybe a
    Nothing

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

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

    -- | Like 'splitPiTys' but split off only /named/ binders
    --   and returns 'TyCoVarBinder's rather than 'TyCoBinder's
    splitForAllTyCoVarBinders :: Type -> ([TyCoVarBinder], Type)
    splitForAllTyCoVarBinders :: Type -> ([VarBndr TyVar ArgFlag], Type)
    splitForAllTyCoVarBinders Type
    ty = Type
    -> Type
    -> [VarBndr TyVar ArgFlag]
    -> ([VarBndr TyVar ArgFlag], Type)
    split Type
    ty Type
    ty []
      where
        split :: Type
    -> Type
    -> [VarBndr TyVar ArgFlag]
    -> ([VarBndr TyVar ArgFlag], Type)
    split Type
    orig_ty Type
    ty [VarBndr TyVar ArgFlag]
    bs | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type
    -> Type
    -> [VarBndr TyVar ArgFlag]
    -> ([VarBndr TyVar ArgFlag], Type)
    split Type
    orig_ty Type
    ty' [VarBndr TyVar ArgFlag]
    bs
        split Type
    _       (ForAllTy VarBndr TyVar ArgFlag
    b Type
    res) [VarBndr TyVar ArgFlag]
    bs = Type
    -> Type
    -> [VarBndr TyVar ArgFlag]
    -> ([VarBndr TyVar ArgFlag], Type)
    split Type
    res Type
    res (VarBndr TyVar ArgFlag
    bforall a. a -> [a] -> [a]
    :[VarBndr TyVar ArgFlag]
    bs)
        split Type
    orig_ty Type
    _                [VarBndr TyVar ArgFlag]
    bs = (forall a. [a] -> [a]
    reverse [VarBndr TyVar ArgFlag]
    bs, Type
    orig_ty)
    {-# INLINE splitForAllTyCoVarBinders #-}

    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 -> Int
    invisibleTyBndrCount Type
    ty = forall (t :: * -> *) a. Foldable t => t a -> Int
    length (forall a b. (a, b) -> a
    fst (Type -> ([TyCoBinder], Type)
    splitInvisPiTys Type
    ty))

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

    splitInvisPiTysN :: Int -> Type -> ([TyCoBinder], Type)
    -- ^ Same as 'splitInvisPiTys', but stop when
    --   - you have found @n@ 'TyCoBinder's,
    --   - or you run out of invisible binders
    splitInvisPiTysN :: Int -> Type -> ([TyCoBinder], Type)
    splitInvisPiTysN Int
    n Type
    ty = forall {t}.
    (Eq t, Num t) =>
    t -> Type -> Type -> [TyCoBinder] -> ([TyCoBinder], Type)
    split Int
    n Type
    ty Type
    ty []
       where
        split :: t -> Type -> Type -> [TyCoBinder] -> ([TyCoBinder], Type)
    split t
    n Type
    orig_ty Type
    ty [TyCoBinder]
    bs
          | t
    n forall a. Eq a => a -> a -> Bool
    == t
    0                  = (forall a. [a] -> [a]
    reverse [TyCoBinder]
    bs, Type
    orig_ty)
          | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = t -> Type -> Type -> [TyCoBinder] -> ([TyCoBinder], Type)
    split t
    n Type
    orig_ty Type
    ty' [TyCoBinder]
    bs
          | ForAllTy VarBndr TyVar ArgFlag
    b Type
    res <- Type
    ty
          , Bndr TyVar
    _ ArgFlag
    vis <- VarBndr TyVar ArgFlag
    b
          , ArgFlag -> Bool
    isInvisibleArgFlag ArgFlag
    vis  = t -> Type -> Type -> [TyCoBinder] -> ([TyCoBinder], Type)
    split (t
    nforall a. Num a => a -> a -> a
    -t
    1) Type
    res Type
    res (VarBndr TyVar ArgFlag -> TyCoBinder
    Named VarBndr TyVar ArgFlag
    b  forall a. a -> [a] -> [a]
    : [TyCoBinder]
    bs)
          | FunTy { ft_af :: Type -> AnonArgFlag
    ft_af = AnonArgFlag
    InvisArg, 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
                                    = t -> Type -> Type -> [TyCoBinder] -> ([TyCoBinder], Type)
    split (t
    nforall a. Num a => a -> a -> a
    -t
    1) Type
    res Type
    res (AnonArgFlag -> Scaled Type -> TyCoBinder
    Anon AnonArgFlag
    InvisArg (forall a. Type -> a -> Scaled a
    Scaled Type
    mult Type
    arg) forall a. a -> [a] -> [a]
    : [TyCoBinder]
    bs)
          | Bool
    otherwise               = (forall a. [a] -> [a]
    reverse [TyCoBinder]
    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 = forall a b. (a, b) -> b
    snd 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 =
      forall a. [Bool] -> [a] -> [a]
    filterByList (forall a b. (a -> b) -> [a] -> [b]
    map (forall a. Eq a => a -> a -> Bool
    /= ArgFlag
    Inferred) forall a b. (a -> b) -> a -> b
    $ TyCon -> [Type] -> [ArgFlag]
    tyConArgFlags 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 =
      forall a. [Bool] -> [a] -> ([a], [a])
    partitionByList (forall a b. (a -> b) -> [a] -> [b]
    map ArgFlag -> Bool
    isInvisibleArgFlag forall a b. (a -> b) -> a -> b
    $ TyCon -> [Type] -> [ArgFlag]
    tyConArgFlags 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, ArgFlag)] -> ([a], [a])
    partitionInvisibles :: forall a. [(a, ArgFlag)] -> ([a], [a])
    partitionInvisibles = forall a b c. (a -> Either b c) -> [a] -> ([b], [c])
    partitionWith forall a. (a, ArgFlag) -> Either a a
    pick_invis
      where
        pick_invis :: (a, ArgFlag) -> Either a a
        pick_invis :: forall a. (a, ArgFlag) -> Either a a
    pick_invis (a
    thing, ArgFlag
    vis) | ArgFlag -> Bool
    isInvisibleArgFlag ArgFlag
    vis = forall a b. a -> Either a b
    Left a
    thing
                                | Bool
    otherwise              = 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
    -- > tyConArgFlags 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.
    tyConArgFlags :: TyCon -> [Type] -> [ArgFlag]
    tyConArgFlags :: TyCon -> [Type] -> [ArgFlag]
    tyConArgFlags TyCon
    tc = Type -> [Type] -> [ArgFlag]
    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 'appTyArgFlags' comes in handy,
    -- since @f Type Bool@ would be represented in Core using 'AppTy's.
    -- (See also #15792).
    appTyArgFlags :: Type -> [Type] -> [ArgFlag]
    appTyArgFlags :: Type -> [Type] -> [ArgFlag]
    appTyArgFlags Type
    ty = Type -> [Type] -> [ArgFlag]
    fun_kind_arg_flags (HasDebugCallStack => 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] -> [ArgFlag]
    fun_kind_arg_flags :: Type -> [Type] -> [ArgFlag]
    fun_kind_arg_flags = TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    emptyTCvSubst
      where
        go :: TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    subst Type
    ki [Type]
    arg_tys
          | Just Type
    ki' <- Type -> Maybe Type
    coreView Type
    ki = TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    subst Type
    ki' [Type]
    arg_tys
        go TCvSubst
    _ Type
    _ [] = []
        go TCvSubst
    subst (ForAllTy (Bndr TyVar
    tv ArgFlag
    argf) Type
    res_ki) (Type
    arg_ty:[Type]
    arg_tys)
          = ArgFlag
    argf forall a. a -> [a] -> [a]
    : TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    subst' Type
    res_ki [Type]
    arg_tys
          where
            subst' :: TCvSubst
    subst' = TCvSubst -> TyVar -> Type -> TCvSubst
    extendTvSubst TCvSubst
    subst TyVar
    tv Type
    arg_ty
        go TCvSubst
    subst (TyVarTy TyVar
    tv) [Type]
    arg_tys
          | Just Type
    ki <- TCvSubst -> TyVar -> Maybe Type
    lookupTyVar TCvSubst
    subst TyVar
    tv = TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    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 ArgFlags:
        --
        -- [Inferred,   Specified, Required, Required, Specified, Required]
        -- forall {k1}. forall k2. k1 ->     k2 ->     forall k3. k3 ->     Type
        go TCvSubst
    subst (FunTy{ft_af :: Type -> AnonArgFlag
    ft_af = AnonArgFlag
    af, ft_res :: Type -> Type
    ft_res = Type
    res_ki}) (Type
    _:[Type]
    arg_tys)
          = ArgFlag
    argf forall a. a -> [a] -> [a]
    : TCvSubst -> Type -> [Type] -> [ArgFlag]
    go TCvSubst
    subst Type
    res_ki [Type]
    arg_tys
          where
            argf :: ArgFlag
    argf = case AnonArgFlag
    af of
                     AnonArgFlag
    VisArg   -> ArgFlag
    Required
                     AnonArgFlag
    InvisArg -> ArgFlag
    Inferred
        go TCvSubst
    _ Type
    _ [Type]
    arg_tys = forall a b. (a -> b) -> [a] -> [b]
    map (forall a b. a -> b -> a
    const ArgFlag
    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) = 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 AnonArgFlag
    af Type
    w Type
    a Type
    b)    = case AnonArgFlag
    af of
                                    AnonArgFlag
    InvisArg -> Bool
    False                               -- e.g., Eq a => b
                                    AnonArgFlag
    VisArg   -> 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

    {-
    %************************************************************************
    %*                                                                      *
       TyCoBinders
    %*                                                                      *
    %************************************************************************
    -}

    -- | Make an anonymous binder
    mkAnonBinder :: AnonArgFlag -> Scaled Type -> TyCoBinder
    mkAnonBinder :: AnonArgFlag -> Scaled Type -> TyCoBinder
    mkAnonBinder = AnonArgFlag -> Scaled Type -> TyCoBinder
    Anon

    -- | Does this binder bind a variable that is /not/ erased? Returns
    -- 'True' for anonymous binders.
    isAnonTyCoBinder :: TyCoBinder -> Bool
    isAnonTyCoBinder :: TyCoBinder -> Bool
    isAnonTyCoBinder (Named {}) = Bool
    False
    isAnonTyCoBinder (Anon {})  = Bool
    True

    tyCoBinderVar_maybe :: TyCoBinder -> Maybe TyCoVar
    tyCoBinderVar_maybe :: TyCoBinder -> Maybe TyVar
    tyCoBinderVar_maybe (Named VarBndr TyVar ArgFlag
    tv) = forall a. a -> Maybe a
    Just forall a b. (a -> b) -> a -> b
    $ forall tv argf. VarBndr tv argf -> tv
    binderVar VarBndr TyVar ArgFlag
    tv
    tyCoBinderVar_maybe TyCoBinder
    _          = forall a. Maybe a
    Nothing

    tyCoBinderType :: TyCoBinder -> Type
    tyCoBinderType :: TyCoBinder -> Type
    tyCoBinderType (Named VarBndr TyVar ArgFlag
    tvb) = forall argf. VarBndr TyVar argf -> Type
    binderType VarBndr TyVar ArgFlag
    tvb
    tyCoBinderType (Anon AnonArgFlag
    _ Scaled Type
    ty)   = forall a. Scaled a -> a
    scaledThing Scaled Type
    ty

    tyBinderType :: TyBinder -> Type
    tyBinderType :: TyCoBinder -> Type
    tyBinderType (Named (Bndr TyVar
    tv ArgFlag
    _))
      = ASSERT( isTyVar tv )
        TyVar -> Type
    tyVarKind TyVar
    tv
    tyBinderType (Anon AnonArgFlag
    _ Scaled Type
    ty)   = forall a. Scaled a -> a
    scaledThing Scaled Type
    ty

    -- | Extract a relevant type, if there is one.
    binderRelevantType_maybe :: TyCoBinder -> Maybe Type
    binderRelevantType_maybe :: TyCoBinder -> Maybe Type
    binderRelevantType_maybe (Named {}) = forall a. Maybe a
    Nothing
    binderRelevantType_maybe (Anon AnonArgFlag
    _ Scaled Type
    ty)  = forall a. a -> Maybe a
    Just (forall a. Scaled a -> a
    scaledThing Scaled Type
    ty)

    {-
    ************************************************************************
    *                                                                      *
    \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 :: TCvSubst
    fam_subst = ASSERT2( tvs `equalLength` tys, ppr tc <+> ppr tys )
                        HasDebugCallStack => [TyVar] -> [Type] -> TCvSubst
    zipTvSubst [TyVar]
    tvs [Type]
    tys
      = TyCon -> [Type] -> Type
    mkTyConApp TyCon
    fam_tc (HasCallStack => TCvSubst -> [Type] -> [Type]
    substTys TCvSubst
    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 -> Int -> Type
    coAxNthLHS CoAxiom br
    ax Int
    ind =
      TyCon -> [Type] -> Type
    mkTyConApp (forall (br :: BranchFlag). CoAxiom br -> TyCon
    coAxiomTyCon CoAxiom br
    ax) (CoAxBranch -> [Type]
    coAxBranchLHS (forall (br :: BranchFlag). CoAxiom br -> Int -> CoAxBranch
    coAxiomNthBranch CoAxiom br
    ax Int
    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) = 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 AnonArgFlag
    _ 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 ArgFlag
    _ 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

    -- | 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 forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    eqPrimTyConKey Bool -> Bool -> Bool
    || TyCon
    tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    eqReprPrimTyConKey
      | Bool
    otherwise
      = Bool
    False

    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
    -> TyCon
    mkSynonymTyCon Name
    name [TyConBinder]
    binders Type
    res_kind [Role]
    roles Type
    rhs Bool
    is_tau Bool
    is_fam_free Bool
    is_forgetful
      where
        is_tau :: Bool
    is_tau       = Type -> Bool
    isTauTy Type
    rhs
        is_fam_free :: Bool
    is_fam_free  = Type -> Bool
    isFamFreeTy Type
    rhs
        is_forgetful :: Bool
    is_forgetful = forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    any (Bool -> Bool
    not forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (TyVar -> TyCoVarSet -> Bool
    `elemVarSet` Type -> TyCoVarSet
    tyCoVarsOfType Type
    rhs) forall b c a. (b -> c) -> (a -> b) -> a -> c
    . forall tv argf. VarBndr tv argf -> tv
    binderVar) [TyConBinder]
    binders Bool -> Bool -> Bool
    ||
                       forall a. (a -> Bool) -> UniqSet a -> Bool
    uniqSetAny TyCon -> Bool
    isForgetfulSynTyCon (Type -> UniqSet TyCon
    tyConsOfType Type
    rhs)
             -- NB: This is allowed to be conservative, returning True more often
             -- than it should. See comments on GHC.Core.TyCon.isForgetfulSynTyCon

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

    -- | Returns Just True if this type is surely lifted, Just False
    -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is
    -- levity polymorphic), and panics if the kind does not have the shape
    -- TYPE r.
    isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
    isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
    isLiftedType_maybe Type
    ty = case Type -> Type
    coreFullView (HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty) of
      Type
    ty' | Type -> Bool
    isLiftedRuntimeRep Type
    ty'  -> forall a. a -> Maybe a
    Just Bool
    True
      TyConApp {}                   -> forall a. a -> Maybe a
    Just Bool
    False  -- Everything else is unlifted
      Type
    _                             -> forall a. Maybe a
    Nothing     -- levity polymorphic

    -- | See "Type#type_classification" for what an unlifted type is.
    -- Panics on levity polymorphic types; See 'mightBeUnliftedType' for
    -- a more approximate predicate that behaves better in the presence of
    -- levity 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.
            -- They are pretty bogus types, mind you.  It would be better never to
            -- construct them
    isUnliftedType :: HasDebugCallStack => Type -> Bool
    isUnliftedType Type
    ty
      = Bool -> Bool
    not (HasDebugCallStack => Type -> Maybe Bool
    isLiftedType_maybe Type
    ty forall a. Maybe a -> a -> a
    `orElse`
             forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "isUnliftedType" (forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    <+> forall a. Outputable a => a -> SDoc
    ppr (HasDebugCallStack => Type -> Type
    typeKind Type
    ty)))

    -- | Returns:
    --
    -- * 'False' if the type is /guaranteed/ lifted or
    -- * 'True' if it is unlifted, OR we aren't sure (e.g. in a levity-polymorphic case)
    mightBeUnliftedType :: Type -> Bool
    mightBeUnliftedType :: Type -> Bool
    mightBeUnliftedType Type
    ty
      = case HasDebugCallStack => Type -> Maybe Bool
    isLiftedType_maybe Type
    ty of
          Just Bool
    is_lifted -> Bool -> Bool
    not Bool
    is_lifted
          Maybe Bool
    Nothing -> Bool
    True

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

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

    isUnboxedTupleType :: Type -> Bool
    isUnboxedTupleType :: Type -> Bool
    isUnboxedTupleType Type
    ty
      = Type -> TyCon
    tyConAppTyCon (HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty) 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
      = Type -> TyCon
    tyConAppTyCon (HasDebugCallStack => Type -> Type
    getRuntimeRep Type
    ty) 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])
    splitTyConApp_maybe Type
    ty of
          Just (TyCon
    tc, [Type]
    ty_args) -> ASSERT( ty_args `lengthIs` tyConArity 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 levity-polymorphic types.
    isStrictType :: HasDebugCallStack => Type -> Bool
    isStrictType :: HasDebugCallStack => Type -> Bool
    isStrictType = HasDebugCallStack => Type -> Bool
    isUnliftedType

    isPrimitiveType :: Type -> Bool
    -- ^ Returns true of types that are opaque to Haskell.
    isPrimitiveType :: Type -> Bool
    isPrimitiveType Type
    ty = case HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    splitTyConApp_maybe Type
    ty of
                            Just (TyCon
    tc, [Type]
    ty_args) -> ASSERT( ty_args `lengthIs` tyConArity 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 :: Int -> Type -> Bool
    isValidJoinPointType Int
    arity Type
    ty
      = forall {t}. (Eq t, Num t) => TyCoVarSet -> t -> Type -> Bool
    valid_under TyCoVarSet
    emptyVarSet Int
    arity Type
    ty
      where
        valid_under :: TyCoVarSet -> t -> Type -> Bool
    valid_under TyCoVarSet
    tvs t
    arity Type
    ty
          | t
    arity forall a. Eq a => a -> a -> Bool
    == t
    0
          = TyCoVarSet
    tvs TyCoVarSet -> TyCoVarSet -> Bool
    `disjointVarSet` Type -> TyCoVarSet
    tyCoVarsOfType Type
    ty
          | Just (TyVar
    t, Type
    ty') <- Type -> Maybe (TyVar, Type)
    splitForAllTyCoVar_maybe Type
    ty
          = TyCoVarSet -> t -> Type -> Bool
    valid_under (TyCoVarSet
    tvs TyCoVarSet -> TyVar -> TyCoVarSet
    `extendVarSet` TyVar
    t) (t
    arityforall a. Num a => a -> a -> a
    -t
    1) Type
    ty'
          | Just (Type
    _, Type
    _, Type
    res_ty) <- Type -> Maybe (Type, Type, Type)
    splitFunTy_maybe Type
    ty
          = TyCoVarSet -> t -> Type -> Bool
    valid_under TyCoVarSet
    tvs (t
    arityforall 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 seq :: forall a b. a -> b -> b
    `seq` ()
    seqType (TyVarTy TyVar
    tv)                = TyVar
    tv seq :: forall a b. a -> b -> b
    `seq` ()
    seqType (AppTy Type
    t1 Type
    t2)               = Type -> ()
    seqType Type
    t1 seq :: forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t2
    seqType (FunTy AnonArgFlag
    _ Type
    w Type
    t1 Type
    t2)           = Type -> ()
    seqType Type
    w seq :: forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t1 seq :: forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    t2
    seqType (TyConApp TyCon
    tc [Type]
    tys)           = TyCon
    tc seq :: forall a b. a -> b -> b
    `seq` [Type] -> ()
    seqTypes [Type]
    tys
    seqType (ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    ty)   = Type -> ()
    seqType (TyVar -> Type
    varType TyVar
    tv) seq :: forall a b. a -> b -> b
    `seq` Type -> ()
    seqType Type
    ty
    seqType (CastTy Type
    ty KindCoercion
    co)              = Type -> ()
    seqType Type
    ty seq :: 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 seq :: forall a b. a -> b -> b
    `seq` [Type] -> ()
    seqTypes [Type]
    tys

    {-
    ************************************************************************
    *                                                                      *
                    Comparison for types
            (We don't use instances so that we know where it happens)
    *                                                                      *
    ************************************************************************

    Note [Equality on AppTys]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    In our cast-ignoring equality, we want to say that the following two
    are equal:

      (Maybe |> co) (Int |> co')   ~?       Maybe Int

    But the left is an AppTy while the right is a TyConApp. The solution is
    to use repSplitAppTy_maybe to break up the TyConApp into its pieces and
    then continue. Easy to do, but also easy to forget to do.

    Note [Comparing nullary type synonyms]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider the task of testing equality between two 'Type's of the form

      TyConApp tc []

    where @tc@ is a type synonym. A naive way to perform this comparison these
    would first expand the synonym and then compare the resulting expansions.

    However, this is obviously wasteful and the RHS of @tc@ may be large; it is
    much better to rather compare the TyCons directly. Consequently, before
    expanding type synonyms in type comparisons we first look for a nullary
    TyConApp and simply compare the TyCons if we find one. Of course, if we find
    that the TyCons are *not* equal then we still need to perform the expansion as
    their RHSs may still be equal.

    We perform this optimisation in a number of places:

     * GHC.Core.Types.eqType
     * GHC.Core.Types.nonDetCmpType
     * GHC.Core.Unify.unify_ty
     * TcCanonical.can_eq_nc'
     * TcUnify.uType

    This optimisation is especially helpful for the ubiquitous GHC.Types.Type,
    since GHC prefers to use the type synonym over @TYPE 'LiftedRep@ applications
    whenever possible. See Note [Prefer Type over TYPE 'LiftedRep] in
    GHC.Core.TyCo.Rep for details.

    -}

    eqType :: Type -> Type -> Bool
    -- ^ Type equality on source types. Does not look through @newtypes@ or
    -- 'PredType's, but it does look through type synonyms.
    -- This first checks that the kinds of the types are equal and then
    -- checks whether the types are equal, ignoring casts and coercions.
    -- (The kind check is a recursive call, but since all kinds have type
    -- @Type@, there is no need to check the types of kinds.)
    -- See also Note [Non-trivial definitional equality] in "GHC.Core.TyCo.Rep".
    eqType :: Type -> Type -> Bool
    eqType Type
    t1 Type
    t2 = Ordering -> Bool
    isEqual forall a b. (a -> b) -> a -> b
    $ Type -> Type -> Ordering
    nonDetCmpType Type
    t1 Type
    t2
      -- It's OK to use nonDetCmpType here and eqType is deterministic,
      -- nonDetCmpType does equality deterministically

    -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'.
    eqTypeX :: RnEnv2 -> Type -> Type -> Bool
    eqTypeX :: RnEnv2 -> Type -> Type -> Bool
    eqTypeX RnEnv2
    env Type
    t1 Type
    t2 = Ordering -> Bool
    isEqual forall a b. (a -> b) -> a -> b
    $ RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    env Type
    t1 Type
    t2
      -- It's OK to use nonDetCmpType here and eqTypeX is deterministic,
      -- nonDetCmpTypeX does equality deterministically

    -- | Type equality on lists of types, looking through type synonyms
    -- but not newtypes.
    eqTypes :: [Type] -> [Type] -> Bool
    eqTypes :: [Type] -> [Type] -> Bool
    eqTypes [Type]
    tys1 [Type]
    tys2 = Ordering -> Bool
    isEqual forall a b. (a -> b) -> a -> b
    $ [Type] -> [Type] -> Ordering
    nonDetCmpTypes [Type]
    tys1 [Type]
    tys2
      -- It's OK to use nonDetCmpType here and eqTypes is deterministic,
      -- nonDetCmpTypes does equality deterministically

    eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
    -- Check that the var lists are the same length
    -- and have matching kinds; if so, extend the RnEnv2
    -- Returns Nothing if they don't match
    eqVarBndrs :: RnEnv2 -> [TyVar] -> [TyVar] -> Maybe RnEnv2
    eqVarBndrs RnEnv2
    env [] []
     = forall a. a -> Maybe a
    Just RnEnv2
    env
    eqVarBndrs RnEnv2
    env (TyVar
    tv1:[TyVar]
    tvs1) (TyVar
    tv2:[TyVar]
    tvs2)
     | RnEnv2 -> Type -> Type -> Bool
    eqTypeX RnEnv2
    env (TyVar -> Type
    varType TyVar
    tv1) (TyVar -> Type
    varType TyVar
    tv2)
     = RnEnv2 -> [TyVar] -> [TyVar] -> Maybe RnEnv2
    eqVarBndrs (RnEnv2 -> TyVar -> TyVar -> RnEnv2
    rnBndr2 RnEnv2
    env TyVar
    tv1 TyVar
    tv2) [TyVar]
    tvs1 [TyVar]
    tvs2
    eqVarBndrs RnEnv2
    _ [TyVar]
    _ [TyVar]
    _= forall a. Maybe a
    Nothing

    -- Now here comes the real worker

    {-
    Note [nonDetCmpType nondeterminism]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX
    uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for
    ordering leads to nondeterminism. We hit the same problem in the TyVarTy case,
    comparing type variables is nondeterministic, note the call to nonDetCmpVar in
    nonDetCmpTypeX.
    See Note [Unique Determinism] for more details.

    Note [Computing equality on types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    There are several places within GHC that depend on the precise choice of
    definitional equality used. If we change that definition, all these places
    must be updated. This Note merely serves as a place for all these places
    to refer to, so searching for references to this Note will find every place
    that needs to be updated.

    See also Note [Non-trivial definitional equality] in GHC.Core.TyCo.Rep.

    -}

    nonDetCmpType :: Type -> Type -> Ordering
    nonDetCmpType :: Type -> Type -> Ordering
    nonDetCmpType (TyConApp TyCon
    tc1 []) (TyConApp TyCon
    tc2 []) | TyCon
    tc1 forall a. Eq a => a -> a -> Bool
    == TyCon
    tc2
      = Ordering
    EQ
    nonDetCmpType Type
    t1 Type
    t2
      -- we know k1 and k2 have the same kind, because they both have kind *.
      = RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    rn_env Type
    t1 Type
    t2
      where
        rn_env :: RnEnv2
    rn_env = InScopeSet -> RnEnv2
    mkRnEnv2 (TyCoVarSet -> InScopeSet
    mkInScopeSet ([Type] -> TyCoVarSet
    tyCoVarsOfTypes [Type
    t1, Type
    t2]))
    {-# INLINE nonDetCmpType #-}

    nonDetCmpTypes :: [Type] -> [Type] -> Ordering
    nonDetCmpTypes :: [Type] -> [Type] -> Ordering
    nonDetCmpTypes [Type]
    ts1 [Type]
    ts2 = RnEnv2 -> [Type] -> [Type] -> Ordering
    nonDetCmpTypesX RnEnv2
    rn_env [Type]
    ts1 [Type]
    ts2
      where
        rn_env :: RnEnv2
    rn_env = InScopeSet -> RnEnv2
    mkRnEnv2 (TyCoVarSet -> InScopeSet
    mkInScopeSet ([Type] -> TyCoVarSet
    tyCoVarsOfTypes ([Type]
    ts1 forall a. [a] -> [a] -> [a]
    ++ [Type]
    ts2)))

    -- | An ordering relation between two 'Type's (known below as @t1 :: k1@
    -- and @t2 :: k2@)
    data TypeOrdering = TLT  -- ^ @t1 < t2@
                      | TEQ  -- ^ @t1 ~ t2@ and there are no casts in either,
                             -- therefore we can conclude @k1 ~ k2@
                      | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so
                             -- they may differ in kind.
                      | TGT  -- ^ @t1 > t2@
                      deriving (TypeOrdering -> TypeOrdering -> Bool
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    /= :: TypeOrdering -> TypeOrdering -> Bool
    $c/= :: TypeOrdering -> TypeOrdering -> Bool
    == :: TypeOrdering -> TypeOrdering -> Bool
    $c== :: TypeOrdering -> TypeOrdering -> Bool
    Eq, Eq TypeOrdering
    TypeOrdering -> TypeOrdering -> Bool
    TypeOrdering -> TypeOrdering -> Ordering
    TypeOrdering -> TypeOrdering -> TypeOrdering
    forall a.
    Eq a
    -> (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    min :: TypeOrdering -> TypeOrdering -> TypeOrdering
    $cmin :: TypeOrdering -> TypeOrdering -> TypeOrdering
    max :: TypeOrdering -> TypeOrdering -> TypeOrdering
    $cmax :: TypeOrdering -> TypeOrdering -> TypeOrdering
    >= :: TypeOrdering -> TypeOrdering -> Bool
    $c>= :: TypeOrdering -> TypeOrdering -> Bool
    > :: TypeOrdering -> TypeOrdering -> Bool
    $c> :: TypeOrdering -> TypeOrdering -> Bool
    <= :: TypeOrdering -> TypeOrdering -> Bool
    $c<= :: TypeOrdering -> TypeOrdering -> Bool
    < :: TypeOrdering -> TypeOrdering -> Bool
    $c< :: TypeOrdering -> TypeOrdering -> Bool
    compare :: TypeOrdering -> TypeOrdering -> Ordering
    $ccompare :: TypeOrdering -> TypeOrdering -> Ordering
    Ord, Int -> TypeOrdering
    TypeOrdering -> Int
    TypeOrdering -> [TypeOrdering]
    TypeOrdering -> TypeOrdering
    TypeOrdering -> TypeOrdering -> [TypeOrdering]
    TypeOrdering -> TypeOrdering -> TypeOrdering -> [TypeOrdering]
    forall a.
    (a -> a)
    -> (a -> a)
    -> (Int -> a)
    -> (a -> Int)
    -> (a -> [a])
    -> (a -> a -> [a])
    -> (a -> a -> [a])
    -> (a -> a -> a -> [a])
    -> Enum a
    enumFromThenTo :: TypeOrdering -> TypeOrdering -> TypeOrdering -> [TypeOrdering]
    $cenumFromThenTo :: TypeOrdering -> TypeOrdering -> TypeOrdering -> [TypeOrdering]
    enumFromTo :: TypeOrdering -> TypeOrdering -> [TypeOrdering]
    $cenumFromTo :: TypeOrdering -> TypeOrdering -> [TypeOrdering]
    enumFromThen :: TypeOrdering -> TypeOrdering -> [TypeOrdering]
    $cenumFromThen :: TypeOrdering -> TypeOrdering -> [TypeOrdering]
    enumFrom :: TypeOrdering -> [TypeOrdering]
    $cenumFrom :: TypeOrdering -> [TypeOrdering]
    fromEnum :: TypeOrdering -> Int
    $cfromEnum :: TypeOrdering -> Int
    toEnum :: Int -> TypeOrdering
    $ctoEnum :: Int -> TypeOrdering
    pred :: TypeOrdering -> TypeOrdering
    $cpred :: TypeOrdering -> TypeOrdering
    succ :: TypeOrdering -> TypeOrdering
    $csucc :: TypeOrdering -> TypeOrdering
    Enum, TypeOrdering
    forall a. a -> a -> Bounded a
    maxBound :: TypeOrdering
    $cmaxBound :: TypeOrdering
    minBound :: TypeOrdering
    $cminBound :: TypeOrdering
    Bounded)

    nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering  -- Main workhorse
        -- See Note [Non-trivial definitional equality] in GHC.Core.TyCo.Rep
        -- See Note [Computing equality on types]
    nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    env Type
    orig_t1 Type
    orig_t2 =
        case RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    orig_t1 Type
    orig_t2 of
          -- If there are casts then we also need to do a comparison of the kinds of
          -- the types being compared
          TypeOrdering
    TEQX          -> TypeOrdering -> Ordering
    toOrdering forall a b. (a -> b) -> a -> b
    $ RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    k1 Type
    k2
          TypeOrdering
    ty_ordering   -> TypeOrdering -> Ordering
    toOrdering TypeOrdering
    ty_ordering
      where
        k1 :: Type
    k1 = HasDebugCallStack => Type -> Type
    typeKind Type
    orig_t1
        k2 :: Type
    k2 = HasDebugCallStack => Type -> Type
    typeKind Type
    orig_t2

        toOrdering :: TypeOrdering -> Ordering
        toOrdering :: TypeOrdering -> Ordering
    toOrdering TypeOrdering
    TLT  = Ordering
    LT
        toOrdering TypeOrdering
    TEQ  = Ordering
    EQ
        toOrdering TypeOrdering
    TEQX = Ordering
    EQ
        toOrdering TypeOrdering
    TGT  = Ordering
    GT

        liftOrdering :: Ordering -> TypeOrdering
        liftOrdering :: Ordering -> TypeOrdering
    liftOrdering Ordering
    LT = TypeOrdering
    TLT
        liftOrdering Ordering
    EQ = TypeOrdering
    TEQ
        liftOrdering Ordering
    GT = TypeOrdering
    TGT

        thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
        thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
    thenCmpTy TypeOrdering
    TEQ  TypeOrdering
    rel  = TypeOrdering
    rel
        thenCmpTy TypeOrdering
    TEQX TypeOrdering
    rel  = TypeOrdering -> TypeOrdering
    hasCast TypeOrdering
    rel
        thenCmpTy TypeOrdering
    rel  TypeOrdering
    _    = TypeOrdering
    rel

        hasCast :: TypeOrdering -> TypeOrdering
        hasCast :: TypeOrdering -> TypeOrdering
    hasCast TypeOrdering
    TEQ = TypeOrdering
    TEQX
        hasCast TypeOrdering
    rel = TypeOrdering
    rel

        -- Returns both the resulting ordering relation between the two types
        -- and whether either contains a cast.
        go :: RnEnv2 -> Type -> Type -> TypeOrdering
        -- See Note [Comparing nullary type synonyms].
        go :: RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    _   (TyConApp TyCon
    tc1 []) (TyConApp TyCon
    tc2 [])
          | TyCon
    tc1 forall a. Eq a => a -> a -> Bool
    == TyCon
    tc2
          = TypeOrdering
    TEQ
        go RnEnv2
    env Type
    t1 Type
    t2
          | Just Type
    t1' <- Type -> Maybe Type
    coreView Type
    t1 = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1' Type
    t2
          | Just Type
    t2' <- Type -> Maybe Type
    coreView Type
    t2 = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1 Type
    t2'

        go RnEnv2
    env (TyVarTy TyVar
    tv1)       (TyVarTy TyVar
    tv2)
          = Ordering -> TypeOrdering
    liftOrdering forall a b. (a -> b) -> a -> b
    $ RnEnv2 -> TyVar -> TyVar
    rnOccL RnEnv2
    env TyVar
    tv1 TyVar -> TyVar -> Ordering
    `nonDetCmpVar` RnEnv2 -> TyVar -> TyVar
    rnOccR RnEnv2
    env TyVar
    tv2
        go RnEnv2
    env (ForAllTy (Bndr TyVar
    tv1 ArgFlag
    _) Type
    t1) (ForAllTy (Bndr TyVar
    tv2 ArgFlag
    _) Type
    t2)
          = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env (TyVar -> Type
    varType TyVar
    tv1) (TyVar -> Type
    varType TyVar
    tv2)
            TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> Type -> Type -> TypeOrdering
    go (RnEnv2 -> TyVar -> TyVar -> RnEnv2
    rnBndr2 RnEnv2
    env TyVar
    tv1 TyVar
    tv2) Type
    t1 Type
    t2
            -- See Note [Equality on AppTys]
        go RnEnv2
    env (AppTy Type
    s1 Type
    t1) Type
    ty2
          | Just (Type
    s2, Type
    t2) <- HasDebugCallStack => Type -> Maybe (Type, Type)
    repSplitAppTy_maybe Type
    ty2
          = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    s1 Type
    s2 TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1 Type
    t2
        go RnEnv2
    env Type
    ty1 (AppTy Type
    s2 Type
    t2)
          | Just (Type
    s1, Type
    t1) <- HasDebugCallStack => Type -> Maybe (Type, Type)
    repSplitAppTy_maybe Type
    ty1
          = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    s1 Type
    s2 TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1 Type
    t2
        go RnEnv2
    env (FunTy AnonArgFlag
    _ Type
    w1 Type
    s1 Type
    t1) (FunTy AnonArgFlag
    _ Type
    w2 Type
    s2 Type
    t2)
            -- NB: nonDepCmpTypeX does the kind check requested by
            -- Note [Equality on FunTys] in GHC.Core.TyCo.Rep
          = Ordering -> TypeOrdering
    liftOrdering (RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    env Type
    s1 Type
    s2 Ordering -> Ordering -> Ordering
    `thenCmp` RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    env Type
    t1 Type
    t2)
              TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    w1 Type
    w2
            -- Comparing multiplicities last because the test is usually true
        go RnEnv2
    env (TyConApp TyCon
    tc1 [Type]
    tys1) (TyConApp TyCon
    tc2 [Type]
    tys2)
          = Ordering -> TypeOrdering
    liftOrdering (TyCon
    tc1 TyCon -> TyCon -> Ordering
    `nonDetCmpTc` TyCon
    tc2) TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> [Type] -> [Type] -> TypeOrdering
    gos RnEnv2
    env [Type]
    tys1 [Type]
    tys2
        go RnEnv2
    _   (LitTy TyLit
    l1)          (LitTy TyLit
    l2)          = Ordering -> TypeOrdering
    liftOrdering (TyLit -> TyLit -> Ordering
    nonDetCmpTyLit TyLit
    l1 TyLit
    l2)
        go RnEnv2
    env (CastTy Type
    t1 KindCoercion
    _)       Type
    t2                  = TypeOrdering -> TypeOrdering
    hasCast forall a b. (a -> b) -> a -> b
    $ RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1 Type
    t2
        go RnEnv2
    env Type
    t1                  (CastTy Type
    t2 KindCoercion
    _)       = TypeOrdering -> TypeOrdering
    hasCast forall a b. (a -> b) -> a -> b
    $ RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    t1 Type
    t2

        go RnEnv2
    _   (CoercionTy {})     (CoercionTy {})     = TypeOrdering
    TEQ

            -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy
        go RnEnv2
    _ Type
    ty1 Type
    ty2
          = Ordering -> TypeOrdering
    liftOrdering forall a b. (a -> b) -> a -> b
    $ (Type -> Int
    get_rank Type
    ty1) forall a. Ord a => a -> a -> Ordering
    `compare` (Type -> Int
    get_rank Type
    ty2)
          where get_rank :: Type -> Int
                get_rank :: Type -> Int
    get_rank (CastTy {})
                  = forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "nonDetCmpTypeX.get_rank" (forall a. Outputable a => a -> SDoc
    ppr [Type
    ty1,Type
    ty2])
                get_rank (TyVarTy {})    = Int
    0
                get_rank (CoercionTy {}) = Int
    1
                get_rank (AppTy {})      = Int
    3
                get_rank (LitTy {})      = Int
    4
                get_rank (TyConApp {})   = Int
    5
                get_rank (FunTy {})      = Int
    6
                get_rank (ForAllTy {})   = Int
    7

        gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
        gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
    gos RnEnv2
    _   []         []         = TypeOrdering
    TEQ
        gos RnEnv2
    _   []         [Type]
    _          = TypeOrdering
    TLT
        gos RnEnv2
    _   [Type]
    _          []         = TypeOrdering
    TGT
        gos RnEnv2
    env (Type
    ty1:[Type]
    tys1) (Type
    ty2:[Type]
    tys2) = RnEnv2 -> Type -> Type -> TypeOrdering
    go RnEnv2
    env Type
    ty1 Type
    ty2 TypeOrdering -> TypeOrdering -> TypeOrdering
    `thenCmpTy` RnEnv2 -> [Type] -> [Type] -> TypeOrdering
    gos RnEnv2
    env [Type]
    tys1 [Type]
    tys2

    -------------
    nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
    nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
    nonDetCmpTypesX RnEnv2
    _   []        []        = Ordering
    EQ
    nonDetCmpTypesX RnEnv2
    env (Type
    t1:[Type]
    tys1) (Type
    t2:[Type]
    tys2) = RnEnv2 -> Type -> Type -> Ordering
    nonDetCmpTypeX RnEnv2
    env Type
    t1 Type
    t2
                                              Ordering -> Ordering -> Ordering
    `thenCmp`
                                              RnEnv2 -> [Type] -> [Type] -> Ordering
    nonDetCmpTypesX RnEnv2
    env [Type]
    tys1 [Type]
    tys2
    nonDetCmpTypesX RnEnv2
    _   []        [Type]
    _         = Ordering
    LT
    nonDetCmpTypesX RnEnv2
    _   [Type]
    _         []        = Ordering
    GT

    -------------
    -- | Compare two 'TyCon's. NB: This should /never/ see 'Constraint' (as
    -- recognized by Kind.isConstraintKindCon) which is considered a synonym for
    -- 'Type' in Core.
    -- See Note [Kind Constraint and kind Type] in "GHC.Core.Type".
    -- See Note [nonDetCmpType nondeterminism]
    nonDetCmpTc :: TyCon -> TyCon -> Ordering
    nonDetCmpTc :: TyCon -> TyCon -> Ordering
    nonDetCmpTc TyCon
    tc1 TyCon
    tc2
      = ASSERT( not (isConstraintKindCon tc1) && not (isConstraintKindCon tc2) )
        Unique
    u1 Unique -> Unique -> Ordering
    `nonDetCmpUnique` Unique
    u2
      where
        u1 :: Unique
    u1  = TyCon -> Unique
    tyConUnique TyCon
    tc1
        u2 :: Unique
    u2  = TyCon -> Unique
    tyConUnique TyCon
    tc2

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

    Note [typeKind vs tcTypeKind]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We have two functions to get the kind of a type

      * typeKind   ignores  the distinction between Constraint and *
      * tcTypeKind respects the distinction between Constraint and *

    tcTypeKind is used by the type inference engine, for which Constraint
    and * are different; after that we use typeKind.

    See also Note [coreView vs tcView]

    Note [Kinding rules for types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In typeKind we consider Constraint and (TYPE LiftedRep) to be identical.
    We then have

             t1 : TYPE rep1
             t2 : TYPE rep2
       (FUN) ----------------
             t1 -> t2 : Type

             ty : TYPE rep
             `a` is not free in rep
    (FORALL) -----------------------
             forall a. ty : TYPE rep

    In tcTypeKind we consider Constraint and (TYPE LiftedRep) to be distinct:

              t1 : TYPE rep1
              t2 : TYPE rep2
        (FUN) ----------------
              t1 -> t2 : Type

              t1 : Constraint
              t2 : TYPE rep
      (PRED1) ----------------
              t1 => t2 : Type

              t1 : Constraint
              t2 : Constraint
      (PRED2) ---------------------
              t1 => t2 : Constraint

              ty : TYPE rep
              `a` is not free in rep
    (FORALL1) -----------------------
              forall a. ty : TYPE rep

              ty : Constraint
    (FORALL2) -------------------------
              forall a. ty : Constraint

    Note that:
    * The only way we distinguish '->' from '=>' is by the fact
      that the argument is a PredTy.  Both are FunTys

    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) exapands
    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
    piResultTys (TyCon -> Type
    tyConKind TyCon
    tc) [Type]
    tys
    typeKind (LitTy TyLit
    l)         = TyLit -> Type
    typeLiteralKind TyLit
    l
    typeKind (FunTy {})        = Type
    liftedTypeKind
    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
    argforall a. a -> [a] -> [a]
    :[Type]
    args)
        go Type
    fun             [Type]
    args = HasDebugCallStack => Type -> [Type] -> Type
    piResultTys (HasDebugCallStack => Type -> Type
    typeKind Type
    fun) [Type]
    args

    typeKind ty :: Type
    ty@(ForAllTy {})
      = case [TyVar] -> Type -> Maybe Type
    occCheckExpand [TyVar]
    tvs Type
    body_kind of
          -- We must make sure tv does not occur in kind
          -- As it is already out of scope!
          -- See Note [Phantom type variables in kinds]
          Just Type
    k' -> Type
    k'
          Maybe Type
    Nothing -> forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "typeKind"
                      (forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr Type
    body SDoc -> SDoc -> SDoc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    <+> forall a. Outputable a => a -> SDoc
    ppr Type
    body_kind)
      where
        ([TyVar]
    tvs, Type
    body) = Type -> ([TyVar], Type)
    splitForAllTyVars Type
    ty
        body_kind :: Type
    body_kind   = HasDebugCallStack => Type -> Type
    typeKind Type
    body

    ---------------------------------------------
    -- Utilities to be used in GHC.Core.Unify,
    -- which uses "tc" functions
    ---------------------------------------------

    tcTypeKind :: HasDebugCallStack => Type -> Kind
    -- No need to expand synonyms
    tcTypeKind :: HasDebugCallStack => Type -> Type
    tcTypeKind (TyConApp TyCon
    tc [Type]
    tys) = HasDebugCallStack => Type -> [Type] -> Type
    piResultTys (TyCon -> Type
    tyConKind TyCon
    tc) [Type]
    tys
    tcTypeKind (LitTy TyLit
    l)         = TyLit -> Type
    typeLiteralKind TyLit
    l
    tcTypeKind (TyVarTy TyVar
    tyvar)   = TyVar -> Type
    tyVarKind TyVar
    tyvar
    tcTypeKind (CastTy Type
    _ty KindCoercion
    co)   = KindCoercion -> Type
    coercionRKind KindCoercion
    co
    tcTypeKind (CoercionTy KindCoercion
    co)   = KindCoercion -> Type
    coercionType KindCoercion
    co

    tcTypeKind (FunTy { ft_af :: Type -> AnonArgFlag
    ft_af = AnonArgFlag
    af, ft_res :: Type -> Type
    ft_res = Type
    res })
      | AnonArgFlag
    InvisArg <- AnonArgFlag
    af
      , Type -> Bool
    tcIsConstraintKind (HasDebugCallStack => Type -> Type
    tcTypeKind Type
    res)
      = Type
    constraintKind     -- Eq a => Ord a         :: Constraint
      | Bool
    otherwise          -- Eq a => a -> a        :: TYPE LiftedRep
      = Type
    liftedTypeKind     -- Eq a => Array# Int    :: Type LiftedRep (not TYPE PtrRep)

    tcTypeKind (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
    argforall a. a -> [a] -> [a]
    :[Type]
    args)
        go Type
    fun             [Type]
    args = HasDebugCallStack => Type -> [Type] -> Type
    piResultTys (HasDebugCallStack => Type -> Type
    tcTypeKind Type
    fun) [Type]
    args

    tcTypeKind ty :: Type
    ty@(ForAllTy {})
      | Type -> Bool
    tcIsConstraintKind Type
    body_kind
      = Type
    constraintKind

      | Bool
    otherwise
      = case [TyVar] -> Type -> Maybe Type
    occCheckExpand [TyVar]
    tvs Type
    body_kind of
          -- We must make sure tv does not occur in kind
          -- As it is already out of scope!
          -- See Note [Phantom type variables in kinds]
          Just Type
    k' -> Type
    k'
          Maybe Type
    Nothing -> forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "tcTypeKind"
                      (forall a. Outputable a => a -> SDoc
    ppr Type
    ty SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr [TyVar]
    tvs SDoc -> SDoc -> SDoc
    $$ forall a. Outputable a => a -> SDoc
    ppr Type
    body SDoc -> SDoc -> SDoc
    <+> SDoc
    dcolon SDoc -> SDoc -> SDoc
    <+> forall a. Outputable a => a -> SDoc
    ppr Type
    body_kind)
      where
        ([TyVar]
    tvs, Type
    body) = Type -> ([TyVar], Type)
    splitForAllTyVars Type
    ty
        body_kind :: Type
    body_kind = HasDebugCallStack => Type -> Type
    tcTypeKind Type
    body

    isPredTy :: HasDebugCallStack => Type -> Bool
    -- See Note [Types for coercions, predicates, and evidence] in GHC.Core.TyCo.Rep
    isPredTy :: HasDebugCallStack => Type -> Bool
    isPredTy Type
    ty = Type -> Bool
    tcIsConstraintKind (HasDebugCallStack => Type -> Type
    tcTypeKind Type
    ty)

    -- tcIsConstraintKind stuff only makes sense in the typechecker
    -- After that Constraint = Type
    -- See Note [coreView vs tcView]
    -- Defined here because it is used in isPredTy and tcRepSplitAppTy_maybe (sigh)
    tcIsConstraintKind :: Kind -> Bool
    tcIsConstraintKind :: Type -> Bool
    tcIsConstraintKind Type
    ty
      | Just (TyCon
    tc, [Type]
    args) <- HasCallStack => Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    ty    -- Note: tcSplit here
      , TyCon -> Bool
    isConstraintKindCon TyCon
    tc
      = ASSERT2( null args, ppr ty ) True

      | Bool
    otherwise
      = Bool
    False

    -- | Like 'kindRep_maybe', but considers 'Constraint' to be distinct
    -- from 'Type'. For a version that treats them as the same type, see
    -- 'kindRep_maybe'.
    tcKindRep_maybe :: HasDebugCallStack => Kind -> Maybe Type
    tcKindRep_maybe :: HasDebugCallStack => Type -> Maybe Type
    tcKindRep_maybe Type
    kind
      | Just (TyCon
    tc, [Type
    arg]) <- HasCallStack => Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    kind    -- Note: tcSplit here
      , TyCon
    tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    tYPETyConKey    = forall a. a -> Maybe a
    Just Type
    arg
      | Bool
    otherwise                   = forall a. Maybe a
    Nothing

    -- | Is this kind equivalent to 'Type'?
    --
    -- This considers 'Constraint' to be distinct from 'Type'. For a version that
    -- treats them as the same type, see 'isLiftedTypeKind'.
    tcIsLiftedTypeKind :: Kind -> Bool
    tcIsLiftedTypeKind :: Type -> Bool
    tcIsLiftedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    tcKindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isLiftedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    -- | Is this kind equivalent to @TYPE (BoxedRep l)@ for some @l :: Levity@?
    --
    -- This considers 'Constraint' to be distinct from 'Type'. For a version that
    -- treats them as the same type, see 'isLiftedTypeKind'.
    tcIsBoxedTypeKind :: Kind -> Bool
    tcIsBoxedTypeKind :: Type -> Bool
    tcIsBoxedTypeKind Type
    kind
      = case HasDebugCallStack => Type -> Maybe Type
    tcKindRep_maybe Type
    kind of
          Just Type
    rep -> Type -> Bool
    isBoxedRuntimeRep Type
    rep
          Maybe Type
    Nothing  -> Bool
    False

    -- | Is this kind equivalent to @TYPE r@ (for some unknown r)?
    --
    -- This considers 'Constraint' to be distinct from @*@.
    tcIsRuntimeTypeKind :: Kind -> Bool
    tcIsRuntimeTypeKind :: Type -> Bool
    tcIsRuntimeTypeKind Type
    kind = forall a. Maybe a -> Bool
    isJust (HasDebugCallStack => Type -> Maybe Type
    tcKindRep_maybe Type
    kind)

    tcReturnsConstraintKind :: Kind -> Bool
    -- True <=> the Kind ultimately returns a Constraint
    --   E.g.  * -> Constraint
    --         forall k. k -> Constraint
    tcReturnsConstraintKind :: Type -> Bool
    tcReturnsConstraintKind Type
    kind
      | Just Type
    kind' <- Type -> Maybe Type
    tcView Type
    kind = Type -> Bool
    tcReturnsConstraintKind Type
    kind'
    tcReturnsConstraintKind (ForAllTy VarBndr TyVar ArgFlag
    _ Type
    ty)         = Type -> Bool
    tcReturnsConstraintKind Type
    ty
    tcReturnsConstraintKind (FunTy { ft_res :: Type -> Type
    ft_res = Type
    ty }) = Type -> Bool
    tcReturnsConstraintKind Type
    ty
    tcReturnsConstraintKind (TyConApp TyCon
    tc [Type]
    _)         = TyCon -> Bool
    isConstraintKindCon TyCon
    tc
    tcReturnsConstraintKind Type
    _                       = Bool
    False

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

    -- | Returns True if a type is levity polymorphic. Should be the same
    -- as (isKindLevPoly . typeKind) but much faster.
    -- Precondition: The type has kind (TYPE blah)
    isTypeLevPoly :: Type -> Bool
    isTypeLevPoly :: Type -> Bool
    isTypeLevPoly = Type -> Bool
    go
      where
        go :: Type -> Bool
    go ty :: Type
    ty@(TyVarTy {})                           = Type -> Bool
    check_kind Type
    ty
        go ty :: Type
    ty@(AppTy {})                             = Type -> Bool
    check_kind Type
    ty
        go ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    _) | Bool -> Bool
    not (TyCon -> Bool
    isTcLevPoly TyCon
    tc) = Bool
    False
                              | Bool
    otherwise            = Type -> Bool
    check_kind Type
    ty
        go (ForAllTy VarBndr TyVar ArgFlag
    _ Type
    ty)                           = Type -> Bool
    go Type
    ty
        go (FunTy {})                                = Bool
    False
        go (LitTy {})                                = Bool
    False
        go ty :: Type
    ty@(CastTy {})                            = Type -> Bool
    check_kind Type
    ty
        go ty :: Type
    ty@(CoercionTy {})                        = forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "isTypeLevPoly co" (forall a. Outputable a => a -> SDoc
    ppr Type
    ty)

        check_kind :: Type -> Bool
    check_kind = Type -> Bool
    isKindLevPoly forall b c a. (b -> c) -> (a -> b) -> a -> c
    . HasDebugCallStack => Type -> Type
    typeKind

    -- | Looking past all pi-types, is the end result potentially levity polymorphic?
    -- Example: True for (forall r (a :: TYPE r). String -> a)
    -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)
    resultIsLevPoly :: Type -> Bool
    resultIsLevPoly :: Type -> Bool
    resultIsLevPoly = Type -> Bool
    isTypeLevPoly forall b c a. (b -> c) -> (a -> b) -> a -> c
    . forall a b. (a, b) -> b
    snd forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> ([TyCoBinder], Type)
    splitPiTys

    {- **********************************************************************
    *                                                                       *
               Occurs check expansion
    %*                                                                      *
    %********************************************************************* -}

    {- Note [Occurs check expansion]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    (occurCheckExpand tv xi) expands synonyms in xi just enough to get rid
    of occurrences of tv outside type function arguments, if that is
    possible; otherwise, it returns Nothing.

    For example, suppose we have
      type F a b = [a]
    Then
      occCheckExpand b (F Int b) = Just [Int]
    but
      occCheckExpand a (F a Int) = Nothing

    We don't promise to do the absolute minimum amount of expanding
    necessary, but we try not to do expansions we don't need to.  We
    prefer doing inner expansions first.  For example,
      type F a b = (a, Int, a, [a])
      type G b   = Char
    We have
      occCheckExpand b (F (G b)) = Just (F Char)
    even though we could also expand F to get rid of b.

    Note [Occurrence checking: look inside kinds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we are considering unifying
       (alpha :: *)  ~  Int -> (beta :: alpha -> alpha)
    This may be an error (what is that alpha doing inside beta's kind?),
    but we must not make the mistake of actually unifying or we'll
    build an infinite data structure.  So when looking for occurrences
    of alpha in the rhs, we must look in the kinds of type variables
    that occur there.

    occCheckExpand tries to expand type synonyms to remove
    unnecessary occurrences of a variable, and thereby get past an
    occurs-check failure.  This is good; but
         we can't do it in the /kind/ of a variable /occurrence/

    For example #18451 built an infinite type:
        type Const a b = a
        data SameKind :: k -> k -> Type
        type T (k :: Const Type a) = forall (b :: k). SameKind a b

    We have
      b :: k
      k :: Const Type a
      a :: k   (must be same as b)

    So if we aren't careful, a's kind mentions a, which is bad.
    And expanding an /occurrence/ of 'a' doesn't help, because the
    /binding site/ is the master copy and all the occurrences should
    match it.

    Here's a related example:
       f :: forall a b (c :: Const Type b). Proxy '[a, c]

    The list means that 'a' gets the same kind as 'c'; but that
    kind mentions 'b', so the binders are out of order.

    Bottom line: in occCheckExpand, do not expand inside the kinds
    of occurrences.  See bad_var_occ in occCheckExpand.  And
    see #18451 for more debate.
    -}

    occCheckExpand :: [Var] -> Type -> Maybe Type
    -- See Note [Occurs check expansion]
    -- We may have needed to do some type synonym unfolding in order to
    -- get rid of the variable (or forall), so we also return the unfolded
    -- version of the type, which is guaranteed to be syntactically free
    -- of the given type variable.  If the type is already syntactically
    -- free of the variable, then the same type is returned.
    occCheckExpand :: [TyVar] -> Type -> Maybe Type
    occCheckExpand [TyVar]
    vs_to_avoid Type
    ty
      | forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [TyVar]
    vs_to_avoid  -- Efficient shortcut
      = forall a. a -> Maybe a
    Just Type
    ty           -- Can happen, eg. GHC.Core.Utils.mkSingleAltCase

      | Bool
    otherwise
      = (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go ([TyVar] -> TyCoVarSet
    mkVarSet [TyVar]
    vs_to_avoid, forall a. VarEnv a
    emptyVarEnv) Type
    ty
      where
        go :: (VarSet, VarEnv TyCoVar) -> Type -> Maybe Type
              -- The VarSet is the set of variables we are trying to avoid
              -- The VarEnv carries mappings necessary
              -- because of kind expansion
        go :: (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet
    as, VarEnv TyVar
    env) ty :: Type
    ty@(TyVarTy TyVar
    tv)
          | Just TyVar
    tv' <- forall a. VarEnv a -> TyVar -> Maybe a
    lookupVarEnv VarEnv TyVar
    env TyVar
    tv = forall (m :: * -> *) a. Monad m => a -> m a
    return (TyVar -> Type
    mkTyVarTy TyVar
    tv')
          | TyCoVarSet -> TyVar -> Bool
    bad_var_occ TyCoVarSet
    as TyVar
    tv               = forall a. Maybe a
    Nothing
          | Bool
    otherwise                       = forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    ty

        go (TyCoVarSet, VarEnv TyVar)
    _   ty :: Type
    ty@(LitTy {}) = forall (m :: * -> *) a. Monad m => a -> m a
    return Type
    ty
        go (TyCoVarSet, VarEnv TyVar)
    cxt (AppTy Type
    ty1 Type
    ty2) = do { Type
    ty1' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty1
                                    ; Type
    ty2' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty2
                                    ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Type -> Type -> Type
    mkAppTy Type
    ty1' Type
    ty2') }
        go (TyCoVarSet, VarEnv TyVar)
    cxt ty :: Type
    ty@(FunTy AnonArgFlag
    _ Type
    w Type
    ty1 Type
    ty2)
           = do { Type
    w'   <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    w
                ; Type
    ty1' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty1
                ; Type
    ty2' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty2
                ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Type
    ty { ft_mult :: Type
    ft_mult = Type
    w', ft_arg :: Type
    ft_arg = Type
    ty1', ft_res :: Type
    ft_res = Type
    ty2' }) }
        go cxt :: (TyCoVarSet, VarEnv TyVar)
    cxt@(TyCoVarSet
    as, VarEnv TyVar
    env) (ForAllTy (Bndr TyVar
    tv ArgFlag
    vis) Type
    body_ty)
           = do { Type
    ki' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt (TyVar -> Type
    varType TyVar
    tv)
                ; let tv' :: TyVar
    tv'  = TyVar -> Type -> TyVar
    setVarType TyVar
    tv Type
    ki'
                      env' :: VarEnv TyVar
    env' = forall a. VarEnv a -> TyVar -> a -> VarEnv a
    extendVarEnv VarEnv TyVar
    env TyVar
    tv TyVar
    tv'
                      as' :: TyCoVarSet
    as'  = TyCoVarSet
    as TyCoVarSet -> TyVar -> TyCoVarSet
    `delVarSet` TyVar
    tv
                ; Type
    body' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet
    as', VarEnv TyVar
    env') Type
    body_ty
                ; forall (m :: * -> *) a. Monad m => a -> m a
    return (VarBndr TyVar ArgFlag -> Type -> Type
    ForAllTy (forall var argf. var -> argf -> VarBndr var argf
    Bndr TyVar
    tv' ArgFlag
    vis) Type
    body') }

        -- For a type constructor application, first try expanding away the
        -- offending variable from the arguments.  If that doesn't work, next
        -- see if the type constructor is a type synonym, and if so, expand
        -- it and try again.
        go (TyCoVarSet, VarEnv TyVar)
    cxt ty :: Type
    ty@(TyConApp TyCon
    tc [Type]
    tys)
          = case forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    mapM ((TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt) [Type]
    tys of
              Just [Type]
    tys' -> forall (m :: * -> *) a. Monad m => a -> m a
    return (TyCon -> [Type] -> Type
    mkTyConApp TyCon
    tc [Type]
    tys')
              Maybe [Type]
    Nothing | Just Type
    ty' <- Type -> Maybe Type
    tcView Type
    ty -> (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty'
                      | Bool
    otherwise             -> forall a. Maybe a
    Nothing
                          -- Failing that, try to expand a synonym

        go (TyCoVarSet, VarEnv TyVar)
    cxt (CastTy Type
    ty KindCoercion
    co) =  do { Type
    ty' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty
                                    ; KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                    ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Type -> KindCoercion -> Type
    mkCastTy Type
    ty' KindCoercion
    co') }
        go (TyCoVarSet, VarEnv TyVar)
    cxt (CoercionTy KindCoercion
    co) = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                    ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> Type
    mkCoercionTy KindCoercion
    co') }

        ------------------
        bad_var_occ :: VarSet -> Var -> Bool
        -- Works for TyVar and CoVar
        -- See Note [Occurrence checking: look inside kinds]
        bad_var_occ :: TyCoVarSet -> TyVar -> Bool
    bad_var_occ TyCoVarSet
    vs_to_avoid TyVar
    v
           =  TyVar
    v                          TyVar -> TyCoVarSet -> Bool
    `elemVarSet`       TyCoVarSet
    vs_to_avoid
           Bool -> Bool -> Bool
    || Type -> TyCoVarSet
    tyCoVarsOfType (TyVar -> Type
    varType TyVar
    v) TyCoVarSet -> TyCoVarSet -> Bool
    `intersectsVarSet` TyCoVarSet
    vs_to_avoid

        ------------------
        go_mco :: (TyCoVarSet, VarEnv TyVar) -> MCoercionN -> Maybe MCoercionN
    go_mco (TyCoVarSet, VarEnv TyVar)
    _   MCoercionN
    MRefl = forall (m :: * -> *) a. Monad m => a -> m a
    return MCoercionN
    MRefl
        go_mco (TyCoVarSet, VarEnv TyVar)
    ctx (MCo KindCoercion
    co) = KindCoercion -> MCoercionN
    MCo forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    ctx KindCoercion
    co

        ------------------
        go_co :: (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt (Refl Type
    ty)                 = do { Type
    ty' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Type -> KindCoercion
    mkNomReflCo Type
    ty') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (GRefl Role
    r Type
    ty MCoercionN
    mco)          = do { MCoercionN
    mco' <- (TyCoVarSet, VarEnv TyVar) -> MCoercionN -> Maybe MCoercionN
    go_mco (TyCoVarSet, VarEnv TyVar)
    cxt MCoercionN
    mco
                                                 ; Type
    ty' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Role -> Type -> MCoercionN -> KindCoercion
    mkGReflCo Role
    r Type
    ty' MCoercionN
    mco') }
          -- Note: Coercions do not contain type synonyms
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (TyConAppCo Role
    r TyCon
    tc [KindCoercion]
    args)    = do { [KindCoercion]
    args' <- forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    mapM ((TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt) [KindCoercion]
    args
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (HasDebugCallStack =>
    Role -> TyCon -> [KindCoercion] -> KindCoercion
    mkTyConAppCo Role
    r TyCon
    tc [KindCoercion]
    args') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (AppCo KindCoercion
    co KindCoercion
    arg)            = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; KindCoercion
    arg' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    arg
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> KindCoercion -> KindCoercion
    mkAppCo KindCoercion
    co' KindCoercion
    arg') }
        go_co cxt :: (TyCoVarSet, VarEnv TyVar)
    cxt@(TyCoVarSet
    as, VarEnv TyVar
    env) (ForAllCo TyVar
    tv KindCoercion
    kind_co KindCoercion
    body_co)
          = do { KindCoercion
    kind_co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    kind_co
               ; let tv' :: TyVar
    tv' = TyVar -> Type -> TyVar
    setVarType TyVar
    tv forall a b. (a -> b) -> a -> b
    $
                           KindCoercion -> Type
    coercionLKind KindCoercion
    kind_co'
                     env' :: VarEnv TyVar
    env' = forall a. VarEnv a -> TyVar -> a -> VarEnv a
    extendVarEnv VarEnv TyVar
    env TyVar
    tv TyVar
    tv'
                     as' :: TyCoVarSet
    as'  = TyCoVarSet
    as TyCoVarSet -> TyVar -> TyCoVarSet
    `delVarSet` TyVar
    tv
               ; KindCoercion
    body' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet
    as', VarEnv TyVar
    env') KindCoercion
    body_co
               ; forall (m :: * -> *) a. Monad m => a -> m a
    return (TyVar -> KindCoercion -> KindCoercion -> KindCoercion
    ForAllCo TyVar
    tv' KindCoercion
    kind_co' KindCoercion
    body') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (FunCo Role
    r KindCoercion
    w KindCoercion
    co1 KindCoercion
    co2)       = do { KindCoercion
    co1' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co1
                                                 ; KindCoercion
    co2' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co2
                                                 ; KindCoercion
    w' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    w
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (Role
    -> KindCoercion -> KindCoercion -> KindCoercion -> KindCoercion
    mkFunCo Role
    r KindCoercion
    w' KindCoercion
    co1' KindCoercion
    co2') }
        go_co (TyCoVarSet
    as,VarEnv TyVar
    env) co :: KindCoercion
    co@(CoVarCo TyVar
    c)
          | Just TyVar
    c' <- forall a. VarEnv a -> TyVar -> Maybe a
    lookupVarEnv VarEnv TyVar
    env TyVar
    c   = forall (m :: * -> *) a. Monad m => a -> m a
    return (TyVar -> KindCoercion
    mkCoVarCo TyVar
    c')
          | TyCoVarSet -> TyVar -> Bool
    bad_var_occ TyCoVarSet
    as TyVar
    c                = forall a. Maybe a
    Nothing
          | Bool
    otherwise                       = forall (m :: * -> *) a. Monad m => a -> m a
    return KindCoercion
    co

        go_co (TyCoVarSet
    as,VarEnv TyVar
    _) co :: KindCoercion
    co@(HoleCo CoercionHole
    h)
          | TyCoVarSet -> TyVar -> Bool
    bad_var_occ TyCoVarSet
    as (CoercionHole -> TyVar
    ch_co_var CoercionHole
    h)    = forall a. Maybe a
    Nothing
          | Bool
    otherwise                       = forall (m :: * -> *) a. Monad m => a -> m a
    return KindCoercion
    co

        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (AxiomInstCo CoAxiom Branched
    ax Int
    ind [KindCoercion]
    args) = do { [KindCoercion]
    args' <- forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    mapM ((TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt) [KindCoercion]
    args
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (CoAxiom Branched -> Int -> [KindCoercion] -> KindCoercion
    mkAxiomInstCo CoAxiom Branched
    ax Int
    ind [KindCoercion]
    args') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (UnivCo UnivCoProvenance
    p Role
    r Type
    ty1 Type
    ty2)      = do { UnivCoProvenance
    p' <- (TyCoVarSet, VarEnv TyVar)
    -> UnivCoProvenance -> Maybe UnivCoProvenance
    go_prov (TyCoVarSet, VarEnv TyVar)
    cxt UnivCoProvenance
    p
                                                 ; Type
    ty1' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty1
                                                 ; Type
    ty2' <- (TyCoVarSet, VarEnv TyVar) -> Type -> Maybe Type
    go (TyCoVarSet, VarEnv TyVar)
    cxt Type
    ty2
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (UnivCoProvenance -> Role -> Type -> Type -> KindCoercion
    mkUnivCo UnivCoProvenance
    p' Role
    r Type
    ty1' Type
    ty2') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (SymCo KindCoercion
    co)                = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> KindCoercion
    mkSymCo KindCoercion
    co') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (TransCo KindCoercion
    co1 KindCoercion
    co2)         = do { KindCoercion
    co1' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co1
                                                 ; KindCoercion
    co2' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co2
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> KindCoercion -> KindCoercion
    mkTransCo KindCoercion
    co1' KindCoercion
    co2') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (NthCo Role
    r Int
    n KindCoercion
    co)            = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (HasDebugCallStack => Role -> Int -> KindCoercion -> KindCoercion
    mkNthCo Role
    r Int
    n KindCoercion
    co') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (LRCo LeftOrRight
    lr KindCoercion
    co)              = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (LeftOrRight -> KindCoercion -> KindCoercion
    mkLRCo LeftOrRight
    lr KindCoercion
    co') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (InstCo KindCoercion
    co KindCoercion
    arg)           = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; KindCoercion
    arg' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    arg
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> KindCoercion -> KindCoercion
    mkInstCo KindCoercion
    co' KindCoercion
    arg') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (KindCo KindCoercion
    co)               = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (KindCoercion -> KindCoercion
    mkKindCo KindCoercion
    co') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (SubCo KindCoercion
    co)                = do { KindCoercion
    co' <- (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (HasDebugCallStack => KindCoercion -> KindCoercion
    mkSubCo KindCoercion
    co') }
        go_co (TyCoVarSet, VarEnv TyVar)
    cxt (AxiomRuleCo CoAxiomRule
    ax [KindCoercion]
    cs)       = do { [KindCoercion]
    cs' <- forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    mapM ((TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt) [KindCoercion]
    cs
                                                 ; forall (m :: * -> *) a. Monad m => a -> m a
    return (CoAxiomRule -> [KindCoercion] -> KindCoercion
    mkAxiomRuleCo CoAxiomRule
    ax [KindCoercion]
    cs') }

        ------------------
        go_prov :: (TyCoVarSet, VarEnv TyVar)
    -> UnivCoProvenance -> Maybe UnivCoProvenance
    go_prov (TyCoVarSet, VarEnv TyVar)
    cxt (PhantomProv KindCoercion
    co)    = KindCoercion -> UnivCoProvenance
    PhantomProv forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
        go_prov (TyCoVarSet, VarEnv TyVar)
    cxt (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UnivCoProvenance
    ProofIrrelProv forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (TyCoVarSet, VarEnv TyVar) -> KindCoercion -> Maybe KindCoercion
    go_co (TyCoVarSet, VarEnv TyVar)
    cxt KindCoercion
    co
        go_prov (TyCoVarSet, VarEnv TyVar)
    _   p :: UnivCoProvenance
    p@(PluginProv String
    _)    = forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    p
        go_prov (TyCoVarSet, VarEnv TyVar)
    _   p :: UnivCoProvenance
    p@(CorePrepProv Bool
    _)  = forall (m :: * -> *) a. Monad m => a -> m a
    return UnivCoProvenance
    p

    {-
    %************************************************************************
    %*                                                                      *
            Miscellaneous functions
    %*                                                                      *
    %************************************************************************

    -}
    -- | All type constructors occurring in the type; looking through type
    --   synonyms, but not newtypes.
    --  When it finds a Class, it returns the class TyCon.
    tyConsOfType :: Type -> UniqSet TyCon
    tyConsOfType :: Type -> UniqSet TyCon
    tyConsOfType Type
    ty
      = Type -> UniqSet TyCon
    go Type
    ty
      where
         go :: Type -> UniqSet TyCon  -- The UniqSet does duplicate elim
         go :: Type -> UniqSet TyCon
    go Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> UniqSet TyCon
    go Type
    ty'
         go (TyVarTy {})                = forall a. UniqSet a
    emptyUniqSet
         go (LitTy {})                  = forall a. UniqSet a
    emptyUniqSet
         go (TyConApp TyCon
    tc [Type]
    tys)           = forall {a}. Uniquable a => a -> UniqSet a
    go_tc TyCon
    tc forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` forall {t :: * -> *}. Foldable t => t Type -> UniqSet TyCon
    go_s [Type]
    tys
         go (AppTy Type
    a Type
    b)                 = Type -> UniqSet TyCon
    go Type
    a forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` Type -> UniqSet TyCon
    go Type
    b
         go (FunTy AnonArgFlag
    _ Type
    w Type
    a Type
    b)             = Type -> UniqSet TyCon
    go Type
    w forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets`
                                          Type -> UniqSet TyCon
    go Type
    a forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` Type -> UniqSet TyCon
    go Type
    b forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` forall {a}. Uniquable a => a -> UniqSet a
    go_tc TyCon
    funTyCon
         go (ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    ty)   = Type -> UniqSet TyCon
    go Type
    ty forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` Type -> UniqSet TyCon
    go (TyVar -> Type
    varType TyVar
    tv)
         go (CastTy Type
    ty KindCoercion
    co)              = Type -> UniqSet TyCon
    go Type
    ty forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go (CoercionTy KindCoercion
    co)             = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co

         go_co :: KindCoercion -> UniqSet TyCon
    go_co (Refl Type
    ty)               = Type -> UniqSet TyCon
    go Type
    ty
         go_co (GRefl Role
    _ Type
    ty MCoercionN
    mco)        = Type -> UniqSet TyCon
    go Type
    ty forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` MCoercionN -> UniqSet TyCon
    go_mco MCoercionN
    mco
         go_co (TyConAppCo Role
    _ TyCon
    tc [KindCoercion]
    args)  = forall {a}. Uniquable a => a -> UniqSet a
    go_tc TyCon
    tc forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` [KindCoercion] -> UniqSet TyCon
    go_cos [KindCoercion]
    args
         go_co (AppCo KindCoercion
    co KindCoercion
    arg)          = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    arg
         go_co (ForAllCo TyVar
    _ KindCoercion
    kind_co KindCoercion
    co) = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    kind_co forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (FunCo Role
    _ KindCoercion
    co_mult KindCoercion
    co1 KindCoercion
    co2) = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co_mult forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co1 forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co2
         go_co (AxiomInstCo CoAxiom Branched
    ax Int
    _ [KindCoercion]
    args) = forall {br :: BranchFlag}. CoAxiom br -> UniqSet TyCon
    go_ax CoAxiom Branched
    ax forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` [KindCoercion] -> UniqSet TyCon
    go_cos [KindCoercion]
    args
         go_co (UnivCo UnivCoProvenance
    p Role
    _ Type
    t1 Type
    t2)      = UnivCoProvenance -> UniqSet TyCon
    go_prov UnivCoProvenance
    p forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` Type -> UniqSet TyCon
    go Type
    t1 forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` Type -> UniqSet TyCon
    go Type
    t2
         go_co (CoVarCo {})            = forall a. UniqSet a
    emptyUniqSet
         go_co (HoleCo {})             = forall a. UniqSet a
    emptyUniqSet
         go_co (SymCo KindCoercion
    co)              = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (TransCo KindCoercion
    co1 KindCoercion
    co2)       = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co1 forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co2
         go_co (NthCo Role
    _ Int
    _ KindCoercion
    co)          = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (LRCo LeftOrRight
    _ KindCoercion
    co)             = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (InstCo KindCoercion
    co KindCoercion
    arg)         = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co forall a. UniqSet a -> UniqSet a -> UniqSet a
    `unionUniqSets` KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    arg
         go_co (KindCo KindCoercion
    co)             = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (SubCo KindCoercion
    co)              = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_co (AxiomRuleCo CoAxiomRule
    _ [KindCoercion]
    cs)      = [KindCoercion] -> UniqSet TyCon
    go_cos [KindCoercion]
    cs

         go_mco :: MCoercionN -> UniqSet TyCon
    go_mco MCoercionN
    MRefl    = forall a. UniqSet a
    emptyUniqSet
         go_mco (MCo KindCoercion
    co) = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co

         go_prov :: UnivCoProvenance -> UniqSet TyCon
    go_prov (PhantomProv KindCoercion
    co)    = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_prov (ProofIrrelProv KindCoercion
    co) = KindCoercion -> UniqSet TyCon
    go_co KindCoercion
    co
         go_prov (PluginProv String
    _)      = forall a. UniqSet a
    emptyUniqSet
         go_prov (CorePrepProv Bool
    _)    = forall a. UniqSet a
    emptyUniqSet
            -- this last case can happen from the tyConsOfType used from
            -- checkTauTvUpdate

         go_s :: t Type -> UniqSet TyCon
    go_s t Type
    tys     = forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (forall a. UniqSet a -> UniqSet a -> UniqSet a
    unionUniqSets forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Type -> UniqSet TyCon
    go)     forall a. UniqSet a
    emptyUniqSet t Type
    tys
         go_cos :: [KindCoercion] -> UniqSet TyCon
    go_cos [KindCoercion]
    cos   = forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (forall a. UniqSet a -> UniqSet a -> UniqSet a
    unionUniqSets forall b c a. (b -> c) -> (a -> b) -> a -> c
    . KindCoercion -> UniqSet TyCon
    go_co)  forall a. UniqSet a
    emptyUniqSet [KindCoercion]
    cos

         go_tc :: a -> UniqSet a
    go_tc a
    tc = forall {a}. Uniquable a => a -> UniqSet a
    unitUniqSet a
    tc
         go_ax :: CoAxiom br -> UniqSet TyCon
    go_ax CoAxiom br
    ax = forall {a}. Uniquable a => a -> UniqSet a
    go_tc forall a b. (a -> b) -> a -> b
    $ forall (br :: BranchFlag). CoAxiom br -> TyCon
    coAxiomTyCon CoAxiom br
    ax

    -- | Retrieve the free variables in this type, splitting them based
    -- on whether they are used visibly or invisibly. Invisible ones come
    -- first.
    splitVisVarsOfType :: Type -> Pair TyCoVarSet
    splitVisVarsOfType :: Type -> Pair TyCoVarSet
    splitVisVarsOfType Type
    orig_ty = forall a. a -> a -> Pair a
    Pair TyCoVarSet
    invis_vars TyCoVarSet
    vis_vars
      where
        Pair TyCoVarSet
    invis_vars1 TyCoVarSet
    vis_vars = Type -> Pair TyCoVarSet
    go Type
    orig_ty
        invis_vars :: TyCoVarSet
    invis_vars = TyCoVarSet
    invis_vars1 TyCoVarSet -> TyCoVarSet -> TyCoVarSet
    `minusVarSet` TyCoVarSet
    vis_vars

        go :: Type -> Pair TyCoVarSet
    go (TyVarTy TyVar
    tv)      = forall a. a -> a -> Pair a
    Pair (Type -> TyCoVarSet
    tyCoVarsOfType forall a b. (a -> b) -> a -> b
    $ TyVar -> Type
    tyVarKind TyVar
    tv) (TyVar -> TyCoVarSet
    unitVarSet TyVar
    tv)
        go (AppTy Type
    t1 Type
    t2)     = Type -> Pair TyCoVarSet
    go Type
    t1 forall a. Monoid a => a -> a -> a
    `mappend` Type -> Pair TyCoVarSet
    go Type
    t2
        go (TyConApp TyCon
    tc [Type]
    tys) = TyCon -> [Type] -> Pair TyCoVarSet
    go_tc TyCon
    tc [Type]
    tys
        go (FunTy AnonArgFlag
    _ Type
    w Type
    t1 Type
    t2) = Type -> Pair TyCoVarSet
    go Type
    w forall a. Monoid a => a -> a -> a
    `mappend` Type -> Pair TyCoVarSet
    go Type
    t1 forall a. Monoid a => a -> a -> a
    `mappend` Type -> Pair TyCoVarSet
    go Type
    t2
        go (ForAllTy (Bndr TyVar
    tv ArgFlag
    _) Type
    ty)
          = ((TyCoVarSet -> TyVar -> TyCoVarSet
    `delVarSet` TyVar
    tv) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Type -> Pair TyCoVarSet
    go Type
    ty) forall a. Monoid a => a -> a -> a
    `mappend`
            (TyCoVarSet -> Pair TyCoVarSet
    invisible (Type -> TyCoVarSet
    tyCoVarsOfType forall a b. (a -> b) -> a -> b
    $ TyVar -> Type
    varType TyVar
    tv))
        go (LitTy {}) = forall a. Monoid a => a
    mempty
        go (CastTy Type
    ty KindCoercion
    co) = Type -> Pair TyCoVarSet
    go Type
    ty forall a. Monoid a => a -> a -> a
    `mappend` TyCoVarSet -> Pair TyCoVarSet
    invisible (KindCoercion -> TyCoVarSet
    tyCoVarsOfCo KindCoercion
    co)
        go (CoercionTy KindCoercion
    co) = TyCoVarSet -> Pair TyCoVarSet
    invisible forall a b. (a -> b) -> a -> b
    $ KindCoercion -> TyCoVarSet
    tyCoVarsOfCo KindCoercion
    co

        invisible :: TyCoVarSet -> Pair TyCoVarSet
    invisible TyCoVarSet
    vs = forall a. a -> a -> Pair a
    Pair TyCoVarSet
    vs TyCoVarSet
    emptyVarSet

        go_tc :: TyCon -> [Type] -> Pair TyCoVarSet
    go_tc TyCon
    tc [Type]
    tys = let ([Type]
    invis, [Type]
    vis) = TyCon -> [Type] -> ([Type], [Type])
    partitionInvisibleTypes TyCon
    tc [Type]
    tys in
                       TyCoVarSet -> Pair TyCoVarSet
    invisible ([Type] -> TyCoVarSet
    tyCoVarsOfTypes [Type]
    invis) forall a. Monoid a => a -> a -> a
    `mappend` forall (t :: * -> *) m a.
    (Foldable t, Monoid m) =>
    (a -> m) -> t a -> m
    foldMap Type -> Pair TyCoVarSet
    go [Type]
    vis

    splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
    splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
    splitVisVarsOfTypes = forall (t :: * -> *) m a.
    (Foldable t, Monoid m) =>
    (a -> m) -> t a -> m
    foldMap Type -> Pair TyCoVarSet
    splitVisVarsOfType

    {-
    ************************************************************************
    *                                                                      *
            Functions over Kinds
    *                                                                      *
    ************************************************************************

    Note [Kind Constraint and kind Type]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The kind Constraint is the kind of classes and other type constraints.
    The special thing about types of kind Constraint is that
     * They are displayed with double arrow:
         f :: Ord a => a -> a
     * They are implicitly instantiated at call sites; so the type inference
       engine inserts an extra argument of type (Ord a) at every call site
       to f.

    However, once type inference is over, there is *no* distinction between
    Constraint and Type. Indeed we can have coercions between the two. Consider
       class C a where
         op :: a -> a
    For this single-method class we may generate a newtype, which in turn
    generates an axiom witnessing
        C a ~ (a -> a)
    so on the left we have Constraint, and on the right we have Type.
    See #7451.

    Because we treat Constraint/Type differently during and after type inference,
    GHC has two notions of equality that differ in whether they equate
    Constraint/Type or not:

    * GHC.Tc.Utils.TcType.tcEqType implements typechecker equality (see
      Note [Typechecker equality vs definitional equality] in GHC.Tc.Utils.TcType),
      which treats Constraint and Type as distinct. This is used during type
      inference. See #11715 for issues that arise from this.
    * GHC.Core.TyCo.Rep.eqType implements definitional equality (see
      Note [Non-trivial definitional equality] in GHC.Core.TyCo.Rep), which treats
      Constraint and Type as equal. This is used after type inference.

    Bottom line: although 'Type' and 'Constraint' are distinct TyCons, with
    distinct uniques, they are treated as equal at all times except
    during type inference.
    -}

    -- | Tests whether the given kind (which should look like @TYPE x@)
    -- is something other than a constructor tree (that is, constructors at every node).
    -- E.g.  True of   TYPE k, TYPE (F Int)
    --       False of  TYPE 'LiftedRep
    isKindLevPoly :: Kind -> Bool
    isKindLevPoly :: Type -> Bool
    isKindLevPoly Type
    k = ASSERT2( isLiftedTypeKind k || _is_type, ppr k )
                        -- the isLiftedTypeKind check is necessary b/c of Constraint
                      Type -> Bool
    go Type
    k
      where
        go :: Type -> Bool
    go Type
    ty | Just Type
    ty' <- Type -> Maybe Type
    coreView Type
    ty = Type -> Bool
    go Type
    ty'
        go TyVarTy{}         = Bool
    True
        go AppTy{}           = Bool
    True  -- it can't be a TyConApp
        go (TyConApp TyCon
    tc [Type]
    tys) = TyCon -> Bool
    isFamilyTyCon TyCon
    tc Bool -> Bool -> Bool
    || forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    any Type -> Bool
    go [Type]
    tys
        go ForAllTy{}        = Bool
    True
        go (FunTy AnonArgFlag
    _ Type
    w Type
    t1 Type
    t2) = Type -> Bool
    go Type
    w Bool -> Bool -> Bool
    || Type -> Bool
    go Type
    t1 Bool -> Bool -> Bool
    || Type -> Bool
    go Type
    t2
        go LitTy{}           = Bool
    False
        go CastTy{}          = Bool
    True
        go CoercionTy{}      = Bool
    True

        _is_type :: Bool
    _is_type = Type -> Bool
    classifiesTypeWithValues Type
    k

    -----------------------------------------
    --              Subkinding
    -- The tc variants are used during type-checking, where ConstraintKind
    -- is distinct from all other kinds
    -- After type-checking (in core), Constraint and liftedTypeKind are
    -- indistinguishable

    -- | Does this classify a type allowed to have values? Responds True to things
    -- like *, #, TYPE Lifted, TYPE v, Constraint.
    classifiesTypeWithValues :: Kind -> Bool
    -- ^ True of any sub-kind of OpenTypeKind
    classifiesTypeWithValues :: Type -> Bool
    classifiesTypeWithValues Type
    k = forall a. Maybe a -> Bool
    isJust (HasDebugCallStack => Type -> Maybe Type
    kindRep_maybe Type
    k)

    {-
    %************************************************************************
    %*                                                                      *
             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 -> Int -> Bool
    tyConAppNeedsKindSig Bool
    spec_inj_pos TyCon
    tc Int
    n_args
      | Ordering
    LT <- forall a. [a] -> Int -> Ordering
    listLengthCmp [TyConBinder]
    tc_binders Int
    n_args
      = Bool
    False
      | Bool
    otherwise
      = let ([TyConBinder]
    dropped_binders, [TyConBinder]
    remaining_binders)
              = forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    n_args [TyConBinder]
    tc_binders
            result_kind :: Type
    result_kind  = [TyConBinder] -> Type -> Type
    mkTyConKind [TyConBinder]
    remaining_binders Type
    tc_res_kind
            result_vars :: TyCoVarSet
    result_vars  = Type -> TyCoVarSet
    tyCoVarsOfType Type
    result_kind
            dropped_vars :: TyCoVarSet
    dropped_vars = FV -> TyCoVarSet
    fvVarSet forall a b. (a -> b) -> a -> b
    $
                           forall a. (a -> FV) -> [a] -> FV
    mapUnionFV TyConBinder -> FV
    injective_vars_of_binder [TyConBinder]
    dropped_binders

        in Bool -> Bool
    not (TyCoVarSet -> TyCoVarSet -> Bool
    subVarSet TyCoVarSet
    result_vars TyCoVarSet
    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
            AnonTCB AnonArgFlag
    VisArg -> Bool -> Type -> FV
    injectiveVarsOfType Bool
    False -- conservative choice
                                                  (TyVar -> Type
    varType TyVar
    tv)
            NamedTCB ArgFlag
    argf  | ArgFlag -> Bool
    source_of_injectivity ArgFlag
    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 :: ArgFlag -> Bool
    source_of_injectivity ArgFlag
    Required  = Bool
    True
        -- See Note [Explicit Case Statement for Specificity]
        source_of_injectivity (Invisible Specificity
    spec) = case Specificity
    spec of
          Specificity
    SpecifiedSpec -> Bool
    spec_inj_pos
          Specificity
    InferredSpec  -> Bool
    False

    {-
    Note [Explicit Case Statement for Specificity]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When pattern matching against an `ArgFlag`, you should not pattern match against
    the pattern synonyms 'Specified' or 'Inferred', as this results in a
    non-exhaustive pattern match warning.
    Instead, pattern match against 'Invisible spec' and do another case analysis on
    this specificity argument.
    The issue has been fixed in GHC 8.10 (ticket #17876). This hack can thus be
    dropped once version 8.10 is used as the minimum version for building GHC.

    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-wavey, 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 parametrized 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 = forall a. Type -> a -> Scaled a
    Scaled Type
    Many

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

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

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

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

    pattern One :: Mult
    pattern $mOne :: forall {r}. Type -> ((# #) -> r) -> ((# #) -> r) -> r
    $bOne :: Type
    One <- (isOneDataConTy -> True)
      where One = Type
    oneDataConTy

    pattern Many :: Mult
    pattern $mMany :: forall {r}. Type -> ((# #) -> r) -> ((# #) -> r) -> r
    $bMany :: Type
    Many <- (isManyDataConTy -> True)
      where Many = Type
    manyDataConTy

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

    isOneDataConTy :: Mult -> Bool
    isOneDataConTy :: Type -> Bool
    isOneDataConTy Type
    ty
      | Just TyCon
    tc <- Type -> Maybe TyCon
    tyConAppTyCon_maybe Type
    ty
      = TyCon
    tc forall a. Uniquable a => a -> Unique -> Bool
    `hasKey` Unique
    oneDataConKey
    isOneDataConTy 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 AnonArgFlag
    _ Type
    Many Type
    _ Type
    res -> Type -> Bool
    isLinearType Type
    res
                          FunTy AnonArgFlag
    _ Type
    _ Type
    _ Type
    _ -> Bool
    True
                          ForAllTy VarBndr TyVar ArgFlag
    _ Type
    res -> Type -> Bool
    isLinearType Type
    res
                          Type
    _ -> Bool
    False