{-# LANGUAGE CPP #-} {-# LANGUAGE DeriveDataTypeable #-} {-# OPTIONS_HADDOCK not-home #-} {- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1998 \section[GHC.Core.TyCo.Rep]{Type and Coercion - friends' interface} Note [The Type-related module hierarchy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ GHC.Core.Class GHC.Core.Coercion.Axiom GHC.Core.TyCon imports GHC.Core.{Class, Coercion.Axiom} GHC.Core.TyCo.Rep imports GHC.Core.{Class, Coercion.Axiom, TyCon} GHC.Core.TyCo.Ppr imports GHC.Core.TyCo.Rep GHC.Core.TyCo.FVs imports GHC.Core.TyCo.Rep GHC.Core.TyCo.Subst imports GHC.Core.TyCo.{Rep, FVs, Ppr} GHC.Core.TyCo.Tidy imports GHC.Core.TyCo.{Rep, FVs} GHC.Builtin.Types.Prim imports GHC.Core.TyCo.Rep ( including mkTyConTy ) GHC.Core.Coercion imports GHC.Core.Type -} -- We expose the relevant stuff from this module via the Type module module GHC.Core.TyCo.Rep ( -- * Types Type(..), TyLit(..), KindOrType, Kind, KnotTied, PredType, ThetaType, -- Synonyms ArgFlag(..), AnonArgFlag(..), -- * Coercions Coercion(..), UnivCoProvenance(..), CoercionHole(..), coHoleCoVar, setCoHoleCoVar, CoercionN, CoercionR, CoercionP, KindCoercion, MCoercion(..), MCoercionR, MCoercionN, -- * Functions over types mkTyConTy_, mkTyVarTy, mkTyVarTys, mkTyCoVarTy, mkTyCoVarTys, mkFunTy, mkVisFunTy, mkInvisFunTy, mkVisFunTys, mkForAllTy, mkForAllTys, mkInvisForAllTys, mkPiTy, mkPiTys, mkFunTyMany, mkScaledFunTy, mkVisFunTyMany, mkVisFunTysMany, mkInvisFunTyMany, mkInvisFunTysMany, nonDetCmpTyLit, cmpTyLit, -- * Functions over binders TyCoBinder(..), TyCoVarBinder, TyBinder, binderVar, binderVars, binderType, binderArgFlag, delBinderVar, isInvisibleArgFlag, isVisibleArgFlag, isInvisibleBinder, isVisibleBinder, isTyBinder, isNamedBinder, -- * Functions over coercions pickLR, -- ** Analyzing types TyCoFolder(..), foldTyCo, -- * Sizes typeSize, coercionSize, provSize, -- * Multiplicities Scaled(..), scaledMult, scaledThing, mapScaledType, Mult ) where #include "HsVersions.h" import GHC.Prelude import {-# SOURCE #-} GHC.Core.TyCo.Ppr ( pprType, pprCo, pprTyLit ) -- Transitively pulls in a LOT of stuff, better to break the loop -- friends: import GHC.Iface.Type import GHC.Types.Var import GHC.Types.Var.Set import GHC.Core.TyCon import GHC.Core.Coercion.Axiom -- others import {-# SOURCE #-} GHC.Builtin.Types ( manyDataConTy ) import GHC.Types.Basic ( LeftOrRight(..), pickLR ) import GHC.Types.Unique ( Uniquable(..) ) import GHC.Utils.Outputable import GHC.Data.FastString import GHC.Utils.Misc import GHC.Utils.Panic -- libraries import qualified Data.Data as Data hiding ( TyCon ) import Data.IORef ( IORef ) -- for CoercionHole {- ********************************************************************** * * Type * * ********************************************************************** -} -- | The key representation of types within the compiler type KindOrType = Type -- See Note [Arguments to type constructors] -- | The key type representing kinds in the compiler. type Kind = Type -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in GHC.Core.Lint data Type -- See Note [Non-trivial definitional equality] = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable) | AppTy Type Type -- ^ Type application to something other than a 'TyCon'. Parameters: -- -- 1) Function: must /not/ be a 'TyConApp' or 'CastTy', -- must be another 'AppTy', or 'TyVarTy' -- See Note [Respecting definitional equality] \(EQ1) about the -- no 'CastTy' requirement -- -- 2) Argument type | TyConApp TyCon [KindOrType] -- ^ Application of a 'TyCon', including newtypes /and/ synonyms. -- Invariant: saturated applications of 'FunTyCon' must -- use 'FunTy' and saturated synonyms must use their own -- constructors. However, /unsaturated/ 'FunTyCon's -- do appear as 'TyConApp's. -- Parameters: -- -- 1) Type constructor being applied to. -- -- 2) Type arguments. Might not have enough type arguments -- here to saturate the constructor. -- Even type synonyms are not necessarily saturated; -- for example unsaturated type synonyms -- can appear as the right hand side of a type synonym. | ForAllTy {-# UNPACK #-} !TyCoVarBinder Type -- ^ A Π type. -- INVARIANT: If the binder is a coercion variable, it must -- be mentioned in the Type. See -- Note [Unused coercion variable in ForAllTy] | FunTy -- ^ FUN m t1 t2 Very common, so an important special case -- See Note [Function types] { Type -> AnonArgFlag ft_af :: AnonArgFlag -- Is this (->) or (=>)? , Type -> Type ft_mult :: Mult -- Multiplicity , Type -> Type ft_arg :: Type -- Argument type , Type -> Type ft_res :: Type } -- Result type | LitTy TyLit -- ^ Type literals are similar to type constructors. | CastTy Type KindCoercion -- ^ A kind cast. The coercion is always nominal. -- INVARIANT: The cast is never reflexive \(EQ2) -- INVARIANT: The Type is not a CastTy (use TransCo instead) \(EQ3) -- INVARIANT: The Type is not a ForAllTy over a tyvar \(EQ4) -- See Note [Respecting definitional equality] | CoercionTy Coercion -- ^ Injection of a Coercion into a type -- This should only ever be used in the RHS of an AppTy, -- in the list of a TyConApp, when applying a promoted -- GADT data constructor deriving Typeable Type Type -> DataType Type -> Constr (forall b. Data b => b -> b) -> Type -> Type forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> Type -> u forall u. (forall d. Data d => d -> u) -> Type -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Type -> m Type forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Type forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Type -> c Type forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Type) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Type) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Type -> m Type gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Type -> m Type $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Type -> m Type gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Type -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Type -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> Type -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> Type -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Type -> r gmapT :: (forall b. Data b => b -> b) -> Type -> Type $cgmapT :: (forall b. Data b => b -> b) -> Type -> Type dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Type) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Type) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Type) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Type) dataTypeOf :: Type -> DataType $cdataTypeOf :: Type -> DataType toConstr :: Type -> Constr $ctoConstr :: Type -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Type $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Type gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Type -> c Type $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Type -> c Type Data.Data instance Outputable Type where ppr :: Type -> SDoc ppr = Type -> SDoc pprType -- NOTE: Other parts of the code assume that type literals do not contain -- types or type variables. data TyLit = NumTyLit Integer | StrTyLit FastString | CharTyLit Char deriving (TyLit -> TyLit -> Bool forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a /= :: TyLit -> TyLit -> Bool $c/= :: TyLit -> TyLit -> Bool == :: TyLit -> TyLit -> Bool $c== :: TyLit -> TyLit -> Bool Eq, Typeable TyLit TyLit -> DataType TyLit -> Constr (forall b. Data b => b -> b) -> TyLit -> TyLit forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u forall u. (forall d. Data d => d -> u) -> TyLit -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyLit -> m TyLit gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyLit -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> TyLit -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> TyLit -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyLit -> r gmapT :: (forall b. Data b => b -> b) -> TyLit -> TyLit $cgmapT :: (forall b. Data b => b -> b) -> TyLit -> TyLit dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyLit) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyLit) dataTypeOf :: TyLit -> DataType $cdataTypeOf :: TyLit -> DataType toConstr :: TyLit -> Constr $ctoConstr :: TyLit -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyLit gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyLit -> c TyLit Data.Data) -- Non-determinism arises due to uniqCompareFS nonDetCmpTyLit :: TyLit -> TyLit -> Ordering nonDetCmpTyLit :: TyLit -> TyLit -> Ordering nonDetCmpTyLit = forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> NonDetFastString NonDetFastString -- Slower than nonDetCmpTyLit but deterministic cmpTyLit :: TyLit -> TyLit -> Ordering cmpTyLit :: TyLit -> TyLit -> Ordering cmpTyLit = forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> LexicalFastString LexicalFastString {-# INLINE cmpTyLitWith #-} cmpTyLitWith :: Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith :: forall r. Ord r => (FastString -> r) -> TyLit -> TyLit -> Ordering cmpTyLitWith FastString -> r _ (NumTyLit Integer x) (NumTyLit Integer y) = forall a. Ord a => a -> a -> Ordering compare Integer x Integer y cmpTyLitWith FastString -> r w (StrTyLit FastString x) (StrTyLit FastString y) = forall a. Ord a => a -> a -> Ordering compare (FastString -> r w FastString x) (FastString -> r w FastString y) cmpTyLitWith FastString -> r _ (CharTyLit Char x) (CharTyLit Char y) = forall a. Ord a => a -> a -> Ordering compare Char x Char y cmpTyLitWith FastString -> r _ TyLit a TyLit b = forall a. Ord a => a -> a -> Ordering compare (TyLit -> Int tag TyLit a) (TyLit -> Int tag TyLit b) where tag :: TyLit -> Int tag :: TyLit -> Int tag NumTyLit{} = Int 0 tag StrTyLit{} = Int 1 tag CharTyLit{} = Int 2 instance Outputable TyLit where ppr :: TyLit -> SDoc ppr = TyLit -> SDoc pprTyLit {- Note [Function types] ~~~~~~~~~~~~~~~~~~~~~~~~ FFunTy is the constructor for a function type. Lots of things to say about it! * FFunTy is the data constructor, meaning "full function type". * The function type constructor (->) has kind (->) :: forall {r1} {r2}. TYPE r1 -> TYPE r2 -> Type LiftedRep mkTyConApp ensure that we convert a saturated application TyConApp (->) [r1,r2,t1,t2] into FunTy t1 t2 dropping the 'r1' and 'r2' arguments; they are easily recovered from 't1' and 't2'. * For the time being its RuntimeRep quantifiers are left inferred. This is to allow for it to evolve. * The ft_af field says whether or not this is an invisible argument VisArg: t1 -> t2 Ordinary function type InvisArg: t1 => t2 t1 is guaranteed to be a predicate type, i.e. t1 :: Constraint See Note [Types for coercions, predicates, and evidence] This visibility info makes no difference in Core; it matters only when we regard the type as a Haskell source type. * FunTy is a (unidirectional) pattern synonym that allows positional pattern matching (FunTy arg res), ignoring the ArgFlag. -} {- ----------------------- Commented out until the pattern match checker can handle it; see #16185 For now we use the CPP macro #define FunTy FFunTy _ (see HsVersions.h) to allow pattern matching on a (positional) FunTy constructor. {-# COMPLETE FunTy, TyVarTy, AppTy, TyConApp , ForAllTy, LitTy, CastTy, CoercionTy :: Type #-} -- | 'FunTy' is a (uni-directional) pattern synonym for the common -- case where we want to match on the argument/result type, but -- ignoring the AnonArgFlag pattern FunTy :: Type -> Type -> Type pattern FunTy arg res <- FFunTy { ft_arg = arg, ft_res = res } End of commented out block ---------------------------------- -} {- Note [Types for coercions, predicates, and evidence] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We treat differently: (a) Predicate types Test: isPredTy Binders: DictIds Kind: Constraint Examples: (Eq a), and (a ~ b) (b) Coercion types are primitive, unboxed equalities Test: isCoVarTy Binders: CoVars (can appear in coercions) Kind: TYPE (TupleRep []) Examples: (t1 ~# t2) or (t1 ~R# t2) (c) Evidence types is the type of evidence manipulated by the type constraint solver. Test: isEvVarType Binders: EvVars Kind: Constraint or TYPE (TupleRep []) Examples: all coercion types and predicate types Coercion types and predicate types are mutually exclusive, but evidence types are a superset of both. When treated as a user type, - Predicates (of kind Constraint) are invisible and are implicitly instantiated - Coercion types, and non-pred evidence types (i.e. not of kind Constrain), are just regular old types, are visible, and are not implicitly instantiated. In a FunTy { ft_af = InvisArg }, the argument type is always a Predicate type. Note [Weird typing rule for ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Here are the typing rules for ForAllTy: tyvar : Type inner : TYPE r tyvar does not occur in r ------------------------------------ ForAllTy (Bndr tyvar vis) inner : TYPE r inner : TYPE r ------------------------------------ ForAllTy (Bndr covar vis) inner : Type Note that the kind of the result depends on whether the binder is a tyvar or a covar. The kind of a forall-over-tyvar is the same as the kind of the inner type. This is because quantification over types is erased before runtime. By contrast, the kind of a forall-over-covar is always Type, because a forall-over-covar is compiled into a function taking a 0-bit-wide erased coercion argument. Because the tyvar form above includes r in its result, we must be careful not to let any variables escape -- thus the last premise of the rule above. Note [Constraints in kinds] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Do we allow a type constructor to have a kind like S :: Eq a => a -> Type No, we do not. Doing so would mean would need a TyConApp like S @k @(d :: Eq k) (ty :: k) and we have no way to build, or decompose, evidence like (d :: Eq k) at the type level. But we admit one exception: equality. We /do/ allow, say, MkT :: (a ~ b) => a -> b -> Type a b Why? Because we can, without much difficulty. Moreover we can promote a GADT data constructor (see TyCon Note [Promoted data constructors]), like data GT a b where MkGT : a -> a -> GT a a so programmers might reasonably expect to be able to promote MkT as well. How does this work? * In GHC.Tc.Validity.checkConstraintsOK we reject kinds that have constraints other than (a~b) and (a~~b). * In Inst.tcInstInvisibleTyBinder we instantiate a call of MkT by emitting [W] co :: alpha ~# beta and producing the elaborated term MkT @alpha @beta (Eq# alpha beta co) We don't generate a boxed "Wanted"; we generate only a regular old /unboxed/ primitive-equality Wanted, and build the box on the spot. * How can we get such a MkT? By promoting a GADT-style data constructor data T a b where MkT :: (a~b) => a -> b -> T a b See DataCon.mkPromotedDataCon and Note [Promoted data constructors] in GHC.Core.TyCon * We support both homogeneous (~) and heterogeneous (~~) equality. (See Note [The equality types story] in GHC.Builtin.Types.Prim for a primer on these equality types.) * How do we prevent a MkT having an illegal constraint like Eq a? We check for this at use-sites; see GHC.Tc.Gen.HsType.tcTyVar, specifically dc_theta_illegal_constraint. * Notice that nothing special happens if K :: (a ~# b) => blah because (a ~# b) is not a predicate type, and is never implicitly instantiated. (Mind you, it's not clear how you could creates a type constructor with such a kind.) See Note [Types for coercions, predicates, and evidence] * The existence of promoted MkT with an equality-constraint argument is the (only) reason that the AnonTCB constructor of TyConBndrVis carries an AnonArgFlag (VisArg/InvisArg). For example, when we promote the data constructor MkT :: forall a b. (a~b) => a -> b -> T a b we get a PromotedDataCon with tyConBinders Bndr (a :: Type) (NamedTCB Inferred) Bndr (b :: Type) (NamedTCB Inferred) Bndr (_ :: a ~ b) (AnonTCB InvisArg) Bndr (_ :: a) (AnonTCB VisArg)) Bndr (_ :: b) (AnonTCB VisArg)) * One might reasonably wonder who *unpacks* these boxes once they are made. After all, there is no type-level `case` construct. The surprising answer is that no one ever does. Instead, if a GADT constructor is used on the left-hand side of a type family equation, that occurrence forces GHC to unify the types in question. For example: data G a where MkG :: G Bool type family F (x :: G a) :: a where F MkG = False When checking the LHS `F MkG`, GHC sees the MkG constructor and then must unify F's implicit parameter `a` with Bool. This succeeds, making the equation F Bool (MkG @Bool <Bool>) = False Note that we never need unpack the coercion. This is because type family equations are *not* parametric in their kind variables. That is, we could have just said type family H (x :: G a) :: a where H _ = False The presence of False on the RHS also forces `a` to become Bool, giving us H Bool _ = False The fact that any of this works stems from the lack of phase separation between types and kinds (unlike the very present phase separation between terms and types). Once we have the ability to pattern-match on types below top-level, this will no longer cut it, but it seems fine for now. Note [Arguments to type constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Because of kind polymorphism, in addition to type application we now have kind instantiation. We reuse the same notations to do so. For example: Just (* -> *) Maybe Right * Nat Zero are represented by: TyConApp (PromotedDataCon Just) [* -> *, Maybe] TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)] Important note: Nat is used as a *kind* and not as a type. This can be confusing, since type-level Nat and kind-level Nat are identical. We use the kind of (PromotedDataCon Right) to know if its arguments are kinds or types. This kind instantiation only happens in TyConApp currently. Note [Non-trivial definitional equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Is Int |> <*> the same as Int? YES! In order to reduce headaches, we decide that any reflexive casts in types are just ignored. (Indeed they must be. See Note [Respecting definitional equality].) More generally, the `eqType` function, which defines Core's type equality relation, ignores casts and coercion arguments, as long as the two types have the same kind. This allows us to be a little sloppier in keeping track of coercions, which is a good thing. It also means that eqType does not depend on eqCoercion, which is also a good thing. Why is this sensible? That is, why is something different than α-equivalence appropriate for the implementation of eqType? Anything smaller than ~ and homogeneous is an appropriate definition for equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any expression of type τ can be transmuted to one of type σ at any point by casting. The same is true of expressions of type σ. So in some sense, τ and σ are interchangeable. But let's be more precise. If we examine the typing rules of FC (say, those in https://richarde.dev/papers/2015/equalities/equalities.pdf) there are several places where the same metavariable is used in two different premises to a rule. (For example, see Ty_App.) There is an implicit equality check here. What definition of equality should we use? By convention, we use α-equivalence. Take any rule with one (or more) of these implicit equality checks. Then there is an admissible rule that uses ~ instead of the implicit check, adding in casts as appropriate. The only problem here is that ~ is heterogeneous. To make the kinds work out in the admissible rule that uses ~, it is necessary to homogenize the coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η; we use η |> kind η, which is homogeneous. The effect of this all is that eqType, the implementation of the implicit equality check, can use any homogeneous relation that is smaller than ~, as those rules must also be admissible. A more drawn out argument around all of this is presented in Section 7.2 of Richard E's thesis (http://richarde.dev/papers/2016/thesis/eisenberg-thesis.pdf). What would go wrong if we insisted on the casts matching? See the beginning of Section 8 in the unpublished paper above. Theoretically, nothing at all goes wrong. But in practical terms, getting the coercions right proved to be nightmarish. And types would explode: during kind-checking, we often produce reflexive kind coercions. When we try to cast by these, mkCastTy just discards them. But if we used an eqType that distinguished between Int and Int |> <*>, then we couldn't discard -- the output of kind-checking would be enormous, and we would need enormous casts with lots of CoherenceCo's to straighten them out. Would anything go wrong if eqType looked through type families? No, not at all. But that makes eqType rather hard to implement. Thus, the guideline for eqType is that it should be the largest easy-to-implement relation that is still smaller than ~ and homogeneous. The precise choice of relation is somewhat incidental, as long as the smart constructors and destructors in Type respect whatever relation is chosen. Another helpful principle with eqType is this: (EQ) If (t1 `eqType` t2) then I can replace t1 by t2 anywhere. This principle also tells us that eqType must relate only types with the same kinds. Interestingly, it must be the case that the free variables of t1 and t2 might be different, even if t1 `eqType` t2. A simple example of this is if we have both cv1 :: k1 ~ k2 and cv2 :: k1 ~ k2 in the environment. Then t1 = t |> cv1 and t2 = t |> cv2 are eqType; yet cv1 is in the free vars of t1 and cv2 is in the free vars of t2. Unless we choose to implement eqType to be just α-equivalence, this wrinkle around free variables remains. Yet not all is lost: we can say that any two equal types share the same *relevant* free variables. Here, a relevant variable is a shallow free variable (see Note [Shallow and deep free variables] in GHC.Core.TyCo.FVs) that does not appear within a coercion. Note that type variables can appear within coercions (in, say, a Refl node), but that coercion variables cannot appear outside a coercion. We do not (yet) have a function to extract relevant free variables, but it would not be hard to write if the need arises. Besides eqType, another equality relation that upholds the (EQ) property above is /typechecker equality/, which is implemented as GHC.Tc.Utils.TcType.tcEqType. See Note [Typechecker equality vs definitional equality] in GHC.Tc.Utils.TcType for what the difference between eqType and tcEqType is. Note [Respecting definitional equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Note [Non-trivial definitional equality] introduces the property (EQ). How is this upheld? Any function that pattern matches on all the constructors will have to consider the possibility of CastTy. Presumably, those functions will handle CastTy appropriately and we'll be OK. More dangerous are the splitXXX functions. Let's focus on splitTyConApp. We don't want it to fail on (T a b c |> co). Happily, if we have (T a b c |> co) `eqType` (T d e f) then co must be reflexive. Why? eqType checks that the kinds are equal, as well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f). By the kind check, we know that (T a b c |> co) and (T d e f) have the same kind. So the only way that co could be non-reflexive is for (T a b c) to have a different kind than (T d e f). But because T's kind is closed (all tycon kinds are closed), the only way for this to happen is that one of the arguments has to differ, leading to a contradiction. Thus, co is reflexive. Accordingly, by eliminating reflexive casts, splitTyConApp need not worry about outermost casts to uphold (EQ). Eliminating reflexive casts is done in mkCastTy. This is (EQ1) below. Unforunately, that's not the end of the story. Consider comparing (T a b c) =? (T a b |> (co -> <Type>)) (c |> co) These two types have the same kind (Type), but the left type is a TyConApp while the right type is not. To handle this case, we say that the right-hand type is ill-formed, requiring an AppTy never to have a casted TyConApp on its left. It is easy enough to pull around the coercions to maintain this invariant, as done in Type.mkAppTy. In the example above, trying to form the right-hand type will instead yield (T a b (c |> co |> sym co) |> <Type>). Both the casts there are reflexive and will be dropped. Huzzah. This idea of pulling coercions to the right works for splitAppTy as well. However, there is one hiccup: it's possible that a coercion doesn't relate two Pi-types. For example, if we have @type family Fun a b where Fun a b = a -> b@, then we might have (T :: Fun Type Type) and (T |> axFun) Int. That axFun can't be pulled to the right. But we don't need to pull it: (T |> axFun) Int is not `eqType` to any proper TyConApp -- thus, leaving it where it is doesn't violate our (EQ) property. In order to detect reflexive casts reliably, we must make sure not to have nested casts: we update (t |> co1 |> co2) to (t |> (co1 `TransCo` co2)). This is (EQ2) below. One other troublesome case is ForAllTy. See Note [Weird typing rule for ForAllTy]. The kind of the body is the same as the kind of the ForAllTy. Accordingly, ForAllTy tv (ty |> co) and (ForAllTy tv ty) |> co are `eqType`. But only the first can be split by splitForAllTy. So we forbid the second form, instead pushing the coercion inside to get the first form. This is done in mkCastTy. In sum, in order to uphold (EQ), we need the following invariants: (EQ1) No decomposable CastTy to the left of an AppTy, where a decomposable cast is one that relates either a FunTy to a FunTy or a ForAllTy to a ForAllTy. (EQ2) No reflexive casts in CastTy. (EQ3) No nested CastTys. (EQ4) No CastTy over (ForAllTy (Bndr tyvar vis) body). See Note [Weird typing rule for ForAllTy] These invariants are all documented above, in the declaration for Type. Note [Equality on FunTys] ~~~~~~~~~~~~~~~~~~~~~~~~~ A (FunTy vis mult arg res) is just an abbreviation for a TyConApp funTyCon [mult, arg_rep, res_rep, arg, res] where arg :: TYPE arg_rep res :: TYPE res_rep Note that the vis field of a FunTy appears nowhere in the equivalent TyConApp. In Core, this is OK, because we no longer care about the visibility of the argument in a FunTy (the vis distinguishes between arg -> res and arg => res). In the type-checker, we are careful not to decompose FunTys with an invisible argument. See also Note [Decomposing fat arrow c=>t] in GHC.Core.Type. In order to compare FunTys while respecting how they could expand into TyConApps, we must check the kinds of the arg and the res. Note [Unused coercion variable in ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have \(co:t1 ~ t2). e What type should we give to this expression? (1) forall (co:t1 ~ t2) -> t (2) (t1 ~ t2) -> t If co is used in t, (1) should be the right choice. if co is not used in t, we would like to have (1) and (2) equivalent. However, we want to keep eqType simple and don't want eqType (1) (2) to return True in any case. We decide to always construct (2) if co is not used in t. Thus in mkLamType, we check whether the variable is a coercion variable (of type (t1 ~# t2), and whether it is un-used in the body. If so, it returns a FunTy instead of a ForAllTy. There are cases we want to skip the check. For example, the check is unnecessary when it is known from the context that the input variable is a type variable. In those cases, we use mkForAllTy. Note [Weird typing rule for ForAllTy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Here is the (truncated) typing rule for the dependent ForAllTy: inner : TYPE r tyvar is not free in r ---------------------------------------- ForAllTy (Bndr tyvar vis) inner : TYPE r Note that the kind of `inner` is the kind of the overall ForAllTy. This is necessary because every ForAllTy over a type variable is erased at runtime. Thus the runtime representation of a ForAllTy (as encoded, via TYPE rep, in the kind) must be the same as the representation of the body. We must check for skolem-escape, though. The skolem-escape would prevent a definition like undefined :: forall (r :: RuntimeRep) (a :: TYPE r). a because the type's kind (TYPE r) mentions the out-of-scope r. Luckily, the real type of undefined is undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a and that HasCallStack constraint neatly sidesteps the potential skolem-escape problem. If the bound variable is a coercion variable: inner : TYPE r covar is free in inner ------------------------------------ ForAllTy (Bndr covar vis) inner : Type Here, the kind of the ForAllTy is just Type, because coercion abstractions are *not* erased. The "covar is free in inner" premise is solely to maintain the representation invariant documented in Note [Unused coercion variable in ForAllTy]. Though there is surface similarity between this free-var check and the one in the tyvar rule, these two restrictions are truly unrelated. -} -- | A type labeled 'KnotTied' might have knot-tied tycons in it. See -- Note [Type checking recursive type and class declarations] in -- "GHC.Tc.TyCl" type KnotTied ty = ty {- ********************************************************************** * * TyCoBinder and ArgFlag * * ********************************************************************** -} -- | A 'TyCoBinder' represents an argument to a function. TyCoBinders can be -- dependent ('Named') or nondependent ('Anon'). They may also be visible or -- not. See Note [TyCoBinders] data TyCoBinder = Named TyCoVarBinder -- A type-lambda binder | Anon AnonArgFlag (Scaled Type) -- A term-lambda binder. Type here can be CoercionTy. -- Visibility is determined by the AnonArgFlag deriving Typeable TyCoBinder TyCoBinder -> DataType TyCoBinder -> Constr (forall b. Data b => b -> b) -> TyCoBinder -> TyCoBinder forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> TyCoBinder -> u forall u. (forall d. Data d => d -> u) -> TyCoBinder -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyCoBinder forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyCoBinder -> c TyCoBinder forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyCoBinder) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyCoBinder) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> TyCoBinder -> m TyCoBinder gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyCoBinder -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> TyCoBinder -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> TyCoBinder -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> TyCoBinder -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TyCoBinder -> r gmapT :: (forall b. Data b => b -> b) -> TyCoBinder -> TyCoBinder $cgmapT :: (forall b. Data b => b -> b) -> TyCoBinder -> TyCoBinder dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyCoBinder) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TyCoBinder) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyCoBinder) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TyCoBinder) dataTypeOf :: TyCoBinder -> DataType $cdataTypeOf :: TyCoBinder -> DataType toConstr :: TyCoBinder -> Constr $ctoConstr :: TyCoBinder -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyCoBinder $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TyCoBinder gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyCoBinder -> c TyCoBinder $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TyCoBinder -> c TyCoBinder Data.Data instance Outputable TyCoBinder where ppr :: TyCoBinder -> SDoc ppr (Anon AnonArgFlag af Scaled Type ty) = forall a. Outputable a => a -> SDoc ppr AnonArgFlag af SDoc -> SDoc -> SDoc <+> forall a. Outputable a => a -> SDoc ppr Scaled Type ty ppr (Named (Bndr TyVar v ArgFlag Required)) = forall a. Outputable a => a -> SDoc ppr TyVar v -- See Note [Explicit Case Statement for Specificity] ppr (Named (Bndr TyVar v (Invisible Specificity spec))) = case Specificity spec of Specificity SpecifiedSpec -> Char -> SDoc char Char '@' SDoc -> SDoc -> SDoc <> forall a. Outputable a => a -> SDoc ppr TyVar v Specificity InferredSpec -> SDoc -> SDoc braces (forall a. Outputable a => a -> SDoc ppr TyVar v) -- | 'TyBinder' is like 'TyCoBinder', but there can only be 'TyVarBinder' -- in the 'Named' field. type TyBinder = TyCoBinder -- | Remove the binder's variable from the set, if the binder has -- a variable. delBinderVar :: VarSet -> TyCoVarBinder -> VarSet delBinderVar :: VarSet -> TyCoVarBinder -> VarSet delBinderVar VarSet vars (Bndr TyVar tv ArgFlag _) = VarSet vars VarSet -> TyVar -> VarSet `delVarSet` TyVar tv -- | Does this binder bind an invisible argument? isInvisibleBinder :: TyCoBinder -> Bool isInvisibleBinder :: TyCoBinder -> Bool isInvisibleBinder (Named (Bndr TyVar _ ArgFlag vis)) = ArgFlag -> Bool isInvisibleArgFlag ArgFlag vis isInvisibleBinder (Anon AnonArgFlag InvisArg Scaled Type _) = Bool True isInvisibleBinder (Anon AnonArgFlag VisArg Scaled Type _) = Bool False -- | Does this binder bind a visible argument? isVisibleBinder :: TyCoBinder -> Bool isVisibleBinder :: TyCoBinder -> Bool isVisibleBinder = Bool -> Bool not forall b c a. (b -> c) -> (a -> b) -> a -> c . TyCoBinder -> Bool isInvisibleBinder isNamedBinder :: TyCoBinder -> Bool isNamedBinder :: TyCoBinder -> Bool isNamedBinder (Named {}) = Bool True isNamedBinder (Anon {}) = Bool False -- | If its a named binder, is the binder a tyvar? -- Returns True for nondependent binder. -- This check that we're really returning a *Ty*Binder (as opposed to a -- coercion binder). That way, if/when we allow coercion quantification -- in more places, we'll know we missed updating some function. isTyBinder :: TyCoBinder -> Bool isTyBinder :: TyCoBinder -> Bool isTyBinder (Named TyCoVarBinder bnd) = TyCoVarBinder -> Bool isTyVarBinder TyCoVarBinder bnd isTyBinder TyCoBinder _ = Bool True {- Note [TyCoBinders] ~~~~~~~~~~~~~~~~~~~ A ForAllTy contains a TyCoVarBinder. But a type can be decomposed to a telescope consisting of a [TyCoBinder] A TyCoBinder represents the type of binders -- that is, the type of an argument to a Pi-type. GHC Core currently supports two different Pi-types: * A non-dependent function type, written with ->, e.g. ty1 -> ty2 represented as FunTy ty1 ty2. These are lifted to Coercions with the corresponding FunCo. * A dependent compile-time-only polytype, written with forall, e.g. forall (a:*). ty represented as ForAllTy (Bndr a v) ty Both Pi-types classify terms/types that take an argument. In other words, if `x` is either a function or a polytype, `x arg` makes sense (for an appropriate `arg`). Note [VarBndrs, TyCoVarBinders, TyConBinders, and visibility] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * A ForAllTy (used for both types and kinds) contains a TyCoVarBinder. Each TyCoVarBinder Bndr a tvis is equipped with tvis::ArgFlag, which says whether or not arguments for this binder should be visible (explicit) in source Haskell. * A TyCon contains a list of TyConBinders. Each TyConBinder Bndr a cvis is equipped with cvis::TyConBndrVis, which says whether or not type and kind arguments for this TyCon should be visible (explicit) in source Haskell. This table summarises the visibility rules: --------------------------------------------------------------------------------------- | Occurrences look like this | GHC displays type as in Haskell source code |-------------------------------------------------------------------------------------- | Bndr a tvis :: TyCoVarBinder, in the binder of ForAllTy for a term | tvis :: ArgFlag | tvis = Inferred: f :: forall {a}. type Arg not allowed: f f :: forall {co}. type Arg not allowed: f | tvis = Specified: f :: forall a. type Arg optional: f or f @Int | tvis = Required: T :: forall k -> type Arg required: T * | This last form is illegal in terms: See Note [No Required TyCoBinder in terms] | | Bndr k cvis :: TyConBinder, in the TyConBinders of a TyCon | cvis :: TyConBndrVis | cvis = AnonTCB: T :: kind -> kind Required: T * | cvis = NamedTCB Inferred: T :: forall {k}. kind Arg not allowed: T | T :: forall {co}. kind Arg not allowed: T | cvis = NamedTCB Specified: T :: forall k. kind Arg not allowed[1]: T | cvis = NamedTCB Required: T :: forall k -> kind Required: T * --------------------------------------------------------------------------------------- [1] In types, in the Specified case, it would make sense to allow optional kind applications, thus (T @*), but we have not yet implemented that ---- In term declarations ---- * Inferred. Function defn, with no signature: f1 x = x We infer f1 :: forall {a}. a -> a, with 'a' Inferred It's Inferred because it doesn't appear in any user-written signature for f1 * Specified. Function defn, with signature (implicit forall): f2 :: a -> a; f2 x = x So f2 gets the type f2 :: forall a. a -> a, with 'a' Specified even though 'a' is not bound in the source code by an explicit forall * Specified. Function defn, with signature (explicit forall): f3 :: forall a. a -> a; f3 x = x So f3 gets the type f3 :: forall a. a -> a, with 'a' Specified * Inferred. Function defn, with signature (explicit forall), marked as inferred: f4 :: forall {a}. a -> a; f4 x = x So f4 gets the type f4 :: forall {a}. a -> a, with 'a' Inferred It's Inferred because the user marked it as such, even though it does appear in the user-written signature for f4 * Inferred/Specified. Function signature with inferred kind polymorphism. f5 :: a b -> Int So 'f5' gets the type f5 :: forall {k} (a:k->*) (b:k). a b -> Int Here 'k' is Inferred (it's not mentioned in the type), but 'a' and 'b' are Specified. * Specified. Function signature with explicit kind polymorphism f6 :: a (b :: k) -> Int This time 'k' is Specified, because it is mentioned explicitly, so we get f6 :: forall (k:*) (a:k->*) (b:k). a b -> Int * Similarly pattern synonyms: Inferred - from inferred types (e.g. no pattern type signature) - or from inferred kind polymorphism ---- In type declarations ---- * Inferred (k) data T1 a b = MkT1 (a b) Here T1's kind is T1 :: forall {k:*}. (k->*) -> k -> * The kind variable 'k' is Inferred, since it is not mentioned Note that 'a' and 'b' correspond to /Anon/ TyCoBinders in T1's kind, and Anon binders don't have a visibility flag. (Or you could think of Anon having an implicit Required flag.) * Specified (k) data T2 (a::k->*) b = MkT (a b) Here T's kind is T :: forall (k:*). (k->*) -> k -> * The kind variable 'k' is Specified, since it is mentioned in the signature. * Required (k) data T k (a::k->*) b = MkT (a b) Here T's kind is T :: forall k:* -> (k->*) -> k -> * The kind is Required, since it bound in a positional way in T's declaration Every use of T must be explicitly applied to a kind * Inferred (k1), Specified (k) data T a b (c :: k) = MkT (a b) (Proxy c) Here T's kind is T :: forall {k1:*} (k:*). (k1->*) -> k1 -> k -> * So 'k' is Specified, because it appears explicitly, but 'k1' is Inferred, because it does not Generally, in the list of TyConBinders for a TyCon, * Inferred arguments always come first * Specified, Anon and Required can be mixed e.g. data Foo (a :: Type) :: forall b. (a -> b -> Type) -> Type where ... Here Foo's TyConBinders are [Required 'a', Specified 'b', Anon] and its kind prints as Foo :: forall a -> forall b. (a -> b -> Type) -> Type See also Note [Required, Specified, and Inferred for types] in GHC.Tc.TyCl ---- Printing ----- We print forall types with enough syntax to tell you their visibility flag. But this is not source Haskell, and these types may not all be parsable. Specified: a list of Specified binders is written between `forall` and `.`: const :: forall a b. a -> b -> a Inferred: like Specified, but every binder is written in braces: f :: forall {k} (a:k). S k a -> Int Required: binders are put between `forall` and `->`: T :: forall k -> * ---- Other points ----- * In classic Haskell, all named binders (that is, the type variables in a polymorphic function type f :: forall a. a -> a) have been Inferred. * Inferred variables correspond to "generalized" variables from the Visible Type Applications paper (ESOP'16). Note [No Required TyCoBinder in terms] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We don't allow Required foralls for term variables, including pattern synonyms and data constructors. Why? Because then an application would need a /compulsory/ type argument (possibly without an "@"?), thus (f Int); and we don't have concrete syntax for that. We could change this decision, but Required, Named TyCoBinders are rare anyway. (Most are Anons.) However the type of a term can (just about) have a required quantifier; see Note [Required quantifiers in the type of a term] in GHC.Tc.Gen.Expr. -} {- ********************************************************************** * * PredType * * ********************************************************************** -} -- | A type of the form @p@ of constraint kind represents a value whose type is -- the Haskell predicate @p@, where a predicate is what occurs before -- the @=>@ in a Haskell type. -- -- We use 'PredType' as documentation to mark those types that we guarantee to -- have this kind. -- -- It can be expanded into its representation, but: -- -- * The type checker must treat it as opaque -- -- * The rest of the compiler treats it as transparent -- -- Consider these examples: -- -- > f :: (Eq a) => a -> Int -- > g :: (?x :: Int -> Int) => a -> Int -- > h :: (r\l) => {r} => {l::Int | r} -- -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\" type PredType = Type -- | A collection of 'PredType's type ThetaType = [PredType] {- (We don't support TREX records yet, but the setup is designed to expand to allow them.) A Haskell qualified type, such as that for f,g,h above, is represented using * a FunTy for the double arrow * with a type of kind Constraint as the function argument The predicate really does turn into a real extra argument to the function. If the argument has type (p :: Constraint) then the predicate p is represented by evidence of type p. %************************************************************************ %* * Simple constructors %* * %************************************************************************ These functions are here so that they can be used by GHC.Builtin.Types.Prim, which in turn is imported by Type -} mkTyVarTy :: TyVar -> Type mkTyVarTy :: TyVar -> Type mkTyVarTy TyVar v = ASSERT2( isTyVar v, ppr v <+> dcolon <+> ppr (tyVarKind v) ) TyVar -> Type TyVarTy TyVar v mkTyVarTys :: [TyVar] -> [Type] mkTyVarTys :: [TyVar] -> [Type] mkTyVarTys = forall a b. (a -> b) -> [a] -> [b] map TyVar -> Type mkTyVarTy -- a common use of mkTyVarTy mkTyCoVarTy :: TyCoVar -> Type mkTyCoVarTy :: TyVar -> Type mkTyCoVarTy TyVar v | TyVar -> Bool isTyVar TyVar v = TyVar -> Type TyVarTy TyVar v | Bool otherwise = Coercion -> Type CoercionTy (TyVar -> Coercion CoVarCo TyVar v) mkTyCoVarTys :: [TyCoVar] -> [Type] mkTyCoVarTys :: [TyVar] -> [Type] mkTyCoVarTys = forall a b. (a -> b) -> [a] -> [b] map TyVar -> Type mkTyCoVarTy infixr 3 `mkFunTy`, `mkVisFunTy`, `mkInvisFunTy`, `mkVisFunTyMany`, `mkInvisFunTyMany` -- Associates to the right mkFunTy :: AnonArgFlag -> Mult -> Type -> Type -> Type mkFunTy :: AnonArgFlag -> Type -> Type -> Type -> Type mkFunTy AnonArgFlag af Type mult Type arg Type res = FunTy { ft_af :: AnonArgFlag ft_af = AnonArgFlag af , ft_mult :: Type ft_mult = Type mult , ft_arg :: Type ft_arg = Type arg , ft_res :: Type ft_res = Type res } mkScaledFunTy :: AnonArgFlag -> Scaled Type -> Type -> Type mkScaledFunTy :: AnonArgFlag -> Scaled Type -> Type -> Type mkScaledFunTy AnonArgFlag af (Scaled Type mult Type arg) Type res = AnonArgFlag -> Type -> Type -> Type -> Type mkFunTy AnonArgFlag af Type mult Type arg Type res mkVisFunTy, mkInvisFunTy :: Mult -> Type -> Type -> Type mkVisFunTy :: Type -> Type -> Type -> Type mkVisFunTy = AnonArgFlag -> Type -> Type -> Type -> Type mkFunTy AnonArgFlag VisArg mkInvisFunTy :: Type -> Type -> Type -> Type mkInvisFunTy = AnonArgFlag -> Type -> Type -> Type -> Type mkFunTy AnonArgFlag InvisArg mkFunTyMany :: AnonArgFlag -> Type -> Type -> Type mkFunTyMany :: AnonArgFlag -> Type -> Type -> Type mkFunTyMany AnonArgFlag af = AnonArgFlag -> Type -> Type -> Type -> Type mkFunTy AnonArgFlag af Type manyDataConTy -- | Special, common, case: Arrow type with mult Many mkVisFunTyMany :: Type -> Type -> Type mkVisFunTyMany :: Type -> Type -> Type mkVisFunTyMany = Type -> Type -> Type -> Type mkVisFunTy Type manyDataConTy mkInvisFunTyMany :: Type -> Type -> Type mkInvisFunTyMany :: Type -> Type -> Type mkInvisFunTyMany = Type -> Type -> Type -> Type mkInvisFunTy Type manyDataConTy -- | Make nested arrow types mkVisFunTys :: [Scaled Type] -> Type -> Type mkVisFunTys :: [Scaled Type] -> Type -> Type mkVisFunTys [Scaled Type] tys Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr (AnonArgFlag -> Scaled Type -> Type -> Type mkScaledFunTy AnonArgFlag VisArg) Type ty [Scaled Type] tys mkVisFunTysMany :: [Type] -> Type -> Type mkVisFunTysMany :: [Type] -> Type -> Type mkVisFunTysMany [Type] tys Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Type -> Type -> Type mkVisFunTyMany Type ty [Type] tys mkInvisFunTysMany :: [Type] -> Type -> Type mkInvisFunTysMany :: [Type] -> Type -> Type mkInvisFunTysMany [Type] tys Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr Type -> Type -> Type mkInvisFunTyMany Type ty [Type] tys -- | Like 'mkTyCoForAllTy', but does not check the occurrence of the binder -- See Note [Unused coercion variable in ForAllTy] mkForAllTy :: TyCoVar -> ArgFlag -> Type -> Type mkForAllTy :: TyVar -> ArgFlag -> Type -> Type mkForAllTy TyVar tv ArgFlag vis Type ty = TyCoVarBinder -> Type -> Type ForAllTy (forall var argf. var -> argf -> VarBndr var argf Bndr TyVar tv ArgFlag vis) Type ty -- | Wraps foralls over the type using the provided 'TyCoVar's from left to right mkForAllTys :: [TyCoVarBinder] -> Type -> Type mkForAllTys :: [TyCoVarBinder] -> Type -> Type mkForAllTys [TyCoVarBinder] tyvars Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr TyCoVarBinder -> Type -> Type ForAllTy Type ty [TyCoVarBinder] tyvars -- | Wraps foralls over the type using the provided 'InvisTVBinder's from left to right mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type mkInvisForAllTys :: [InvisTVBinder] -> Type -> Type mkInvisForAllTys [InvisTVBinder] tyvars Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr TyCoVarBinder -> Type -> Type ForAllTy Type ty forall a b. (a -> b) -> a -> b $ forall a. [VarBndr a Specificity] -> [VarBndr a ArgFlag] tyVarSpecToBinders [InvisTVBinder] tyvars mkPiTy :: TyCoBinder -> Type -> Type mkPiTy :: TyCoBinder -> Type -> Type mkPiTy (Anon AnonArgFlag af Scaled Type ty1) Type ty2 = AnonArgFlag -> Scaled Type -> Type -> Type mkScaledFunTy AnonArgFlag af Scaled Type ty1 Type ty2 mkPiTy (Named (Bndr TyVar tv ArgFlag vis)) Type ty = TyVar -> ArgFlag -> Type -> Type mkForAllTy TyVar tv ArgFlag vis Type ty mkPiTys :: [TyCoBinder] -> Type -> Type mkPiTys :: [TyCoBinder] -> Type -> Type mkPiTys [TyCoBinder] tbs Type ty = forall (t :: * -> *) a b. Foldable t => (a -> b -> b) -> b -> t a -> b foldr TyCoBinder -> Type -> Type mkPiTy Type ty [TyCoBinder] tbs -- | Create a nullary 'TyConApp'. In general you should rather use -- 'GHC.Core.Type.mkTyConTy'. This merely exists to break the import cycle -- between 'GHC.Core.TyCon' and this module. mkTyConTy_ :: TyCon -> Type mkTyConTy_ :: TyCon -> Type mkTyConTy_ TyCon tycon = TyCon -> [Type] -> Type TyConApp TyCon tycon [] {- %************************************************************************ %* * Coercions %* * %************************************************************************ -} -- | A 'Coercion' is concrete evidence of the equality/convertibility -- of two types. -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in GHC.Core.Lint data Coercion -- Each constructor has a "role signature", indicating the way roles are -- propagated through coercions. -- - P, N, and R stand for coercions of the given role -- - e stands for a coercion of a specific unknown role -- (think "role polymorphism") -- - "e" stands for an explicit role parameter indicating role e. -- - _ stands for a parameter that is not a Role or Coercion. -- These ones mirror the shape of types = -- Refl :: _ -> N -- A special case reflexivity for a very common case: Nominal reflexivity -- If you need Representational, use (GRefl Representational ty MRefl) -- not (SubCo (Refl ty)) Refl Type -- See Note [Refl invariant] -- GRefl :: "e" -> _ -> Maybe N -> e -- See Note [Generalized reflexive coercion] | GRefl Role Type MCoercionN -- See Note [Refl invariant] -- Use (Refl ty), not (GRefl Nominal ty MRefl) -- Use (GRefl Representational _ _), not (SubCo (GRefl Nominal _ _)) -- These ones simply lift the correspondingly-named -- Type constructors into Coercions -- TyConAppCo :: "e" -> _ -> ?? -> e -- See Note [TyConAppCo roles] | TyConAppCo Role TyCon [Coercion] -- lift TyConApp -- The TyCon is never a synonym; -- we expand synonyms eagerly -- But it can be a type function -- TyCon is never a saturated (->); use FunCo instead | AppCo Coercion CoercionN -- lift AppTy -- AppCo :: e -> N -> e -- See Note [Forall coercions] | ForAllCo TyCoVar KindCoercion Coercion -- ForAllCo :: _ -> N -> e -> e | FunCo Role CoercionN Coercion Coercion -- lift FunTy -- FunCo :: "e" -> N -> e -> e -> e -- Note: why doesn't FunCo have a AnonArgFlag, like FunTy? -- Because the AnonArgFlag has no impact on Core; it is only -- there to guide implicit instantiation of Haskell source -- types, and that is irrelevant for coercions, which are -- Core-only. -- These are special | CoVarCo CoVar -- :: _ -> (N or R) -- result role depends on the tycon of the variable's type -- AxiomInstCo :: e -> _ -> ?? -> e | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion] -- See also [CoAxiom index] -- The coercion arguments always *precisely* saturate -- arity of (that branch of) the CoAxiom. If there are -- any left over, we use AppCo. -- See [Coercion axioms applied to coercions] -- The roles of the argument coercions are determined -- by the cab_roles field of the relevant branch of the CoAxiom | AxiomRuleCo CoAxiomRule [Coercion] -- AxiomRuleCo is very like AxiomInstCo, but for a CoAxiomRule -- The number coercions should match exactly the expectations -- of the CoAxiomRule (i.e., the rule is fully saturated). | UnivCo UnivCoProvenance Role Type Type -- :: _ -> "e" -> _ -> _ -> e | SymCo Coercion -- :: e -> e | TransCo Coercion Coercion -- :: e -> e -> e | NthCo Role Int Coercion -- Zero-indexed; decomposes (T t0 ... tn) -- :: "e" -> _ -> e0 -> e (inverse of TyConAppCo, see Note [TyConAppCo roles]) -- Using NthCo on a ForAllCo gives an N coercion always -- See Note [NthCo and newtypes] -- -- Invariant: (NthCo r i co), it is always the case that r = role of (Nth i co) -- That is: the role of the entire coercion is redundantly cached here. -- See Note [NthCo Cached Roles] | LRCo LeftOrRight CoercionN -- Decomposes (t_left t_right) -- :: _ -> N -> N | InstCo Coercion CoercionN -- :: e -> N -> e -- See Note [InstCo roles] -- Extract a kind coercion from a (heterogeneous) type coercion -- NB: all kind coercions are Nominal | KindCo Coercion -- :: e -> N | SubCo CoercionN -- Turns a ~N into a ~R -- :: N -> R | HoleCo CoercionHole -- ^ See Note [Coercion holes] -- Only present during typechecking deriving Typeable Coercion Coercion -> DataType Coercion -> Constr (forall b. Data b => b -> b) -> Coercion -> Coercion forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> Coercion -> u forall u. (forall d. Data d => d -> u) -> Coercion -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Coercion forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Coercion -> c Coercion forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Coercion) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Coercion) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Coercion -> m Coercion gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Coercion -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Coercion -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> Coercion -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> Coercion -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Coercion -> r gmapT :: (forall b. Data b => b -> b) -> Coercion -> Coercion $cgmapT :: (forall b. Data b => b -> b) -> Coercion -> Coercion dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Coercion) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Coercion) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Coercion) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Coercion) dataTypeOf :: Coercion -> DataType $cdataTypeOf :: Coercion -> DataType toConstr :: Coercion -> Constr $ctoConstr :: Coercion -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Coercion $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Coercion gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Coercion -> c Coercion $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Coercion -> c Coercion Data.Data type CoercionN = Coercion -- always nominal type CoercionR = Coercion -- always representational type CoercionP = Coercion -- always phantom type KindCoercion = CoercionN -- always nominal instance Outputable Coercion where ppr :: Coercion -> SDoc ppr = Coercion -> SDoc pprCo -- | A semantically more meaningful type to represent what may or may not be a -- useful 'Coercion'. data MCoercion = MRefl -- A trivial Reflexivity coercion | MCo Coercion -- Other coercions deriving Typeable MCoercion MCoercion -> DataType MCoercion -> Constr (forall b. Data b => b -> b) -> MCoercion -> MCoercion forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> MCoercion -> u forall u. (forall d. Data d => d -> u) -> MCoercion -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercion forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercion -> c MCoercion forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercion) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercion) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> MCoercion -> m MCoercion gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercion -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MCoercion -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercion -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> MCoercion -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MCoercion -> r gmapT :: (forall b. Data b => b -> b) -> MCoercion -> MCoercion $cgmapT :: (forall b. Data b => b -> b) -> MCoercion -> MCoercion dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercion) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MCoercion) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercion) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c MCoercion) dataTypeOf :: MCoercion -> DataType $cdataTypeOf :: MCoercion -> DataType toConstr :: MCoercion -> Constr $ctoConstr :: MCoercion -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercion $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c MCoercion gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercion -> c MCoercion $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MCoercion -> c MCoercion Data.Data type MCoercionR = MCoercion type MCoercionN = MCoercion instance Outputable MCoercion where ppr :: MCoercion -> SDoc ppr MCoercion MRefl = String -> SDoc text String "MRefl" ppr (MCo Coercion co) = String -> SDoc text String "MCo" SDoc -> SDoc -> SDoc <+> forall a. Outputable a => a -> SDoc ppr Coercion co {- Note [Refl invariant] ~~~~~~~~~~~~~~~~~~~~~~~~ Invariant 1: Refl lifting Refl (similar for GRefl r ty MRefl) is always lifted as far as possible. For example (Refl T) (Refl a) (Refl b) is normalised (by mkAPpCo) to (Refl (T a b)). You might think that a consequences is: Every identity coercion has Refl at the root But that's not quite true because of coercion variables. Consider g where g :: Int~Int Left h where h :: Maybe Int ~ Maybe Int etc. So the consequence is only true of coercions that have no coercion variables. Invariant 2: TyConAppCo An application of (Refl T) to some coercions, at least one of which is NOT the identity, is normalised to TyConAppCo. (They may not be fully saturated however.) TyConAppCo coercions (like all coercions other than Refl) are NEVER the identity. Note [Generalized reflexive coercion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ GRefl is a generalized reflexive coercion (see #15192). It wraps a kind coercion, which might be reflexive (MRefl) or any coercion (MCo co). The typing rules for GRefl: ty : k1 ------------------------------------ GRefl r ty MRefl: ty ~r ty ty : k1 co :: k1 ~ k2 ------------------------------------ GRefl r ty (MCo co) : ty ~r ty |> co Consider we have g1 :: s ~r t s :: k1 g2 :: k1 ~ k2 and we want to construct a coercions co which has type (s |> g2) ~r t We can define co = Sym (GRefl r s g2) ; g1 It is easy to see that Refl == GRefl Nominal ty MRefl :: ty ~n ty A nominal reflexive coercion is quite common, so we keep the special form Refl to save allocation. Note [Coercion axioms applied to coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The reason coercion axioms can be applied to coercions and not just types is to allow for better optimization. There are some cases where we need to be able to "push transitivity inside" an axiom in order to expose further opportunities for optimization. For example, suppose we have C a : t[a] ~ F a g : b ~ c and we want to optimize sym (C b) ; t[g] ; C c which has the kind F b ~ F c (stopping through t[b] and t[c] along the way). We'd like to optimize this to just F g -- but how? The key is that we need to allow axioms to be instantiated by *coercions*, not just by types. Then we can (in certain cases) push transitivity inside the axiom instantiations, and then react opposite-polarity instantiations of the same axiom. In this case, e.g., we match t[g] against the LHS of (C c)'s kind, to obtain the substitution a |-> g (note this operation is sort of the dual of lifting!) and hence end up with C g : t[b] ~ F c which indeed has the same kind as t[g] ; C c. Now we have sym (C b) ; C g which can be optimized to F g. Note [CoAxiom index] ~~~~~~~~~~~~~~~~~~~~ A CoAxiom has 1 or more branches. Each branch has contains a list of the free type variables in that branch, the LHS type patterns, and the RHS type for that branch. When we apply an axiom to a list of coercions, we must choose which branch of the axiom we wish to use, as the different branches may have different numbers of free type variables. (The number of type patterns is always the same among branches, but that doesn't quite concern us here.) The Int in the AxiomInstCo constructor is the 0-indexed number of the chosen branch. Note [Forall coercions] ~~~~~~~~~~~~~~~~~~~~~~~ Constructing coercions between forall-types can be a bit tricky, because the kinds of the bound tyvars can be different. The typing rule is: kind_co : k1 ~ k2 tv1:k1 |- co : t1 ~ t2 ------------------------------------------------------------------- ForAllCo tv1 kind_co co : all tv1:k1. t1 ~ all tv1:k2. (t2[tv1 |-> tv1 |> sym kind_co]) First, the TyCoVar stored in a ForAllCo is really an optimisation: this field should be a Name, as its kind is redundant. Thinking of the field as a Name is helpful in understanding what a ForAllCo means. The kind of TyCoVar always matches the left-hand kind of the coercion. The idea is that kind_co gives the two kinds of the tyvar. See how, in the conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right. Of course, a type variable can't have different kinds at the same time. So, we arbitrarily prefer the first kind when using tv1 in the inner coercion co, which shows that t1 equals t2. The last wrinkle is that we need to fix the kinds in the conclusion. In t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it mentions the same name with different kinds, but it *is* well-kinded, noting that `(tv1:k2) |> sym kind_co` has kind k1. This all really would work storing just a Name in the ForAllCo. But we can't add Names to, e.g., VarSets, and there generally is just an impedance mismatch in a bunch of places. So we use tv1. When we need tv2, we can use setTyVarKind. Note [Predicate coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have g :: a~b How can we coerce between types ([c]~a) => [a] -> c and ([c]~b) => [b] -> c where the equality predicate *itself* differs? Answer: we simply treat (~) as an ordinary type constructor, so these types really look like ((~) [c] a) -> [a] -> c ((~) [c] b) -> [b] -> c So the coercion between the two is obviously ((~) [c] g) -> [g] -> c Another way to see this to say that we simply collapse predicates to their representation type (see Type.coreView and Type.predTypeRep). This collapse is done by mkPredCo; there is no PredCo constructor in Coercion. This is important because we need Nth to work on predicates too: Nth 1 ((~) [c] g) = g See Simplify.simplCoercionF, which generates such selections. Note [Roles] ~~~~~~~~~~~~ Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated in #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see https://gitlab.haskell.org/ghc/ghc/wikis/roles-implementation Here is one way to phrase the problem: Given: newtype Age = MkAge Int type family F x type instance F Age = Bool type instance F Int = Char This compiles down to: axAge :: Age ~ Int axF1 :: F Age ~ Bool axF2 :: F Int ~ Char Then, we can make: (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char Yikes! The solution is _roles_, as articulated in "Generative Type Abstraction and Type-level Computation" (POPL 2010), available at http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf The specification for roles has evolved somewhat since that paper. For the current full details, see the documentation in docs/core-spec. Here are some highlights. We label every equality with a notion of type equivalence, of which there are three options: Nominal, Representational, and Phantom. A ground type is nominally equivalent only with itself. A newtype (which is considered a ground type in Haskell) is representationally equivalent to its representation. Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P" to denote the equivalences. The axioms above would be: axAge :: Age ~R Int axF1 :: F Age ~N Bool axF2 :: F Age ~N Char Then, because transitivity applies only to coercions proving the same notion of equivalence, the above construction is impossible. However, there is still an escape hatch: we know that any two types that are nominally equivalent are representationally equivalent as well. This is what the form SubCo proves -- it "demotes" a nominal equivalence into a representational equivalence. So, it would seem the following is possible: sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char -- WRONG What saves us here is that the arguments to a type function F, lifted into a coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and we are safe. Roles are attached to parameters to TyCons. When lifting a TyCon into a coercion (through TyConAppCo), we need to ensure that the arguments to the TyCon respect their roles. For example: data T a b = MkT a (F b) If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because the type function F branches on b's *name*, not representation. So, we say that 'a' has role Representational and 'b' has role Nominal. The third role, Phantom, is for parameters not used in the type's definition. Given the following definition data Q a = MkQ Int the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we can construct the coercion Bool ~P Char (using UnivCo). See the paper cited above for more examples and information. Note [TyConAppCo roles] ~~~~~~~~~~~~~~~~~~~~~~~ The TyConAppCo constructor has a role parameter, indicating the role at which the coercion proves equality. The choice of this parameter affects the required roles of the arguments of the TyConAppCo. To help explain it, assume the following definition: type instance F Int = Bool -- Axiom axF : F Int ~N Bool newtype Age = MkAge Int -- Axiom axAge : Age ~R Int data Foo a = MkFoo a -- Role on Foo's parameter is Representational TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool For (TyConAppCo Nominal) all arguments must have role Nominal. Why? So that Foo Age ~N Foo Int does *not* hold. TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool TyConAppCo Representational Foo axAge : Foo Age ~R Foo Int For (TyConAppCo Representational), all arguments must have the roles corresponding to the result of tyConRoles on the TyCon. This is the whole point of having roles on the TyCon to begin with. So, we can have Foo Age ~R Foo Int, if Foo's parameter has role R. If a Representational TyConAppCo is over-saturated (which is otherwise fine), the spill-over arguments must all be at Nominal. This corresponds to the behavior for AppCo. TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool All arguments must have role Phantom. This one isn't strictly necessary for soundness, but this choice removes ambiguity. The rules here dictate the roles of the parameters to mkTyConAppCo (should be checked by Lint). Note [NthCo and newtypes] ~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have newtype N a = MkN Int type role N representational This yields axiom NTCo:N :: forall a. N a ~R Int We can then build co :: forall a b. N a ~R N b co = NTCo:N a ; sym (NTCo:N b) for any `a` and `b`. Because of the role annotation on N, if we use NthCo, we'll get out a representational coercion. That is: NthCo r 0 co :: forall a b. a ~R b Yikes! Clearly, this is terrible. The solution is simple: forbid NthCo to be used on newtypes if the internal coercion is representational. This is not just some corner case discovered by a segfault somewhere; it was discovered in the proof of soundness of roles and described in the "Safe Coercions" paper (ICFP '14). Note [NthCo Cached Roles] ~~~~~~~~~~~~~~~~~~~~~~~~~ Why do we cache the role of NthCo in the NthCo constructor? Because computing role(Nth i co) involves figuring out that co :: T tys1 ~ T tys2 using coercionKind, and finding (coercionRole co), and then looking at the tyConRoles of T. Avoiding bad asymptotic behaviour here means we have to compute the kind and role of a coercion simultaneously, which makes the code complicated and inefficient. This only happens for NthCo. Caching the role solves the problem, and allows coercionKind and coercionRole to be simple. See #11735 Note [InstCo roles] ~~~~~~~~~~~~~~~~~~~ Here is (essentially) the typing rule for InstCo: g :: (forall a. t1) ~r (forall a. t2) w :: s1 ~N s2 ------------------------------- InstCo InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2]) Note that the Coercion w *must* be nominal. This is necessary because the variable a might be used in a "nominal position" (that is, a place where role inference would require a nominal role) in t1 or t2. If we allowed w to be representational, we could get bogus equalities. A more nuanced treatment might be able to relax this condition somewhat, by checking if t1 and/or t2 use their bound variables in nominal ways. If not, having w be representational is OK. %************************************************************************ %* * UnivCoProvenance %* * %************************************************************************ A UnivCo is a coercion whose proof does not directly express its role and kind (indeed for some UnivCos, like PluginProv, there /is/ no proof). The different kinds of UnivCo are described by UnivCoProvenance. Really each is entirely separate, but they all share the need to represent their role and kind, which is done in the UnivCo constructor. -} -- | For simplicity, we have just one UnivCo that represents a coercion from -- some type to some other type, with (in general) no restrictions on the -- type. The UnivCoProvenance specifies more exactly what the coercion really -- is and why a program should (or shouldn't!) trust the coercion. -- It is reasonable to consider each constructor of 'UnivCoProvenance' -- as a totally independent coercion form; their only commonality is -- that they don't tell you what types they coercion between. (That info -- is in the 'UnivCo' constructor of 'Coercion'. data UnivCoProvenance = PhantomProv KindCoercion -- ^ See Note [Phantom coercions]. Only in Phantom -- roled coercions | ProofIrrelProv KindCoercion -- ^ From the fact that any two coercions are -- considered equivalent. See Note [ProofIrrelProv]. -- Can be used in Nominal or Representational coercions | PluginProv String -- ^ From a plugin, which asserts that this coercion -- is sound. The string is for the use of the plugin. | CorePrepProv -- See Note [Unsafe coercions] in GHC.Core.CoreToStg.Prep Bool -- True <=> the UnivCo must be homogeneously kinded -- False <=> allow hetero-kinded, e.g. Int ~ Int# deriving Typeable UnivCoProvenance UnivCoProvenance -> DataType UnivCoProvenance -> Constr (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance $cgmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance $cgmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance $cgmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> UnivCoProvenance -> m UnivCoProvenance gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> UnivCoProvenance -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] $cgmapQ :: forall u. (forall d. Data d => d -> u) -> UnivCoProvenance -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r $cgmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r $cgmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> UnivCoProvenance -> r gmapT :: (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance $cgmapT :: (forall b. Data b => b -> b) -> UnivCoProvenance -> UnivCoProvenance dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c UnivCoProvenance) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) $cdataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c UnivCoProvenance) dataTypeOf :: UnivCoProvenance -> DataType $cdataTypeOf :: UnivCoProvenance -> DataType toConstr :: UnivCoProvenance -> Constr $ctoConstr :: UnivCoProvenance -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance $cgunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c UnivCoProvenance gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance $cgfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> UnivCoProvenance -> c UnivCoProvenance Data.Data instance Outputable UnivCoProvenance where ppr :: UnivCoProvenance -> SDoc ppr (PhantomProv Coercion _) = String -> SDoc text String "(phantom)" ppr (ProofIrrelProv Coercion _) = String -> SDoc text String "(proof irrel.)" ppr (PluginProv String str) = SDoc -> SDoc parens (String -> SDoc text String "plugin" SDoc -> SDoc -> SDoc <+> SDoc -> SDoc brackets (String -> SDoc text String str)) ppr (CorePrepProv Bool _) = String -> SDoc text String "(CorePrep)" -- | A coercion to be filled in by the type-checker. See Note [Coercion holes] data CoercionHole = CoercionHole { CoercionHole -> TyVar ch_co_var :: CoVar -- See Note [CoercionHoles and coercion free variables] , CoercionHole -> IORef (Maybe Coercion) ch_ref :: IORef (Maybe Coercion) } coHoleCoVar :: CoercionHole -> CoVar coHoleCoVar :: CoercionHole -> TyVar coHoleCoVar = CoercionHole -> TyVar ch_co_var setCoHoleCoVar :: CoercionHole -> CoVar -> CoercionHole setCoHoleCoVar :: CoercionHole -> TyVar -> CoercionHole setCoHoleCoVar CoercionHole h TyVar cv = CoercionHole h { ch_co_var :: TyVar ch_co_var = TyVar cv } instance Data.Data CoercionHole where -- don't traverse? toConstr :: CoercionHole -> Constr toConstr CoercionHole _ = String -> Constr abstractConstr String "CoercionHole" gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CoercionHole gunfold forall b r. Data b => c (b -> r) -> c r _ forall r. r -> c r _ = forall a. HasCallStack => String -> a error String "gunfold" dataTypeOf :: CoercionHole -> DataType dataTypeOf CoercionHole _ = String -> DataType mkNoRepType String "CoercionHole" instance Outputable CoercionHole where ppr :: CoercionHole -> SDoc ppr (CoercionHole { ch_co_var :: CoercionHole -> TyVar ch_co_var = TyVar cv }) = SDoc -> SDoc braces (forall a. Outputable a => a -> SDoc ppr TyVar cv) instance Uniquable CoercionHole where getUnique :: CoercionHole -> Unique getUnique (CoercionHole { ch_co_var :: CoercionHole -> TyVar ch_co_var = TyVar cv }) = forall a. Uniquable a => a -> Unique getUnique TyVar cv {- Note [Phantom coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider data T a = T1 | T2 Then we have T s ~R T t for any old s,t. The witness for this is (TyConAppCo T Rep co), where (co :: s ~P t) is a phantom coercion built with PhantomProv. The role of the UnivCo is always Phantom. The Coercion stored is the (nominal) kind coercion between the types kind(s) ~N kind (t) Note [Coercion holes] ~~~~~~~~~~~~~~~~~~~~~~~~ During typechecking, constraint solving for type classes works by - Generate an evidence Id, d7 :: Num a - Wrap it in a Wanted constraint, [W] d7 :: Num a - Use the evidence Id where the evidence is needed - Solve the constraint later - When solved, add an enclosing let-binding let d7 = .... in .... which actually binds d7 to the (Num a) evidence For equality constraints we use a different strategy. See Note [The equality types story] in GHC.Builtin.Types.Prim for background on equality constraints. - For /boxed/ equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just like type classes above. (Indeed, boxed equality constraints *are* classes.) - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2) we use a different plan For unboxed equalities: - Generate a CoercionHole, a mutable variable just like a unification variable - Wrap the CoercionHole in a Wanted constraint; see GHC.Tc.Utils.TcEvDest - Use the CoercionHole in a Coercion, via HoleCo - Solve the constraint later - When solved, fill in the CoercionHole by side effect, instead of doing the let-binding thing The main reason for all this is that there may be no good place to let-bind the evidence for unboxed equalities: - We emit constraints for kind coercions, to be used to cast a type's kind. These coercions then must be used in types. Because they might appear in a top-level type, there is no place to bind these (unlifted) coercions in the usual way. - A coercion for (forall a. t1) ~ (forall a. t2) will look like forall a. (coercion for t1~t2) But the coercion for (t1~t2) may mention 'a', and we don't have let-bindings within coercions. We could add them, but coercion holes are easier. - Moreover, nothing is lost from the lack of let-bindings. For dictionaries want to achieve sharing to avoid recomoputing the dictionary. But coercions are entirely erased, so there's little benefit to sharing. Indeed, even if we had a let-binding, we always inline types and coercions at every use site and drop the binding. Other notes about HoleCo: * INVARIANT: CoercionHole and HoleCo are used only during type checking, and should never appear in Core. Just like unification variables; a Type can contain a TcTyVar, but only during type checking. If, one day, we use type-level information to separate out forms that can appear during type-checking vs forms that can appear in core proper, holes in Core will be ruled out. * See Note [CoercionHoles and coercion free variables] * Coercion holes can be compared for equality like other coercions: by looking at the types coerced. Note [CoercionHoles and coercion free variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Why does a CoercionHole contain a CoVar, as well as reference to fill in? Because we want to treat that CoVar as a free variable of the coercion. See #14584, and Note [What prevents a constraint from floating] in GHC.Tc.Solver, item (4): forall k. [W] co1 :: t1 ~# t2 |> co2 [W] co2 :: k ~# * Here co2 is a CoercionHole. But we /must/ know that it is free in co1, because that's all that stops it floating outside the implication. Note [ProofIrrelProv] ~~~~~~~~~~~~~~~~~~~~~ A ProofIrrelProv is a coercion between coercions. For example: data G a where MkG :: G Bool In core, we get G :: * -> * MkG :: forall (a :: *). (a ~ Bool) -> G a Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want a proof that ('MkG a1 co1) ~ ('MkG a2 co2). This will have to be TyConAppCo Nominal MkG [co3, co4] where co3 :: co1 ~ co2 co4 :: a1 ~ a2 Note that co1 :: a1 ~ Bool co2 :: a2 ~ Bool Here, co3 = UnivCo (ProofIrrelProv co5) Nominal (CoercionTy co1) (CoercionTy co2) where co5 :: (a1 ~ Bool) ~ (a2 ~ Bool) co5 = TyConAppCo Nominal (~#) [<*>, <*>, co4, <Bool>] -} {- ********************************************************************* * * foldType and foldCoercion * * ********************************************************************* -} {- Note [foldType] ~~~~~~~~~~~~~~~~~~ foldType is a bit more powerful than perhaps it looks: * You can fold with an accumulating parameter, via TyCoFolder env (Endo a) Recall newtype Endo a = Endo (a->a) * You can fold monadically with a monad M, via TyCoFolder env (M a) provided you have instance .. => Monoid (M a) Note [mapType vs foldType] ~~~~~~~~~~~~~~~~~~~~~~~~~~ We define foldType here, but mapType in module Type. Why? * foldType is used in GHC.Core.TyCo.FVs for finding free variables. It's a very simple function that analyses a type, but does not construct one. * mapType constructs new types, and so it needs to call the "smart constructors", mkAppTy, mkCastTy, and so on. These are sophisticated functions, and can't be defined here in GHC.Core.TyCo.Rep. Note [Specialising foldType] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We inline foldType at every call site (there are not many), so that it becomes specialised for the particular monoid *and* TyCoFolder at that site. This is just for efficiency, but walking over types is done a *lot* in GHC, so worth optimising. We were worried that TyCoFolder env (Endo a) might not eta-expand. Recall newtype Endo a = Endo (a->a). In particular, given fvs :: Type -> TyCoVarSet fvs ty = appEndo (foldType tcf emptyVarSet ty) emptyVarSet tcf :: TyCoFolder enf (Endo a) tcf = TyCoFolder { tcf_tyvar = do_tv, ... } where do_tvs is tv = Endo do_it where do_it acc | tv `elemVarSet` is = acc | tv `elemVarSet` acc = acc | otherwise = acc `extendVarSet` tv we want to end up with fvs ty = go emptyVarSet ty emptyVarSet where go env (TyVarTy tv) acc = acc `extendVarSet` tv ..etc.. And indeed this happens. - Selections from 'tcf' are done at compile time - 'go' is nicely eta-expanded. We were also worried about deep_fvs :: Type -> TyCoVarSet deep_fvs ty = appEndo (foldType deep_tcf emptyVarSet ty) emptyVarSet deep_tcf :: TyCoFolder enf (Endo a) deep_tcf = TyCoFolder { tcf_tyvar = do_tv, ... } where do_tvs is tv = Endo do_it where do_it acc | tv `elemVarSet` is = acc | tv `elemVarSet` acc = acc | otherwise = deep_fvs (varType tv) `unionVarSet` acc `extendVarSet` tv Here deep_fvs and deep_tcf are mutually recursive, unlike fvs and tcf. But, amazingly, we get good code here too. GHC is careful not to makr TyCoFolder data constructor for deep_tcf as a loop breaker, so the record selections still cancel. And eta expansion still happens too. -} data TyCoFolder env a = TyCoFolder { forall env a. TyCoFolder env a -> Type -> Maybe Type tcf_view :: Type -> Maybe Type -- Optional "view" function -- E.g. expand synonyms , forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_tyvar :: env -> TyVar -> a , forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_covar :: env -> CoVar -> a , forall env a. TyCoFolder env a -> env -> CoercionHole -> a tcf_hole :: env -> CoercionHole -> a -- ^ What to do with coercion holes. -- See Note [Coercion holes] in "GHC.Core.TyCo.Rep". , forall env a. TyCoFolder env a -> env -> TyVar -> ArgFlag -> env tcf_tycobinder :: env -> TyCoVar -> ArgFlag -> env -- ^ The returned env is used in the extended scope } {-# INLINE foldTyCo #-} -- See Note [Specialising foldType] foldTyCo :: Monoid a => TyCoFolder env a -> env -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a) foldTyCo :: forall a env. Monoid a => TyCoFolder env a -> env -> (Type -> a, [Type] -> a, Coercion -> a, [Coercion] -> a) foldTyCo (TyCoFolder { tcf_view :: forall env a. TyCoFolder env a -> Type -> Maybe Type tcf_view = Type -> Maybe Type view , tcf_tyvar :: forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_tyvar = env -> TyVar -> a tyvar , tcf_tycobinder :: forall env a. TyCoFolder env a -> env -> TyVar -> ArgFlag -> env tcf_tycobinder = env -> TyVar -> ArgFlag -> env tycobinder , tcf_covar :: forall env a. TyCoFolder env a -> env -> TyVar -> a tcf_covar = env -> TyVar -> a covar , tcf_hole :: forall env a. TyCoFolder env a -> env -> CoercionHole -> a tcf_hole = env -> CoercionHole -> a cohole }) env env = (env -> Type -> a go_ty env env, env -> [Type] -> a go_tys env env, env -> Coercion -> a go_co env env, env -> [Coercion] -> a go_cos env env) where go_ty :: env -> Type -> a go_ty env env Type ty | Just Type ty' <- Type -> Maybe Type view Type ty = env -> Type -> a go_ty env env Type ty' go_ty env env (TyVarTy TyVar tv) = env -> TyVar -> a tyvar env env TyVar tv go_ty env env (AppTy Type t1 Type t2) = env -> Type -> a go_ty env env Type t1 forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env Type t2 go_ty env _ (LitTy {}) = forall a. Monoid a => a mempty go_ty env env (CastTy Type ty Coercion co) = env -> Type -> a go_ty env env Type ty forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion co go_ty env env (CoercionTy Coercion co) = env -> Coercion -> a go_co env env Coercion co go_ty env env (FunTy AnonArgFlag _ Type w Type arg Type res) = env -> Type -> a go_ty env env Type w forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env Type arg forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env Type res go_ty env env (TyConApp TyCon _ [Type] tys) = env -> [Type] -> a go_tys env env [Type] tys go_ty env env (ForAllTy (Bndr TyVar tv ArgFlag vis) Type inner) = let !env' :: env env' = env -> TyVar -> ArgFlag -> env tycobinder env env TyVar tv ArgFlag vis -- Avoid building a thunk here in env -> Type -> a go_ty env env (TyVar -> Type varType TyVar tv) forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env' Type inner -- Explicit recursion because using foldr builds a local -- loop (with env free) and I'm not confident it'll be -- lambda lifted in the end go_tys :: env -> [Type] -> a go_tys env _ [] = forall a. Monoid a => a mempty go_tys env env (Type t:[Type] ts) = env -> Type -> a go_ty env env Type t forall a. Monoid a => a -> a -> a `mappend` env -> [Type] -> a go_tys env env [Type] ts go_cos :: env -> [Coercion] -> a go_cos env _ [] = forall a. Monoid a => a mempty go_cos env env (Coercion c:[Coercion] cs) = env -> Coercion -> a go_co env env Coercion c forall a. Monoid a => a -> a -> a `mappend` env -> [Coercion] -> a go_cos env env [Coercion] cs go_co :: env -> Coercion -> a go_co env env (Refl Type ty) = env -> Type -> a go_ty env env Type ty go_co env env (GRefl Role _ Type ty MCoercion MRefl) = env -> Type -> a go_ty env env Type ty go_co env env (GRefl Role _ Type ty (MCo Coercion co)) = env -> Type -> a go_ty env env Type ty forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion co go_co env env (TyConAppCo Role _ TyCon _ [Coercion] args) = env -> [Coercion] -> a go_cos env env [Coercion] args go_co env env (AppCo Coercion c1 Coercion c2) = env -> Coercion -> a go_co env env Coercion c1 forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion c2 go_co env env (FunCo Role _ Coercion cw Coercion c1 Coercion c2) = env -> Coercion -> a go_co env env Coercion cw forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion c1 forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion c2 go_co env env (CoVarCo TyVar cv) = env -> TyVar -> a covar env env TyVar cv go_co env env (AxiomInstCo CoAxiom Branched _ Int _ [Coercion] args) = env -> [Coercion] -> a go_cos env env [Coercion] args go_co env env (HoleCo CoercionHole hole) = env -> CoercionHole -> a cohole env env CoercionHole hole go_co env env (UnivCo UnivCoProvenance p Role _ Type t1 Type t2) = env -> UnivCoProvenance -> a go_prov env env UnivCoProvenance p forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env Type t1 forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env Type t2 go_co env env (SymCo Coercion co) = env -> Coercion -> a go_co env env Coercion co go_co env env (TransCo Coercion c1 Coercion c2) = env -> Coercion -> a go_co env env Coercion c1 forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion c2 go_co env env (AxiomRuleCo CoAxiomRule _ [Coercion] cos) = env -> [Coercion] -> a go_cos env env [Coercion] cos go_co env env (NthCo Role _ Int _ Coercion co) = env -> Coercion -> a go_co env env Coercion co go_co env env (LRCo LeftOrRight _ Coercion co) = env -> Coercion -> a go_co env env Coercion co go_co env env (InstCo Coercion co Coercion arg) = env -> Coercion -> a go_co env env Coercion co forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env Coercion arg go_co env env (KindCo Coercion co) = env -> Coercion -> a go_co env env Coercion co go_co env env (SubCo Coercion co) = env -> Coercion -> a go_co env env Coercion co go_co env env (ForAllCo TyVar tv Coercion kind_co Coercion co) = env -> Coercion -> a go_co env env Coercion kind_co forall a. Monoid a => a -> a -> a `mappend` env -> Type -> a go_ty env env (TyVar -> Type varType TyVar tv) forall a. Monoid a => a -> a -> a `mappend` env -> Coercion -> a go_co env env' Coercion co where env' :: env env' = env -> TyVar -> ArgFlag -> env tycobinder env env TyVar tv ArgFlag Inferred go_prov :: env -> UnivCoProvenance -> a go_prov env env (PhantomProv Coercion co) = env -> Coercion -> a go_co env env Coercion co go_prov env env (ProofIrrelProv Coercion co) = env -> Coercion -> a go_co env env Coercion co go_prov env _ (PluginProv String _) = forall a. Monoid a => a mempty go_prov env _ (CorePrepProv Bool _) = forall a. Monoid a => a mempty {- ********************************************************************* * * typeSize, coercionSize * * ********************************************************************* -} -- NB: We put typeSize/coercionSize here because they are mutually -- recursive, and have the CPR property. If we have mutual -- recursion across a hi-boot file, we don't get the CPR property -- and these functions allocate a tremendous amount of rubbish. -- It's not critical (because typeSize is really only used in -- debug mode, but I tripped over an example (T5642) in which -- typeSize was one of the biggest single allocators in all of GHC. -- And it's easy to fix, so I did. -- NB: typeSize does not respect `eqType`, in that two types that -- are `eqType` may return different sizes. This is OK, because this -- function is used only in reporting, not decision-making. typeSize :: Type -> Int typeSize :: Type -> Int typeSize (LitTy {}) = Int 1 typeSize (TyVarTy {}) = Int 1 typeSize (AppTy Type t1 Type t2) = Type -> Int typeSize Type t1 forall a. Num a => a -> a -> a + Type -> Int typeSize Type t2 typeSize (FunTy AnonArgFlag _ Type _ Type t1 Type t2) = Type -> Int typeSize Type t1 forall a. Num a => a -> a -> a + Type -> Int typeSize Type t2 typeSize (ForAllTy (Bndr TyVar tv ArgFlag _) Type t) = Type -> Int typeSize (TyVar -> Type varType TyVar tv) forall a. Num a => a -> a -> a + Type -> Int typeSize Type t typeSize (TyConApp TyCon _ [Type] ts) = Int 1 forall a. Num a => a -> a -> a + forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum (forall a b. (a -> b) -> [a] -> [b] map Type -> Int typeSize [Type] ts) typeSize (CastTy Type ty Coercion co) = Type -> Int typeSize Type ty forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co typeSize (CoercionTy Coercion co) = Coercion -> Int coercionSize Coercion co coercionSize :: Coercion -> Int coercionSize :: Coercion -> Int coercionSize (Refl Type ty) = Type -> Int typeSize Type ty coercionSize (GRefl Role _ Type ty MCoercion MRefl) = Type -> Int typeSize Type ty coercionSize (GRefl Role _ Type ty (MCo Coercion co)) = Int 1 forall a. Num a => a -> a -> a + Type -> Int typeSize Type ty forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (TyConAppCo Role _ TyCon _ [Coercion] args) = Int 1 forall a. Num a => a -> a -> a + forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum (forall a b. (a -> b) -> [a] -> [b] map Coercion -> Int coercionSize [Coercion] args) coercionSize (AppCo Coercion co Coercion arg) = Coercion -> Int coercionSize Coercion co forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion arg coercionSize (ForAllCo TyVar _ Coercion h Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion h coercionSize (FunCo Role _ Coercion w Coercion co1 Coercion co2) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co2 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion w coercionSize (CoVarCo TyVar _) = Int 1 coercionSize (HoleCo CoercionHole _) = Int 1 coercionSize (AxiomInstCo CoAxiom Branched _ Int _ [Coercion] args) = Int 1 forall a. Num a => a -> a -> a + forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum (forall a b. (a -> b) -> [a] -> [b] map Coercion -> Int coercionSize [Coercion] args) coercionSize (UnivCo UnivCoProvenance p Role _ Type t1 Type t2) = Int 1 forall a. Num a => a -> a -> a + UnivCoProvenance -> Int provSize UnivCoProvenance p forall a. Num a => a -> a -> a + Type -> Int typeSize Type t1 forall a. Num a => a -> a -> a + Type -> Int typeSize Type t2 coercionSize (SymCo Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (TransCo Coercion co1 Coercion co2) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co2 coercionSize (NthCo Role _ Int _ Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (LRCo LeftOrRight _ Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (InstCo Coercion co Coercion arg) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion arg coercionSize (KindCo Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (SubCo Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co coercionSize (AxiomRuleCo CoAxiomRule _ [Coercion] cs) = Int 1 forall a. Num a => a -> a -> a + forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a sum (forall a b. (a -> b) -> [a] -> [b] map Coercion -> Int coercionSize [Coercion] cs) provSize :: UnivCoProvenance -> Int provSize :: UnivCoProvenance -> Int provSize (PhantomProv Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co provSize (ProofIrrelProv Coercion co) = Int 1 forall a. Num a => a -> a -> a + Coercion -> Int coercionSize Coercion co provSize (PluginProv String _) = Int 1 provSize (CorePrepProv Bool _) = Int 1 {- ************************************************************************ * * Multiplicities * * ************************************************************************ These definitions are here to avoid module loops, and to keep GHC.Core.Multiplicity above this module. -} -- | A shorthand for data with an attached 'Mult' element (the multiplicity). data Scaled a = Scaled !Mult a deriving (Scaled a -> DataType Scaled a -> Constr forall {a}. Data a => Typeable (Scaled a) forall a. Data a => Scaled a -> DataType forall a. Data a => Scaled a -> Constr forall a. Data a => (forall b. Data b => b -> b) -> Scaled a -> Scaled a forall a u. Data a => Int -> (forall d. Data d => d -> u) -> Scaled a -> u forall a u. Data a => (forall d. Data d => d -> u) -> Scaled a -> [u] forall a r r'. Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall a r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r forall a (m :: * -> *). (Data a, Monad m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) forall a (c :: * -> *). Data a => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) forall a (c :: * -> *). Data a => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) forall a (t :: * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) forall a (t :: * -> * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) $cgmapMo :: forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) $cgmapMp :: forall a (m :: * -> *). (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) $cgmapM :: forall a (m :: * -> *). (Data a, Monad m) => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Scaled a -> u $cgmapQi :: forall a u. Data a => Int -> (forall d. Data d => d -> u) -> Scaled a -> u gmapQ :: forall u. (forall d. Data d => d -> u) -> Scaled a -> [u] $cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> Scaled a -> [u] gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r $cgmapQr :: forall a r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r $cgmapQl :: forall a r r'. Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r gmapT :: (forall b. Data b => b -> b) -> Scaled a -> Scaled a $cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> Scaled a -> Scaled a dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) $cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) $cdataCast1 :: forall a (t :: * -> *) (c :: * -> *). (Data a, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) dataTypeOf :: Scaled a -> DataType $cdataTypeOf :: forall a. Data a => Scaled a -> DataType toConstr :: Scaled a -> Constr $ctoConstr :: forall a. Data a => Scaled a -> Constr gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) $cgunfold :: forall a (c :: * -> *). Data a => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) $cgfoldl :: forall a (c :: * -> *). Data a => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) Data.Data) -- You might think that this would be a natural candidate for -- Functor, Traversable but Krzysztof says (!3674) "it was too easy -- to accidentally lift functions (substitutions, zonking etc.) from -- Type -> Type to Scaled Type -> Scaled Type, ignoring -- multiplicities and causing bugs". So we don't. -- -- Being strict in a is worse for performance, so we are only strict on the -- Mult part of scaled. instance (Outputable a) => Outputable (Scaled a) where ppr :: Scaled a -> SDoc ppr (Scaled Type _cnt a t) = forall a. Outputable a => a -> SDoc ppr a t -- Do not print the multiplicity here because it tends to be too verbose scaledMult :: Scaled a -> Mult scaledMult :: forall a. Scaled a -> Type scaledMult (Scaled Type m a _) = Type m scaledThing :: Scaled a -> a scaledThing :: forall a. Scaled a -> a scaledThing (Scaled Type _ a t) = a t -- | Apply a function to both the Mult and the Type in a 'Scaled Type' mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type mapScaledType Type -> Type f (Scaled Type m Type t) = forall a. Type -> a -> Scaled a Scaled (Type -> Type f Type m) (Type -> Type f Type t) {- | Mult is a type alias for Type. Mult must contain Type because multiplicity variables are mere type variables (of kind Multiplicity) in Haskell. So the simplest implementation is to make Mult be Type. Multiplicities can be formed with: - One: GHC.Types.One (= oneDataCon) - Many: GHC.Types.Many (= manyDataCon) - Multiplication: GHC.Types.MultMul (= multMulTyCon) So that Mult feels a bit more structured, we provide pattern synonyms and smart constructors for these. -} type Mult = Type