+%
+% (c) The University of Glasgow 2006
+%
- Module for type coercions, as in System FC.
+Module for type coercions, as in System FC.
Coercions are represented as types, and their kinds tell what types the
coercion works on.
typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
\begin{code}
+{-# OPTIONS -w #-}
+-- The above warning supression flag is a temporary kludge.
+-- While working on this module you are encouraged to remove it and fix
+-- any warnings in the module. See
+-- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
+-- for details
+
module Coercion (
Coercion,
isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
-- Coercion transformations
+ mkCoercion,
mkSymCoercion, mkTransCoercion,
- mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion,
+ mkLeftCoercion, mkRightCoercion, mkRightCoercions,
+ mkInstCoercion, mkAppCoercion,
mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
- mkNewTypeCoercion, mkDataInstCoercion, mkAppsCoercion,
+ mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
- splitNewTypeRepCo_maybe, decomposeCo,
+ splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
unsafeCoercionTyCon, symCoercionTyCon,
transCoercionTyCon, leftCoercionTyCon,
- rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn
+ rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
+
+ -- CoercionI
+ CoercionI(..),
+ isIdentityCoercion,
+ mkSymCoI, mkTransCoI,
+ mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI,
+ mkNoteTyCoI, mkForAllTyCoI,
+ fromCoI, fromACo,
+ mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI
+
) where
#include "HsVersions.h"
import TypeRep
-import Type ( Type, Kind, PredType, substTyWith, mkAppTy, mkForAllTy,
- mkFunTy, splitAppTy_maybe, splitForAllTy_maybe, coreView,
- kindView, mkTyConApp, isCoercionKind, isEqPred, mkAppTys,
- coreEqType, splitAppTys, isTyVarTy, splitTyConApp_maybe
- )
-import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isClosedNewTyCon,
- newTyConRhs, newTyConCo_maybe,
- isCoercionTyCon, isCoercionTyCon_maybe )
-import Var ( Var, TyVar, isTyVar, tyVarKind )
-import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName )
-import OccName ( mkOccNameFS )
-import PrelNames ( symCoercionTyConKey,
- transCoercionTyConKey, leftCoercionTyConKey,
- rightCoercionTyConKey, instCoercionTyConKey,
- unsafeCoercionTyConKey, gHC_PRIM
- )
-import Util ( lengthIs, snocView )
-import Unique ( hasKey )
-import BasicTypes ( Arity )
+import Type
+import TyCon
+import Class
+import Var
+import Name
+import OccName
+import PrelNames
+import Util
+import Unique
+import BasicTypes
import Outputable
+type Coercion = Type
+type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
------------------------------
decomposeCo :: Arity -> Coercion -> [Coercion]
splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
splitCoercionKind_maybe other = Nothing
-isCoVar :: Var -> Bool
-isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)
-
-type Coercion = Type
-type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
-
coercionKind :: Coercion -> (Type, Type)
-- c :: (t1 :=: t2)
-- Then (coercionKind c) = (t1,t2)
-coercionKind (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
- | otherwise = let t = (TyVarTy a) in (t, t)
+coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
+ | otherwise = (ty, ty)
coercionKind (AppTy ty1 ty2)
= let (t1, t2) = coercionKind ty1
(s1, s2) = coercionKind ty2 in
coercionKind (TyConApp tc args)
| Just (ar, rule) <- isCoercionTyCon_maybe tc
-- CoercionTyCons carry their kinding rule, so we use it here
- = if length args >= ar
- then splitCoercionKind (rule args)
- else pprPanic ("arity/arguments mismatch in coercionKind:")
- (ppr ar $$ ppr tc <+> ppr args)
+ = ASSERT( length args >= ar ) -- Always saturated
+ let (ty1,ty2) = rule (take ar args) -- Apply the rule to the right number of args
+ (tys1, tys2) = coercionKinds (drop ar args)
+ in (mkAppTys ty1 tys1, mkAppTys ty2 tys2)
+
| otherwise
= let (lArgs, rArgs) = coercionKinds args in
(TyConApp tc lArgs, TyConApp tc rArgs)
mkFunCoercion co1 co2 = mkFunTy co1 co2
+-------------------------------
-- This smart constructor creates a sym'ed version its argument,
-- but tries to push the sym's down to the leaves. If we come to
-- sym tv or sym tycon then we can drop the sym because tv and tycon
-- are reflexive coercions
mkSymCoercion co
- | Just co2 <- splitSymCoercion_maybe co = co2
- -- sym (sym co) --> co
- | Just (co1, arg_tys) <- splitTyConApp_maybe co
- , not (isCoercionTyCon co1) = mkTyConApp co1 (map mkSymCoercion arg_tys)
- -- we can drop the sym for a TyCon
- -- sym (ty [t1, ..., tn]) --> ty [sym t1, ..., sym tn]
- | (co1, arg_tys) <- splitAppTys co
- , isTyVarTy co1 = mkAppTys (maybe_drop co1) (map mkSymCoercion arg_tys)
- -- sym (tv [t1, ..., tn]) --> tv [sym t1, ..., sym tn]
- -- if tv type variable
- -- sym (cv [t1, ..., tn]) --> (sym cv) [sym t1, ..., sym tn]
- -- if cv is a coercion variable
- -- fall through if head is a CoercionTyCon
- | Just (co1, co2) <- splitTransCoercion_maybe co
+ | Just co' <- coreView co = mkSymCoercion co'
+
+mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
+mkSymCoercion (AppTy co1 co2) = AppTy (mkSymCoercion co1) (mkSymCoercion co2)
+mkSymCoercion (FunTy co1 co2) = FunTy (mkSymCoercion co1) (mkSymCoercion co2)
+
+mkSymCoercion (TyConApp tc cos)
+ | not (isCoercionTyCon tc) = mkTyConApp tc (map mkSymCoercion cos)
+
+mkSymCoercion (TyConApp tc [co])
+ | tc `hasKey` symCoercionTyConKey = co -- sym (sym co) --> co
+ | tc `hasKey` leftCoercionTyConKey = mkLeftCoercion (mkSymCoercion co)
+ | tc `hasKey` rightCoercionTyConKey = mkRightCoercion (mkSymCoercion co)
+
+mkSymCoercion (TyConApp tc [co1,co2])
+ | tc `hasKey` transCoercionTyConKey
-- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2)
+ -- Note reversal of arguments!
= mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
- | Just (co, ty) <- splitInstCoercion_maybe co
+
+ | tc `hasKey` instCoercionTyConKey
-- sym (co @ ty) --> (sym co) @ ty
- = mkInstCoercion (mkSymCoercion co) ty
- | Just co <- splitLeftCoercion_maybe co
- -- sym (left co) --> left (sym co)
- = mkLeftCoercion (mkSymCoercion co)
- | Just co <- splitRightCoercion_maybe co
- -- sym (right co) --> right (sym co)
- = mkRightCoercion (mkSymCoercion co)
- where
- maybe_drop (TyVarTy tv)
- | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
- | otherwise = TyVarTy tv
- maybe_drop other = other
-mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
--- for atomic types and constructors, we can just ignore sym since these
--- are reflexive coercions
+ -- Note: sym is not applied to 'ty'
+ = mkInstCoercion (mkSymCoercion co1) co2
+
+mkSymCoercion (TyConApp tc cos) -- Other coercion tycons, such as those
+ = mkCoercion symCoercionTyCon [TyConApp tc cos] -- arising from newtypes
+
mkSymCoercion (TyVarTy tv)
| isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
- | otherwise = TyVarTy tv
-mkSymCoercion co = mkCoercion symCoercionTyCon [co]
+ | otherwise = TyVarTy tv -- Reflexive
+-------------------------------
+-- ToDo: we should be cleverer about transitivity
+mkTransCoercion g1 g2 -- sym g `trans` g = id
+ | (t1,_) <- coercionKind g1
+ , (_,t2) <- coercionKind g2
+ , t1 `coreEqType` t2
+ = t1
+
+ | otherwise
+ = mkCoercion transCoercionTyCon [g1, g2]
+
+
+-------------------------------
-- Smart constructors for left and right
mkLeftCoercion co
| Just (co', _) <- splitAppCoercion_maybe co = co'
- | otherwise = mkCoercion leftCoercionTyCon [co]
+ | otherwise = mkCoercion leftCoercionTyCon [co]
mkRightCoercion co
| Just (co1, co2) <- splitAppCoercion_maybe co = co2
| otherwise = mkCoercion rightCoercionTyCon [co]
-mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]
-
-mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
+mkRightCoercions n co
+ = go n co []
+ where
+ go n co acc
+ | n > 0
+ = case splitAppCoercion_maybe co of
+ Just (co1,co2) -> go (n-1) co1 (co2:acc)
+ Nothing -> go (n-1) (mkCoercion leftCoercionTyCon [co]) (mkCoercion rightCoercionTyCon [co]:acc)
+ | otherwise
+ = acc
+
+mkInstCoercion co ty
+ | Just (tv,co') <- splitForAllTy_maybe co
+ = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a]
+ | otherwise
+ = mkCoercion instCoercionTyCon [co, ty]
mkInstsCoercion co tys = foldl mkInstCoercion co tys
-- See note [Newtype coercions] in TyCon
-mkNewTypeCoercion :: Name -> TyCon -> ([TyVar], Type) -> TyCon
-mkNewTypeCoercion name tycon (tvs, rhs_ty)
- = mkCoercionTyCon name co_con_arity (mkKindingFun rule)
+mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
+mkNewTypeCoercion name tycon tvs rhs_ty
+ = mkCoercionTyCon name co_con_arity rule
where
co_con_arity = length tvs
- rule args = (TyConApp tycon tys, substTyWith tvs tys rhs_ty, rest)
- where
- tys = take co_con_arity args
- rest = drop co_con_arity args
+ rule args = ASSERT( co_con_arity == length args )
+ (TyConApp tycon args, substTyWith tvs args rhs_ty)
--- Coercion identifying a data/newtype representation type and its family
--- instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is the
--- coercion tycon built here, `F' the family tycon and `R' the (derived)
+-- Coercion identifying a data/newtype/synonym representation type and its
+-- family instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is
+-- the coercion tycon built here, `F' the family tycon and `R' the (derived)
-- representation tycon.
--
-mkDataInstCoercion :: Name -- unique name for the coercion tycon
- -> [TyVar] -- type parameters of the coercion (`tvs')
- -> TyCon -- family tycon (`F')
- -> [Type] -- type instance (`ts')
- -> TyCon -- representation tycon (`R')
- -> TyCon -- => coercion tycon (`Co')
-mkDataInstCoercion name tvs family instTys rep_tycon
- = mkCoercionTyCon name coArity (mkKindingFun rule)
+mkFamInstCoercion :: Name -- unique name for the coercion tycon
+ -> [TyVar] -- type parameters of the coercion (`tvs')
+ -> TyCon -- family tycon (`F')
+ -> [Type] -- type instance (`ts')
+ -> TyCon -- representation tycon (`R')
+ -> TyCon -- => coercion tycon (`Co')
+mkFamInstCoercion name tvs family instTys rep_tycon
+ = mkCoercionTyCon name coArity rule
where
coArity = length tvs
-
- rule args = (substTyWith tvs tys $ -- with sigma = [tys/tvs],
+ rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs],
TyConApp family instTys, -- sigma (F ts)
- TyConApp rep_tycon tys, -- :=: R tys
- rest) -- surplus arguments
- where
- tys = take coArity args
- rest = drop coArity args
+ TyConApp rep_tycon args) -- :=: R tys
--------------------------------------
-- Coercion Type Constructors...
-- sym d :: p2=q2
-- sym e :: p3=q3
-- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)
---
--- (mkKindingFun f) is given the args [c, sym d, sym e]
-mkKindingFun :: ([Type] -> (Type, Type, [Type]))
- -> [Type] -> Kind
-mkKindingFun f args =
- let (ty1, ty2, rest) = f args in
- let (argtys1, argtys2) = unzip (map coercionKind rest) in
- mkCoKind (mkAppTys ty1 argtys1) (mkAppTys ty2 argtys2)
-
symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon
-- Each coercion TyCon is built with the special CoercionTyCon record and
-- by any TyConApp in which they are applied, however they may also be over
-- applied (see example above) and the kinding function must deal with this.
symCoercionTyCon =
- mkCoercionTyCon symCoercionTyConName 1 (mkKindingFun flipCoercionKindOf)
+ mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf
where
- flipCoercionKindOf (co:rest) = (ty2, ty1, rest)
+ flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1)
where
(ty1, ty2) = coercionKind co
transCoercionTyCon =
- mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf)
+ mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf
where
- composeCoercionKindsOf (co1:co2:rest) =
+ composeCoercionKindsOf (co1:co2:rest)
+ = ASSERT( null rest )
WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug")
- (a1, r2, rest)
+ (a1, r2)
where
(a1, r1) = coercionKind co1
(a2, r2) = coercionKind co2
leftCoercionTyCon =
- mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf)
+ mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf
where
- leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
+ leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
where
(ty1,ty2) = fst (splitCoercionKindOf co)
rightCoercionTyCon =
- mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf)
+ mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
where
- rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
+ rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
where
(ty1,ty2) = snd (splitCoercionKindOf co)
= ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
instCoercionTyCon
- = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind)
+ = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
where
instantiateCo t s =
let Just (tv, ty) = splitForAllTy_maybe t in
substTyWith [tv] [s] ty
- instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest)
+ instCoercionKind (co1:ty:rest) = ASSERT( null rest )
+ (instantiateCo t1 ty, instantiateCo t2 ty)
where (t1, t2) = coercionKind co1
unsafeCoercionTyCon
- = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind)
+ = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
where
- unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest)
+ unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
--------------------------------------
-- ...and their names
mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
- key Nothing (ATyCon coCon) BuiltInSyntax
+ key (ATyCon coCon) BuiltInSyntax
transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon
symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon
+instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI)
+-- instNewTyCon_maybe T ts
+-- = Just (rep_ty, co) if co : T ts ~ rep_ty
+instNewTyCon_maybe tc tys
+ | Just (tvs, ty, mb_co_tc) <- unwrapNewTyCon_maybe tc
+ = ASSERT( tys `lengthIs` tyConArity tc )
+ Just (substTyWith tvs tys ty,
+ case mb_co_tc of
+ Nothing -> IdCo
+ Just co_tc -> ACo (mkTyConApp co_tc tys))
+ | otherwise
+ = Nothing
+
-- this is here to avoid module loops
splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion)
-- Sometimes we want to look through a newtype and get its associated coercion
-- It only strips *one layer* off, so the caller will usually call itself recursively
-- Only applied to types of kind *, hence the newtype is always saturated
+-- splitNewTypeRepCo_maybe ty
+-- = Just (ty', co) if co : ty ~ ty'
+-- Returns Nothing for non-newtypes or fully-transparent newtypes
splitNewTypeRepCo_maybe ty
| Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
splitNewTypeRepCo_maybe (TyConApp tc tys)
- | isClosedNewTyCon tc
- = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied
- -- to *types* (of kind *)
- case newTyConRhs tc of
- (tvs, rep_ty) ->
- ASSERT( length tvs == length tys )
- Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)
- where
- co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo_maybe tc)
-splitNewTypeRepCo_maybe other = Nothing
+ | Just (ty', coi) <- instNewTyCon_maybe tc tys
+ = case coi of
+ ACo co -> Just (ty', co)
+ IdCo -> panic "splitNewTypeRepCo_maybe"
+ -- This case handled by coreView
+splitNewTypeRepCo_maybe other
+ = Nothing
+\end{code}
+
+
+--------------------------------------
+-- CoercionI smart constructors
+-- lifted smart constructors of ordinary coercions
+
+\begin{code}
+ -- CoercionI is either
+ -- (a) proper coercion
+ -- (b) the identity coercion
+data CoercionI = IdCo | ACo Coercion
+
+isIdentityCoercion :: CoercionI -> Bool
+isIdentityCoercion IdCo = True
+isIdentityCoercion _ = False
+
+allIdCos :: [CoercionI] -> Bool
+allIdCos = all isIdentityCoercion
+
+zipCoArgs :: [CoercionI] -> [Type] -> [Coercion]
+zipCoArgs cois tys = zipWith fromCoI cois tys
+
+fromCoI :: CoercionI -> Type -> Type
+fromCoI IdCo ty = ty -- Identity coercion represented
+fromCoI (ACo co) ty = co -- by the type itself
+
+mkSymCoI :: CoercionI -> CoercionI
+mkSymCoI IdCo = IdCo
+mkSymCoI (ACo co) = ACo $ mkCoercion symCoercionTyCon [co]
+ -- the smart constructor
+ -- is too smart with tyvars
+
+mkTransCoI :: CoercionI -> CoercionI -> CoercionI
+mkTransCoI IdCo aco = aco
+mkTransCoI aco IdCo = aco
+mkTransCoI (ACo co1) (ACo co2) = ACo $ mkTransCoercion co1 co2
+
+mkTyConAppCoI :: TyCon -> [Type] -> [CoercionI] -> CoercionI
+mkTyConAppCoI tyCon tys cois
+ | allIdCos cois = IdCo
+ | otherwise = ACo (TyConApp tyCon (zipCoArgs cois tys))
+
+mkAppTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+mkAppTyCoI ty1 IdCo ty2 IdCo = IdCo
+mkAppTyCoI ty1 coi1 ty2 coi2 =
+ ACo $ AppTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
+
+mkFunTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+mkFunTyCoI ty1 IdCo ty2 IdCo = IdCo
+mkFunTyCoI ty1 coi1 ty2 coi2 =
+ ACo $ FunTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
+
+mkNoteTyCoI :: TyNote -> CoercionI -> CoercionI
+mkNoteTyCoI _ IdCo = IdCo
+mkNoteTyCoI note (ACo co) = ACo $ NoteTy note co
+
+mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI
+mkForAllTyCoI _ IdCo = IdCo
+mkForAllTyCoI tv (ACo co) = ACo $ ForAllTy tv co
+
+fromACo (ACo co) = co
+
+
+mkClassPPredCoI :: Class -> [Type] -> [CoercionI] -> CoercionI
+-- mkClassPPredCoI cls tys cois = coi
+-- coi : PredTy (cls tys) ~ predTy (cls (tys `cast` cois))
+mkClassPPredCoI cls tys cois
+ | allIdCos cois = IdCo
+ | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys)
+
+mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI
+-- Similar invariant to mkclassPPredCoI
+mkIParamPredCoI ipn IdCo = IdCo
+mkIParamPredCoI ipn (ACo co) = ACo $ PredTy $ IParam ipn co
+
+mkEqPredCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+-- Similar invariant to mkclassPPredCoI
+mkEqPredCoI _ IdCo _ IdCo = IdCo
+mkEqPredCoI ty1 IdCo _ (ACo co2) = ACo $ PredTy $ EqPred ty1 co2
+mkEqPredCoI ty1 (ACo co1) ty2 coi2 = ACo $ PredTy $ EqPred co1 (fromCoI coi2 ty2)
\end{code}
+
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