-T%
+%
% (c) The University of Glasgow 2006
%
\begin{code}
-{-# OPTIONS -fno-warn-incomplete-patterns #-}
+{-# 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
-- * Main data type
Coercion,
- mkCoKind, mkReflCoKind, coVarKind,
+ mkCoKind, mkCoPredTy, coVarKind, coVarKind_maybe,
coercionKind, coercionKinds, isIdentityCoercion,
-- ** Equality predicates
-- ** Coercion transformations
mkCoercion,
mkSymCoercion, mkTransCoercion,
- mkLeftCoercion, mkRightCoercion, mkRightCoercions,
+ mkLeftCoercion, mkRightCoercion,
mkInstCoercion, mkAppCoercion, mkTyConCoercion, mkFunCoercion,
mkForAllCoercion, mkInstsCoercion, mkUnsafeCoercion,
mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon,
+ -- ** Decomposition
+ decompLR_maybe, decompCsel_maybe, decompInst_maybe,
+
-- ** Optimisation
optCoercion,
import Name
import PrelNames
import Util
+import Control.Monad
import BasicTypes
+import MonadUtils
import Outputable
import FastString
coVarKind :: CoVar -> (Type,Type)
-- c :: t1 ~ t2
-coVarKind cv = splitCoVarKind (tyVarKind cv)
+coVarKind cv = case coVarKind_maybe cv of
+ Just ts -> ts
+ Nothing -> pprPanic "coVarKind" (ppr cv $$ ppr (tyVarKind cv))
+
+coVarKind_maybe :: CoVar -> Maybe (Type,Type)
+coVarKind_maybe cv = splitCoKind_maybe (tyVarKind cv)
-- | Take a 'CoercionKind' apart into the two types it relates: see also 'mkCoKind'.
-- Panics if the argument is not a valid 'CoercionKind'
-splitCoVarKind :: Kind -> (Type, Type)
-splitCoVarKind co | Just co' <- kindView co = splitCoVarKind co'
-splitCoVarKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
+splitCoKind_maybe :: Kind -> Maybe (Type, Type)
+splitCoKind_maybe co | Just co' <- kindView co = splitCoKind_maybe co'
+splitCoKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)
+splitCoKind_maybe _ = Nothing
--- | Makes a 'CoercionKind' from two types: the types whose equality is proven by the relevant 'Coercion'
+-- | Makes a 'CoercionKind' from two types: the types whose equality
+-- is proven by the relevant 'Coercion'
mkCoKind :: Type -> Type -> CoercionKind
mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
mkCoPredTy :: Type -> Type -> Type -> Type
mkCoPredTy s t r = ForAllTy (mkWildCoVar (mkCoKind s t)) r
+splitCoPredTy_maybe :: Type -> Maybe (Type, Type, Type)
+splitCoPredTy_maybe ty
+ | Just (cv,r) <- splitForAllTy_maybe ty
+ , isCoVar cv
+ , Just (s,t) <- coVarKind_maybe cv
+ = Just (s,t,r)
+ | otherwise
+ = Nothing
+
-- | Tests whether a type is just a type equality predicate
isEqPredTy :: Type -> Bool
isEqPredTy (PredTy pred) = isEqPred pred
getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
--- | Create a reflexive 'CoercionKind' that asserts that a type can be coerced to itself
-mkReflCoKind :: Type -> CoercionKind
-mkReflCoKind ty = mkCoKind ty ty
-
-- | If it is the case that
--
-- > c :: (t1 ~ t2)
coercionKind ty@(TyVarTy a) | isCoVar a = coVarKind a
| otherwise = (ty, ty)
coercionKind (AppTy ty1 ty2)
- = let (t1, t2) = coercionKind ty1
- (s1, s2) = coercionKind ty2 in
- (mkAppTy t1 s1, mkAppTy t2 s2)
-coercionKind (TyConApp tc args)
+ = let (s1, t1) = coercionKind ty1
+ (s2, t2) = coercionKind ty2 in
+ (mkAppTy s1 s2, mkAppTy t1 t2)
+coercionKind co@(TyConApp tc args)
| Just (ar, rule) <- isCoercionTyCon_maybe tc
-- CoercionTyCons carry their kinding rule, so we use it here
- = 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)
+ = WARN( not (length args >= ar), ppr co ) -- Always saturated
+ (let (ty1,ty2) = runID (rule (return . typeKind)
+ (return . coercionKind)
+ False (take ar args))
+ -- Apply the rule to the right number of args
+ -- Always succeeds (if term is well-kinded!)
+ (tys1, tys2) = coercionKinds (drop ar args)
+ in (mkAppTys ty1 tys1, mkAppTys ty2 tys2))
| otherwise
= let (lArgs, rArgs) = coercionKinds args in
-- ^ Create a symmetric version of the given 'Coercion' that asserts equality
-- between the same types but in the other "direction", so a kind of @t1 ~ t2@
-- becomes the kind @t2 ~ t1@.
---
--- This function attempts to simplify the generated 'Coercion' by removing
--- redundant applications of @sym@. This is done by pushing this new @sym@
--- down into the 'Coercion' and exploiting the fact that @sym (sym co) = co@.
-mkSymCoercion 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)
-
- | tc `hasKey` instCoercionTyConKey
- -- sym (co @ ty) --> (sym co) @ ty
- -- 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 -- Reflexive
-
--------------------------------
--- ToDo: we should be cleverer about transitivity
+mkSymCoercion g = mkCoercion symCoercionTyCon [g]
mkTransCoercion :: Coercion -> Coercion -> Coercion
-- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
---
--- This function attempts to simplify the generated 'Coercion' by exploiting the fact that
--- @sym g `trans` g = id@.
-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
+mkTransCoercion g1 g2 = mkCoercion transCoercionTyCon [g1, g2]
mkLeftCoercion :: Coercion -> Coercion
-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
-- the "functions" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
--
-- > mkLeftCoercion c :: f ~ g
-mkLeftCoercion co
- | Just (co', _) <- splitAppCoercion_maybe co = co'
- | otherwise = mkCoercion leftCoercionTyCon [co]
+mkLeftCoercion co = mkCoercion leftCoercionTyCon [co]
mkRightCoercion :: Coercion -> Coercion
-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
-- the "arguments" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
--
-- > mkLeftCoercion c :: x ~ y
-mkRightCoercion co
- | Just (_, co2) <- splitAppCoercion_maybe co = co2
- | otherwise = mkCoercion rightCoercionTyCon [co]
-
-mkRightCoercions :: Int -> Coercion -> [Coercion]
--- ^ As 'mkRightCoercion', but finds the 'Coercion's available on the right side of @n@
--- nested application 'Coercion's, manufacturing new left or right cooercions as necessary
--- if suffficiently many are not directly available.
-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
-
+mkRightCoercion co = mkCoercion rightCoercionTyCon [co]
mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion :: Coercion -> Coercion
mkCsel1Coercion co = mkCoercion csel1CoercionTyCon [co]
mkInstCoercion :: Coercion -> Type -> Coercion
-- ^ Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
-- the resulting beta-reduction, otherwise it creates a suspended instantiation.
-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]
+mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
mkInstsCoercion :: Coercion -> [Type] -> Coercion
-- ^ As 'mkInstCoercion', but instantiates the coercion with a number of type arguments, left-to-right
mkInstsCoercion co tys = foldl mkInstCoercion co tys
-{-
-splitSymCoercion_maybe :: Coercion -> Maybe Coercion
-splitSymCoercion_maybe (TyConApp tc [co]) =
- if tc `hasKey` symCoercionTyConKey
- then Just co
- else Nothing
-splitSymCoercion_maybe co = Nothing
--}
-
-splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
--- ^ Splits a coercion application, being careful *not* to split @left c@ etc.
--- This is because those are really syntactic constructs, not applications
-splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'
-splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
-splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
-splitAppCoercion_maybe (TyConApp tc tys)
- | not (isCoercionTyCon tc)
- = case snocView tys of
- Just (tys', ty') -> Just (TyConApp tc tys', ty')
- Nothing -> Nothing
-splitAppCoercion_maybe _ = Nothing
-
-{-
-splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
-splitTransCoercion_maybe (TyConApp tc [ty1, ty2])
- = if tc `hasKey` transCoercionTyConKey then
- Just (ty1, ty2)
- else
- Nothing
-splitTransCoercion_maybe other = Nothing
-
-splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)
-splitInstCoercion_maybe (TyConApp tc [ty1, ty2])
- = if tc `hasKey` instCoercionTyConKey then
- Just (ty1, ty2)
- else
- Nothing
-splitInstCoercion_maybe other = Nothing
-
-splitLeftCoercion_maybe :: Coercion -> Maybe Coercion
-splitLeftCoercion_maybe (TyConApp tc [co])
- = if tc `hasKey` leftCoercionTyConKey then
- Just co
- else
- Nothing
-splitLeftCoercion_maybe other = Nothing
-
-splitRightCoercion_maybe :: Coercion -> Maybe Coercion
-splitRightCoercion_maybe (TyConApp tc [co])
- = if tc `hasKey` rightCoercionTyConKey then
- Just co
- else
- Nothing
-splitRightCoercion_maybe other = Nothing
--}
-
-- | Manufacture a coercion from this air. Needless to say, this is not usually safe,
-- but it is used when we know we are dealing with bottom, which is one case in which
-- it is safe. This is also used implement the @unsafeCoerce#@ primitive.
where
co_con_arity = length tvs
- rule args = ASSERT( co_con_arity == length args )
- (TyConApp tycon args, substTyWith tvs args rhs_ty)
+ rule :: CoTyConKindChecker
+ rule kc_ty kc_co checking args
+ = do { ks <- mapM kc_ty args
+ ; unless (not checking || kindAppOk (tyConKind tycon) ks)
+ (fail "Argument kind mis-match")
+ ; return (TyConApp tycon args, substTyWith tvs args rhs_ty) }
-- | Create a coercion identifying a @data@, @newtype@ or @type@ representation type
-- and its family instance. It has the form @Co tvs :: F ts ~ R tvs@, where @Co@ is
= mkCoercionTyCon name coArity rule
where
coArity = length tvs
- rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs],
- TyConApp family instTys, -- sigma (F ts)
- TyConApp rep_tycon args) -- ~ R tys
+
+ rule :: CoTyConKindChecker
+ rule kc_ty kc_co checking args
+ = do { ks <- mapM kc_ty args
+ ; unless (not checking || kindAppOk (tyConKind rep_tycon) ks)
+ (fail "Argument kind mis-match")
+ ; return (substTyWith tvs args $ -- with sigma = [tys/tvs],
+ TyConApp family instTys -- sigma (F ts)
+ , TyConApp rep_tycon args) } -- ~ R tys
+
+kindAppOk :: Kind -> [Kind] -> Bool
+kindAppOk kfn [] = True
+kindAppOk kfn (k:ks)
+ = case splitKindFunTy_maybe kfn of
+ Just (kfa, kfb) | k `isSubKind` kfa -> kindAppOk kfb ks
+ _other -> False
\end{code}
rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon,
csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon :: TyCon
-symCoercionTyCon =
- mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf
+symCoercionTyCon
+ = mkCoercionTyCon symCoercionTyConName 1 kc_sym
where
- flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1)
- where
- (ty1, ty2) = coercionKind co
+ kc_sym :: CoTyConKindChecker
+ kc_sym kc_ty kc_co _ (co:_)
+ = do { (ty1,ty2) <- kc_co co
+ ; return (ty2,ty1) }
-transCoercionTyCon =
- mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf
+transCoercionTyCon
+ = mkCoercionTyCon transCoercionTyConName 2 kc_trans
where
- composeCoercionKindsOf (co1:co2:rest)
- = ASSERT( null rest )
- WARN( not (r1 `coreEqType` a2),
- text "Strange! Type mismatch in trans coercion, probably a bug"
- $$
- _err_stuff )
- (a1, r2)
- where
- (a1, r1) = coercionKind co1
- (a2, r2) = coercionKind co2
-
- _err_stuff = vcat [ text "co1:" <+> ppr co1
- , text "co1 kind left:" <+> ppr a1
- , text "co1 kind right:" <+> ppr r1
- , text "co2:" <+> ppr co2
- , text "co2 kind left:" <+> ppr a2
- , text "co2 kind right:" <+> ppr r2 ]
+ kc_trans :: CoTyConKindChecker
+ kc_trans kc_ty kc_co checking (co1:co2:_)
+ = do { (a1, r1) <- kc_co co1
+ ; (a2, r2) <- kc_co co2
+ ; unless (not checking || (r1 `coreEqType` a2))
+ (fail "Trans coercion mis-match")
+ ; return (a1, r2) }
---------------------------------------------------
-leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 (fst . decompLR)
-rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 (snd . decompLR)
+leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 (kcLR_help fst)
+rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 (kcLR_help snd)
+
+kcLR_help :: (forall a. (a,a)->a) -> CoTyConKindChecker
+kcLR_help select kc_ty kc_co _checking (co : _)
+ = do { (ty1, ty2) <- kc_co co
+ ; case decompLR_maybe ty1 ty2 of
+ Nothing -> fail "decompLR"
+ Just res -> return (select res) }
-decompLR :: [Type] -> ((Type,Type), (Type,Type))
+decompLR_maybe :: Type -> Type -> Maybe ((Type,Type), (Type,Type))
-- Helper for left and right. Finds coercion kind of its input and
-- returns the left and right projections of the coercion...
--
-- if c :: t1 s1 ~ t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))
-decompLR (co : rest)
- | (ty1, ty2) <- coercionKind co
- , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
+decompLR_maybe ty1 ty2
+ | Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
, Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
- = ASSERT( null rest)
- ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
-decompLR cos
- = pprPanic "Coercion.decompLR"
- (ppr cos $$ vcat (map (pprEqPred .coercionKind) cos))
+ = Just ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
+decompLR_maybe _ _ = Nothing
---------------------------------------------------
instCoercionTyCon
- = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
+ = mkCoercionTyCon instCoercionTyConName 2 kcInst_help
where
- instantiateCo t s =
- let Just (tv, ty) = splitForAllTy_maybe t in
- substTyWith [tv] [s] ty
+ kcInst_help :: CoTyConKindChecker
+ kcInst_help kc_ty kc_co checking (co : ty : _)
+ = do { (t1,t2) <- kc_co co
+ ; k <- kc_ty ty
+ ; case decompInst_maybe t1 t2 of
+ Nothing -> fail "decompInst"
+ Just ((tv1,tv2), (ty1,ty2)) -> do
+ { unless (not checking || (k `isSubKind` tyVarKind tv1))
+ (fail "Coercion instantation kind mis-match")
+ ; return (substTyWith [tv1] [ty] ty1,
+ substTyWith [tv2] [ty] ty2) } }
+
+decompInst_maybe :: Type -> Type -> Maybe ((TyVar,TyVar), (Type,Type))
+decompInst_maybe ty1 ty2
+ | Just (tv1,r1) <- splitForAllTy_maybe ty1
+ , Just (tv2,r2) <- splitForAllTy_maybe ty2
+ = Just ((tv1,tv2), (r1,r2))
- instCoercionKind (co1:ty:rest) = ASSERT( null rest )
- (instantiateCo t1 ty, instantiateCo t2 ty)
- where (t1, t2) = coercionKind co1
---------------------------------------------------
unsafeCoercionTyCon
- = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
+ = mkCoercionTyCon unsafeCoercionTyConName 2 kc_unsafe
where
- unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
+ kc_unsafe kc_ty kc_co _checking (ty1:ty2:_)
+ = do { k1 <- kc_ty ty1
+ ; k2 <- kc_ty ty2
+ ; return (ty1,ty2) }
---------------------------------------------------
-- The csel* family
+
+csel1CoercionTyCon = mkCoercionTyCon csel1CoercionTyConName 1 (kcCsel_help fstOf3)
+csel2CoercionTyCon = mkCoercionTyCon csel2CoercionTyConName 1 (kcCsel_help sndOf3)
+cselRCoercionTyCon = mkCoercionTyCon cselRCoercionTyConName 1 (kcCsel_help thirdOf3)
+
+kcCsel_help :: (forall a. (a,a,a) -> a) -> CoTyConKindChecker
+kcCsel_help select kc_ty kc_co _checking (co : rest)
+ = do { (ty1,ty2) <- kc_co co
+ ; case decompCsel_maybe ty1 ty2 of
+ Nothing -> fail "decompCsel"
+ Just res -> return (select res) }
+
+decompCsel_maybe :: Type -> Type -> Maybe ((Type,Type), (Type,Type), (Type,Type))
-- If co :: (s1~t1 => r1) ~ (s2~t2 => r2)
--- Then csel1 co :: s1 ~ s2
--- csel2 co :: t1 ~ t2
--- cselR co :: r1 ~ r2
-
-csel1CoercionTyCon = mkCoercionTyCon csel1CoercionTyConName 1 (fstOf3 . decompCsel)
-csel2CoercionTyCon = mkCoercionTyCon csel2CoercionTyConName 1 (sndOf3 . decompCsel)
-cselRCoercionTyCon = mkCoercionTyCon cselRCoercionTyConName 1 (thirdOf3 . decompCsel)
-
-decompCsel :: [Coercion] -> ((Type,Type), (Type,Type), (Type,Type))
-decompCsel (co : rest)
- | (ty1,ty2) <- coercionKind co
- , Just (cv1, r1) <- splitForAllTy_maybe ty1
- , Just (cv2, r2) <- splitForAllTy_maybe ty2
- , (s1,t1) <- ASSERT( isCoVar cv1) coVarKind cv1
- , (s2,t2) <- ASSERT( isCoVar cv1) coVarKind cv2
- = ASSERT( null rest )
- ((s1,s2), (t1,t2), (r1,r2))
-decompCsel other = pprPanic "decompCsel" (ppr other)
+-- Then csel1 co :: s1 ~ s2
+-- csel2 co :: t1 ~ t2
+-- cselR co :: r1 ~ r2
+decompCsel_maybe ty1 ty2
+ | Just (s1, t1, r1) <- splitCoPredTy_maybe ty1
+ , Just (s2, t2, r2) <- splitCoPredTy_maybe ty2
+ = Just ((s1,s2), (t1,t2), (r1,r2))
+decompCsel_maybe _ _ = Nothing
fstOf3 :: (a,b,c) -> a
sndOf3 :: (a,b,c) -> b
mkAppTyCoI ty1 coi1 ty2 coi2 =
ACo $ AppTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
--- | Smart constructor for function-'Coercion's on 'CoercionI', see also 'mkFunCoercion'
+
mkFunTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
mkFunTyCoI _ IdCo _ IdCo = IdCo
mkFunTyCoI ty1 coi1 ty2 coi2 =
%************************************************************************
\begin{code}
-optCoercion :: Coercion -> Coercion
-optCoercion co
- = ASSERT2( coercionKind co `eq` coercionKind result,
- ppr co $$ ppr result $$ ppr (coercionKind co) $$ ppr (coercionKind result) )
- result
+type NormalCo = Coercion
+ -- Invariants:
+ -- * For trans coercions (co1 `trans` co2)
+ -- co1 is not a trans, and neither co1 nor co2 is identity
+ -- * If the coercion is the identity, it has no CoVars of CoTyCons in it (just types)
+
+type NormalNonIdCo = NormalCo -- Extra invariant: not the identity
+
+optCoercion :: Coercion -> NormalCo
+optCoercion co = opt_co False co
+
+opt_co :: Bool -- True <=> return (sym co)
+ -> Coercion
+ -> NormalCo
+opt_co = opt_co'
+-- opt_co sym co = pprTrace "opt_co {" (ppr sym <+> ppr co) $
+-- co1 `seq`
+-- pprTrace "opt_co done }" (ppr co1)
+-- WARN( not same_co_kind, ppr co <+> dcolon <+> pprEqPred (s1,t1)
+-- $$ ppr co1 <+> dcolon <+> pprEqPred (s2,t2) )
+-- co1
+-- where
+-- co1 = opt_co' sym co
+-- same_co_kind = s1 `coreEqType` s2 && t1 `coreEqType` t2
+-- (s,t) = coercionKind co
+-- (s1,t1) | sym = (t,s)
+-- | otherwise = (s,t)
+-- (s2,t2) = coercionKind co1
+
+opt_co' sym (AppTy ty1 ty2) = mkAppTy (opt_co sym ty1) (opt_co sym ty2)
+opt_co' sym (FunTy ty1 ty2) = FunTy (opt_co sym ty1) (opt_co sym ty2)
+opt_co' sym (PredTy (ClassP cls tys)) = PredTy (ClassP cls (map (opt_co sym) tys))
+opt_co' sym (PredTy (IParam n ty)) = PredTy (IParam n (opt_co sym ty))
+
+opt_co' sym co@(TyVarTy tv)
+ | not (isCoVar tv) = co -- Identity; does not mention a CoVar
+ | ty1 `coreEqType` ty2 = ty1 -- Identity; ..ditto..
+ | not sym = co
+ | otherwise = mkSymCoercion co
+ where
+ (ty1,ty2) = coVarKind tv
+
+opt_co' sym (ForAllTy tv cor)
+ | isCoVar tv = mkCoPredTy (opt_co sym co1) (opt_co sym co2) (opt_co sym cor)
+ | otherwise = ForAllTy tv (opt_co sym cor)
+ where
+ (co1,co2) = coVarKind tv
+
+opt_co' sym (TyConApp tc cos)
+ | isCoercionTyCon tc
+ = foldl mkAppTy opt_co_tc
+ (map (opt_co sym) (drop arity cos))
+ | otherwise
+ = TyConApp tc (map (opt_co sym) cos)
+ where
+ arity = tyConArity tc
+ opt_co_tc :: NormalCo
+ opt_co_tc = opt_co_tc_app sym tc (take arity cos)
+
+--------
+opt_co_tc_app :: Bool -> TyCon -> [Type] -> NormalCo
+-- Used for CoercionTyCons only
+opt_co_tc_app sym tc cos
+ | tc `hasKey` symCoercionTyConKey
+ = opt_co (not sym) co1
+
+ | tc `hasKey` transCoercionTyConKey
+ = if sym then opt_trans opt_co2 opt_co1
+ else opt_trans opt_co1 opt_co2
+
+ | tc `hasKey` leftCoercionTyConKey
+ , Just (co1, _) <- splitAppTy_maybe opt_co1
+ = co1
+
+ | tc `hasKey` rightCoercionTyConKey
+ , Just (_, co2) <- splitAppTy_maybe opt_co1
+ = co2
+
+ | tc `hasKey` csel1CoercionTyConKey
+ , Just (s1,_,_) <- splitCoPredTy_maybe opt_co1
+ = s1
+
+ | tc `hasKey` csel2CoercionTyConKey
+ , Just (_,s2,_) <- splitCoPredTy_maybe opt_co1
+ = s2
+
+ | tc `hasKey` cselRCoercionTyConKey
+ , Just (_,_,r) <- splitCoPredTy_maybe opt_co1
+ = r
+
+ | tc `hasKey` instCoercionTyConKey
+ , Just (tv, co'') <- splitForAllTy_maybe opt_co1
+ , let ty = co2
+ = substTyWith [tv] [ty] co''
+
+ | otherwise -- Do not push sym inside top-level axioms
+ -- e.g. if g is a top-level axiom
+ -- g a : F a ~ a
+ -- Then (sym (g ty)) /= g (sym ty) !!
+ = if sym then mkSymCoercion the_co
+ else the_co
+ where
+ the_co = TyConApp tc cos
+ (co1 : cos1) = cos
+ (co2 : _) = cos1
+ opt_co1 = opt_co sym co1
+ opt_co2 = opt_co sym co2
+
+-------------
+opt_trans :: NormalCo -> NormalCo -> NormalCo
+opt_trans co1 co2
+ | isIdNormCo co1 = co2
+ | otherwise = opt_trans1 co1 co2
+
+opt_trans1 :: NormalNonIdCo -> NormalCo -> NormalCo
+-- First arg is not the identity
+opt_trans1 co1 co2
+ | isIdNormCo co2 = co1
+ | otherwise = opt_trans2 co1 co2
+
+opt_trans2 :: NormalNonIdCo -> NormalNonIdCo -> NormalCo
+-- Neither arg is the identity
+opt_trans2 (TyConApp tc [co1a,co1b]) co2
+ | tc `hasKey` transCoercionTyConKey
+ = opt_trans1 co1a (opt_trans2 co1b co2)
+
+opt_trans2 co1 co2
+ | Just co <- opt_trans_rule co1 co2
+ = co
+
+opt_trans2 co1 (TyConApp tc [co2a,co2b])
+ | tc `hasKey` transCoercionTyConKey
+ , Just co1_2a <- opt_trans_rule co1 co2a
+ = if isIdNormCo co1_2a
+ then co2b
+ else opt_trans2 co1_2a co2b
+
+opt_trans2 co1 co2
+ = mkTransCoercion co1 co2
+
+------
+opt_trans_rule :: NormalNonIdCo -> NormalNonIdCo -> Maybe NormalCo
+opt_trans_rule (TyConApp tc [co1]) co2
+ | tc `hasKey` symCoercionTyConKey
+ , co1 `coreEqType` co2
+ , (_,ty2) <- coercionKind co2
+ = Just ty2
+
+opt_trans_rule co1 (TyConApp tc [co2])
+ | tc `hasKey` symCoercionTyConKey
+ , co1 `coreEqType` co2
+ , (ty1,_) <- coercionKind co1
+ = Just ty1
+
+opt_trans_rule (TyConApp tc1 [co1,ty1]) (TyConApp tc2 [co2,ty2])
+ | tc1 `hasKey` instCoercionTyConKey
+ , tc1 == tc2
+ , ty1 `coreEqType` ty2
+ = Just (mkInstCoercion (opt_trans2 co1 co2) ty1)
+
+opt_trans_rule (TyConApp tc1 cos1) (TyConApp tc2 cos2)
+ | not (isCoercionTyCon tc1) ||
+ getUnique tc1 `elem` [ leftCoercionTyConKey, rightCoercionTyConKey
+ , csel1CoercionTyConKey, csel2CoercionTyConKey
+ , cselRCoercionTyConKey ] --Yuk!
+ , tc1 == tc2 -- Works for left,right, and csel* family
+ -- BUT NOT equality axioms
+ -- E.g. (g Int) `trans` (g Bool)
+ -- /= g (Int . Bool)
+ = Just (TyConApp tc1 (zipWith opt_trans cos1 cos2))
+
+opt_trans_rule co1 co2
+ | Just (co1a, co1b) <- splitAppTy_maybe co1
+ , Just (co2a, co2b) <- splitAppTy_maybe co2
+ = Just (mkAppTy (opt_trans co1a co2a) (opt_trans co1b co2b))
+
+ | Just (s1,t1,r1) <- splitCoPredTy_maybe co1
+ , Just (s2,t2,r2) <- splitCoPredTy_maybe co1
+ = Just (mkCoPredTy (opt_trans s1 s2)
+ (opt_trans t1 t2)
+ (opt_trans r1 r2))
+
+ | Just (tv1,r1) <- splitForAllTy_maybe co1
+ , Just (tv2,r2) <- splitForAllTy_maybe co2
+ , not (isCoVar tv1) -- Both have same kind
+ , let r2' = substTyWith [tv2] [TyVarTy tv1] r2
+ = Just (ForAllTy tv1 (opt_trans2 r1 r2'))
+
+opt_trans_rule _ _ = Nothing
+
+
+-------------
+isIdNormCo :: NormalCo -> Bool
+-- Cheap identity test: look for coercions with no coercion variables at all
+-- So it'll return False for (sym g `trans` g)
+isIdNormCo ty = go ty
where
- (s1,t1) `eq` (s2,t2) = s1 `coreEqType` s2 && t1 `coreEqType` t2
-
- (result,_,_) = go co
- -- optimized, changed?, identity?
- go :: Coercion -> ( Coercion, Bool, Bool )
- -- traverse coercion term bottom up and return
- --
- -- 1) equivalent coercion, in optimized form
- --
- -- 2) whether the output coercion differs from
- -- the input coercion
- --
- -- 3) whether the coercion is an identity coercion
- --
- -- Performs the following optimizations:
- --
- -- sym id >-> id
- -- trans id co >-> co
- -- trans co id >-> co
- -- sym (sym co) >-> co
- -- trans g (sym g) >-> id
- -- trans (sym g) g >-> id
- --
- go ty@(TyVarTy a) | isCoVar a = let (ty1,ty2) = coercionKind ty
- in (ty, False, ty1 `coreEqType` ty2)
- | otherwise = (ty, False, True)
- go ty@(AppTy ty1 ty2)
- = let (ty1', chan1, id1) = go ty1
- (ty2', chan2, id2) = go ty2
- in if chan1 || chan2
- then (AppTy ty1' ty2', True, id1 && id2)
- else (ty , False, id1 && id2)
- go ty@(TyConApp tc args)
- | tc == symCoercionTyCon, (ty1:tys) <- args
- = goSym ty ty1 tys
- | tc == transCoercionTyCon, [ty1,ty2] <- args
- = goTrans ty ty1 ty2
- | tc == leftCoercionTyCon, [ty1] <- args
- = goLeft ty ty1
- | tc == rightCoercionTyCon, [ty1] <- args
- = goRight ty ty1
- | tc == instCoercionTyCon, [ty1,ty2] <- args
- = goInst ty ty1 ty2
- | not (isCoercionTyCon tc)
- = let (args', chans, ids) = mapAndUnzip3 go args
- in if or chans
- then (TyConApp tc args', True , and ids)
- else (ty , False, and ids)
- | otherwise
- = (ty, False, False)
- go ty@(FunTy ty1 ty2)
- = let (ty1',chan1,id1) = go ty1
- (ty2',chan2,id2) = go ty2
- in if chan1 || chan2
- then (FunTy ty1' ty2', True , id1 && id2)
- else (ty , False, id1 && id2)
- go ty@(ForAllTy tv ty1)
- = let (ty1', chan1, id1) = go ty1
- in if chan1
- then (ForAllTy tv ty1', True , id1)
- else (ty , False, id1)
- go ty@(PredTy (EqPred ty1 ty2))
- = let (ty1', chan1, id1) = go ty1
- (ty2', chan2, id2) = go ty2
- in if chan1 || chan2
- then (PredTy (EqPred ty1' ty2'), True , id1 && id2)
- else (ty , False, id1 && id2)
- go ty@(PredTy (ClassP cl args))
- = let (args', chans, ids) = mapAndUnzip3 go args
- in if or chans
- then (PredTy (ClassP cl args'), True , and ids)
- else (ty , False, and ids)
- go ty@(PredTy (IParam name ty1))
- = let (ty1', chan1, id1) = go ty1
- in if chan1
- then (PredTy (IParam name ty1'), True , id1)
- else (ty , False, id1)
-
- goSym :: Coercion -> Coercion -> [Coercion] -> ( Coercion, Bool, Bool )
- --
- -- pushes the sym constructor inwards, if possible
- --
- -- takes original coercion term
- -- first argument
- -- rest of arguments
- goSym ty ty1 tys
- = case mkSymCoercion ty1 of
- (TyConApp tc _ ) | tc == symCoercionTyCon
- -> let (tys',chans',ids) = mapAndUnzip3 go (ty1:tys)
- in if or chans'
- then (TyConApp symCoercionTyCon tys', True , and ids)
- else (ty , False, and ids)
- ty1' -> let (ty',_ ,id') = go (mkAppsCoercion ty1' tys)
- in (ty',True,id')
-
-
- goRight :: Coercion -> Coercion -> ( Coercion, Bool, Bool )
- --
- -- reduces the right constructor, if possible
- --
- -- takes original coercion term
- -- argument
- --
- goRight ty ty1
- = case mkRightCoercion ty1 of
- (TyConApp tc _ ) | tc == rightCoercionTyCon
- -> let (ty1',chan1,id1) = go ty1
- in if chan1
- then (TyConApp rightCoercionTyCon [ty1'], True , id1)
- else (ty , False, id1)
- ty1' -> let (ty',_ ,id') = go ty1'
- in (ty',True,id')
-
- goLeft :: Coercion -> Coercion -> ( Coercion, Bool, Bool )
- --
- -- reduces the left constructor, if possible
- --
- -- takes original coercion term
- -- argument
- --
- goLeft ty ty1
- = case mkLeftCoercion ty1 of
- (TyConApp tc _ ) | tc == leftCoercionTyCon
- -> let (ty1',chan1,id1) = go ty1
- in if chan1
- then (TyConApp leftCoercionTyCon [ty1'], True , id1)
- else (ty , False, id1)
- ty1' -> let (ty',_ ,id') = go ty1'
- in (ty',True,id')
-
- goInst :: Coercion -> Coercion -> Coercion -> ( Coercion, Bool, Bool )
- --
- -- reduces the inst constructor, if possible
- --
- -- takes original coercion term
- -- coercion argument
- -- type argument
- --
- goInst ty ty1 ty2
- = case mkInstCoercion ty1 ty2 of
- (TyConApp tc _ ) | tc == instCoercionTyCon
- -> let (ty1',chan1,id1) = go ty1
- in if chan1
- then (TyConApp instCoercionTyCon [ty1',ty2], True , id1)
- else (ty , False, id1)
- ty1' -> let (ty',_ ,id') = go ty1'
- in (ty',True,id')
-
- goTrans :: Coercion -> Coercion -> Coercion -> ( Coercion, Bool, Bool )
- --
- -- trans id co >-> co
- -- trans co id >-> co
- -- trans g (sym g) >-> id
- -- trans (sym g) g >-> id
- --
- goTrans ty ty1 ty2
- | id1
- = (ty2', True, id2)
- | id2
- = (ty1', True, False)
- | chan1 || chan2
- = (TyConApp transCoercionTyCon [ty1',ty2'], True , False)
- | Just ty' <- mty'
- = (ty', True, True)
- | otherwise
- = (ty, False, False)
- where (ty1', chan1, id1) = go ty1
- (ty2', chan2, id2) = go ty2
- mty' = case mkTransCoercion ty1' ty2'
- of (TyConApp tc _) | tc == transCoercionTyCon
- -> Nothing
- ty' -> Just ty'
+ go (TyVarTy tv) = not (isCoVar tv)
+ go (AppTy t1 t2) = go t1 && go t2
+ go (FunTy t1 t2) = go t1 && go t2
+ go (ForAllTy tv ty) = go (tyVarKind tv) && go ty
+ go (TyConApp tc tys) = not (isCoercionTyCon tc) && all go tys
+ go (PredTy (IParam _ ty)) = go ty
+ go (PredTy (ClassP _ tys)) = all go tys
+ go (PredTy (EqPred t1 t2)) = go t1 && go t2
\end{code}
projects / ghc-hetmet.git / blobdiff