X-Git-Url: http://git.megacz.com/?p=ghc-hetmet.git;a=blobdiff_plain;f=compiler%2Ftypes%2FCoercion.lhs;h=faab46304421562cc7ab117447019d7bf650a5b7;hp=fb91a0de67d9d14d63e8e9d637e903c04e37aaee;hb=c80364f8e4681b34e974f5df36ecdacec7cd9cd8;hpb=a7a32655a398d0bad611314f0f73c0dcbf2588f4 diff --git a/compiler/types/Coercion.lhs b/compiler/types/Coercion.lhs index fb91a0d..faab463 100644 --- a/compiler/types/Coercion.lhs +++ b/compiler/types/Coercion.lhs @@ -1,464 +1,857 @@ +% +% (c) The University of Glasgow 2006 +% - Module for type coercions, as in System FC. +\begin{code} +-- | Module for (a) type kinds and (b) type coercions, +-- as used in System FC. See 'CoreSyn.Expr' for +-- more on System FC and how coercions fit into it. +-- +-- Coercions are represented as types, and their kinds tell what types the +-- coercion works on. The coercion kind constructor is a special TyCon that +-- must always be saturated, like so: +-- +-- > typeKind (symCoercion type) :: TyConApp CoTyCon{...} [type, type] +module Coercion ( + -- * Main data type + Coercion, Kind, + typeKind, -Coercions are represented as types, and their kinds tell what types the -coercion works on. + -- ** Deconstructing Kinds + kindFunResult, kindAppResult, synTyConResKind, + splitKindFunTys, splitKindFunTysN, splitKindFunTy_maybe, -The coercion kind constructor is a special TyCon that must always be saturated + -- ** Predicates on Kinds + isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind, + isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind, + isCoSuperKind, isSuperKind, isCoercionKind, + mkArrowKind, mkArrowKinds, - typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type] + isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind, + isSubKindCon, -\begin{code} -module Coercion ( - Coercion, - - mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind, - coercionKind, coercionKinds, coercionKindPredTy, + mkCoKind, mkCoPredTy, coVarKind, coVarKind_maybe, + coercionKind, coercionKinds, isIdentityCoercion, - -- Equality predicates + -- ** Equality predicates isEqPred, mkEqPred, getEqPredTys, isEqPredTy, - -- Coercion transformations + -- ** Coercion transformations + mkCoercion, mkSymCoercion, mkTransCoercion, - mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion, - mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion, - mkNewTypeCoercion, mkDataInstCoercion, mkAppsCoercion, + mkLeftCoercion, mkRightCoercion, + mkInstCoercion, mkAppCoercion, mkTyConCoercion, mkFunCoercion, + mkForAllCoercion, mkInstsCoercion, mkUnsafeCoercion, + mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion, + mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion, + + mkClassPPredCo, mkIParamPredCo, mkEqPredCo, + mkCoVarCoercion, mkCoPredCo, - splitNewTypeRepCo_maybe, decomposeCo, unsafeCoercionTyCon, symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, - rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn + rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn + csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon, + + -- ** Decomposition + decompLR_maybe, decompCsel_maybe, decompInst_maybe, + splitCoPredTy_maybe, + splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo, + + -- ** Comparison + coreEqCoercion, coreEqCoercion2, + + -- * CoercionI + CoercionI(..), + isIdentityCoI, + mkSymCoI, mkTransCoI, + mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI, + mkForAllTyCoI, + fromCoI, + mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI, mkCoPredCoI + ) 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, - tyVarsOfType, mkTyVarTys - ) -import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isNewTyCon, - newTyConRhs, newTyConCo, - isCoercionTyCon, isCoercionTyCon_maybe ) -import Var ( Var, TyVar, isTyVar, tyVarKind ) -import VarSet ( elemVarSet ) -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 VarEnv +import VarSet +import Name +import PrelNames +import Util +import BasicTypes import Outputable +import FastString +\end{code} +%************************************************************************ +%* * + Functions over Kinds +%* * +%************************************************************************ +\begin{code} +-- | Essentially 'funResultTy' on kinds +kindFunResult :: Kind -> Kind +kindFunResult k = funResultTy k + +kindAppResult :: Kind -> [arg] -> Kind +kindAppResult k [] = k +kindAppResult k (_:as) = kindAppResult (kindFunResult k) as + +-- | Essentially 'splitFunTys' on kinds +splitKindFunTys :: Kind -> ([Kind],Kind) +splitKindFunTys k = splitFunTys k + +splitKindFunTy_maybe :: Kind -> Maybe (Kind,Kind) +splitKindFunTy_maybe = splitFunTy_maybe + +-- | Essentially 'splitFunTysN' on kinds +splitKindFunTysN :: Int -> Kind -> ([Kind],Kind) +splitKindFunTysN k = splitFunTysN k + +-- | Find the result 'Kind' of a type synonym, +-- after applying it to its 'arity' number of type variables +-- Actually this function works fine on data types too, +-- but they'd always return '*', so we never need to ask +synTyConResKind :: TyCon -> Kind +synTyConResKind tycon = kindAppResult (tyConKind tycon) (tyConTyVars tycon) + +-- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's +isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool +isOpenTypeKindCon, isUbxTupleKindCon, isArgTypeKindCon, + isUnliftedTypeKindCon, isSubArgTypeKindCon :: TyCon -> Bool + +isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey + +isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc +isOpenTypeKind _ = False + +isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey + +isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc +isUbxTupleKind _ = False + +isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey + +isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc +isArgTypeKind _ = False + +isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey + +isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc +isUnliftedTypeKind _ = False + +isSubOpenTypeKind :: Kind -> Bool +-- ^ True of any sub-kind of OpenTypeKind (i.e. anything except arrow) +isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) ) + ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) ) + False +isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True +isSubOpenTypeKind other = ASSERT( isKind other ) False + -- This is a conservative answer + -- It matters in the call to isSubKind in + -- checkExpectedKind. + +isSubArgTypeKindCon kc + | isUnliftedTypeKindCon kc = True + | isLiftedTypeKindCon kc = True + | isArgTypeKindCon kc = True + | otherwise = False + +isSubArgTypeKind :: Kind -> Bool +-- ^ True of any sub-kind of ArgTypeKind +isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc +isSubArgTypeKind _ = False + +-- | Is this a super-kind (i.e. a type-of-kinds)? +isSuperKind :: Type -> Bool +isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc +isSuperKind _ = False + +-- | Is this a kind (i.e. a type-of-types)? +isKind :: Kind -> Bool +isKind k = isSuperKind (typeKind k) + +isSubKind :: Kind -> Kind -> Bool +-- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@ +isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2 +isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2) +isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2')) + = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2' +isSubKind _ _ = False + +eqKind :: Kind -> Kind -> Bool +eqKind = tcEqType + +isSubKindCon :: TyCon -> TyCon -> Bool +-- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@ +isSubKindCon kc1 kc2 + | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True + | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True + | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True + | isOpenTypeKindCon kc2 = True + -- we already know kc1 is not a fun, its a TyCon + | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True + | otherwise = False + +defaultKind :: Kind -> Kind +-- ^ Used when generalising: default kind ? and ?? to *. See "Type#kind_subtyping" for more +-- information on what that means + +-- When we generalise, we make generic type variables whose kind is +-- simple (* or *->* etc). So generic type variables (other than +-- built-in constants like 'error') always have simple kinds. This is important; +-- consider +-- f x = True +-- We want f to get type +-- f :: forall (a::*). a -> Bool +-- Not +-- f :: forall (a::??). a -> Bool +-- because that would allow a call like (f 3#) as well as (f True), +--and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr. +defaultKind k + | isSubOpenTypeKind k = liftedTypeKind + | isSubArgTypeKind k = liftedTypeKind + | otherwise = k +\end{code} + +%************************************************************************ +%* * + Coercions +%* * +%************************************************************************ + + +\begin{code} +-- | A 'Coercion' represents a 'Type' something should be coerced to. +type Coercion = Type + +-- | A 'CoercionKind' is always of form @ty1 ~ ty2@ and indicates the +-- types that a 'Coercion' will work on. +type CoercionKind = Kind ------------------------------ + +-- | This breaks a 'Coercion' with 'CoercionKind' @T A B C ~ T D E F@ into +-- a list of 'Coercion's of kinds @A ~ D@, @B ~ E@ and @E ~ F@. Hence: +-- +-- > decomposeCo 3 c = [right (left (left c)), right (left c), right c] decomposeCo :: Arity -> Coercion -> [Coercion] --- (decomposeCo 3 c) = [right (left (left c)), right (left c), right c] --- So this breaks a coercion with kind T A B C :=: T D E F into --- a list of coercions of kinds A :=: D, B :=: E and E :=: F decomposeCo n co = go n co [] where - go 0 co cos = cos + go 0 _ cos = cos go n co cos = go (n-1) (mkLeftCoercion co) (mkRightCoercion co : cos) ------------------------------- ------------------------------------------------------- -- and some coercion kind stuff +coVarKind :: CoVar -> (Type,Type) +-- c :: t1 ~ t2 +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' +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' +mkCoKind :: Type -> Type -> CoercionKind +mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2) + +-- | (mkCoPredTy s t r) produces the type: (s~t) => r +mkCoPredTy :: Type -> Type -> Type -> Type +mkCoPredTy s t r = ASSERT( not (co_var `elemVarSet` tyVarsOfType r) ) + ForAllTy co_var r + where + co_var = mkWildCoVar (mkCoKind s t) + +mkCoPredCo :: Coercion -> Coercion -> Coercion -> Coercion +-- Creates a coercion between (s1~t1) => r1 and (s2~t2) => r2 +mkCoPredCo = mkCoPredTy + + +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 -isEqPredTy other = False +isEqPredTy _ = False +-- | Creates a type equality predicate mkEqPred :: (Type, Type) -> PredType mkEqPred (ty1, ty2) = EqPred ty1 ty2 +-- | Splits apart a type equality predicate, if the supplied 'PredType' is one. +-- Panics otherwise getEqPredTys :: PredType -> (Type,Type) getEqPredTys (EqPred ty1 ty2) = (ty1, ty2) getEqPredTys other = pprPanic "getEqPredTys" (ppr other) -mkCoKind :: Type -> Type -> CoercionKind -mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2) +isIdentityCoercion :: Coercion -> Bool +isIdentityCoercion co + = case coercionKind co of + (t1,t2) -> t1 `coreEqType` t2 +\end{code} -mkReflCoKind :: Type -> CoercionKind -mkReflCoKind ty = mkCoKind ty ty +%************************************************************************ +%* * + Building coercions +%* * +%************************************************************************ -splitCoercionKind :: CoercionKind -> (Type, Type) -splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co' -splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2) +Coercion kind and type mk's (make saturated TyConApp CoercionTyCon{...} args) -splitCoercionKind_maybe :: Kind -> Maybe (Type, Type) -splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co' -splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2) -splitCoercionKind_maybe other = Nothing +\begin{code} +-- | Make a coercion from the specified coercion 'TyCon' and the 'Type' arguments to +-- that coercion. Try to use the @mk*Coercion@ family of functions instead of using this function +-- if possible +mkCoercion :: TyCon -> [Type] -> Coercion +mkCoercion coCon args = ASSERT( tyConArity coCon == length args ) + TyConApp coCon args -isCoVar :: Var -> Bool -isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv) +mkCoVarCoercion :: CoVar -> Coercion +mkCoVarCoercion cv = mkTyVarTy cv -type Coercion = Type -type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2) +-- | Apply a 'Coercion' to another 'Coercion', which is presumably a +-- 'Coercion' constructor of some kind +mkAppCoercion :: Coercion -> Coercion -> Coercion +mkAppCoercion co1 co2 = mkAppTy co1 co2 -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 (AppTy ty1 ty2) - = let (t1, t2) = coercionKind ty1 - (s1, s2) = coercionKind ty2 in - (mkAppTy t1 s1, mkAppTy t2 s2) -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) - | otherwise - = let (lArgs, rArgs) = coercionKinds args in - (TyConApp tc lArgs, TyConApp tc rArgs) -coercionKind (FunTy ty1 ty2) - = let (t1, t2) = coercionKind ty1 - (s1, s2) = coercionKind ty2 in - (mkFunTy t1 s1, mkFunTy t2 s2) -coercionKind (ForAllTy tv ty) - = let (ty1, ty2) = coercionKind ty in - (ForAllTy tv ty1, ForAllTy tv ty2) -coercionKind (NoteTy _ ty) = coercionKind ty -coercionKind (PredTy (EqPred c1 c2)) - = let k1 = coercionKindPredTy c1 - k2 = coercionKindPredTy c2 in - (k1,k2) -coercionKind (PredTy (ClassP cl args)) - = let (lArgs, rArgs) = coercionKinds args in - (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs)) -coercionKind (PredTy (IParam name ty)) - = let (ty1, ty2) = coercionKind ty in - (PredTy (IParam name ty1), PredTy (IParam name ty2)) +-- | Applies multiple 'Coercion's to another 'Coercion', from left to right. +-- See also 'mkAppCoercion' +mkAppsCoercion :: Coercion -> [Coercion] -> Coercion +mkAppsCoercion co1 tys = foldl mkAppTy co1 tys -coercionKindPredTy :: Coercion -> CoercionKind -coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2 +-- | Apply a type constructor to a list of coercions. +mkTyConCoercion :: TyCon -> [Coercion] -> Coercion +mkTyConCoercion con cos = mkTyConApp con cos -coercionKinds :: [Coercion] -> ([Type], [Type]) -coercionKinds tys = unzip $ map coercionKind tys +-- | Make a function 'Coercion' between two other 'Coercion's +mkFunCoercion :: Coercion -> Coercion -> Coercion +mkFunCoercion co1 co2 = mkFunTy co1 co2 -- NB: Handles correctly the forall for eqpreds! -------------------------------------- --- Coercion kind and type mk's --- (make saturated TyConApp CoercionTyCon{...} args) +-- | Make a 'Coercion' which binds a variable within an inner 'Coercion' +mkForAllCoercion :: Var -> Coercion -> Coercion +-- note that a TyVar should be used here, not a CoVar (nor a TcTyVar) +mkForAllCoercion tv co = ASSERT ( isTyCoVar tv ) mkForAllTy tv co -mkCoercion coCon args = ASSERT( tyConArity coCon == length args ) - TyConApp coCon args -mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion -mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion +------------------------------- -mkAppCoercion co1 co2 = mkAppTy co1 co2 -mkAppsCoercion co1 tys = foldl mkAppTy co1 tys --- note that a TyVar should be used here, not a CoVar (nor a TcTyVar) -mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co -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 - -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2) - = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1) - | Just (co, ty) <- splitInstCoercion_maybe co - -- 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 -mkSymCoercion (TyVarTy tv) - | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv] - | otherwise = TyVarTy tv -mkSymCoercion co = mkCoercion symCoercionTyCon [co] - --- Smart constructors for left and right -mkLeftCoercion co - | Just (co', _) <- splitAppCoercion_maybe co = 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] +mkSymCoercion :: Coercion -> Coercion +-- ^ 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@. +mkSymCoercion g = mkCoercion symCoercionTyCon [g] + +mkTransCoercion :: Coercion -> Coercion -> Coercion +-- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's. +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 = 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 = mkCoercion rightCoercionTyCon [co] + +mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion :: Coercion -> Coercion +mkCsel1Coercion co = mkCoercion csel1CoercionTyCon [co] +mkCsel2Coercion co = mkCoercion csel2CoercionTyCon [co] +mkCselRCoercion co = mkCoercion cselRCoercionTyCon [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 = 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 --- which are really sytactic 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 co = 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 - --- Unsafe coercion is not safe, it is used when we know we are dealing with --- bottom, which is one case in which it is safe. It is also used to --- implement the unsafeCoerce# primitive. +-- | 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. +-- Optimise by pushing down through type constructors mkUnsafeCoercion :: Type -> Type -> Coercion -mkUnsafeCoercion ty1 ty2 - = mkCoercion unsafeCoercionTyCon [ty1, ty2] +mkUnsafeCoercion (TyConApp tc1 tys1) (TyConApp tc2 tys2) + | tc1 == tc2 + = TyConApp tc1 (zipWith mkUnsafeCoercion tys1 tys2) +mkUnsafeCoercion (FunTy a1 r1) (FunTy a2 r2) + = FunTy (mkUnsafeCoercion a1 a2) (mkUnsafeCoercion r1 r2) + +mkUnsafeCoercion ty1 ty2 + | ty1 `coreEqType` ty2 = ty1 + | otherwise = mkCoercion unsafeCoercionTyCon [ty1, ty2] -- See note [Newtype coercions] in TyCon + +-- | Create a coercion suitable for the given 'TyCon'. The 'Name' should be that of a +-- new coercion 'TyCon', the 'TyVar's the arguments expected by the @newtype@ and the +-- type the appropriate right hand side of the @newtype@, with the free variables +-- a subset of those 'TyVar's. mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon -mkNewTypeCoercion name tycon tvs rhs_ty - = ASSERT (length tvs == tyConArity tycon) - mkCoercionTyCon name co_con_arity (mkKindingFun rule) +mkNewTypeCoercion name tycon tvs rhs_ty + = mkCoercionTyCon name arity desc where - rule args = (TyConApp tycon tys, substTyWith tvs_eta tys rhs_eta, rest) - where - tys = take co_con_arity args - rest = drop co_con_arity args + arity = length tvs + desc = CoAxiom { co_ax_tvs = tvs + , co_ax_lhs = mkTyConApp tycon (mkTyVarTys tvs) + , co_ax_rhs = 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 +-- the coercion tycon built here, @F@ the family tycon and @R@ the (derived) +-- representation tycon. +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 inst_tys rep_tycon + = mkCoercionTyCon name arity desc + where + arity = length tvs + desc = CoAxiom { co_ax_tvs = tvs + , co_ax_lhs = mkTyConApp family inst_tys + , co_ax_rhs = mkTyConApp rep_tycon (mkTyVarTys tvs) } - -- if the rhs_ty is a type application and it has a tail equal to a tail - -- of the tvs, then we eta-contract the type of the coercion - rhs_args = let (ty, ty_args) = splitAppTys rhs_ty in ty_args - n_eta_tys = count_eta (reverse rhs_args) (reverse tvs) +mkClassPPredCo :: Class -> [Coercion] -> Coercion +mkClassPPredCo cls = (PredTy . ClassP cls) - count_eta ((TyVarTy tv):rest_ty) (tv':rest_tv) - | tv == tv' && (not $ any (elemVarSet tv . tyVarsOfType) rest_ty) - -- if the last types are the same, and not free anywhere else - -- then eta contract - = 1 + (count_eta rest_ty rest_tv) - | otherwise -- don't - = 0 - count_eta _ _ = 0 - +mkIParamPredCo :: (IPName Name) -> Coercion -> Coercion +mkIParamPredCo ipn = (PredTy . IParam ipn) - eqVar (TyVarTy tv) tv' = tv == tv' - eqVar _ _ = False +mkEqPredCo :: Coercion -> Coercion -> Coercion +mkEqPredCo co1 co2 = PredTy (EqPred co1 co2) - co_con_arity = (tyConArity tycon) - n_eta_tys - tvs_eta = (reverse (drop n_eta_tys (reverse tvs))) +\end{code} - rhs_eta - | (ty, ty_args) <- splitAppTys rhs_ty - = mkAppTys ty (reverse (drop n_eta_tys (reverse ty_args))) --- 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) --- 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) - where - coArity = length tvs +%************************************************************************ +%* * + Coercion Type Constructors +%* * +%************************************************************************ - rule args = (substTyWith tvs tys $ -- 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 +Example. The coercion ((sym c) (sym d) (sym e)) +will be represented by (TyConApp sym [c, sym d, sym e]) +If sym c :: p1=q1 + sym d :: p2=q2 + sym e :: p3=q3 +then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3) --------------------------------------- --- Coercion Type Constructors... - --- Example. The coercion ((sym c) (sym d) (sym e)) --- will be represented by (TyConApp sym [c, sym d, sym e]) --- If sym c :: p1=q1 --- sym d :: p2=q2 --- sym e :: p3=q3 --- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3) +\begin{code} +-- | Coercion type constructors: avoid using these directly and instead use +-- the @mk*Coercion@ and @split*Coercion@ family of functions if possible. -- --- (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 -- carries its own kinding rule. Such CoercionTyCons must be fully applied -- 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) - where - flipCoercionKindOf (co:rest) = (ty2, ty1, rest) - where - (ty1, ty2) = coercionKind co - -transCoercionTyCon = - mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf) - where - composeCoercionKindsOf (co1:co2:rest) = - WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug") - (a1, r2, rest) - where - (a1, r1) = coercionKind co1 - (a2, r2) = coercionKind co2 - -leftCoercionTyCon = - mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf) - where - leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest) - where - (ty1,ty2) = fst (splitCoercionKindOf co) - -rightCoercionTyCon = - mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf) - where - rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest) - where - (ty1,ty2) = snd (splitCoercionKindOf co) +symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, + rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon, + csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon :: TyCon + +symCoercionTyCon = mkCoercionTyCon symCoercionTyConName 1 CoSym +transCoercionTyCon = mkCoercionTyCon transCoercionTyConName 2 CoTrans +leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 CoLeft +rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 CoRight +instCoercionTyCon = mkCoercionTyCon instCoercionTyConName 2 CoInst +csel1CoercionTyCon = mkCoercionTyCon csel1CoercionTyConName 1 CoCsel1 +csel2CoercionTyCon = mkCoercionTyCon csel2CoercionTyConName 1 CoCsel2 +cselRCoercionTyCon = mkCoercionTyCon cselRCoercionTyConName 1 CoCselR +unsafeCoercionTyCon = mkCoercionTyCon unsafeCoercionTyConName 2 CoUnsafe + +transCoercionTyConName, symCoercionTyConName, leftCoercionTyConName, + rightCoercionTyConName, instCoercionTyConName, unsafeCoercionTyConName, + csel1CoercionTyConName, csel2CoercionTyConName, cselRCoercionTyConName :: Name + +transCoercionTyConName = mkCoConName (fsLit "trans") transCoercionTyConKey transCoercionTyCon +symCoercionTyConName = mkCoConName (fsLit "sym") symCoercionTyConKey symCoercionTyCon +leftCoercionTyConName = mkCoConName (fsLit "left") leftCoercionTyConKey leftCoercionTyCon +rightCoercionTyConName = mkCoConName (fsLit "right") rightCoercionTyConKey rightCoercionTyCon +instCoercionTyConName = mkCoConName (fsLit "inst") instCoercionTyConKey instCoercionTyCon +csel1CoercionTyConName = mkCoConName (fsLit "csel1") csel1CoercionTyConKey csel1CoercionTyCon +csel2CoercionTyConName = mkCoConName (fsLit "csel2") csel2CoercionTyConKey csel2CoercionTyCon +cselRCoercionTyConName = mkCoConName (fsLit "cselR") cselRCoercionTyConKey cselRCoercionTyCon +unsafeCoercionTyConName = mkCoConName (fsLit "CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon + +mkCoConName :: FastString -> Unique -> TyCon -> Name +mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkTcOccFS occ) + key (ATyCon coCon) BuiltInSyntax +\end{code} -splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type)) +\begin{code} +------------ +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)) -splitCoercionKindOf co - | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co) - , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1 +-- if c :: t1 s1 ~ t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2)) +decompLR_maybe (ty1,ty2) + | Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2 - = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2)) - -instCoercionTyCon - = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun 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) - where (t1, t2) = coercionKind co1 - -unsafeCoercionTyCon - = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind) - where - unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest) - --------------------------------------- --- ...and their names - -mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ) - key Nothing (ATyCon coCon) BuiltInSyntax + = Just ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2)) +decompLR_maybe _ = Nothing + +------------ +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)) +decompInst_maybe _ = Nothing + +------------ +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 +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 +\end{code} -transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon -symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon -leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon -rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon -instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon -unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon +%************************************************************************ +%* * + Newtypes +%* * +%************************************************************************ +\begin{code} +instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI) +-- ^ If @co :: T ts ~ rep_ty@ then: +-- +-- > instNewTyCon_maybe T ts = Just (rep_ty, co) +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 (mkTyConApp tc tys) + 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 +-- ^ Sometimes we want to look through a @newtype@ and get its associated coercion. +-- This function only strips *one layer* of @newtype@ off, so the caller will usually call +-- itself recursively. Furthermore, this function should only be applied to types of kind @*@, +-- hence the newtype is always saturated. If @co : ty ~ ty'@ then: +-- +-- > splitNewTypeRepCo_maybe ty = Just (ty', co) +-- +-- The function returns @Nothing@ for non-@newtypes@ or fully-transparent @newtype@s. splitNewTypeRepCo_maybe ty | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty' splitNewTypeRepCo_maybe (TyConApp tc tys) - | isNewTyCon 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) + | 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 _ + = Nothing + +-- | Determines syntactic equality of coercions +coreEqCoercion :: Coercion -> Coercion -> Bool +coreEqCoercion = coreEqType + +coreEqCoercion2 :: RnEnv2 -> Coercion -> Coercion -> Bool +coreEqCoercion2 = coreEqType2 +\end{code} + + +%************************************************************************ +%* * + CoercionI and its constructors +%* * +%************************************************************************ + +-------------------------------------- +-- CoercionI smart constructors +-- lifted smart constructors of ordinary coercions + +\begin{code} +-- | 'CoercionI' represents a /lifted/ ordinary 'Coercion', in that it +-- can represent either one of: +-- +-- 1. A proper 'Coercion' +-- +-- 2. The identity coercion +data CoercionI = IdCo Type | ACo Coercion + +liftCoI :: (Type -> Type) -> CoercionI -> CoercionI +liftCoI f (IdCo ty) = IdCo (f ty) +liftCoI f (ACo ty) = ACo (f ty) + +liftCoI2 :: (Type -> Type -> Type) -> CoercionI -> CoercionI -> CoercionI +liftCoI2 f (IdCo ty1) (IdCo ty2) = IdCo (f ty1 ty2) +liftCoI2 f coi1 coi2 = ACo (f (fromCoI coi1) (fromCoI coi2)) + +liftCoIs :: ([Type] -> Type) -> [CoercionI] -> CoercionI +liftCoIs f cois = go_id [] cois + where + go_id rev_tys [] = IdCo (f (reverse rev_tys)) + go_id rev_tys (IdCo ty : cois) = go_id (ty:rev_tys) cois + go_id rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois + + go_aco rev_tys [] = ACo (f (reverse rev_tys)) + go_aco rev_tys (IdCo ty : cois) = go_aco (ty:rev_tys) cois + go_aco rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois + +instance Outputable CoercionI where + ppr (IdCo _) = ptext (sLit "IdCo") + ppr (ACo co) = ppr co + +isIdentityCoI :: CoercionI -> Bool +isIdentityCoI (IdCo _) = True +isIdentityCoI (ACo _) = False + +-- | Return either the 'Coercion' contained within the 'CoercionI' or the given +-- 'Type' if the 'CoercionI' is the identity 'Coercion' +fromCoI :: CoercionI -> Type +fromCoI (IdCo ty) = ty -- Identity coercion represented +fromCoI (ACo co) = co -- by the type itself + +-- | Smart constructor for @sym@ on 'CoercionI', see also 'mkSymCoercion' +mkSymCoI :: CoercionI -> CoercionI +mkSymCoI (IdCo ty) = IdCo ty +mkSymCoI (ACo co) = ACo $ mkCoercion symCoercionTyCon [co] + -- the smart constructor + -- is too smart with tyvars + +-- | Smart constructor for @trans@ on 'CoercionI', see also 'mkTransCoercion' +mkTransCoI :: CoercionI -> CoercionI -> CoercionI +mkTransCoI (IdCo _) aco = aco +mkTransCoI aco (IdCo _) = aco +mkTransCoI (ACo co1) (ACo co2) = ACo $ mkTransCoercion co1 co2 + +-- | Smart constructor for type constructor application on 'CoercionI', see also 'mkAppCoercion' +mkTyConAppCoI :: TyCon -> [CoercionI] -> CoercionI +mkTyConAppCoI tyCon cois = liftCoIs (mkTyConApp tyCon) cois + +-- | Smart constructor for honest-to-god 'Coercion' application on 'CoercionI', see also 'mkAppCoercion' +mkAppTyCoI :: CoercionI -> CoercionI -> CoercionI +mkAppTyCoI = liftCoI2 mkAppTy + +mkFunTyCoI :: CoercionI -> CoercionI -> CoercionI +mkFunTyCoI = liftCoI2 mkFunTy + +-- | Smart constructor for quantified 'Coercion's on 'CoercionI', see also 'mkForAllCoercion' +mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI +mkForAllTyCoI tv = liftCoI (ForAllTy tv) + +-- | Smart constructor for class 'Coercion's on 'CoercionI'. Satisfies: +-- +-- > mkClassPPredCoI cls tys cois :: PredTy (cls tys) ~ PredTy (cls (tys `cast` cois)) +mkClassPPredCoI :: Class -> [CoercionI] -> CoercionI +mkClassPPredCoI cls = liftCoIs (PredTy . ClassP cls) + +-- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI' +mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI +mkIParamPredCoI ipn = liftCoI (PredTy . IParam ipn) + +-- | Smart constructor for type equality 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI' +mkEqPredCoI :: CoercionI -> CoercionI -> CoercionI +mkEqPredCoI = liftCoI2 (\t1 t2 -> PredTy (EqPred t1 t2)) + +mkCoPredCoI :: CoercionI -> CoercionI -> CoercionI -> CoercionI +mkCoPredCoI coi1 coi2 coi3 = mkFunTyCoI (mkEqPredCoI coi1 coi2) coi3 + + +\end{code} + +%************************************************************************ +%* * + The kind of a type, and of a coercion +%* * +%************************************************************************ + +\begin{code} +typeKind :: Type -> Kind +typeKind ty@(TyConApp tc tys) + | isCoercionTyCon tc = typeKind (fst (coercionKind ty)) + | otherwise = kindAppResult (tyConKind tc) tys + -- During coercion optimisation we *do* match a type + -- against a coercion (see OptCoercion.matchesAxiomLhs) + -- So the use of typeKind in Unify.match_kind must work on coercions too + -- Hence the isCoercionTyCon case above + +typeKind (PredTy pred) = predKind pred +typeKind (AppTy fun _) = kindFunResult (typeKind fun) +typeKind (ForAllTy _ ty) = typeKind ty +typeKind (TyVarTy tyvar) = tyVarKind tyvar +typeKind (FunTy _arg res) + -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*), + -- not unliftedTypKind (#) + -- The only things that can be after a function arrow are + -- (a) types (of kind openTypeKind or its sub-kinds) + -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *)) + | isTySuperKind k = k + | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind + where + k = typeKind res + +------------------ +predKind :: PredType -> Kind +predKind (EqPred {}) = coSuperKind -- A coercion kind! +predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are +predKind (IParam {}) = liftedTypeKind -- always represented by lifted types + +------------------ +-- | If it is the case that +-- +-- > c :: (t1 ~ t2) +-- +-- i.e. the kind of @c@ is a 'CoercionKind' relating @t1@ and @t2@, +-- then @coercionKind c = (t1, t2)@. +coercionKind :: Coercion -> (Type, Type) +coercionKind ty@(TyVarTy a) | isCoVar a = coVarKind a + | otherwise = (ty, ty) +coercionKind (AppTy ty1 ty2) + = let (s1, t1) = coercionKind ty1 + (s2, t2) = coercionKind ty2 in + (mkAppTy s1 s2, mkAppTy t1 t2) +coercionKind co@(TyConApp tc args) + | Just (ar, desc) <- isCoercionTyCon_maybe tc + -- CoercionTyCons carry their kinding rule, so we use it here + = WARN( not (length args >= ar), ppr co ) -- Always saturated + (let (ty1, ty2) = coTyConAppKind desc (take ar 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) + +coercionKind (FunTy ty1 ty2) + = let (t1, t2) = coercionKind ty1 + (s1, s2) = coercionKind ty2 in + (mkFunTy t1 s1, mkFunTy t2 s2) + +coercionKind (ForAllTy tv ty) + | isCoVar tv +-- c1 :: s1~s2 c2 :: t1~t2 c3 :: r1~r2 +-- ---------------------------------------------- +-- c1~c2 => c3 :: (s1~t1) => r1 ~ (s2~t2) => r2 +-- or +-- forall (_:c1~c2) + = let (c1,c2) = coVarKind tv + (s1,s2) = coercionKind c1 + (t1,t2) = coercionKind c2 + (r1,r2) = coercionKind ty + in + (mkCoPredTy s1 t1 r1, mkCoPredTy s2 t2 r2) + + | otherwise +-- c1 :: s1~s2 c2 :: t1~t2 c3 :: r1~r2 +-- ---------------------------------------------- +-- forall a:k. c :: forall a:k. t1 ~ forall a:k. t2 + = let (ty1, ty2) = coercionKind ty in + (ForAllTy tv ty1, ForAllTy tv ty2) + +coercionKind (PredTy (ClassP cl args)) + = let (lArgs, rArgs) = coercionKinds args in + (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs)) +coercionKind (PredTy (IParam name ty)) + = let (ty1, ty2) = coercionKind ty in + (PredTy (IParam name ty1), PredTy (IParam name ty2)) +coercionKind (PredTy (EqPred c1 c2)) + = pprTrace "coercionKind" (pprEqPred (c1,c2)) $ + -- These should not show up in coercions at all + -- becuase they are in the form of for-alls + let k1 = coercionKindPredTy c1 + k2 = coercionKindPredTy c2 in + (k1,k2) + where + coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2 + +------------------ +-- | Apply 'coercionKind' to multiple 'Coercion's +coercionKinds :: [Coercion] -> ([Type], [Type]) +coercionKinds tys = unzip $ map coercionKind tys + +------------------ +-- | 'coTyConAppKind' is given a list of the type arguments to the 'CoTyCon', +-- and constructs the types that the resulting coercion relates. +-- Fails (in the monad) if ill-kinded. +-- Typically the monad is +-- either the Lint monad (with the consistency-check flag = True), +-- or the ID monad with a panic on failure (and the consistency-check flag = False) +coTyConAppKind + :: CoTyConDesc + -> [Type] -- Exactly right number of args + -> (Type, Type) -- Kind of this application +coTyConAppKind CoUnsafe (ty1:ty2:_) + = (ty1,ty2) +coTyConAppKind CoSym (co:_) + | (ty1,ty2) <- coercionKind co = (ty2,ty1) +coTyConAppKind CoTrans (co1:co2:_) + = (fst (coercionKind co1), snd (coercionKind co2)) +coTyConAppKind CoLeft (co:_) + | Just (res,_) <- decompLR_maybe (coercionKind co) = res +coTyConAppKind CoRight (co:_) + | Just (_,res) <- decompLR_maybe (coercionKind co) = res +coTyConAppKind CoCsel1 (co:_) + | Just (res,_,_) <- decompCsel_maybe (coercionKind co) = res +coTyConAppKind CoCsel2 (co:_) + | Just (_,res,_) <- decompCsel_maybe (coercionKind co) = res +coTyConAppKind CoCselR (co:_) + | Just (_,_,res) <- decompCsel_maybe (coercionKind co) = res +coTyConAppKind CoInst (co:ty:_) + | Just ((tv1,tv2), (ty1,ty2)) <- decompInst_maybe (coercionKind co) + = (substTyWith [tv1] [ty] ty1, substTyWith [tv2] [ty] ty2) +coTyConAppKind (CoAxiom { co_ax_tvs = tvs + , co_ax_lhs = lhs_ty, co_ax_rhs = rhs_ty }) cos + = (substTyWith tvs tys1 lhs_ty, substTyWith tvs tys2 rhs_ty) where - co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo tc) -splitNewTypeRepCo_maybe other = Nothing + (tys1, tys2) = coercionKinds cos +coTyConAppKind desc cos = pprTrace "coTyConAppKind" (ppr desc $$ braces (vcat + [ ppr co <+> dcolon <+> pprEqPred (coercionKind co) + | co <- cos ])) $ + coercionKind (head cos) \end{code}