X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=compiler%2Ftypes%2FCoercion.lhs;h=08f593e9bd0c984e49ca56070162151c7dc350f9;hb=0e73a9fbdc8555ffb948cfd72401a700b122c395;hp=672deae68be2163872948f37a7d084f5d69dac93;hpb=ab22f4e6456820c1b5169d75f5975a94e61f54ce;p=ghc-hetmet.git diff --git a/compiler/types/Coercion.lhs b/compiler/types/Coercion.lhs index 672deae..08f593e 100644 --- a/compiler/types/Coercion.lhs +++ b/compiler/types/Coercion.lhs @@ -2,36 +2,64 @@ % (c) The University of Glasgow 2006 % -Module for type coercions, as in System FC. - -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 - - typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type] - \begin{code} +-- 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 for 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 CoercionTyCon{...} [type, type] module Coercion ( + -- * Main data type 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, - splitNewTypeRepCo_maybe, decomposeCo, + splitNewTypeRepCo_maybe, instNewTyCon_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, + + -- ** Optimisation + optCoercion, + + -- ** Comparison + coreEqCoercion, coreEqCoercion2, + + -- * CoercionI + CoercionI(..), + isIdentityCoI, + mkSymCoI, mkTransCoI, + mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI, + mkForAllTyCoI, + fromCoI, fromACo, + mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI + ) where #include "HsVersions.h" @@ -39,25 +67,36 @@ module Coercion ( import TypeRep import Type import TyCon -import Var hiding (isCoVar) +import Class +import Var +import VarEnv import Name -import OccName import PrelNames import Util -import Unique +import Control.Monad import BasicTypes +import MonadUtils import Outputable +import FastString + +-- | 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) @@ -66,53 +105,78 @@ decomposeCo n co ------------------------------------------------------- -- and some coercion kind stuff -isEqPredTy (PredTy pred) = isEqPred pred -isEqPredTy other = False +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)) -mkEqPred :: (Type, Type) -> PredType -mkEqPred (ty1, ty2) = EqPred ty1 ty2 +coVarKind_maybe :: CoVar -> Maybe (Type,Type) +coVarKind_maybe cv = splitCoKind_maybe (tyVarKind cv) -getEqPredTys :: PredType -> (Type,Type) -getEqPredTys (EqPred ty1 ty2) = (ty1, ty2) -getEqPredTys other = pprPanic "getEqPredTys" (ppr other) +-- | 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) -mkReflCoKind :: Type -> CoercionKind -mkReflCoKind ty = mkCoKind ty ty +-- | (mkCoPredTy s t r) produces the type: (s~t) => r +mkCoPredTy :: Type -> Type -> Type -> Type +mkCoPredTy s t r = ForAllTy (mkWildCoVar (mkCoKind s t)) r -splitCoercionKind :: CoercionKind -> (Type, Type) -splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co' -splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2) +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 -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 +-- | Tests whether a type is just a type equality predicate +isEqPredTy :: Type -> Bool +isEqPredTy (PredTy pred) = isEqPred pred +isEqPredTy _ = False -isCoVar :: Var -> Bool -isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv) +-- | Creates a type equality predicate +mkEqPred :: (Type, Type) -> PredType +mkEqPred (ty1, ty2) = EqPred ty1 ty2 -type Coercion = Type -type CoercionKind = Kind -- A CoercionKind is always of form (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) +-- | 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) --- c :: (t1 :=: t2) --- Then (coercionKind c) = (t1,t2) -coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a) +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 @@ -121,14 +185,40 @@ coercionKind (FunTy ty1 ty2) = let (t1, t2) = coercionKind ty1 (s1, s2) = coercionKind ty2 in (mkFunTy t1 s1, mkFunTy t2 s2) -coercionKind (ForAllTy tv ty) + +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 (NoteTy _ ty) = coercionKind ty + coercionKind (PredTy (EqPred c1 c2)) - = let k1 = coercionKindPredTy c1 + = pprTrace "coercionKind" (pprEqPred (c1,c2)) $ + let k1 = coercionKindPredTy c1 k2 = coercionKindPredTy c2 in (k1,k2) + -- These should not show up in coercions at all + -- becuase they are in the form of for-alls + where + coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2 + + + coercionKind (PredTy (ClassP cl args)) = let (lArgs, rArgs) = coercionKinds args in (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs)) @@ -136,281 +226,682 @@ coercionKind (PredTy (IParam name ty)) = let (ty1, ty2) = coercionKind ty in (PredTy (IParam name ty1), PredTy (IParam name ty2)) -coercionKindPredTy :: Coercion -> CoercionKind -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 ------------------------------------- --- Coercion kind and type mk's --- (make saturated TyConApp CoercionTyCon{...} args) +isIdentityCoercion :: Coercion -> Bool +isIdentityCoercion co + = case coercionKind co of + (t1,t2) -> t1 `coreEqType` t2 +\end{code} + +%************************************************************************ +%* * + Building coercions +%* * +%************************************************************************ + +Coercion kind and type mk's (make saturated TyConApp CoercionTyCon{...} args) +\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 -mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion -mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion +-- | 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 + +-- | 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 + +-- | Apply a type constructor to a list of coercions. +mkTyConCoercion :: TyCon -> [Coercion] -> Coercion +mkTyConCoercion con cos = mkTyConApp con cos -mkAppCoercion co1 co2 = mkAppTy co1 co2 -mkAppsCoercion co1 tys = foldl mkAppTy co1 tys +-- | Make a function 'Coercion' between two other 'Coercion's +mkFunCoercion :: Coercion -> Coercion -> Coercion +mkFunCoercion co1 co2 = mkFunTy co1 co2 + +-- | 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 ( 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. mkUnsafeCoercion :: Type -> Type -> Coercion mkUnsafeCoercion ty1 ty2 = mkCoercion unsafeCoercionTyCon [ty1, ty2] -- See note [Newtype coercions] in TyCon -mkNewTypeCoercion :: Name -> TyCon -> ([TyVar], Type) -> TyCon -mkNewTypeCoercion name tycon (tvs, rhs_ty) + +-- | 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 = mkCoercionTyCon name co_con_arity rule 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) } --- 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) +-- | 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. --- -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 +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 args $ -- with sigma = [tys/tvs], - TyConApp family instTys, -- sigma (F ts) - TyConApp rep_tycon args) -- :=: R tys --------------------------------------- --- Coercion Type Constructors... + 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 _ [] = True +kindAppOk kfn (k:ks) + = case splitKindFunTy_maybe kfn of + Just (kfa, kfb) | k `isSubKind` kfa -> kindAppOk kfb ks + _other -> False +\end{code} --- 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) -symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon +%************************************************************************ +%* * + 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. +-- -- 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 flipCoercionKindOf - where - flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1) - where - (ty1, ty2) = coercionKind co +symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, + rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon, + csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon :: TyCon -transCoercionTyCon = - mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf - where - composeCoercionKindsOf (co1:co2:rest) - = ASSERT( null rest ) - WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug") - (a1, r2) - where - (a1, r1) = coercionKind co1 - (a2, r2) = coercionKind co2 - -leftCoercionTyCon = - mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf +symCoercionTyCon + = mkCoercionTyCon symCoercionTyConName 1 kc_sym where - leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2) - where - (ty1,ty2) = fst (splitCoercionKindOf co) - -rightCoercionTyCon = - mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf + kc_sym :: CoTyConKindChecker + kc_sym _kc_ty kc_co _ (co:_) + = do { (ty1,ty2) <- kc_co co + ; return (ty2,ty1) } + kc_sym _ _ _ _ = panic "kc_sym" + +transCoercionTyCon + = mkCoercionTyCon transCoercionTyConName 2 kc_trans where - rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2) - where - (ty1,ty2) = snd (splitCoercionKindOf co) - -splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type)) + 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) } + kc_trans _ _ _ _ = panic "kc_sym" + +--------------------------------------------------- +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) } +kcLR_help _ _ _ _ _ = panic "kcLR_help" + +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)) + = 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 - - instCoercionKind (co1:ty:rest) = ASSERT( null rest ) - (instantiateCo t1 ty, instantiateCo t2 ty) - where (t1, t2) = coercionKind co1 - + 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) } } + kcInst_help _ _ _ _ = panic "kcInst_help" + +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 + +--------------------------------------------------- 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 { _ <- kc_ty ty1 + ; _ <- kc_ty ty2 + ; return (ty1,ty2) } + kc_unsafe _ _ _ _ = panic "kc_unsafe" --------------------------------------- --- ...and their names +--------------------------------------------------- +-- 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 : _) + = do { (ty1,ty2) <- kc_co co + ; case decompCsel_maybe ty1 ty2 of + Nothing -> fail "decompCsel" + Just res -> return (select res) } +kcCsel_help _ _ _ _ _ = panic "kcCsel_help" + +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 + +fstOf3 :: (a,b,c) -> a +sndOf3 :: (a,b,c) -> b +thirdOf3 :: (a,b,c) -> c +fstOf3 (a,_,_) = a +sndOf3 (_,b,_) = b +thirdOf3 (_,_,c) = c -mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ) +-------------------------------------- +-- Their Names + +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} -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 + 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) - | 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 _ + = 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 | ACo Coercion + +instance Outputable CoercionI where + ppr IdCo = ptext (sLit "IdCo") + ppr (ACo co) = ppr co + +isIdentityCoI :: CoercionI -> Bool +isIdentityCoI IdCo = True +isIdentityCoI _ = False + +-- | Tests whether all the given 'CoercionI's represent the identity coercion +allIdCoIs :: [CoercionI] -> Bool +allIdCoIs = all isIdentityCoI + +-- | For each 'CoercionI' in the input list, return either the 'Coercion' it +-- contains or the corresponding 'Type' from the other list +zipCoArgs :: [CoercionI] -> [Type] -> [Coercion] +zipCoArgs cois tys = zipWith fromCoI cois tys + +-- | Return either the 'Coercion' contained within the 'CoercionI' or the given +-- 'Type' if the 'CoercionI' is the identity 'Coercion' +fromCoI :: CoercionI -> Type -> 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 = IdCo +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 -> [Type] -> [CoercionI] -> CoercionI +mkTyConAppCoI tyCon tys cois + | allIdCoIs cois = IdCo + | otherwise = ACo (TyConApp tyCon (zipCoArgs cois tys)) + +-- | Smart constructor for honest-to-god 'Coercion' application on 'CoercionI', see also 'mkAppCoercion' +mkAppTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI +mkAppTyCoI _ IdCo _ IdCo = IdCo +mkAppTyCoI ty1 coi1 ty2 coi2 = + ACo $ AppTy (fromCoI coi1 ty1) (fromCoI coi2 ty2) + + +mkFunTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI +mkFunTyCoI _ IdCo _ IdCo = IdCo +mkFunTyCoI ty1 coi1 ty2 coi2 = + ACo $ FunTy (fromCoI coi1 ty1) (fromCoI coi2 ty2) + +-- | Smart constructor for quantified 'Coercion's on 'CoercionI', see also 'mkForAllCoercion' +mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI +mkForAllTyCoI _ IdCo = IdCo +mkForAllTyCoI tv (ACo co) = ACo $ ForAllTy tv co + +-- | Extract a 'Coercion' from a 'CoercionI' if it represents one. If it is the identity coercion, +-- panic +fromACo :: CoercionI -> Coercion +fromACo (ACo co) = co +fromACo (IdCo {}) = panic "fromACo" + +-- | Smart constructor for class 'Coercion's on 'CoercionI'. Satisfies: +-- +-- > mkClassPPredCoI cls tys cois :: PredTy (cls tys) ~ PredTy (cls (tys `cast` cois)) +mkClassPPredCoI :: Class -> [Type] -> [CoercionI] -> CoercionI +mkClassPPredCoI cls tys cois + | allIdCoIs cois = IdCo + | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys) + +-- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI' +mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI +mkIParamPredCoI _ IdCo = IdCo +mkIParamPredCoI ipn (ACo co) = ACo $ PredTy $ IParam ipn co + +-- | Smart constructor for type equality 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI' +mkEqPredCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI +mkEqPredCoI _ IdCo _ IdCo = IdCo +mkEqPredCoI ty1 IdCo _ (ACo co2) = ACo $ PredTy $ EqPred ty1 co2 +mkEqPredCoI _ (ACo co1) ty2 coi2 = ACo $ PredTy $ EqPred co1 (fromCoI coi2 ty2) +\end{code} + +%************************************************************************ +%* * + Optimising coercions +%* * +%************************************************************************ + +\begin{code} +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 + 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}