X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=compiler%2Ftypes%2FCoercion.lhs;h=83a5af341cacc4c33acb5a8a390b2852b47ee2b8;hb=bcadca676448e38427b910bad5d7063f948a99c8;hp=54061ed4fea3cea3a143034e2ebe9e7d74e9ebd9;hpb=a92db2a52d056ab962e4f55d5d8e3997ac3b8e4f;p=ghc-hetmet.git diff --git a/compiler/types/Coercion.lhs b/compiler/types/Coercion.lhs index 54061ed..83a5af3 100644 --- a/compiler/types/Coercion.lhs +++ b/compiler/types/Coercion.lhs @@ -1,70 +1,97 @@ - - 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] +T% +% (c) The University of Glasgow 2006 +% \begin{code} +{-# OPTIONS -fno-warn-incomplete-patterns #-} +-- 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, mkReflCoKind, coVarKind, + 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, mkAppsCoercion, + mkLeftCoercion, mkRightCoercion, mkRightCoercions, + 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, + + -- ** Optimisation + optCoercion, + + -- ** Comparison + coreEqCoercion, + + -- * CoercionI + CoercionI(..), + isIdentityCoI, + mkSymCoI, mkTransCoI, + mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI, + mkForAllTyCoI, + fromCoI, fromACo, + mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI + ) where #include "HsVersions.h" import TypeRep -import Type ( Type, Kind, PredType, substTyWith, mkAppTy, mkForAllTy, - mkFunTy, splitAppTy_maybe, splitForAllTy_maybe, coreView, - kindView, mkTyConApp, isCoercionKind, isEqPred, mkAppTys - ) -import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isNewTyCon, - newTyConRhs, newTyConCo, - isCoercionTyCon, isCoercionTyCon_maybe ) -import Var ( Var, TyVar, isTyVar, tyVarKind ) -import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName ) -import OccName ( mkOccNameFS ) -import PrelNames ( symCoercionTyConKey, - transCoercionTyConKey, leftCoercionTyConKey, - rightCoercionTyConKey, instCoercionTyConKey, - unsafeCoercionTyConKey, gHC_PRIM - ) -import Util ( lengthIs, snocView ) -import Unique ( hasKey ) -import BasicTypes ( Arity ) +import Type +import TyCon +import Class +import Var +import Name +import PrelNames +import Util +import BasicTypes 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) @@ -73,42 +100,51 @@ decomposeCo n co ------------------------------------------------------- -- and some coercion kind stuff +coVarKind :: CoVar -> (Type,Type) +-- c :: t1 ~ t2 +coVarKind cv = splitCoVarKind (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) + +-- | 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 = ForAllTy (mkWildCoVar (mkCoKind s t)) r + +-- | 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) - +-- | Create a reflexive 'CoercionKind' that asserts that a type can be coerced to itself mkReflCoKind :: Type -> CoercionKind mkReflCoKind ty = mkCoKind ty ty -splitCoercionKind :: CoercionKind -> (Type, Type) -splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co' -splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2) - -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 - -isCoVar :: Var -> Bool -isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv) - -type Coercion = Type -type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2) - +-- | 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 (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a) - | otherwise = let t = (TyVarTy a) in (t, t) +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 @@ -116,10 +152,11 @@ coercionKind (AppTy ty1 ty2) coercionKind (TyConApp tc args) | Just (ar, rule) <- isCoercionTyCon_maybe tc -- CoercionTyCons carry their kinding rule, so we use it here - = if length args >= ar - then splitCoercionKind (rule args) - else pprPanic ("arity/arguments mismatch in coercionKind:") - (ppr ar $$ ppr tc <+> ppr args) + = ASSERT( length args >= ar ) -- Always saturated + let (ty1,ty2) = rule (take ar args) -- Apply the rule to the right number of args + (tys1, tys2) = coercionKinds (drop ar args) + in (mkAppTys ty1 tys1, mkAppTys ty2 tys2) + | otherwise = let (lArgs, rArgs) = coercionKinds args in (TyConApp tc lArgs, TyConApp tc rArgs) @@ -127,14 +164,40 @@ 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)) @@ -142,75 +205,186 @@ 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 -mkAppCoercion co1 co2 = mkAppTy co1 co2 -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 + +-- | 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 + +------------------------------- + +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@. +-- +-- 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 co2 <- splitSymCoercion_maybe co = co2 - | Just (co1, co2) <- splitAppCoercion_maybe co - -- should make this case better - = mkAppCoercion (mkSymCoercion co1) (mkSymCoercion co2) - | Just (co1, co2) <- splitTransCoercion_maybe co + | Just co' <- coreView co = mkSymCoercion co' + +mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty) +mkSymCoercion (AppTy co1 co2) = AppTy (mkSymCoercion co1) (mkSymCoercion co2) +mkSymCoercion (FunTy co1 co2) = FunTy (mkSymCoercion co1) (mkSymCoercion co2) + +mkSymCoercion (TyConApp tc cos) + | not (isCoercionTyCon tc) = mkTyConApp tc (map mkSymCoercion cos) + +mkSymCoercion (TyConApp tc [co]) + | tc `hasKey` symCoercionTyConKey = co -- sym (sym co) --> co + | tc `hasKey` leftCoercionTyConKey = mkLeftCoercion (mkSymCoercion co) + | tc `hasKey` rightCoercionTyConKey = mkRightCoercion (mkSymCoercion co) + +mkSymCoercion (TyConApp tc [co1,co2]) + | tc `hasKey` transCoercionTyConKey + -- sym (co1 `trans` co2) --> (sym co2) `trans (sym co2) + -- Note reversal of arguments! = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1) - | Just (co, ty) <- splitInstCoercion_maybe co - = mkInstCoercion (mkSymCoercion co) ty - | Just co <- splitLeftCoercion_maybe co - = mkLeftCoercion (mkSymCoercion co) - | Just co <- splitRightCoercion_maybe co - = mkRightCoercion (mkSymCoercion co) -mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty) --- for atomic types and constructors, we can just ignore sym since these --- are reflexive coercions + + | 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 -mkSymCoercion co = mkCoercion symCoercionTyCon [co] - -- this should not happen but does + | otherwise = TyVarTy tv -- Reflexive + +------------------------------- +-- ToDo: we should be cleverer about transitivity + +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 + +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] + | otherwise = 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 (co1, co2) <- splitAppCoercion_maybe co = co2 + | Just (_, co2) <- splitAppCoercion_maybe co = co2 | otherwise = mkCoercion rightCoercionTyCon [co] -mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2] - -mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty] +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 + + +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 + | Just (tv,co') <- splitForAllTy_maybe co + = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a] + | otherwise + = 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 +-- ^ 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) @@ -219,8 +393,9 @@ splitAppCoercion_maybe (TyConApp tc tys) = case snocView tys of Just (tys', ty') -> Just (TyConApp tc tys', ty') Nothing -> Nothing -splitAppCoercion_maybe co = Nothing +splitAppCoercion_maybe _ = Nothing +{- splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion) splitTransCoercion_maybe (TyConApp tc [ty1, ty2]) = if tc `hasKey` transCoercionTyConKey then @@ -252,139 +427,444 @@ splitRightCoercion_maybe (TyConApp tc [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 the 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] --- Make the coercion associated with a newtype. If we have --- --- newtype T a b = MkT (Int, a, b) --- --- Then (mkNewTypeCoercion CoT T [a,b] (Int, a, b)) creates the coercion --- CoT, such kinding rule such that --- --- CoT S U :: (Int, S, U) :=: T S U +-- 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 (tyConArity tycon) rule +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) + +-- | 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 instTys rep_tycon + = mkCoercionTyCon name coArity rule where - rule args = mkCoKind (substTyWith tvs args rhs_ty) (TyConApp tycon args) + coArity = length tvs + rule args = (substTyWith tvs args $ -- with sigma = [tys/tvs], + TyConApp family instTys, -- sigma (F ts) + TyConApp rep_tycon args) -- ~ R tys +\end{code} --------------------------------------- --- 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) --- --- (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 +%************************************************************************ +%* * + 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, transCoercionTyCon, leftCoercionTyCon, + rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon, + csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon :: TyCon + symCoercionTyCon = - mkCoercionTyCon symCoercionTyConName 1 (mkKindingFun flipCoercionKindOf) + mkCoercionTyCon symCoercionTyConName 1 flipCoercionKindOf where - flipCoercionKindOf (co:rest) = (ty2, ty1, rest) + flipCoercionKindOf (co:rest) = ASSERT( null rest ) (ty2, ty1) where (ty1, ty2) = coercionKind co transCoercionTyCon = - mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf) + mkCoercionTyCon transCoercionTyConName 2 composeCoercionKindsOf where - composeCoercionKindsOf (co1:co2:rest) = (a1, r2, rest) + 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 -leftCoercionTyCon = - mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf) - where - leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest) - where - (ty1,ty2) = fst (splitCoercionKindOf co) + _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 ] -rightCoercionTyCon = - mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf) - where - rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest) - where - (ty1,ty2) = snd (splitCoercionKindOf co) +--------------------------------------------------- +leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 (fst . decompLR) +rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 (snd . decompLR) -splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type)) +decompLR :: [Type] -> ((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) +-- 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 , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2 - = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2)) + = ASSERT( null rest) + ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2)) +decompLR cos + = pprPanic "Coercion.decompLR" + (ppr cos $$ vcat (map (pprEqPred .coercionKind) cos)) +--------------------------------------------------- instCoercionTyCon - = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind) + = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind where instantiateCo t s = let Just (tv, ty) = splitForAllTy_maybe t in substTyWith [tv] [s] ty - instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest) + instCoercionKind (co1:ty:rest) = ASSERT( null rest ) + (instantiateCo t1 ty, instantiateCo t2 ty) where (t1, t2) = coercionKind co1 +--------------------------------------------------- unsafeCoercionTyCon - = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind) + = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind where - unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest) + unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2) --------------------------------------- --- ...and their names +--------------------------------------------------- +-- The csel* family +-- 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) + +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) - key Nothing (ATyCon coCon) BuiltInSyntax +-------------------------------------- +-- 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) - | 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 +\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) + +-- | 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 = + 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 + +-- | 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} +optCoercion :: Coercion -> Coercion +optCoercion co + = ASSERT2( coercionKind co `eq` coercionKind result, + ppr co $$ ppr result $$ ppr (coercionKind co) $$ ppr (coercionKind result) ) + result where - co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo tc) -splitNewTypeRepCo_maybe other = Nothing + (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 + -- + 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] <- args + = case go ty1 of + (ty1', _ , True) -> (ty1', True, True) + (ty1', True, _ ) -> (TyConApp tc [ty1'], True, False) + (_ , _ , _ ) -> (ty, False, False) + | tc == transCoercionTyCon, [ty1,ty2] <- args + = let (ty1', chan1, id1) = go ty1 + (ty2', chan2, id2) = go ty2 + in if id1 + then (ty2', True, id2) + else if id2 + then (ty1', True, False) + else if chan1 || chan2 + then (TyConApp tc [ty1',ty2'], True , False) + else (ty , False, False) + | tc == leftCoercionTyCon, [ty1] <- args + = let (ty1', chan1, id1) = go ty1 + in if chan1 + then (TyConApp tc [ty1'], True , id1) + else (ty , False, id1) + | tc == rightCoercionTyCon, [ty1] <- args + = let (ty1', chan1, id1) = go ty1 + in if chan1 + then (TyConApp tc [ty1'], True , id1) + else (ty , False, id1) + | 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) \end{code}