From 1fa25d26f6bc9ab6def35b272405bad5bd23f6bf Mon Sep 17 00:00:00 2001 From: Max Bolingbroke Date: Thu, 31 Jul 2008 01:23:51 +0000 Subject: [PATCH] Document Coercion --- compiler/types/Coercion.lhs | 212 ++++++++++++++++++++++++++++++------------- 1 file changed, 149 insertions(+), 63 deletions(-) diff --git a/compiler/types/Coercion.lhs b/compiler/types/Coercion.lhs index 3bc5d84..d6b92fa 100644 --- a/compiler/types/Coercion.lhs +++ b/compiler/types/Coercion.lhs @@ -2,15 +2,6 @@ % (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} {-# OPTIONS -fno-warn-incomplete-patterns #-} -- The above warning supression flag is a temporary kludge. @@ -19,16 +10,24 @@ The coercion kind constructor is a special TyCon that must always be saturated -- 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, - -- Equality predicates + -- ** Equality predicates isEqPred, mkEqPred, getEqPredTys, isEqPredTy, - -- Coercion transformations + -- ** Coercion transformations mkCoercion, mkSymCoercion, mkTransCoercion, mkLeftCoercion, mkRightCoercion, mkRightCoercions, @@ -42,10 +41,10 @@ module Coercion ( transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn - -- Comparison + -- ** Comparison coreEqCoercion, - -- CoercionI + -- * CoercionI CoercionI(..), isIdentityCoercion, mkSymCoI, mkTransCoI, @@ -72,14 +71,20 @@ import BasicTypes import Outputable import FastString +-- | A 'Coercion' represents a 'Type' something should be coerced to. type Coercion = Type -type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2) + +-- | 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 @@ -92,35 +97,48 @@ decomposeCo n co ------------------------------------------------------- -- and some coercion kind stuff +-- | Tests whether a type is just a type equality predicate isEqPredTy :: Type -> Bool isEqPredTy (PredTy pred) = isEqPred pred 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) +-- | 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) +-- | Create a reflexive 'CoercionKind' that asserts that a type can be coerced to itself mkReflCoKind :: Type -> CoercionKind mkReflCoKind ty = mkCoKind ty ty +-- | Take a 'CoercionKind' apart into the two types it relates: see also 'mkCoKind'. +-- Panics if the argument is not a valid 'CoercionKind' splitCoercionKind :: CoercionKind -> (Type, Type) splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co' splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2) +-- | Take a 'CoercionKind' apart into the two types it relates, if possible. See also 'splitCoercionKind' 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 _ = Nothing +-- | 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)@. +-- See also 'coercionKindPredTy' coercionKind :: Coercion -> (Type, Type) --- c :: (t1 :=: t2) --- Then (coercionKind c) = (t1,t2) coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a) | otherwise = (ty, ty) coercionKind (AppTy ty1 ty2) @@ -156,9 +174,12 @@ coercionKind (PredTy (IParam name ty)) = let (ty1, ty2) = coercionKind ty in (PredTy (IParam name ty1), PredTy (IParam name ty2)) +-- | Recover the 'CoercionKind' corresponding to a particular 'Coerceion'. See also 'coercionKind' +-- and 'mkCoKind' 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 @@ -166,27 +187,43 @@ coercionKinds tys = unzip $ map coercionKind tys -- Coercion kind and type mk's -- (make saturated TyConApp CoercionTyCon{...} args) +-- | 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 -mkAppsCoercion, mkInstsCoercion :: Coercion -> [Coercion] -> Coercion -mkForAllCoercion :: Var -> 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 + +-- | 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 + +-- | Make a function 'Coercion' between two other 'Coercion's +mkFunCoercion :: Coercion -> Coercion -> Coercion 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 :: 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 co' <- coreView co = mkSymCoercion co' @@ -222,6 +259,12 @@ mkSymCoercion (TyVarTy tv) ------------------------------- -- 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 @@ -234,15 +277,29 @@ mkTransCoercion g1 g2 -- sym g `trans` g = id ------------------------------- -- 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] +mkRightCoercion :: Coercion -> Coercion +-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of +-- the "arguments" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then: +-- +-- > mkLeftCoercion c :: x ~ y mkRightCoercion co | Just (_, co2) <- splitAppCoercion_maybe co = co2 | otherwise = mkCoercion rightCoercionTyCon [co] mkRightCoercions :: Int -> Coercion -> [Coercion] +-- ^ As 'mkRightCoercion', but finds the 'Coercion's available on the right side of @n@ +-- nested application 'Coercion's, manufacturing new left or right cooercions as necessary +-- if suffficiently many are not directly available. mkRightCoercions n co = go n co [] where @@ -254,12 +311,18 @@ mkRightCoercions n co | otherwise = acc + +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 {- @@ -272,8 +335,8 @@ 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) @@ -318,15 +381,20 @@ splitRightCoercion_maybe (TyConApp tc [co]) 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 + +-- | 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 @@ -336,17 +404,16 @@ mkNewTypeCoercion name tycon tvs rhs_ty rule args = ASSERT( co_con_arity == length args ) (TyConApp tycon args, substTyWith tvs args rhs_ty) --- Coercion identifying a data/newtype/synonym representation type and its --- family instance. It has the form `Co tvs :: F ts :=: R tvs', where `Co' is --- the coercion tycon built here, `F' the family tycon and `R' the (derived) +-- | 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 -- ^ 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 @@ -365,6 +432,8 @@ mkFamInstCoercion name tvs family instTys rep_tycon -- sym e :: p3=q3 -- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3) +-- | Coercion type constructors: avoid using these directly and instead use the @mk*Coercion@ and @split*Coercion@ family +-- of functions if possible. symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon, unsafeCoercionTyCon :: TyCon -- Each coercion TyCon is built with the special CoercionTyCon record and -- carries its own kinding rule. Such CoercionTyCons must be fully applied @@ -439,7 +508,7 @@ unsafeCoercionTyCon -- ...and their names mkCoConName :: FastString -> Unique -> TyCon -> Name -mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ) +mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkTcOccFS occ) key (ATyCon coCon) BuiltInSyntax transCoercionTyConName, symCoercionTyConName, leftCoercionTyConName, rightCoercionTyConName, instCoercionTyConName, unsafeCoercionTyConName :: Name @@ -454,8 +523,9 @@ unsafeCoercionTyConName = mkCoConName (fsLit "CoUnsafe") unsafeCoercionTyConKey instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI) --- instNewTyCon_maybe T ts --- = Just (rep_ty, co) if co : T ts ~ rep_ty +-- ^ 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 ) @@ -468,12 +538,14 @@ instNewTyCon_maybe tc tys -- this is here to avoid module loops splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion) --- Sometimes we want to look through a newtype and get its associated coercion --- It only strips *one layer* off, so the caller will usually call itself recursively --- Only applied to types of kind *, hence the newtype is always saturated --- splitNewTypeRepCo_maybe ty --- = Just (ty', co) if co : ty ~ ty' --- Returns Nothing for non-newtypes or fully-transparent newtypes +-- ^ 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) @@ -485,9 +557,7 @@ splitNewTypeRepCo_maybe (TyConApp tc tys) splitNewTypeRepCo_maybe _ = Nothing -------------------------------------- --- Syntactic equality of coercions - +-- | Determines syntactic equality of coercions coreEqCoercion :: Coercion -> Coercion -> Bool coreEqCoercion = coreEqType \end{code} @@ -498,74 +568,90 @@ coreEqCoercion = coreEqType -- lifted smart constructors of ordinary coercions \begin{code} - -- CoercionI is either - -- (a) proper coercion - -- (b) the identity coercion +-- | '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 isIdentityCoercion :: CoercionI -> Bool isIdentityCoercion IdCo = True isIdentityCoercion _ = False +-- | Tests whether all the given 'CoercionI's represent the identity coercion allIdCos :: [CoercionI] -> Bool allIdCos = all isIdentityCoercion +-- | 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 | allIdCos 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 = coi --- coi : PredTy (cls tys) ~ predTy (cls (tys `cast` cois)) mkClassPPredCoI cls tys cois | allIdCos cois = IdCo | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys) +-- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI' mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI --- Similar invariant to mkclassPPredCoI 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 --- Similar invariant to mkclassPPredCoI 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} - -- 1.7.10.4