Commit 1fa25d26 authored by batterseapower's avatar batterseapower
Browse files

Document Coercion

parent fb54e7be
......@@ -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}
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