% (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,
+ 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"
import TypeRep
import Type
import TyCon
+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)
-------------------------------------------------------
-- 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
-type Coercion = Type
-type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
+-- | 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)
+-- | 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
= 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))
= 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
-------------------------------
--- 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 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)
- | tc `hasKey` instCoercionTyConKey
- -- sym (co @ ty) --> (sym co) @ ty
- -- Note: sym is not applied to 'ty'
- = mkInstCoercion (mkSymCoercion 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@.
+mkSymCoercion g = mkCoercion symCoercionTyCon [g]
-mkSymCoercion (TyConApp tc cos) -- Other coercion tycons, such as those
- = mkCoercion symCoercionTyCon [TyConApp tc cos] -- arising from newtypes
+mkTransCoercion :: Coercion -> Coercion -> Coercion
+-- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
+mkTransCoercion g1 g2 = mkCoercion transCoercionTyCon [g1, g2]
-mkSymCoercion (TyVarTy tv)
- | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
- | otherwise = TyVarTy tv -- Reflexive
-
--------------------------------
--- ToDo: we should be cleverer about transitivity
-mkTransCoercion g1 g2 -- sym g `trans` g = id
- | (t1,_) <- coercionKind g1
- , (_,t2) <- coercionKind g2
- , t1 `coreEqType` t2
- = t1
+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]
- | otherwise
- = mkCoercion transCoercionTyCon [g1, g2]
+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]
-------------------------------
--- 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]
-
-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]
+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
+
+-- | 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/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
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}
+optCoercion :: TvSubst -> Coercion -> NormalCo
+-- ^ optCoercion applies a substitution to a coercion,
+-- *and* optimises it to reduce its size
+optCoercion env co = opt_co env False co
+
+type NormalCo = Coercion
+ -- Invariants:
+ -- * The substitution has been fully applied
+ -- * 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
+
+opt_co, opt_co' :: TvSubst
+ -> 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' env sym (AppTy ty1 ty2) = mkAppTy (opt_co env sym ty1) (opt_co env sym ty2)
+opt_co' env sym (FunTy ty1 ty2) = FunTy (opt_co env sym ty1) (opt_co env sym ty2)
+opt_co' env sym (PredTy (ClassP cls tys)) = PredTy (ClassP cls (map (opt_co env sym) tys))
+opt_co' env sym (PredTy (IParam n ty)) = PredTy (IParam n (opt_co env sym ty))
+opt_co' _ _ co@(PredTy (EqPred {})) = pprPanic "optCoercion" (ppr co)
+
+opt_co' env sym co@(TyVarTy tv)
+ | Just ty <- lookupTyVar env tv = opt_co' (zapTvSubstEnv env) sym ty
+ | 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' env sym (ForAllTy tv cor)
+ | isCoVar tv = mkCoPredTy (opt_co env sym co1) (opt_co env sym co2) (opt_co env sym cor)
+ | otherwise = case substTyVarBndr env tv of
+ (env', tv') -> ForAllTy tv' (opt_co env' sym cor)
+ where
+ (co1,co2) = coVarKind tv
+
+opt_co' env sym (TyConApp tc cos)
+ | isCoercionTyCon tc
+ = foldl mkAppTy
+ (opt_co_tc_app env sym tc (take arity cos))
+ (map (opt_co env sym) (drop arity cos))
+ | otherwise
+ = TyConApp tc (map (opt_co env sym) cos)
+ where
+ arity = tyConArity tc
+
+--------
+opt_co_tc_app :: TvSubst -> Bool -> TyCon -> [Coercion] -> NormalCo
+-- Used for CoercionTyCons only
+-- Arguments are *not* already simplified/substituted
+opt_co_tc_app env sym tc cos
+ | tc `hasKey` symCoercionTyConKey
+ = opt_co env (not sym) co1
+
+ | tc `hasKey` transCoercionTyConKey
+ = if sym then opt_trans opt_co2 opt_co1 -- sym (g `o` h) = sym h `o` sym g
+ else opt_trans opt_co1 opt_co2
+
+ | tc `hasKey` leftCoercionTyConKey
+ , Just (opt_co1_left, _) <- splitAppTy_maybe opt_co1
+ = opt_co1_left -- sym (left g) = left (sym g)
+ -- The opt_co has the sym pushed into it
+
+ | tc `hasKey` rightCoercionTyConKey
+ , Just (_, opt_co1_right) <- splitAppTy_maybe opt_co1
+ = opt_co1_right
+
+ | 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 -- See if the first arg
+ -- is already a forall
+ , Just (tv, co1_body) <- splitForAllTy_maybe co1
+ , let ty = substTy env co2
+ = opt_co (extendTvSubst env tv ty) sym co1_body
+
+ | tc `hasKey` instCoercionTyConKey -- See if is *now* a forall
+ , Just (tv, opt_co1_body) <- splitForAllTy_maybe opt_co1
+ , let ty = substTy env co2
+ = substTyWith [tv] [ty] opt_co1_body -- An inefficient one-variable substitution
+
+ | 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
+ (co1 : cos1) = cos
+ (co2 : _) = cos1
+
+ -- These opt_cos have the sym pushed into them
+ opt_co1 = opt_co env sym co1
+ opt_co2 = opt_co env sym co2
+
+ -- However the_co does *not* have sym pushed into it
+ the_co = TyConApp tc (map (opt_co env False) cos)
+
+-------------
+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}
projects / ghc-hetmet.git / blobdiff