%
\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
+-- | Module for (a) type kinds and (b) 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:
+-- 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]
+-- > typeKind (symCoercion type) :: TyConApp CoTyCon{...} [type, type]
module Coercion (
-- * Main data type
- Coercion,
-
- mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
- coercionKind, coercionKinds, coercionKindPredTy,
+ Coercion, Kind,
+ typeKind,
+
+ -- ** Deconstructing Kinds
+ kindFunResult, kindAppResult, synTyConResKind,
+ splitKindFunTys, splitKindFunTysN, splitKindFunTy_maybe,
+
+ -- ** Predicates on Kinds
+ isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
+ isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
+ isCoSuperKind, isSuperKind, isCoercionKind,
+ mkArrowKind, mkArrowKinds,
+
+ isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
+ isSubKindCon,
+
+ mkCoKind, mkCoPredTy, coVarKind, coVarKind_maybe,
+ coercionKind, coercionKinds, isIdentityCoercion,
-- ** Equality predicates
isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
-- ** Coercion transformations
mkCoercion,
mkSymCoercion, mkTransCoercion,
- mkLeftCoercion, mkRightCoercion, mkRightCoercions,
- mkInstCoercion, mkAppCoercion,
- mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
+ mkLeftCoercion, mkRightCoercion,
+ mkInstCoercion, mkAppCoercion, mkTyConCoercion, mkFunCoercion,
+ mkForAllCoercion, mkInstsCoercion, mkUnsafeCoercion,
mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
+ mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion,
+
+ mkClassPPredCo, mkIParamPredCo, mkEqPredCo,
+ mkCoVarCoercion, mkCoPredCo,
- splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
unsafeCoercionTyCon, symCoercionTyCon,
transCoercionTyCon, leftCoercionTyCon,
rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
+ csel1CoercionTyCon, csel2CoercionTyCon, cselRCoercionTyCon,
+
+ -- ** Decomposition
+ decompLR_maybe, decompCsel_maybe, decompInst_maybe,
+ splitCoPredTy_maybe,
+ splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
-- ** Comparison
- coreEqCoercion,
+ coreEqCoercion, coreEqCoercion2,
-- * CoercionI
CoercionI(..),
- isIdentityCoercion,
+ isIdentityCoI,
mkSymCoI, mkTransCoI,
mkTyConAppCoI, mkAppTyCoI, mkFunTyCoI,
mkForAllTyCoI,
- fromCoI, fromACo,
- mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI
+ fromCoI,
+ mkClassPPredCoI, mkIParamPredCoI, mkEqPredCoI, mkCoPredCoI
) where
import TyCon
import Class
import Var
+import VarEnv
+import VarSet
import Name
-import OccName
import PrelNames
import Util
-import Unique
import BasicTypes
import Outputable
import FastString
+\end{code}
+
+%************************************************************************
+%* *
+ Functions over Kinds
+%* *
+%************************************************************************
+
+\begin{code}
+-- | Essentially 'funResultTy' on kinds
+kindFunResult :: Kind -> Kind
+kindFunResult k = funResultTy k
+
+kindAppResult :: Kind -> [arg] -> Kind
+kindAppResult k [] = k
+kindAppResult k (_:as) = kindAppResult (kindFunResult k) as
+
+-- | Essentially 'splitFunTys' on kinds
+splitKindFunTys :: Kind -> ([Kind],Kind)
+splitKindFunTys k = splitFunTys k
+
+splitKindFunTy_maybe :: Kind -> Maybe (Kind,Kind)
+splitKindFunTy_maybe = splitFunTy_maybe
+
+-- | Essentially 'splitFunTysN' on kinds
+splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
+splitKindFunTysN k = splitFunTysN k
+
+-- | Find the result 'Kind' of a type synonym,
+-- after applying it to its 'arity' number of type variables
+-- Actually this function works fine on data types too,
+-- but they'd always return '*', so we never need to ask
+synTyConResKind :: TyCon -> Kind
+synTyConResKind tycon = kindAppResult (tyConKind tycon) (tyConTyVars tycon)
+
+-- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's
+isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
+isOpenTypeKindCon, isUbxTupleKindCon, isArgTypeKindCon,
+ isUnliftedTypeKindCon, isSubArgTypeKindCon :: TyCon -> Bool
+
+isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
+
+isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
+isOpenTypeKind _ = False
+
+isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
+
+isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
+isUbxTupleKind _ = False
+
+isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
+
+isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
+isArgTypeKind _ = False
+
+isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
+
+isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
+isUnliftedTypeKind _ = False
+
+isSubOpenTypeKind :: Kind -> Bool
+-- ^ True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
+isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
+ ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
+ False
+isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
+isSubOpenTypeKind other = ASSERT( isKind other ) False
+ -- This is a conservative answer
+ -- It matters in the call to isSubKind in
+ -- checkExpectedKind.
+
+isSubArgTypeKindCon kc
+ | isUnliftedTypeKindCon kc = True
+ | isLiftedTypeKindCon kc = True
+ | isArgTypeKindCon kc = True
+ | otherwise = False
+
+isSubArgTypeKind :: Kind -> Bool
+-- ^ True of any sub-kind of ArgTypeKind
+isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
+isSubArgTypeKind _ = False
+
+-- | Is this a super-kind (i.e. a type-of-kinds)?
+isSuperKind :: Type -> Bool
+isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
+isSuperKind _ = False
+
+-- | Is this a kind (i.e. a type-of-types)?
+isKind :: Kind -> Bool
+isKind k = isSuperKind (typeKind k)
+
+isSubKind :: Kind -> Kind -> Bool
+-- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@
+isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
+isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
+isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
+ = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
+isSubKind _ _ = False
+
+eqKind :: Kind -> Kind -> Bool
+eqKind = tcEqType
+
+isSubKindCon :: TyCon -> TyCon -> Bool
+-- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@
+isSubKindCon kc1 kc2
+ | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
+ | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
+ | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
+ | isOpenTypeKindCon kc2 = True
+ -- we already know kc1 is not a fun, its a TyCon
+ | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
+ | otherwise = False
+
+defaultKind :: Kind -> Kind
+-- ^ Used when generalising: default kind ? and ?? to *. See "Type#kind_subtyping" for more
+-- information on what that means
+
+-- When we generalise, we make generic type variables whose kind is
+-- simple (* or *->* etc). So generic type variables (other than
+-- built-in constants like 'error') always have simple kinds. This is important;
+-- consider
+-- f x = True
+-- We want f to get type
+-- f :: forall (a::*). a -> Bool
+-- Not
+-- f :: forall (a::??). a -> Bool
+-- because that would allow a call like (f 3#) as well as (f True),
+--and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
+defaultKind k
+ | isSubOpenTypeKind k = liftedTypeKind
+ | isSubArgTypeKind k = liftedTypeKind
+ | otherwise = k
+\end{code}
+%************************************************************************
+%* *
+ Coercions
+%* *
+%************************************************************************
+
+
+\begin{code}
-- | A 'Coercion' represents a 'Type' something should be coerced to.
type Coercion = Type
go n co cos = go (n-1) (mkLeftCoercion co)
(mkRightCoercion co : cos)
-------------------------------
-------------------------------------------------------
-- and some coercion kind stuff
+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))
+
+coVarKind_maybe :: CoVar -> Maybe (Type,Type)
+coVarKind_maybe cv = splitCoKind_maybe (tyVarKind cv)
+
+-- | 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)
+
+-- | (mkCoPredTy s t r) produces the type: (s~t) => r
+mkCoPredTy :: Type -> Type -> Type -> Type
+mkCoPredTy s t r = ASSERT( not (co_var `elemVarSet` tyVarsOfType r) )
+ ForAllTy co_var r
+ where
+ co_var = mkWildCoVar (mkCoKind s t)
+
+mkCoPredCo :: Coercion -> Coercion -> Coercion -> Coercion
+-- Creates a coercion between (s1~t1) => r1 and (s2~t2) => r2
+mkCoPredCo = mkCoPredTy
+
+
+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
+
-- | Tests whether a type is just a type equality predicate
isEqPredTy :: Type -> Bool
isEqPredTy (PredTy pred) = isEqPred pred
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)
-coercionKind ty@(TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind 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)
- | 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)
-
- | otherwise
- = let (lArgs, rArgs) = coercionKinds args in
- (TyConApp tc lArgs, TyConApp tc rArgs)
-coercionKind (FunTy ty1 ty2)
- = let (t1, t2) = coercionKind ty1
- (s1, s2) = coercionKind ty2 in
- (mkFunTy t1 s1, mkFunTy t2 s2)
-coercionKind (ForAllTy tv ty)
- = let (ty1, ty2) = coercionKind ty in
- (ForAllTy tv ty1, ForAllTy tv ty2)
-coercionKind (PredTy (EqPred c1 c2))
- = let k1 = coercionKindPredTy c1
- k2 = coercionKindPredTy c2 in
- (k1,k2)
-coercionKind (PredTy (ClassP cl args))
- = let (lArgs, rArgs) = coercionKinds args in
- (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
-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
+isIdentityCoercion :: Coercion -> Bool
+isIdentityCoercion co
+ = case coercionKind co of
+ (t1,t2) -> t1 `coreEqType` t2
+\end{code}
--- | Apply 'coercionKind' to multiple 'Coercion's
-coercionKinds :: [Coercion] -> ([Type], [Type])
-coercionKinds tys = unzip $ map coercionKind tys
+%************************************************************************
+%* *
+ Building coercions
+%* *
+%************************************************************************
--------------------------------------
--- Coercion kind and type mk's
--- (make saturated TyConApp CoercionTyCon{...} args)
+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 coCon args = ASSERT( tyConArity coCon == length args )
TyConApp coCon args
--- | Apply a 'Coercion' to another 'Coercion', which is presumably a 'Coercion' constructor of some
--- kind
+mkCoVarCoercion :: CoVar -> Coercion
+mkCoVarCoercion cv = mkTyVarTy cv
+
+-- | 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
+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
+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
+-- | 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
+mkFunCoercion co1 co2 = mkFunTy co1 co2 -- NB: Handles correctly the forall for eqpreds!
+
+-- | 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 ( isTyCoVar tv ) mkForAllTy tv co
-------------------------------
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'
-
-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 (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 -- Reflexive
-
--------------------------------
--- ToDo: we should be cleverer about transitivity
+-- ^ Create a symmetric version of the given 'Coercion' that asserts equality
+-- between the same types but in the other "direction", so a kind of @t1 ~ t2@
+-- becomes the kind @t2 ~ t1@.
+mkSymCoercion g = mkCoercion symCoercionTyCon [g]
mkTransCoercion :: Coercion -> Coercion -> Coercion
-- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
---
--- 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
+mkTransCoercion g1 g2 = mkCoercion transCoercionTyCon [g1, g2]
mkLeftCoercion :: Coercion -> Coercion
-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
-- the "functions" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
--
-- > mkLeftCoercion c :: f ~ g
-mkLeftCoercion co
- | Just (co', _) <- splitAppCoercion_maybe co = co'
- | otherwise = mkCoercion leftCoercionTyCon [co]
+mkLeftCoercion co = mkCoercion leftCoercionTyCon [co]
mkRightCoercion :: Coercion -> Coercion
-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
-- the "arguments" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
--
-- > mkLeftCoercion c :: x ~ y
-mkRightCoercion co
- | 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
- 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
+mkRightCoercion co = mkCoercion rightCoercionTyCon [co]
+mkCsel1Coercion, mkCsel2Coercion, mkCselRCoercion :: Coercion -> Coercion
+mkCsel1Coercion co = mkCoercion csel1CoercionTyCon [co]
+mkCsel2Coercion co = mkCoercion csel2CoercionTyCon [co]
+mkCselRCoercion co = mkCoercion cselRCoercionTyCon [co]
+-------------------------------
mkInstCoercion :: Coercion -> Type -> Coercion
-- ^ Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
-- the resulting beta-reduction, otherwise it creates a suspended instantiation.
-mkInstCoercion co ty
- | Just (tv,co') <- splitForAllTy_maybe co
- = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a]
- | otherwise
- = mkCoercion instCoercionTyCon [co, ty]
+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.
--- 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)
-splitAppCoercion_maybe (TyConApp tc tys)
- | not (isCoercionTyCon tc)
- = case snocView tys of
- Just (tys', ty') -> Just (TyConApp tc tys', ty')
- Nothing -> Nothing
-splitAppCoercion_maybe _ = 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
--}
-
-- | 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.
+-- Optimise by pushing down through type constructors
mkUnsafeCoercion :: Type -> Type -> Coercion
-mkUnsafeCoercion ty1 ty2
- = mkCoercion unsafeCoercionTyCon [ty1, ty2]
+mkUnsafeCoercion (TyConApp tc1 tys1) (TyConApp tc2 tys2)
+ | tc1 == tc2
+ = TyConApp tc1 (zipWith mkUnsafeCoercion tys1 tys2)
+mkUnsafeCoercion (FunTy a1 r1) (FunTy a2 r2)
+ = FunTy (mkUnsafeCoercion a1 a2) (mkUnsafeCoercion r1 r2)
+
+mkUnsafeCoercion ty1 ty2
+ | ty1 `coreEqType` ty2 = ty1
+ | otherwise = mkCoercion unsafeCoercionTyCon [ty1, ty2]
-- See note [Newtype coercions] in TyCon
-- a subset of those 'TyVar's.
mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
mkNewTypeCoercion name tycon tvs rhs_ty
- = mkCoercionTyCon name co_con_arity rule
+ = mkCoercionTyCon name arity desc
where
- co_con_arity = length tvs
-
- rule args = ASSERT( co_con_arity == length args )
- (TyConApp tycon args, substTyWith tvs args rhs_ty)
+ arity = length tvs
+ desc = CoAxiom { co_ax_tvs = tvs
+ , co_ax_lhs = mkTyConApp tycon (mkTyVarTys tvs)
+ , co_ax_rhs = 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
-> [Type] -- ^ Type instance (@ts@)
-> TyCon -- ^ Representation tycon (@R@)
-> TyCon -- ^ Coercion tycon (@Co@)
-mkFamInstCoercion name tvs family instTys rep_tycon
- = mkCoercionTyCon name coArity rule
+mkFamInstCoercion name tvs family inst_tys rep_tycon
+ = mkCoercionTyCon name arity desc
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
+ arity = length tvs
+ desc = CoAxiom { co_ax_tvs = tvs
+ , co_ax_lhs = mkTyConApp family inst_tys
+ , co_ax_rhs = mkTyConApp rep_tycon (mkTyVarTys tvs) }
---------------------------------------
--- 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)
-
--- | 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
--- 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
-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"
- $$
- ppr r1 <+> text "=/=" <+> ppr a2)
- (a1, r2)
- where
- (a1, r1) = coercionKind co1
- (a2, r2) = coercionKind co2
-
-leftCoercionTyCon =
- mkCoercionTyCon leftCoercionTyConName 1 leftProjectCoercionKindOf
- where
- leftProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
- where
- (ty1,ty2) = fst (splitCoercionKindOf co)
+mkClassPPredCo :: Class -> [Coercion] -> Coercion
+mkClassPPredCo cls = (PredTy . ClassP cls)
-rightCoercionTyCon =
- mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
- where
- rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
- where
- (ty1,ty2) = snd (splitCoercionKindOf co)
+mkIParamPredCo :: (IPName Name) -> Coercion -> Coercion
+mkIParamPredCo ipn = (PredTy . IParam ipn)
-splitCoercionKindOf :: 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)
- , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
- , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
- = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
-splitCoercionKindOf co
- = pprPanic "Coercion.splitCoercionKindOf"
- (ppr co $$ ppr (coercionKindPredTy co))
+mkEqPredCo :: Coercion -> Coercion -> Coercion
+mkEqPredCo co1 co2 = PredTy (EqPred co1 co2)
-instCoercionTyCon
- = mkCoercionTyCon instCoercionTyConName 2 instCoercionKind
- 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
+\end{code}
-unsafeCoercionTyCon
- = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
- where
- unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
-
---------------------------------------
--- ...and their names
+
+%************************************************************************
+%* *
+ 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 CoSym
+transCoercionTyCon = mkCoercionTyCon transCoercionTyConName 2 CoTrans
+leftCoercionTyCon = mkCoercionTyCon leftCoercionTyConName 1 CoLeft
+rightCoercionTyCon = mkCoercionTyCon rightCoercionTyConName 1 CoRight
+instCoercionTyCon = mkCoercionTyCon instCoercionTyConName 2 CoInst
+csel1CoercionTyCon = mkCoercionTyCon csel1CoercionTyConName 1 CoCsel1
+csel2CoercionTyCon = mkCoercionTyCon csel2CoercionTyConName 1 CoCsel2
+cselRCoercionTyCon = mkCoercionTyCon cselRCoercionTyConName 1 CoCselR
+unsafeCoercionTyCon = mkCoercionTyCon unsafeCoercionTyConName 2 CoUnsafe
+
+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, symCoercionTyConName, leftCoercionTyConName, rightCoercionTyConName, instCoercionTyConName, unsafeCoercionTyConName :: 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
-unsafeCoercionTyConName = mkCoConName (fsLit "CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon
+\begin{code}
+------------
+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))
+decompLR_maybe (ty1,ty2)
+ | Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1
+ , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2
+ = Just ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))
+decompLR_maybe _ = Nothing
+
+------------
+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
+
+------------
+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
+\end{code}
+%************************************************************************
+%* *
+ Newtypes
+%* *
+%************************************************************************
+\begin{code}
instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, CoercionI)
-- ^ If @co :: T ts ~ rep_ty@ then:
--
= 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))
+ Nothing -> IdCo (mkTyConApp tc tys)
+ Just co_tc -> ACo (mkTyConApp co_tc tys))
| otherwise
= Nothing
| Just (ty', coi) <- instNewTyCon_maybe tc tys
= case coi of
ACo co -> Just (ty', co)
- IdCo -> panic "splitNewTypeRepCo_maybe"
+ 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
-- 1. A proper 'Coercion'
--
-- 2. The identity coercion
-data CoercionI = IdCo | ACo Coercion
+data CoercionI = IdCo Type | ACo Coercion
-instance Outputable CoercionI where
- ppr IdCo = ptext (sLit "IdCo")
- ppr (ACo co) = ppr co
+liftCoI :: (Type -> Type) -> CoercionI -> CoercionI
+liftCoI f (IdCo ty) = IdCo (f ty)
+liftCoI f (ACo ty) = ACo (f ty)
+
+liftCoI2 :: (Type -> Type -> Type) -> CoercionI -> CoercionI -> CoercionI
+liftCoI2 f (IdCo ty1) (IdCo ty2) = IdCo (f ty1 ty2)
+liftCoI2 f coi1 coi2 = ACo (f (fromCoI coi1) (fromCoI coi2))
-isIdentityCoercion :: CoercionI -> Bool
-isIdentityCoercion IdCo = True
-isIdentityCoercion _ = False
+liftCoIs :: ([Type] -> Type) -> [CoercionI] -> CoercionI
+liftCoIs f cois = go_id [] cois
+ where
+ go_id rev_tys [] = IdCo (f (reverse rev_tys))
+ go_id rev_tys (IdCo ty : cois) = go_id (ty:rev_tys) cois
+ go_id rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois
--- | Tests whether all the given 'CoercionI's represent the identity coercion
-allIdCos :: [CoercionI] -> Bool
-allIdCos = all isIdentityCoercion
+ go_aco rev_tys [] = ACo (f (reverse rev_tys))
+ go_aco rev_tys (IdCo ty : cois) = go_aco (ty:rev_tys) cois
+ go_aco rev_tys (ACo co : cois) = go_aco (co:rev_tys) cois
--- | 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
+instance Outputable CoercionI where
+ ppr (IdCo _) = ptext (sLit "IdCo")
+ ppr (ACo co) = ppr co
+
+isIdentityCoI :: CoercionI -> Bool
+isIdentityCoI (IdCo _) = True
+isIdentityCoI (ACo _) = False
-- | 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
+fromCoI :: CoercionI -> 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]
+mkSymCoI (IdCo ty) = IdCo ty
+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 (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))
+mkTyConAppCoI :: TyCon -> [CoercionI] -> CoercionI
+mkTyConAppCoI tyCon cois = liftCoIs (mkTyConApp tyCon) cois
-- | 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)
+mkAppTyCoI :: CoercionI -> CoercionI -> CoercionI
+mkAppTyCoI = liftCoI2 mkAppTy
--- | 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)
+mkFunTyCoI :: CoercionI -> CoercionI -> CoercionI
+mkFunTyCoI = liftCoI2 mkFunTy
-- | 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
+mkForAllTyCoI tv = liftCoI (ForAllTy tv)
-- | 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
- | allIdCos cois = IdCo
- | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys)
+mkClassPPredCoI :: Class -> [CoercionI] -> CoercionI
+mkClassPPredCoI cls = liftCoIs (PredTy . ClassP cls)
-- | 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
+mkIParamPredCoI ipn = liftCoI (PredTy . IParam ipn)
-- | 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)
+mkEqPredCoI :: CoercionI -> CoercionI -> CoercionI
+mkEqPredCoI = liftCoI2 (\t1 t2 -> PredTy (EqPred t1 t2))
+
+mkCoPredCoI :: CoercionI -> CoercionI -> CoercionI -> CoercionI
+mkCoPredCoI coi1 coi2 coi3 = mkFunTyCoI (mkEqPredCoI coi1 coi2) coi3
+
+
+\end{code}
+
+%************************************************************************
+%* *
+ The kind of a type, and of a coercion
+%* *
+%************************************************************************
+
+\begin{code}
+typeKind :: Type -> Kind
+typeKind ty@(TyConApp tc tys)
+ | isCoercionTyCon tc = typeKind (fst (coercionKind ty))
+ | otherwise = kindAppResult (tyConKind tc) tys
+ -- During coercion optimisation we *do* match a type
+ -- against a coercion (see OptCoercion.matchesAxiomLhs)
+ -- So the use of typeKind in Unify.match_kind must work on coercions too
+ -- Hence the isCoercionTyCon case above
+
+typeKind (PredTy pred) = predKind pred
+typeKind (AppTy fun _) = kindFunResult (typeKind fun)
+typeKind (ForAllTy _ ty) = typeKind ty
+typeKind (TyVarTy tyvar) = tyVarKind tyvar
+typeKind (FunTy _arg res)
+ -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
+ -- not unliftedTypKind (#)
+ -- The only things that can be after a function arrow are
+ -- (a) types (of kind openTypeKind or its sub-kinds)
+ -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
+ | isTySuperKind k = k
+ | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
+ where
+ k = typeKind res
+
+------------------
+predKind :: PredType -> Kind
+predKind (EqPred {}) = coSuperKind -- A coercion kind!
+predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
+predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
+
+------------------
+-- | 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)
+coercionKind ty@(TyVarTy a) | isCoVar a = coVarKind a
+ | otherwise = (ty, ty)
+coercionKind (AppTy ty1 ty2)
+ = let (s1, t1) = coercionKind ty1
+ (s2, t2) = coercionKind ty2 in
+ (mkAppTy s1 s2, mkAppTy t1 t2)
+coercionKind co@(TyConApp tc args)
+ | Just (ar, desc) <- isCoercionTyCon_maybe tc
+ -- CoercionTyCons carry their kinding rule, so we use it here
+ = WARN( not (length args >= ar), ppr co ) -- Always saturated
+ (let (ty1, ty2) = coTyConAppKind desc (take ar 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)
+
+coercionKind (FunTy ty1 ty2)
+ = let (t1, t2) = coercionKind ty1
+ (s1, s2) = coercionKind ty2 in
+ (mkFunTy t1 s1, mkFunTy t2 s2)
+
+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 (PredTy (ClassP cl args))
+ = let (lArgs, rArgs) = coercionKinds args in
+ (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))
+coercionKind (PredTy (IParam name ty))
+ = let (ty1, ty2) = coercionKind ty in
+ (PredTy (IParam name ty1), PredTy (IParam name ty2))
+coercionKind (PredTy (EqPred c1 c2))
+ = pprTrace "coercionKind" (pprEqPred (c1,c2)) $
+ -- These should not show up in coercions at all
+ -- becuase they are in the form of for-alls
+ let k1 = coercionKindPredTy c1
+ k2 = coercionKindPredTy c2 in
+ (k1,k2)
+ where
+ 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
+
+------------------
+-- | 'coTyConAppKind' is given a list of the type arguments to the 'CoTyCon',
+-- and constructs the types that the resulting coercion relates.
+-- Fails (in the monad) if ill-kinded.
+-- Typically the monad is
+-- either the Lint monad (with the consistency-check flag = True),
+-- or the ID monad with a panic on failure (and the consistency-check flag = False)
+coTyConAppKind
+ :: CoTyConDesc
+ -> [Type] -- Exactly right number of args
+ -> (Type, Type) -- Kind of this application
+coTyConAppKind CoUnsafe (ty1:ty2:_)
+ = (ty1,ty2)
+coTyConAppKind CoSym (co:_)
+ | (ty1,ty2) <- coercionKind co = (ty2,ty1)
+coTyConAppKind CoTrans (co1:co2:_)
+ = (fst (coercionKind co1), snd (coercionKind co2))
+coTyConAppKind CoLeft (co:_)
+ | Just (res,_) <- decompLR_maybe (coercionKind co) = res
+coTyConAppKind CoRight (co:_)
+ | Just (_,res) <- decompLR_maybe (coercionKind co) = res
+coTyConAppKind CoCsel1 (co:_)
+ | Just (res,_,_) <- decompCsel_maybe (coercionKind co) = res
+coTyConAppKind CoCsel2 (co:_)
+ | Just (_,res,_) <- decompCsel_maybe (coercionKind co) = res
+coTyConAppKind CoCselR (co:_)
+ | Just (_,_,res) <- decompCsel_maybe (coercionKind co) = res
+coTyConAppKind CoInst (co:ty:_)
+ | Just ((tv1,tv2), (ty1,ty2)) <- decompInst_maybe (coercionKind co)
+ = (substTyWith [tv1] [ty] ty1, substTyWith [tv2] [ty] ty2)
+coTyConAppKind (CoAxiom { co_ax_tvs = tvs
+ , co_ax_lhs = lhs_ty, co_ax_rhs = rhs_ty }) cos
+ = (substTyWith tvs tys1 lhs_ty, substTyWith tvs tys2 rhs_ty)
+ where
+ (tys1, tys2) = coercionKinds cos
+coTyConAppKind desc cos = pprTrace "coTyConAppKind" (ppr desc $$ braces (vcat
+ [ ppr co <+> dcolon <+> pprEqPred (coercionKind co)
+ | co <- cos ])) $
+ coercionKind (head cos)
\end{code}
projects / ghc-hetmet.git / blobdiff