-\r
- Module for type coercions, as in System FC.\r
-\r
-Coercions are represented as types, and their kinds tell what types the \r
-coercion works on. \r
-\r
-The coercion kind constructor is a special TyCon that must always be saturated\r
-\r
- typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]\r
-\r
-\begin{code}\r
-module Coercion (\r
- Coercion,\r
- \r
- mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,\r
- coercionKind, coercionKinds, coercionKindPredTy,\r
-\r
- -- Equality predicates\r
- isEqPred, mkEqPred, getEqPredTys, isEqPredTy, \r
-\r
- -- Coercion transformations\r
- mkSymCoercion, mkTransCoercion,\r
- mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion,\r
- mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,\r
- mkNewTypeCoercion, mkAppsCoercion,\r
-\r
- splitNewTypeRepCo_maybe, decomposeCo,\r
-\r
- unsafeCoercionTyCon, symCoercionTyCon,\r
- transCoercionTyCon, leftCoercionTyCon, \r
- rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn\r
- ) where \r
-\r
-#include "HsVersions.h"\r
-\r
-import TypeRep\r
-import Type ( Type, Kind, PredType, substTyWith, mkAppTy, mkForAllTy,\r
- mkFunTy, splitAppTy_maybe, splitForAllTy_maybe, coreView,\r
- kindView, mkTyConApp, isCoercionKind, isEqPred, mkAppTys\r
- )\r
-import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isNewTyCon,\r
- newTyConRhs, newTyConCo, \r
- isCoercionTyCon, isCoercionTyCon_maybe )\r
-import Var ( Var, TyVar, isTyVar, tyVarKind )\r
-import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName )\r
-import OccName ( mkOccNameFS )\r
-import PrelNames ( symCoercionTyConKey, \r
- transCoercionTyConKey, leftCoercionTyConKey,\r
- rightCoercionTyConKey, instCoercionTyConKey, \r
- unsafeCoercionTyConKey, gHC_PRIM\r
- )\r
-import Util ( lengthIs, snocView )\r
-import Unique ( hasKey )\r
-import BasicTypes ( Arity )\r
-import Outputable\r
-\r
-\r
-\r
-------------------------------\r
-decomposeCo :: Arity -> Coercion -> [Coercion]\r
--- (decomposeCo 3 c) = [right (left (left c)), right (left c), right c]\r
-decomposeCo n co\r
- = go n co []\r
- where\r
- go 0 co cos = cos\r
- go n co cos = go (n-1) (mkLeftCoercion co)\r
- (mkRightCoercion co : cos)\r
-\r
-------------------------------\r
-\r
--------------------------------------------------------\r
--- and some coercion kind stuff\r
-\r
-isEqPredTy (PredTy pred) = isEqPred pred\r
-isEqPredTy other = False\r
-\r
-mkEqPred :: (Type, Type) -> PredType\r
-mkEqPred (ty1, ty2) = EqPred ty1 ty2\r
-\r
-getEqPredTys :: PredType -> (Type,Type)\r
-getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)\r
-getEqPredTys other = pprPanic "getEqPredTys" (ppr other)\r
-\r
-mkCoKind :: Type -> Type -> CoercionKind\r
-mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)\r
-\r
-mkReflCoKind :: Type -> CoercionKind\r
-mkReflCoKind ty = mkCoKind ty ty\r
-\r
-splitCoercionKind :: CoercionKind -> (Type, Type)\r
-splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'\r
-splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)\r
-\r
-splitCoercionKind_maybe :: Kind -> Maybe (Type, Type)\r
-splitCoercionKind_maybe co | Just co' <- kindView co = splitCoercionKind_maybe co'\r
-splitCoercionKind_maybe (PredTy (EqPred ty1 ty2)) = Just (ty1, ty2)\r
-splitCoercionKind_maybe other = Nothing\r
-\r
-isCoVar :: Var -> Bool\r
-isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)\r
-\r
-type Coercion = Type\r
-type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)\r
-\r
-coercionKind :: Coercion -> (Type, Type)\r
--- c :: (t1 :=: t2)\r
--- Then (coercionKind c) = (t1,t2)\r
-\r
-coercionKind (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)\r
- | otherwise = let t = (TyVarTy a) in (t, t)\r
-coercionKind (AppTy ty1 ty2) \r
- = let (t1, t2) = coercionKind ty1\r
- (s1, s2) = coercionKind ty2 in\r
- (mkAppTy t1 s1, mkAppTy t2 s2)\r
-coercionKind (TyConApp tc args)\r
- | Just (ar, rule) <- isCoercionTyCon_maybe tc \r
- = if length args >= ar \r
- then splitCoercionKind (rule args)\r
- else pprPanic ("arity/arguments mismatch in coercionKind:") \r
- (ppr ar $$ ppr tc <+> ppr args)\r
- | otherwise\r
- = let (lArgs, rArgs) = coercionKinds args in\r
- (TyConApp tc lArgs, TyConApp tc rArgs)\r
-coercionKind (FunTy ty1 ty2) \r
- = let (t1, t2) = coercionKind ty1\r
- (s1, s2) = coercionKind ty2 in\r
- (mkFunTy t1 s1, mkFunTy t2 s2)\r
-coercionKind (ForAllTy tv ty) \r
- = let (ty1, ty2) = coercionKind ty in\r
- (ForAllTy tv ty1, ForAllTy tv ty2)\r
-coercionKind (NoteTy _ ty) = coercionKind ty\r
-coercionKind (PredTy (EqPred c1 c2)) \r
- = let k1 = coercionKindPredTy c1\r
- k2 = coercionKindPredTy c2 in\r
- (k1,k2)\r
-coercionKind (PredTy (ClassP cl args)) \r
- = let (lArgs, rArgs) = coercionKinds args in\r
- (PredTy (ClassP cl lArgs), PredTy (ClassP cl rArgs))\r
-coercionKind (PredTy (IParam name ty))\r
- = let (ty1, ty2) = coercionKind ty in\r
- (PredTy (IParam name ty1), PredTy (IParam name ty2))\r
-\r
-coercionKindPredTy :: Coercion -> CoercionKind\r
-coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2\r
-\r
-coercionKinds :: [Coercion] -> ([Type], [Type])\r
-coercionKinds tys = unzip $ map coercionKind tys\r
-\r
--------------------------------------\r
--- Coercion kind and type mk's\r
--- (make saturated TyConApp CoercionTyCon{...} args)\r
-\r
-mkCoercion coCon args = ASSERT( tyConArity coCon == length args ) \r
- TyConApp coCon args\r
-\r
-mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion\r
-mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion\r
-\r
-mkAppCoercion co1 co2 = mkAppTy co1 co2\r
-mkAppsCoercion co1 tys = foldl mkAppTy co1 tys\r
--- note that a TyVar should be used here, not a CoVar (nor a TcTyVar)\r
-mkForAllCoercion tv co = ASSERT ( isTyVar tv ) mkForAllTy tv co\r
-mkFunCoercion co1 co2 = mkFunTy co1 co2\r
-\r
-mkSymCoercion co \r
- | Just co2 <- splitSymCoercion_maybe co = co2\r
- | Just (co1, co2) <- splitAppCoercion_maybe co \r
- -- should make this case better\r
- = mkAppCoercion (mkSymCoercion co1) (mkSymCoercion co2)\r
- | Just (co1, co2) <- splitTransCoercion_maybe co\r
- = mkTransCoercion (mkSymCoercion co1) (mkSymCoercion co2)\r
- | Just (co, ty) <- splitInstCoercion_maybe co\r
- = mkInstCoercion (mkSymCoercion co) ty\r
- | Just co <- splitLeftCoercion_maybe co\r
- = mkLeftCoercion (mkSymCoercion co)\r
- | Just co <- splitRightCoercion_maybe co\r
- = mkRightCoercion (mkSymCoercion co)\r
-mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)\r
--- for atomic types and constructors, we can just ignore sym since these\r
--- are reflexive coercions\r
-mkSymCoercion (TyVarTy tv) \r
- | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]\r
- | otherwise = TyVarTy tv\r
-mkSymCoercion co = mkCoercion symCoercionTyCon [co] \r
- -- this should not happen but does\r
-\r
--- Smart constructors for left and right\r
-mkLeftCoercion co \r
- | Just (co', _) <- splitAppCoercion_maybe co = co'\r
- | otherwise = mkCoercion leftCoercionTyCon [co]\r
-\r
-mkRightCoercion co \r
- | Just (co1, co2) <- splitAppCoercion_maybe co = co2\r
- | otherwise = mkCoercion rightCoercionTyCon [co]\r
-\r
-mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]\r
-\r
-mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]\r
-\r
-mkInstsCoercion co tys = foldl mkInstCoercion co tys\r
-\r
-splitSymCoercion_maybe :: Coercion -> Maybe Coercion\r
-splitSymCoercion_maybe (TyConApp tc [co]) = \r
- if tc `hasKey` symCoercionTyConKey\r
- then Just co\r
- else Nothing\r
-splitSymCoercion_maybe co = Nothing\r
-\r
-splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)\r
--- Splits a coercion application, being careful *not* to split (left c), etc\r
--- which are really sytactic constructs, not applications\r
-splitAppCoercion_maybe co | Just co' <- coreView co = splitAppCoercion_maybe co'\r
-splitAppCoercion_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)\r
-splitAppCoercion_maybe (AppTy ty1 ty2) = Just (ty1, ty2)\r
-splitAppCoercion_maybe (TyConApp tc tys) \r
- | not (isCoercionTyCon tc)\r
- = case snocView tys of\r
- Just (tys', ty') -> Just (TyConApp tc tys', ty')\r
- Nothing -> Nothing\r
-splitAppCoercion_maybe co = Nothing\r
-\r
-splitTransCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)\r
-splitTransCoercion_maybe (TyConApp tc [ty1, ty2]) \r
- = if tc `hasKey` transCoercionTyConKey then\r
- Just (ty1, ty2)\r
- else\r
- Nothing\r
-splitTransCoercion_maybe other = Nothing\r
-\r
-splitInstCoercion_maybe :: Coercion -> Maybe (Coercion, Type)\r
-splitInstCoercion_maybe (TyConApp tc [ty1, ty2])\r
- = if tc `hasKey` instCoercionTyConKey then\r
- Just (ty1, ty2)\r
- else\r
- Nothing\r
-splitInstCoercion_maybe other = Nothing\r
-\r
-splitLeftCoercion_maybe :: Coercion -> Maybe Coercion\r
-splitLeftCoercion_maybe (TyConApp tc [co])\r
- = if tc `hasKey` leftCoercionTyConKey then\r
- Just co\r
- else\r
- Nothing\r
-splitLeftCoercion_maybe other = Nothing\r
-\r
-splitRightCoercion_maybe :: Coercion -> Maybe Coercion\r
-splitRightCoercion_maybe (TyConApp tc [co])\r
- = if tc `hasKey` rightCoercionTyConKey then\r
- Just co\r
- else\r
- Nothing\r
-splitRightCoercion_maybe other = Nothing\r
-\r
--- Unsafe coercion is not safe, it is used when we know we are dealing with\r
--- bottom, which is the one case in which it is safe\r
-mkUnsafeCoercion :: Type -> Type -> Coercion\r
-mkUnsafeCoercion ty1 ty2 \r
- = mkCoercion unsafeCoercionTyCon [ty1, ty2]\r
-\r
-\r
--- make the coercion associated with a newtype\r
-mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon\r
-mkNewTypeCoercion name tycon tvs rhs_ty \r
- = ASSERT (length tvs == tyConArity tycon)\r
- mkCoercionTyCon name (tyConArity tycon) rule\r
- where\r
- rule args = mkCoKind (substTyWith tvs args rhs_ty) (TyConApp tycon args)\r
-\r
---------------------------------------\r
--- Coercion Type Constructors...\r
-\r
--- Example. The coercion ((sym c) (sym d) (sym e))\r
--- will be represented by (TyConApp sym [c, sym d, sym e])\r
--- If sym c :: p1=q1\r
--- sym d :: p2=q2\r
--- sym e :: p3=q3\r
--- then ((sym c) (sym d) (sym e)) :: (p1 p2 p3)=(q1 q2 q3)\r
---\r
--- (mkKindingFun f) is given the args [c, sym d, sym e]\r
-mkKindingFun :: ([Type] -> (Type, Type, [Type])) -> [Type] -> Kind\r
-mkKindingFun f args = \r
- let (ty1, ty2, rest) = f args in \r
- let (argtys1, argtys2) = unzip (map coercionKind rest) in\r
- mkCoKind (mkAppTys ty1 argtys1) (mkAppTys ty2 argtys2)\r
- \r
-\r
-symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: TyCon\r
--- Each coercion TyCon is built with the special CoercionTyCon record and\r
--- carries its won kinding rule. Such CoercionTyCons must be fully applied\r
--- by any TyConApp in which they are applied, however they may also be over\r
--- applied (see example above) and the kinding function must deal with this.\r
-symCoercionTyCon = \r
- mkCoercionTyCon symCoercionTyConName 1 (mkKindingFun flipCoercionKindOf)\r
- where\r
- flipCoercionKindOf (co:rest) = (ty2, ty1, rest)\r
- where\r
- (ty1, ty2) = coercionKind co\r
-\r
-transCoercionTyCon = \r
- mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf)\r
- where\r
- composeCoercionKindsOf (co1:co2:rest) = (a1, r2, rest)\r
- where\r
- (a1, r1) = coercionKind co1\r
- (a2, r2) = coercionKind co2 \r
-\r
-leftCoercionTyCon =\r
- mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf)\r
- where\r
- leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)\r
- where\r
- (ty1,ty2) = fst (splitCoercionKindOf co)\r
-\r
-rightCoercionTyCon =\r
- mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf)\r
- where\r
- rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)\r
- where\r
- (ty1,ty2) = snd (splitCoercionKindOf co)\r
-\r
-splitCoercionKindOf :: Type -> ((Type,Type), (Type,Type))\r
--- Helper for left and right. Finds coercion kind of its input and\r
--- returns the left and right projections of the coercion...\r
---\r
--- if c :: t1 s1 :=: t2 s2 then splitCoercionKindOf c = ((t1, t2), (s1, s2))\r
-splitCoercionKindOf co\r
- | Just (ty1, ty2) <- splitCoercionKind_maybe (coercionKindPredTy co)\r
- , Just (ty_fun1, ty_arg1) <- splitAppTy_maybe ty1\r
- , Just (ty_fun2, ty_arg2) <- splitAppTy_maybe ty2\r
- = ((ty_fun1, ty_fun2),(ty_arg1, ty_arg2))\r
-\r
-instCoercionTyCon \r
- = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind)\r
- where\r
- instantiateCo t s =\r
- let Just (tv, ty) = splitForAllTy_maybe t in\r
- substTyWith [tv] [s] ty\r
-\r
- instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest)\r
- where (t1, t2) = coercionKind co1\r
-\r
-unsafeCoercionTyCon \r
- = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind)\r
- where\r
- unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest) \r
- \r
---------------------------------------\r
--- ...and their names\r
-\r
-mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)\r
- key Nothing (ATyCon coCon) BuiltInSyntax\r
-\r
-transCoercionTyConName = mkCoConName FSLIT("trans") transCoercionTyConKey transCoercionTyCon\r
-symCoercionTyConName = mkCoConName FSLIT("sym") symCoercionTyConKey symCoercionTyCon\r
-leftCoercionTyConName = mkCoConName FSLIT("left") leftCoercionTyConKey leftCoercionTyCon\r
-rightCoercionTyConName = mkCoConName FSLIT("right") rightCoercionTyConKey rightCoercionTyCon\r
-instCoercionTyConName = mkCoConName FSLIT("inst") instCoercionTyConKey instCoercionTyCon\r
-unsafeCoercionTyConName = mkCoConName FSLIT("CoUnsafe") unsafeCoercionTyConKey unsafeCoercionTyCon\r
-\r
-\r
-\r
--- this is here to avoid module loops\r
-splitNewTypeRepCo_maybe :: Type -> Maybe (Type, Coercion) \r
--- Sometimes we want to look through a recursive newtype, and that's what happens here\r
--- It only strips *one layer* off, so the caller will usually call itself recursively\r
--- Only applied to types of kind *, hence the newtype is always saturated\r
-splitNewTypeRepCo_maybe ty \r
- | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'\r
-splitNewTypeRepCo_maybe (TyConApp tc tys)\r
- | isNewTyCon tc \r
- = ASSERT( tys `lengthIs` tyConArity tc ) -- splitNewTypeRepCo_maybe only be applied \r
- -- to *types* (of kind *)\r
- case newTyConRhs tc of\r
- (tvs, rep_ty) -> \r
- ASSERT( length tvs == length tys )\r
- Just (substTyWith tvs tys rep_ty, mkTyConApp co_con tys)\r
- where\r
- co_con = maybe (pprPanic "splitNewTypeRepCo_maybe" (ppr tc)) id (newTyConCo tc)\r
-\r
-splitNewTypeRepCo_maybe other = Nothing\r
-\end{code}
\ No newline at end of file
+%
+% (c) The University of Glasgow 2006
+%
+
+\begin{code}
+{-# OPTIONS -fno-warn-incomplete-patterns #-}
+-- The above warning supression flag is a temporary kludge.
+-- While working on this module you are encouraged to remove it and fix
+-- any warnings in the module. See
+-- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
+-- for details
+
+-- | Module for type coercions, as used in System FC. See 'CoreSyn.Expr' for
+-- more on System FC and how coercions fit into it.
+--
+-- Coercions are represented as types, and their kinds tell what types the
+-- coercion works on. The coercion kind constructor is a special TyCon that must always be saturated, like so:
+--
+-- > typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
+module Coercion (
+ -- * Main data type
+ Coercion,
+
+ mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
+ coercionKind, coercionKinds, coercionKindPredTy, isIdentityCoercion,
+
+ -- ** Equality predicates
+ isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
+
+ -- ** Coercion transformations
+ mkCoercion,
+ mkSymCoercion, mkTransCoercion,
+ mkLeftCoercion, mkRightCoercion, mkRightCoercions,
+ mkInstCoercion, mkAppCoercion, mkTyConCoercion, mkFunCoercion,
+ mkForAllCoercion, mkInstsCoercion, mkUnsafeCoercion,
+ mkNewTypeCoercion, mkFamInstCoercion, mkAppsCoercion,
+
+ splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
+
+ unsafeCoercionTyCon, symCoercionTyCon,
+ transCoercionTyCon, leftCoercionTyCon,
+ rightCoercionTyCon, instCoercionTyCon, -- needed by TysWiredIn
+
+ -- ** Comparison
+ coreEqCoercion,
+
+ -- * 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 Name
+import PrelNames
+import Util
+import BasicTypes
+import Outputable
+import FastString
+
+-- | A 'Coercion' represents a 'Type' something should be coerced to.
+type Coercion = Type
+
+-- | A 'CoercionKind' is always of form @ty1 ~ ty2@ and indicates the
+-- types that a 'Coercion' will work on.
+type CoercionKind = Kind
+
+------------------------------
+
+-- | This breaks a 'Coercion' with 'CoercionKind' @T A B C ~ T D E F@ into
+-- a list of 'Coercion's of kinds @A ~ D@, @B ~ E@ and @E ~ F@. Hence:
+--
+-- > decomposeCo 3 c = [right (left (left c)), right (left c), right c]
+decomposeCo :: Arity -> Coercion -> [Coercion]
+decomposeCo n co
+ = go n co []
+ where
+ go 0 _ cos = cos
+ go n co cos = go (n-1) (mkLeftCoercion co)
+ (mkRightCoercion co : cos)
+
+------------------------------
+
+-------------------------------------------------------
+-- 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)
+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
+
+-- | Apply 'coercionKind' to multiple 'Coercion's
+coercionKinds :: [Coercion] -> ([Type], [Type])
+coercionKinds tys = unzip $ map coercionKind tys
+
+-------------------------------------
+isIdentityCoercion :: Coercion -> Bool
+isIdentityCoercion co
+ = case coercionKind co of
+ (t1,t2) -> t1 `coreEqType` t2
+
+-------------------------------------
+-- 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
+
+-- | 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
+
+-- | 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
+
+
+-------------------------------
+
+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
+
+mkTransCoercion :: Coercion -> Coercion -> Coercion
+-- ^ Create a new 'Coercion' by exploiting transitivity on the two given 'Coercion's.
+--
+-- This function attempts to simplify the generated 'Coercion' by exploiting the fact that
+-- @sym g `trans` g = id@.
+mkTransCoercion g1 g2 -- sym g `trans` g = id
+ | (t1,_) <- coercionKind g1
+ , (_,t2) <- coercionKind g2
+ , t1 `coreEqType` t2
+ = t1
+
+ | otherwise
+ = mkCoercion transCoercionTyCon [g1, g2]
+
+
+-------------------------------
+-- Smart constructors for left and right
+
+mkLeftCoercion :: Coercion -> Coercion
+-- ^ From an application 'Coercion' build a 'Coercion' that asserts the equality of
+-- the "functions" on either side of the type equality. So if @c@ has kind @f x ~ g y@ then:
+--
+-- > mkLeftCoercion c :: f ~ g
+mkLeftCoercion co
+ | Just (co', _) <- splitAppCoercion_maybe co = co'
+ | otherwise = mkCoercion leftCoercionTyCon [co]
+
+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
+
+
+mkInstCoercion :: Coercion -> Type -> Coercion
+-- ^ Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
+-- the resulting beta-reduction, otherwise it creates a suspended instantiation.
+mkInstCoercion co ty
+ | Just (tv,co') <- splitForAllTy_maybe co
+ = substTyWith [tv] [ty] co' -- (forall a.co) @ ty --> co[ty/a]
+ | otherwise
+ = mkCoercion instCoercionTyCon [co, ty]
+
+mkInstsCoercion :: Coercion -> [Type] -> Coercion
+-- ^ As 'mkInstCoercion', but instantiates the coercion with a number of type arguments, left-to-right
+mkInstsCoercion co tys = foldl mkInstCoercion co tys
+
+{-
+splitSymCoercion_maybe :: Coercion -> Maybe Coercion
+splitSymCoercion_maybe (TyConApp tc [co]) =
+ if tc `hasKey` symCoercionTyConKey
+ then Just co
+ else Nothing
+splitSymCoercion_maybe co = Nothing
+-}
+
+splitAppCoercion_maybe :: Coercion -> Maybe (Coercion, Coercion)
+-- ^ Splits a coercion application, being careful *not* to split @left c@ etc.
+-- 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.
+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)
+
+-- | Create a coercion identifying a @data@, @newtype@ or @type@ representation type
+-- and its family instance. It has the form @Co tvs :: F ts ~ R tvs@, where @Co@ is
+-- the coercion tycon built here, @F@ the family tycon and @R@ the (derived)
+-- representation tycon.
+mkFamInstCoercion :: Name -- ^ Unique name for the coercion tycon
+ -> [TyVar] -- ^ Type parameters of the coercion (@tvs@)
+ -> TyCon -- ^ Family tycon (@F@)
+ -> [Type] -- ^ Type instance (@ts@)
+ -> TyCon -- ^ Representation tycon (@R@)
+ -> TyCon -- ^ Coercion tycon (@Co@)
+mkFamInstCoercion name tvs family instTys rep_tycon
+ = mkCoercionTyCon name coArity rule
+ where
+ 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...
+
+-- 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)
+
+rightCoercionTyCon =
+ mkCoercionTyCon rightCoercionTyConName 1 rightProjectCoercionKindOf
+ where
+ rightProjectCoercionKindOf (co:rest) = ASSERT( null rest ) (ty1, ty2)
+ where
+ (ty1,ty2) = snd (splitCoercionKindOf co)
+
+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))
+
+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
+
+unsafeCoercionTyCon
+ = mkCoercionTyCon unsafeCoercionTyConName 2 unsafeCoercionKind
+ where
+ unsafeCoercionKind (ty1:ty2:rest) = ASSERT( null rest ) (ty1,ty2)
+
+--------------------------------------
+-- ...and their names
+
+mkCoConName :: FastString -> Unique -> TyCon -> Name
+mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkTcOccFS occ)
+ key (ATyCon coCon) BuiltInSyntax
+
+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
+
+
+
+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.
+-- 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)
+ | Just (ty', coi) <- instNewTyCon_maybe tc tys
+ = case coi of
+ ACo co -> Just (ty', co)
+ IdCo -> panic "splitNewTypeRepCo_maybe"
+ -- This case handled by coreView
+splitNewTypeRepCo_maybe _
+ = Nothing
+
+-- | Determines syntactic equality of coercions
+coreEqCoercion :: Coercion -> Coercion -> Bool
+coreEqCoercion = coreEqType
+\end{code}
+
+
+--------------------------------------
+-- CoercionI smart constructors
+-- lifted smart constructors of ordinary coercions
+
+\begin{code}
+-- | 'CoercionI' represents a /lifted/ ordinary 'Coercion', in that it
+-- can represent either one of:
+--
+-- 1. A proper 'Coercion'
+--
+-- 2. The identity coercion
+data CoercionI = IdCo | ACo Coercion
+
+instance Outputable CoercionI where
+ ppr IdCo = ptext (sLit "IdCo")
+ ppr (ACo co) = ppr co
+
+isIdentityCoI :: CoercionI -> Bool
+isIdentityCoI IdCo = True
+isIdentityCoI _ = False
+
+-- | Tests whether all the given 'CoercionI's represent the identity coercion
+allIdCoIs :: [CoercionI] -> Bool
+allIdCoIs = all isIdentityCoI
+
+-- | For each 'CoercionI' in the input list, return either the 'Coercion' it
+-- contains or the corresponding 'Type' from the other list
+zipCoArgs :: [CoercionI] -> [Type] -> [Coercion]
+zipCoArgs cois tys = zipWith fromCoI cois tys
+
+-- | Return either the 'Coercion' contained within the 'CoercionI' or the given
+-- 'Type' if the 'CoercionI' is the identity 'Coercion'
+fromCoI :: CoercionI -> Type -> Type
+fromCoI IdCo ty = ty -- Identity coercion represented
+fromCoI (ACo co) _ = co -- by the type itself
+
+-- | Smart constructor for @sym@ on 'CoercionI', see also 'mkSymCoercion'
+mkSymCoI :: CoercionI -> CoercionI
+mkSymCoI IdCo = IdCo
+mkSymCoI (ACo co) = ACo $ mkCoercion symCoercionTyCon [co]
+ -- the smart constructor
+ -- is too smart with tyvars
+
+-- | Smart constructor for @trans@ on 'CoercionI', see also 'mkTransCoercion'
+mkTransCoI :: CoercionI -> CoercionI -> CoercionI
+mkTransCoI IdCo aco = aco
+mkTransCoI aco IdCo = aco
+mkTransCoI (ACo co1) (ACo co2) = ACo $ mkTransCoercion co1 co2
+
+-- | Smart constructor for type constructor application on 'CoercionI', see also 'mkAppCoercion'
+mkTyConAppCoI :: TyCon -> [Type] -> [CoercionI] -> CoercionI
+mkTyConAppCoI tyCon tys cois
+ | allIdCoIs cois = IdCo
+ | otherwise = ACo (TyConApp tyCon (zipCoArgs cois tys))
+
+-- | Smart constructor for honest-to-god 'Coercion' application on 'CoercionI', see also 'mkAppCoercion'
+mkAppTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+mkAppTyCoI _ IdCo _ IdCo = IdCo
+mkAppTyCoI ty1 coi1 ty2 coi2 =
+ ACo $ AppTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
+
+-- | Smart constructor for function-'Coercion's on 'CoercionI', see also 'mkFunCoercion'
+mkFunTyCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+mkFunTyCoI _ IdCo _ IdCo = IdCo
+mkFunTyCoI ty1 coi1 ty2 coi2 =
+ ACo $ FunTy (fromCoI coi1 ty1) (fromCoI coi2 ty2)
+
+-- | Smart constructor for quantified 'Coercion's on 'CoercionI', see also 'mkForAllCoercion'
+mkForAllTyCoI :: TyVar -> CoercionI -> CoercionI
+mkForAllTyCoI _ IdCo = IdCo
+mkForAllTyCoI tv (ACo co) = ACo $ ForAllTy tv co
+
+-- | Extract a 'Coercion' from a 'CoercionI' if it represents one. If it is the identity coercion,
+-- panic
+fromACo :: CoercionI -> Coercion
+fromACo (ACo co) = co
+
+-- | Smart constructor for class 'Coercion's on 'CoercionI'. Satisfies:
+--
+-- > mkClassPPredCoI cls tys cois :: PredTy (cls tys) ~ PredTy (cls (tys `cast` cois))
+mkClassPPredCoI :: Class -> [Type] -> [CoercionI] -> CoercionI
+mkClassPPredCoI cls tys cois
+ | allIdCoIs cois = IdCo
+ | otherwise = ACo $ PredTy $ ClassP cls (zipCoArgs cois tys)
+
+-- | Smart constructor for implicit parameter 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
+mkIParamPredCoI :: (IPName Name) -> CoercionI -> CoercionI
+mkIParamPredCoI _ IdCo = IdCo
+mkIParamPredCoI ipn (ACo co) = ACo $ PredTy $ IParam ipn co
+
+-- | Smart constructor for type equality 'Coercion's on 'CoercionI'. Similar to 'mkClassPPredCoI'
+mkEqPredCoI :: Type -> CoercionI -> Type -> CoercionI -> CoercionI
+mkEqPredCoI _ IdCo _ IdCo = IdCo
+mkEqPredCoI ty1 IdCo _ (ACo co2) = ACo $ PredTy $ EqPred ty1 co2
+mkEqPredCoI _ (ACo co1) ty2 coi2 = ACo $ PredTy $ EqPred co1 (fromCoI coi2 ty2)
+\end{code}
projects / ghc-hetmet.git / blobdiff