+%
+% (c) The University of Glasgow 2006
+%
- Module for type coercions, as in System FC.
+\begin{code}
+-- | 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.
+--
+module Coercion (
+ -- * Main data type
+ Coercion(..), Var, CoVar,
-Coercions are represented as types, and their kinds tell what types the
-coercion works on.
+ -- ** Deconstructing Kinds
+ kindFunResult, kindAppResult, synTyConResKind,
+ splitKindFunTys, splitKindFunTysN, splitKindFunTy_maybe,
-The coercion kind constructor is a special TyCon that must always be saturated
+ -- ** Predicates on Kinds
+ isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
+ isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
+ isSuperKind, isCoercionKind,
+ mkArrowKind, mkArrowKinds,
- typeKind (symCoercion type) :: TyConApp CoercionTyCon{...} [type, type]
+ isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
+ isSubKindCon,
-\begin{code}
-module Coercion (
- Coercion,
-
- mkCoKind, mkReflCoKind, splitCoercionKind_maybe, splitCoercionKind,
- coercionKind, coercionKinds, coercionKindPredTy,
+ mkCoType, coVarKind, coVarKind_maybe,
+ coercionType, coercionKind, coercionKinds, isReflCo,
+
+ -- ** Constructing coercions
+ mkReflCo, mkCoVarCo,
+ mkAxInstCo, mkPiCo, mkPiCos,
+ mkSymCo, mkTransCo, mkNthCo,
+ mkInstCo, mkAppCo, mkTyConAppCo, mkFunCo,
+ mkForAllCo, mkUnsafeCo,
+ mkNewTypeCo, mkFamInstCo,
+ mkPredCo,
- -- Equality predicates
- isEqPred, mkEqPred, getEqPredTys, isEqPredTy,
+ -- ** Decomposition
+ splitCoPredTy_maybe,
+ splitNewTypeRepCo_maybe, instNewTyCon_maybe, decomposeCo,
+ getCoVar_maybe,
- -- Coercion transformations
- mkSymCoercion, mkTransCoercion,
- mkLeftCoercion, mkRightCoercion, mkInstCoercion, mkAppCoercion,
- mkForAllCoercion, mkFunCoercion, mkInstsCoercion, mkUnsafeCoercion,
- mkNewTypeCoercion, mkAppsCoercion,
+ splitTyConAppCo_maybe,
+ splitAppCo_maybe,
+ splitForAllCo_maybe,
- splitNewTypeRepCo_maybe, decomposeCo,
+ -- ** Coercion variables
+ mkCoVar, isCoVar, isCoVarType, coVarName, setCoVarName, setCoVarUnique,
- unsafeCoercionTyCon, symCoercionTyCon,
- transCoercionTyCon, leftCoercionTyCon,
- rightCoercionTyCon, instCoercionTyCon -- needed by TysWiredIn
+ -- ** Free variables
+ tyCoVarsOfCo, tyCoVarsOfCos, coVarsOfCo, coercionSize,
+
+ -- ** Substitution
+ CvSubstEnv, emptyCvSubstEnv,
+ CvSubst(..), emptyCvSubst, Coercion.lookupTyVar, lookupCoVar,
+ isEmptyCvSubst, zapCvSubstEnv, getCvInScope,
+ substCo, substCos, substCoVar, substCoVars,
+ substCoWithTy, substCoWithTys,
+ cvTvSubst, tvCvSubst, zipOpenCvSubst,
+ substTy, extendTvSubst,
+ substTyVarBndr, substCoVarBndr,
+
+ -- ** Lifting
+ liftCoMatch, liftCoSubst, liftCoSubstTyVar, liftCoSubstWith,
+
+ -- ** Comparison
+ coreEqCoercion, coreEqCoercion2,
+
+ -- ** Forcing evaluation of coercions
+ seqCo,
+
+ -- * Pretty-printing
+ pprCo, pprParendCo, pprCoAxiom,
+
+ -- * Other
+ applyCo, coVarPred
+
) where
#include "HsVersions.h"
+import Unify ( MatchEnv(..), ruleMatchTyX, matchList )
import TypeRep
-import Type ( Type, Kind, PredType, substTyWith, mkAppTy, mkForAllTy,
- mkFunTy, splitAppTy_maybe, splitForAllTy_maybe, coreView,
- kindView, mkTyConApp, isCoercionKind, isEqPred, mkAppTys,
- coreEqType
- )
-import TyCon ( TyCon, tyConArity, mkCoercionTyCon, isNewTyCon,
- newTyConRhs, newTyConCo,
- isCoercionTyCon, isCoercionTyCon_maybe )
-import Var ( Var, TyVar, isTyVar, tyVarKind )
-import Name ( BuiltInSyntax(..), Name, mkWiredInName, tcName )
-import OccName ( mkOccNameFS )
-import PrelNames ( symCoercionTyConKey,
- transCoercionTyConKey, leftCoercionTyConKey,
- rightCoercionTyConKey, instCoercionTyConKey,
- unsafeCoercionTyConKey, gHC_PRIM
- )
-import Util ( lengthIs, snocView )
-import Unique ( hasKey )
-import BasicTypes ( Arity )
+import qualified Type
+import Type hiding( substTy, substTyVarBndr, extendTvSubst )
+import Kind
+import Class ( classTyCon )
+import TyCon
+import Var
+import VarEnv
+import VarSet
+import UniqFM ( minusUFM )
+import Maybes ( orElse )
+import Name ( Name, NamedThing(..), nameUnique )
+import OccName ( isSymOcc )
+import Util
+import BasicTypes
import Outputable
+import Unique
+import Pair
+import TysPrim ( eqPredPrimTyCon )
+import PrelNames ( funTyConKey )
+import Control.Applicative
+import Data.Traversable (traverse, sequenceA)
+import Control.Arrow (second)
+import FastString
+import qualified Data.Data as Data hiding ( TyCon )
+\end{code}
+%************************************************************************
+%* *
+ Coercions
+%* *
+%************************************************************************
-------------------------------
-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 []
+\begin{code}
+-- | A 'Coercion' is concrete evidence of the equality/convertibility
+-- of two types.
+
+data Coercion
+ -- These ones mirror the shape of types
+ = Refl Type -- See Note [Refl invariant]
+ -- Invariant: applications of (Refl T) to a bunch of identity coercions
+ -- always show up as Refl.
+ -- For example (Refl T) (Refl a) (Refl b) shows up as (Refl (T a b)).
+
+ -- Applications of (Refl T) to some coercions, at least one of
+ -- which is NOT the identity, show up as TyConAppCo.
+ -- (They may not be fully saturated however.)
+ -- ConAppCo coercions (like all coercions other than Refl)
+ -- are NEVER the identity.
+
+ -- These ones simply lift the correspondingly-named
+ -- Type constructors into Coercions
+ | TyConAppCo TyCon [Coercion] -- lift TyConApp
+ -- The TyCon is never a synonym;
+ -- we expand synonyms eagerly
+
+ | AppCo Coercion Coercion -- lift AppTy
+
+ -- See Note [Forall coercions]
+ | ForAllCo TyVar Coercion -- forall a. g
+
+ -- These are special
+ | CoVarCo CoVar
+ | AxiomInstCo CoAxiom [Coercion] -- The coercion arguments always *precisely*
+ -- saturate arity of CoAxiom.
+ -- See [Coercion axioms applied to coercions]
+ | UnsafeCo Type Type
+ | SymCo Coercion
+ | TransCo Coercion Coercion
+
+ -- These are destructors
+ | NthCo Int Coercion -- Zero-indexed
+ | InstCo Coercion Type
+ deriving (Data.Data, Data.Typeable)
+\end{code}
+
+Note [Refl invariant]
+~~~~~~~~~~~~~~~~~~~~~
+Coercions have the following invariant
+ Refl is always lifted as far as possible.
+
+You might think that a consequencs is:
+ Every identity coercions has Refl at the root
+
+But that's not quite true because of coercion variables. Consider
+ g where g :: Int~Int
+ Left h where h :: Maybe Int ~ Maybe Int
+etc. So the consequence is only true of coercions that
+have no coercion variables.
+
+Note [Coercion axioms applied to coercions]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The reason coercion axioms can be applied to coercions and not just
+types is to allow for better optimization. There are some cases where
+we need to be able to "push transitivity inside" an axiom in order to
+expose further opportunities for optimization.
+
+For example, suppose we have
+
+ C a : t[a] ~ F a
+ g : b ~ c
+
+and we want to optimize
+
+ sym (C b) ; t[g] ; C c
+
+which has the kind
+
+ F b ~ F c
+
+(stopping through t[b] and t[c] along the way).
+
+We'd like to optimize this to just F g -- but how? The key is
+that we need to allow axioms to be instantiated by *coercions*,
+not just by types. Then we can (in certain cases) push
+transitivity inside the axiom instantiations, and then react
+opposite-polarity instantiations of the same axiom. In this
+case, e.g., we match t[g] against the LHS of (C c)'s kind, to
+obtain the substitution a |-> g (note this operation is sort
+of the dual of lifting!) and hence end up with
+
+ C g : t[b] ~ F c
+
+which indeed has the same kind as t[g] ; C c.
+
+Now we have
+
+ sym (C b) ; C g
+
+which can be optimized to F g.
+
+
+Note [Forall coercions]
+~~~~~~~~~~~~~~~~~~~~~~~
+Constructing coercions between forall-types can be a bit tricky.
+Currently, the situation is as follows:
+
+ ForAllCo TyVar Coercion
+
+represents a coercion between polymorphic types, with the rule
+
+ v : k g : t1 ~ t2
+ ----------------------------------------------
+ ForAllCo v g : (all v:k . t1) ~ (all v:k . t2)
+
+Note that it's only necessary to coerce between polymorphic types
+where the type variables have identical kinds, because equality on
+kinds is trivial.
+
+Note [Predicate coercions]
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+Suppose we have
+ g :: a~b
+How can we coerce between types
+ ([c]~a) => [a] -> c
+and
+ ([c]~b) => [b] -> c
+where the equality predicate *itself* differs?
+
+Answer: we simply treat (~) as an ordinary type constructor, so these
+types really look like
+
+ ((~) [c] a) -> [a] -> c
+ ((~) [c] b) -> [b] -> c
+
+So the coercion between the two is obviously
+
+ ((~) [c] g) -> [g] -> c
+
+Another way to see this to say that we simply collapse predicates to
+their representation type (see Type.coreView and Type.predTypeRep).
+
+This collapse is done by mkPredCo; there is no PredCo constructor
+in Coercion. This is important because we need Nth to work on
+predicates too:
+ Nth 1 ((~) [c] g) = g
+See Simplify.simplCoercionF, which generates such selections.
+
+%************************************************************************
+%* *
+\subsection{Coercion variables}
+%* *
+%************************************************************************
+
+\begin{code}
+coVarName :: CoVar -> Name
+coVarName = varName
+
+setCoVarUnique :: CoVar -> Unique -> CoVar
+setCoVarUnique = setVarUnique
+
+setCoVarName :: CoVar -> Name -> CoVar
+setCoVarName = setVarName
+
+isCoVar :: Var -> Bool
+isCoVar v = isCoVarType (varType v)
+
+isCoVarType :: Type -> Bool
+isCoVarType = isEqPredTy
+\end{code}
+
+
+\begin{code}
+tyCoVarsOfCo :: Coercion -> VarSet
+-- Extracts type and coercion variables from a coercion
+tyCoVarsOfCo (Refl ty) = tyVarsOfType ty
+tyCoVarsOfCo (TyConAppCo _ cos) = tyCoVarsOfCos cos
+tyCoVarsOfCo (AppCo co1 co2) = tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2
+tyCoVarsOfCo (ForAllCo tv co) = tyCoVarsOfCo co `delVarSet` tv
+tyCoVarsOfCo (CoVarCo v) = unitVarSet v
+tyCoVarsOfCo (AxiomInstCo _ cos) = tyCoVarsOfCos cos
+tyCoVarsOfCo (UnsafeCo ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
+tyCoVarsOfCo (SymCo co) = tyCoVarsOfCo co
+tyCoVarsOfCo (TransCo co1 co2) = tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2
+tyCoVarsOfCo (NthCo _ co) = tyCoVarsOfCo co
+tyCoVarsOfCo (InstCo co ty) = tyCoVarsOfCo co `unionVarSet` tyVarsOfType ty
+
+tyCoVarsOfCos :: [Coercion] -> VarSet
+tyCoVarsOfCos cos = foldr (unionVarSet . tyCoVarsOfCo) emptyVarSet cos
+
+coVarsOfCo :: Coercion -> VarSet
+-- Extract *coerction* variables only. Tiresome to repeat the code, but easy.
+coVarsOfCo (Refl _) = emptyVarSet
+coVarsOfCo (TyConAppCo _ cos) = coVarsOfCos cos
+coVarsOfCo (AppCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
+coVarsOfCo (ForAllCo _ co) = coVarsOfCo co
+coVarsOfCo (CoVarCo v) = unitVarSet v
+coVarsOfCo (AxiomInstCo _ cos) = coVarsOfCos cos
+coVarsOfCo (UnsafeCo _ _) = emptyVarSet
+coVarsOfCo (SymCo co) = coVarsOfCo co
+coVarsOfCo (TransCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
+coVarsOfCo (NthCo _ co) = coVarsOfCo co
+coVarsOfCo (InstCo co _) = coVarsOfCo co
+
+coVarsOfCos :: [Coercion] -> VarSet
+coVarsOfCos cos = foldr (unionVarSet . coVarsOfCo) emptyVarSet cos
+
+coercionSize :: Coercion -> Int
+coercionSize (Refl ty) = typeSize ty
+coercionSize (TyConAppCo _ cos) = 1 + sum (map coercionSize cos)
+coercionSize (AppCo co1 co2) = coercionSize co1 + coercionSize co2
+coercionSize (ForAllCo _ co) = 1 + coercionSize co
+coercionSize (CoVarCo _) = 1
+coercionSize (AxiomInstCo _ cos) = 1 + sum (map coercionSize cos)
+coercionSize (UnsafeCo ty1 ty2) = typeSize ty1 + typeSize ty2
+coercionSize (SymCo co) = 1 + coercionSize co
+coercionSize (TransCo co1 co2) = 1 + coercionSize co1 + coercionSize co2
+coercionSize (NthCo _ co) = 1 + coercionSize co
+coercionSize (InstCo co ty) = 1 + coercionSize co + typeSize ty
+\end{code}
+
+%************************************************************************
+%* *
+ Pretty-printing coercions
+%* *
+%************************************************************************
+
+@pprCo@ is the standard @Coercion@ printer; the overloaded @ppr@
+function is defined to use this. @pprParendCo@ is the same, except it
+puts parens around the type, except for the atomic cases.
+@pprParendCo@ works just by setting the initial context precedence
+very high.
+
+\begin{code}
+instance Outputable Coercion where
+ ppr = pprCo
+
+pprCo, pprParendCo :: Coercion -> SDoc
+pprCo co = ppr_co TopPrec co
+pprParendCo co = ppr_co TyConPrec co
+
+ppr_co :: Prec -> Coercion -> SDoc
+ppr_co _ (Refl ty) = angles (ppr ty)
+
+ppr_co p co@(TyConAppCo tc cos)
+ | tc `hasKey` funTyConKey = ppr_fun_co p co
+ | otherwise = pprTcApp p ppr_co tc cos
+
+ppr_co p (AppCo co1 co2) = maybeParen p TyConPrec $
+ pprCo co1 <+> ppr_co TyConPrec co2
+
+ppr_co p co@(ForAllCo {}) = ppr_forall_co p co
+
+ppr_co _ (CoVarCo cv)
+ | isSymOcc (getOccName cv) = parens (ppr cv)
+ | otherwise = ppr cv
+
+ppr_co p (AxiomInstCo con cos) = pprTypeNameApp p ppr_co (getName con) cos
+
+
+ppr_co p (TransCo co1 co2) = maybeParen p FunPrec $
+ ppr_co FunPrec co1
+ <+> ptext (sLit ";")
+ <+> ppr_co FunPrec co2
+ppr_co p (InstCo co ty) = maybeParen p TyConPrec $
+ pprParendCo co <> ptext (sLit "@") <> pprType ty
+
+ppr_co p (UnsafeCo ty1 ty2) = pprPrefixApp p (ptext (sLit "UnsafeCo")) [pprParendType ty1, pprParendType ty2]
+ppr_co p (SymCo co) = pprPrefixApp p (ptext (sLit "Sym")) [pprParendCo co]
+ppr_co p (NthCo n co) = pprPrefixApp p (ptext (sLit "Nth:") <+> int n) [pprParendCo co]
+
+
+angles :: SDoc -> SDoc
+angles p = char '<' <> p <> char '>'
+
+ppr_fun_co :: Prec -> Coercion -> SDoc
+ppr_fun_co p co = pprArrowChain p (split co)
where
- go 0 co cos = cos
- go n co cos = go (n-1) (mkLeftCoercion co)
- (mkRightCoercion co : cos)
+ split (TyConAppCo f [arg,res])
+ | f `hasKey` funTyConKey
+ = ppr_co FunPrec arg : split res
+ split co = [ppr_co TopPrec co]
-------------------------------
+ppr_forall_co :: Prec -> Coercion -> SDoc
+ppr_forall_co p ty
+ = maybeParen p FunPrec $
+ sep [pprForAll tvs, ppr_co TopPrec rho]
+ where
+ (tvs, rho) = split1 [] ty
+ split1 tvs (ForAllCo tv ty) = split1 (tv:tvs) ty
+ split1 tvs ty = (reverse tvs, ty)
+\end{code}
+
+\begin{code}
+pprCoAxiom :: CoAxiom -> SDoc
+pprCoAxiom ax
+ = sep [ ptext (sLit "axiom") <+> ppr ax <+> ppr (co_ax_tvs ax)
+ , nest 2 (dcolon <+> pprEqPred (Pair (co_ax_lhs ax) (co_ax_rhs ax))) ]
+\end{code}
+
+%************************************************************************
+%* *
+ Functions over Kinds
+%* *
+%************************************************************************
+
+\begin{code}
+-- | This breaks a 'Coercion' with type @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 = [nth 0 c, nth 1 c, nth 2 c]
+decomposeCo :: Arity -> Coercion -> [Coercion]
+decomposeCo arity co = [mkNthCo n co | n <- [0..(arity-1)] ]
+
+-- | Attempts to obtain the type variable underlying a 'Coercion'
+getCoVar_maybe :: Coercion -> Maybe CoVar
+getCoVar_maybe (CoVarCo cv) = Just cv
+getCoVar_maybe _ = Nothing
+
+-- | Attempts to tease a coercion apart into a type constructor and the application
+-- of a number of coercion arguments to that constructor
+splitTyConAppCo_maybe :: Coercion -> Maybe (TyCon, [Coercion])
+splitTyConAppCo_maybe (Refl ty) = (fmap . second . map) Refl (splitTyConApp_maybe ty)
+splitTyConAppCo_maybe (TyConAppCo tc cos) = Just (tc, cos)
+splitTyConAppCo_maybe _ = Nothing
+
+splitAppCo_maybe :: Coercion -> Maybe (Coercion, Coercion)
+-- ^ Attempt to take a coercion application apart.
+splitAppCo_maybe (AppCo co1 co2) = Just (co1, co2)
+splitAppCo_maybe (TyConAppCo tc cos)
+ | isDecomposableTyCon tc || cos `lengthExceeds` tyConArity tc
+ , Just (cos', co') <- snocView cos
+ = Just (mkTyConAppCo tc cos', co') -- Never create unsaturated type family apps!
+ -- Use mkTyConAppCo to preserve the invariant
+ -- that identity coercions are always represented by Refl
+splitAppCo_maybe (Refl ty)
+ | Just (ty1, ty2) <- splitAppTy_maybe ty
+ = Just (Refl ty1, Refl ty2)
+splitAppCo_maybe _ = Nothing
+
+splitForAllCo_maybe :: Coercion -> Maybe (TyVar, Coercion)
+splitForAllCo_maybe (ForAllCo tv co) = Just (tv, co)
+splitForAllCo_maybe _ = Nothing
-------------------------------------------------------
-- and some coercion kind stuff
-isEqPredTy (PredTy pred) = isEqPred pred
-isEqPredTy other = False
+coVarPred :: CoVar -> PredType
+coVarPred cv
+ = ASSERT( isCoVar cv )
+ case splitPredTy_maybe (varType cv) of
+ Just pred -> pred
+ other -> pprPanic "coVarPred" (ppr cv $$ ppr other)
-mkEqPred :: (Type, Type) -> PredType
-mkEqPred (ty1, ty2) = EqPred ty1 ty2
+coVarKind :: CoVar -> (Type,Type)
+-- c :: t1 ~ t2
+coVarKind cv = case coVarKind_maybe cv of
+ Just ts -> ts
+ Nothing -> pprPanic "coVarKind" (ppr cv $$ ppr (tyVarKind cv))
-getEqPredTys :: PredType -> (Type,Type)
-getEqPredTys (EqPred ty1 ty2) = (ty1, ty2)
-getEqPredTys other = pprPanic "getEqPredTys" (ppr other)
+coVarKind_maybe :: CoVar -> Maybe (Type,Type)
+coVarKind_maybe cv = splitEqPredTy_maybe (varType cv)
-mkCoKind :: Type -> Type -> CoercionKind
-mkCoKind ty1 ty2 = PredTy (EqPred ty1 ty2)
+-- | Makes a coercion type from two types: the types whose equality
+-- is proven by the relevant 'Coercion'
+mkCoType :: Type -> Type -> Type
+mkCoType ty1 ty2 = PredTy (EqPred ty1 ty2)
-mkReflCoKind :: Type -> CoercionKind
-mkReflCoKind ty = mkCoKind ty ty
+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 :: CoercionKind -> (Type, Type)
-splitCoercionKind co | Just co' <- kindView co = splitCoercionKind co'
-splitCoercionKind (PredTy (EqPred ty1 ty2)) = (ty1, ty2)
+isReflCo :: Coercion -> Bool
+isReflCo (Refl {}) = True
+isReflCo _ = False
-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
+isReflCo_maybe :: Coercion -> Maybe Type
+isReflCo_maybe (Refl ty) = Just ty
+isReflCo_maybe _ = Nothing
+\end{code}
-isCoVar :: Var -> Bool
-isCoVar tv = isTyVar tv && isCoercionKind (tyVarKind tv)
-
-type Coercion = Type
-type CoercionKind = Kind -- A CoercionKind is always of form (ty1 :=: ty2)
-
-coercionKind :: Coercion -> (Type, Type)
--- c :: (t1 :=: t2)
--- Then (coercionKind c) = (t1,t2)
-coercionKind (TyVarTy a) | isCoVar a = splitCoercionKind (tyVarKind a)
- | otherwise = let t = (TyVarTy a) in (t, t)
-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
- = if length args >= ar
- then splitCoercionKind (rule args)
- else pprPanic ("arity/arguments mismatch in coercionKind:")
- (ppr ar $$ ppr tc <+> ppr args)
- | 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 (NoteTy _ ty) = coercionKind ty
-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))
-
-coercionKindPredTy :: Coercion -> CoercionKind
-coercionKindPredTy c = let (t1, t2) = coercionKind c in mkCoKind t1 t2
-
-coercionKinds :: [Coercion] -> ([Type], [Type])
-coercionKinds tys = unzip $ map coercionKind tys
-
--------------------------------------
--- Coercion kind and type mk's
--- (make saturated TyConApp CoercionTyCon{...} args)
-
-mkCoercion coCon args = ASSERT( tyConArity coCon == length args )
- TyConApp coCon args
-
-mkAppCoercion, mkFunCoercion, mkTransCoercion, mkInstCoercion :: Coercion -> Coercion -> Coercion
-mkSymCoercion, mkLeftCoercion, mkRightCoercion :: Coercion -> Coercion
-
-mkAppCoercion co1 co2 = mkAppTy co1 co2
-mkAppsCoercion co1 tys = foldl mkAppTy co1 tys
+%************************************************************************
+%* *
+ Building coercions
+%* *
+%************************************************************************
+
+\begin{code}
+mkCoVarCo :: CoVar -> Coercion
+mkCoVarCo cv
+ | ty1 `eqType` ty2 = Refl ty1
+ | otherwise = CoVarCo cv
+ where
+ (ty1, ty2) = ASSERT( isCoVar cv ) coVarKind cv
+
+mkReflCo :: Type -> Coercion
+mkReflCo = Refl
+
+mkAxInstCo :: CoAxiom -> [Type] -> Coercion
+mkAxInstCo ax tys
+ | arity == n_tys = AxiomInstCo ax rtys
+ | otherwise = ASSERT( arity < n_tys )
+ foldl AppCo (AxiomInstCo ax (take arity rtys))
+ (drop arity rtys)
+ where
+ n_tys = length tys
+ arity = coAxiomArity ax
+ rtys = map Refl tys
+
+-- | Apply a 'Coercion' to another 'Coercion'.
+mkAppCo :: Coercion -> Coercion -> Coercion
+mkAppCo (Refl ty1) (Refl ty2) = Refl (mkAppTy ty1 ty2)
+mkAppCo (Refl (TyConApp tc tys)) co = TyConAppCo tc (map Refl tys ++ [co])
+mkAppCo (TyConAppCo tc cos) co = TyConAppCo tc (cos ++ [co])
+mkAppCo co1 co2 = AppCo co1 co2
+-- Note, mkAppCo is careful to maintain invariants regarding
+-- where Refl constructors appear; see the comments in the definition
+-- of Coercion and the Note [Refl invariant] in types/TypeRep.lhs.
+
+-- | Applies multiple 'Coercion's to another 'Coercion', from left to right.
+-- See also 'mkAppCo'
+mkAppCos :: Coercion -> [Coercion] -> Coercion
+mkAppCos co1 tys = foldl mkAppCo co1 tys
+
+-- | Apply a type constructor to a list of coercions.
+mkTyConAppCo :: TyCon -> [Coercion] -> Coercion
+mkTyConAppCo tc cos
+ -- Expand type synonyms
+ | Just (tv_co_prs, rhs_ty, leftover_cos) <- tcExpandTyCon_maybe tc cos
+ = mkAppCos (liftCoSubst (mkTopCvSubst tv_co_prs) rhs_ty) leftover_cos
+
+ | Just tys <- traverse isReflCo_maybe cos
+ = Refl (mkTyConApp tc tys) -- See Note [Refl invariant]
+
+ | otherwise = TyConAppCo tc cos
+
+-- | Make a function 'Coercion' between two other 'Coercion's
+mkFunCo :: Coercion -> Coercion -> Coercion
+mkFunCo co1 co2 = mkTyConAppCo funTyCon [co1, co2]
+
+-- | Make a 'Coercion' which binds a variable within an inner 'Coercion'
+mkForAllCo :: 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
-
-mkSymCoercion co
- | Just co2 <- splitSymCoercion_maybe co = co2
- | Just (co1, co2) <- splitAppCoercion_maybe co
- -- should make this case better
- = mkAppCoercion (mkSymCoercion co1) (mkSymCoercion co2)
- | Just (co1, co2) <- splitTransCoercion_maybe co
- = mkTransCoercion (mkSymCoercion co2) (mkSymCoercion co1)
- | Just (co, ty) <- splitInstCoercion_maybe co
- = mkInstCoercion (mkSymCoercion co) ty
- | Just co <- splitLeftCoercion_maybe co
- = mkLeftCoercion (mkSymCoercion co)
- | Just co <- splitRightCoercion_maybe co
- = mkRightCoercion (mkSymCoercion co)
-mkSymCoercion (ForAllTy tv ty) = ForAllTy tv (mkSymCoercion ty)
--- for atomic types and constructors, we can just ignore sym since these
--- are reflexive coercions
-mkSymCoercion (TyVarTy tv)
- | isCoVar tv = mkCoercion symCoercionTyCon [TyVarTy tv]
- | otherwise = TyVarTy tv
-mkSymCoercion co = mkCoercion symCoercionTyCon [co]
- -- this should not happen but does
-
--- 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]
-
-mkTransCoercion co1 co2 = mkCoercion transCoercionTyCon [co1, co2]
-
-mkInstCoercion co ty = mkCoercion instCoercionTyCon [co, ty]
-
-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 the one case in which it is safe. It is also used to
--- implement the unsafeCoerce# primitive.
-mkUnsafeCoercion :: Type -> Type -> Coercion
-mkUnsafeCoercion ty1 ty2
- = mkCoercion unsafeCoercionTyCon [ty1, ty2]
-
-
--- Make the coercion associated with a newtype. If we have
+mkForAllCo tv (Refl ty) = ASSERT( isTyVar tv ) Refl (mkForAllTy tv ty)
+mkForAllCo tv co = ASSERT ( isTyVar tv ) ForAllCo tv co
+
+mkPredCo :: Pred Coercion -> Coercion
+-- See Note [Predicate coercions]
+mkPredCo (EqPred co1 co2) = mkTyConAppCo eqPredPrimTyCon [co1,co2]
+mkPredCo (ClassP cls cos) = mkTyConAppCo (classTyCon cls) cos
+mkPredCo (IParam _ co) = co
+
+-------------------------------
+
+-- | 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@.
+mkSymCo :: Coercion -> Coercion
+
+-- Do a few simple optimizations, but don't bother pushing occurrences
+-- of symmetry to the leaves; the optimizer will take care of that.
+mkSymCo co@(Refl {}) = co
+mkSymCo (UnsafeCo ty1 ty2) = UnsafeCo ty2 ty1
+mkSymCo (SymCo co) = co
+mkSymCo co = SymCo co
+
+-- | Create a new 'Coercion' by composing the two given 'Coercion's transitively.
+mkTransCo :: Coercion -> Coercion -> Coercion
+mkTransCo (Refl _) co = co
+mkTransCo co (Refl _) = co
+mkTransCo co1 co2 = TransCo co1 co2
+
+mkNthCo :: Int -> Coercion -> Coercion
+mkNthCo n (Refl ty) = Refl (getNth n ty)
+mkNthCo n co = NthCo n co
+
+-- | Instantiates a 'Coercion' with a 'Type' argument. If possible, it immediately performs
+-- the resulting beta-reduction, otherwise it creates a suspended instantiation.
+mkInstCo :: Coercion -> Type -> Coercion
+mkInstCo (ForAllCo tv co) ty = substCoWithTy tv ty co
+mkInstCo co ty = InstCo co ty
+
+-- | Manufacture a coercion from thin 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
+-- to implement the @unsafeCoerce#@ primitive. Optimise by pushing
+-- down through type constructors.
+mkUnsafeCo :: Type -> Type -> Coercion
+mkUnsafeCo ty1 ty2 | ty1 `eqType` ty2 = Refl ty1
+mkUnsafeCo (TyConApp tc1 tys1) (TyConApp tc2 tys2)
+ | tc1 == tc2
+ = mkTyConAppCo tc1 (zipWith mkUnsafeCo tys1 tys2)
+
+mkUnsafeCo (FunTy a1 r1) (FunTy a2 r2)
+ = mkFunCo (mkUnsafeCo a1 a2) (mkUnsafeCo r1 r2)
+
+mkUnsafeCo ty1 ty2 = UnsafeCo ty1 ty2
+
+-- See note [Newtype coercions] in TyCon
+
+-- | Create a coercion constructor (axiom) suitable for the given
+-- newtype 'TyCon'. The 'Name' should be that of a new coercion
+-- 'CoAxiom', 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.
+mkNewTypeCo :: Name -> TyCon -> [TyVar] -> Type -> CoAxiom
+mkNewTypeCo name tycon tvs rhs_ty
+ = CoAxiom { co_ax_unique = nameUnique name
+ , co_ax_name = name
+ , 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
+-- the coercion constructor built here, @F@ the family tycon and @R@ the (derived)
+-- representation tycon.
+mkFamInstCo :: 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@)
+ -> CoAxiom -- ^ Coercion constructor (@Co@)
+mkFamInstCo name tvs family inst_tys rep_tycon
+ = CoAxiom { co_ax_unique = nameUnique name
+ , co_ax_name = name
+ , co_ax_tvs = tvs
+ , co_ax_lhs = mkTyConApp family inst_tys
+ , co_ax_rhs = mkTyConApp rep_tycon (mkTyVarTys tvs) }
+
+mkPiCos :: [Var] -> Coercion -> Coercion
+mkPiCos vs co = foldr mkPiCo co vs
+
+mkPiCo :: Var -> Coercion -> Coercion
+mkPiCo v co | isTyVar v = mkForAllCo v co
+ | otherwise = mkFunCo (mkReflCo (varType v)) co
+\end{code}
+
+%************************************************************************
+%* *
+ Newtypes
+%* *
+%************************************************************************
+
+\begin{code}
+instNewTyCon_maybe :: TyCon -> [Type] -> Maybe (Type, Coercion)
+-- ^ If @co :: T ts ~ rep_ty@ then:
--
--- newtype T a b = MkT (Int, a, b)
+-- > instNewTyCon_maybe T ts = Just (rep_ty, co)
+instNewTyCon_maybe tc tys
+ | Just (tvs, ty, co_tc) <- unwrapNewTyCon_maybe tc
+ = ASSERT( tys `lengthIs` tyConArity tc )
+ Just (substTyWith tvs tys ty, mkAxInstCo 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:
--
--- Then (mkNewTypeCoercion CoT T [a,b] (Int, a, b)) creates the coercion
--- CoT, such kinding rule such that
+-- > splitNewTypeRepCo_maybe ty = Just (ty', co)
--
--- CoT S U :: (Int, S, U) :=: T S U
-mkNewTypeCoercion :: Name -> TyCon -> [TyVar] -> Type -> TyCon
-mkNewTypeCoercion name tycon tvs rhs_ty
- = ASSERT (length tvs == tyConArity tycon)
- mkCoercionTyCon name (tyConArity tycon) rule
+-- 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', co) <- instNewTyCon_maybe tc tys
+ = case co of
+ Refl _ -> panic "splitNewTypeRepCo_maybe"
+ -- This case handled by coreView
+ _ -> Just (ty', co)
+splitNewTypeRepCo_maybe _
+ = Nothing
+
+-- | Determines syntactic equality of coercions
+coreEqCoercion :: Coercion -> Coercion -> Bool
+coreEqCoercion co1 co2 = coreEqCoercion2 rn_env co1 co2
+ where rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfCo co1 `unionVarSet` tyCoVarsOfCo co2))
+
+coreEqCoercion2 :: RnEnv2 -> Coercion -> Coercion -> Bool
+coreEqCoercion2 env (Refl ty1) (Refl ty2) = eqTypeX env ty1 ty2
+coreEqCoercion2 env (TyConAppCo tc1 cos1) (TyConAppCo tc2 cos2)
+ = tc1 == tc2 && all2 (coreEqCoercion2 env) cos1 cos2
+
+coreEqCoercion2 env (AppCo co11 co12) (AppCo co21 co22)
+ = coreEqCoercion2 env co11 co21 && coreEqCoercion2 env co12 co22
+
+coreEqCoercion2 env (ForAllCo v1 co1) (ForAllCo v2 co2)
+ = coreEqCoercion2 (rnBndr2 env v1 v2) co1 co2
+
+coreEqCoercion2 env (CoVarCo cv1) (CoVarCo cv2)
+ = rnOccL env cv1 == rnOccR env cv2
+
+coreEqCoercion2 env (AxiomInstCo con1 cos1) (AxiomInstCo con2 cos2)
+ = con1 == con2
+ && all2 (coreEqCoercion2 env) cos1 cos2
+
+coreEqCoercion2 env (UnsafeCo ty11 ty12) (UnsafeCo ty21 ty22)
+ = eqTypeX env ty11 ty21 && eqTypeX env ty12 ty22
+
+coreEqCoercion2 env (SymCo co1) (SymCo co2)
+ = coreEqCoercion2 env co1 co2
+
+coreEqCoercion2 env (TransCo co11 co12) (TransCo co21 co22)
+ = coreEqCoercion2 env co11 co21 && coreEqCoercion2 env co12 co22
+
+coreEqCoercion2 env (NthCo d1 co1) (NthCo d2 co2)
+ = d1 == d2 && coreEqCoercion2 env co1 co2
+
+coreEqCoercion2 env (InstCo co1 ty1) (InstCo co2 ty2)
+ = coreEqCoercion2 env co1 co2 && eqTypeX env ty1 ty2
+
+coreEqCoercion2 _ _ _ = False
+\end{code}
+
+%************************************************************************
+%* *
+ Substitution of coercions
+%* *
+%************************************************************************
+
+\begin{code}
+-- | A substitution of 'Coercion's for 'CoVar's (OR 'TyVar's, when
+-- doing a \"lifting\" substitution)
+type CvSubstEnv = VarEnv Coercion
+
+emptyCvSubstEnv :: CvSubstEnv
+emptyCvSubstEnv = emptyVarEnv
+
+data CvSubst
+ = CvSubst InScopeSet -- The in-scope type variables
+ TvSubstEnv -- Substitution of types
+ CvSubstEnv -- Substitution of coercions
+
+instance Outputable CvSubst where
+ ppr (CvSubst ins tenv cenv)
+ = brackets $ sep[ ptext (sLit "CvSubst"),
+ nest 2 (ptext (sLit "In scope:") <+> ppr ins),
+ nest 2 (ptext (sLit "Type env:") <+> ppr tenv),
+ nest 2 (ptext (sLit "Coercion env:") <+> ppr cenv) ]
+
+emptyCvSubst :: CvSubst
+emptyCvSubst = CvSubst emptyInScopeSet emptyVarEnv emptyVarEnv
+
+isEmptyCvSubst :: CvSubst -> Bool
+isEmptyCvSubst (CvSubst _ tenv cenv) = isEmptyVarEnv tenv && isEmptyVarEnv cenv
+
+getCvInScope :: CvSubst -> InScopeSet
+getCvInScope (CvSubst in_scope _ _) = in_scope
+
+zapCvSubstEnv :: CvSubst -> CvSubst
+zapCvSubstEnv (CvSubst in_scope _ _) = CvSubst in_scope emptyVarEnv emptyVarEnv
+
+cvTvSubst :: CvSubst -> TvSubst
+cvTvSubst (CvSubst in_scope tvs _) = TvSubst in_scope tvs
+
+tvCvSubst :: TvSubst -> CvSubst
+tvCvSubst (TvSubst in_scope tenv) = CvSubst in_scope tenv emptyCvSubstEnv
+
+extendTvSubst :: CvSubst -> TyVar -> Type -> CvSubst
+extendTvSubst (CvSubst in_scope tenv cenv) tv ty
+ = CvSubst in_scope (extendVarEnv tenv tv ty) cenv
+
+substCoVarBndr :: CvSubst -> CoVar -> (CvSubst, CoVar)
+substCoVarBndr subst@(CvSubst in_scope tenv cenv) old_var
+ = ASSERT( isCoVar old_var )
+ (CvSubst (in_scope `extendInScopeSet` new_var) tenv new_cenv, new_var)
where
- rule args = mkCoKind (substTyWith tvs args rhs_ty) (TyConApp tycon args)
+ -- When we substitute (co :: t1 ~ t2) we may get the identity (co :: t ~ t)
+ -- In that case, mkCoVarCo will return a ReflCoercion, and
+ -- we want to substitute that (not new_var) for old_var
+ new_co = mkCoVarCo new_var
+ no_change = new_var == old_var && not (isReflCo new_co)
---------------------------------------
--- Coercion Type Constructors...
+ new_cenv | no_change = delVarEnv cenv old_var
+ | otherwise = extendVarEnv cenv old_var new_co
--- 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)
---
--- (mkKindingFun f) is given the args [c, sym d, sym e]
-mkKindingFun :: ([Type] -> (Type, Type, [Type])) -> [Type] -> Kind
-mkKindingFun f args =
- let (ty1, ty2, rest) = f args in
- let (argtys1, argtys2) = unzip (map coercionKind rest) in
- mkCoKind (mkAppTys ty1 argtys1) (mkAppTys ty2 argtys2)
-
+ new_var = uniqAway in_scope subst_old_var
+ subst_old_var = mkCoVar (varName old_var) (substTy subst (varType old_var))
+ -- It's important to do the substitution for coercions,
+ -- because only they can have free type variables
+
+substTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
+substTyVarBndr (CvSubst in_scope tenv cenv) old_var
+ = case Type.substTyVarBndr (TvSubst in_scope tenv) old_var of
+ (TvSubst in_scope' tenv', new_var) -> (CvSubst in_scope' tenv' cenv, new_var)
+
+zipOpenCvSubst :: [Var] -> [Coercion] -> CvSubst
+zipOpenCvSubst vs cos
+ | debugIsOn && (length vs /= length cos)
+ = pprTrace "zipOpenCvSubst" (ppr vs $$ ppr cos) emptyCvSubst
+ | otherwise
+ = CvSubst (mkInScopeSet (tyCoVarsOfCos cos)) emptyTvSubstEnv (zipVarEnv vs cos)
+
+mkTopCvSubst :: [(Var,Coercion)] -> CvSubst
+mkTopCvSubst prs = CvSubst emptyInScopeSet emptyTvSubstEnv (mkVarEnv prs)
-symCoercionTyCon, transCoercionTyCon, leftCoercionTyCon, rightCoercionTyCon, instCoercionTyCon :: 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 (mkKindingFun flipCoercionKindOf)
+substCoWithTy :: TyVar -> Type -> Coercion -> Coercion
+substCoWithTy tv ty = substCoWithTys [tv] [ty]
+
+substCoWithTys :: [TyVar] -> [Type] -> Coercion -> Coercion
+substCoWithTys tvs tys co
+ | debugIsOn && (length tvs /= length tys)
+ = pprTrace "substCoWithTys" (ppr tvs $$ ppr tys) co
+ | otherwise
+ = ASSERT( length tvs == length tys )
+ substCo (CvSubst in_scope (zipVarEnv tvs tys) emptyVarEnv) co
where
- flipCoercionKindOf (co:rest) = (ty2, ty1, rest)
- where
- (ty1, ty2) = coercionKind co
+ in_scope = mkInScopeSet (tyVarsOfTypes tys)
+
+-- | Substitute within a 'Coercion'
+substCo :: CvSubst -> Coercion -> Coercion
+substCo subst co | isEmptyCvSubst subst = co
+ | otherwise = subst_co subst co
+
+-- | Substitute within several 'Coercion's
+substCos :: CvSubst -> [Coercion] -> [Coercion]
+substCos subst cos | isEmptyCvSubst subst = cos
+ | otherwise = map (substCo subst) cos
+
+substTy :: CvSubst -> Type -> Type
+substTy subst = Type.substTy (cvTvSubst subst)
-transCoercionTyCon =
- mkCoercionTyCon transCoercionTyConName 2 (mkKindingFun composeCoercionKindsOf)
+subst_co :: CvSubst -> Coercion -> Coercion
+subst_co subst co
+ = go co
where
- composeCoercionKindsOf (co1:co2:rest) =
- WARN( not (r1 `coreEqType` a2), text "Strange! Type mismatch in trans coercion, probably a bug")
- (a1, r2, rest)
- where
- (a1, r1) = coercionKind co1
- (a2, r2) = coercionKind co2
-
-leftCoercionTyCon =
- mkCoercionTyCon leftCoercionTyConName 1 (mkKindingFun leftProjectCoercionKindOf)
+ go_ty :: Type -> Type
+ go_ty = Coercion.substTy subst
+
+ go :: Coercion -> Coercion
+ go (Refl ty) = Refl $! go_ty ty
+ go (TyConAppCo tc cos) = let args = map go cos
+ in args `seqList` TyConAppCo tc args
+ go (AppCo co1 co2) = mkAppCo (go co1) $! go co2
+ go (ForAllCo tv co) = case substTyVarBndr subst tv of
+ (subst', tv') ->
+ ForAllCo tv' $! subst_co subst' co
+ go (CoVarCo cv) = substCoVar subst cv
+ go (AxiomInstCo con cos) = AxiomInstCo con $! map go cos
+ go (UnsafeCo ty1 ty2) = (UnsafeCo $! go_ty ty1) $! go_ty ty2
+ go (SymCo co) = mkSymCo (go co)
+ go (TransCo co1 co2) = mkTransCo (go co1) (go co2)
+ go (NthCo d co) = mkNthCo d (go co)
+ go (InstCo co ty) = mkInstCo (go co) $! go_ty ty
+
+substCoVar :: CvSubst -> CoVar -> Coercion
+substCoVar (CvSubst in_scope _ cenv) cv
+ | Just co <- lookupVarEnv cenv cv = co
+ | Just cv1 <- lookupInScope in_scope cv = ASSERT( isCoVar cv1 ) CoVarCo cv1
+ | otherwise = WARN( True, ptext (sLit "substCoVar not in scope") <+> ppr cv )
+ ASSERT( isCoVar cv ) CoVarCo cv
+
+substCoVars :: CvSubst -> [CoVar] -> [Coercion]
+substCoVars subst cvs = map (substCoVar subst) cvs
+
+lookupTyVar :: CvSubst -> TyVar -> Maybe Type
+lookupTyVar (CvSubst _ tenv _) tv = lookupVarEnv tenv tv
+
+lookupCoVar :: CvSubst -> Var -> Maybe Coercion
+lookupCoVar (CvSubst _ _ cenv) v = lookupVarEnv cenv v
+\end{code}
+
+%************************************************************************
+%* *
+ "Lifting" substitution
+ [(TyVar,Coercion)] -> Type -> Coercion
+%* *
+%************************************************************************
+
+\begin{code}
+liftCoSubstWith :: [TyVar] -> [Coercion] -> Type -> Coercion
+liftCoSubstWith tvs cos = liftCoSubst (zipOpenCvSubst tvs cos)
+
+-- | The \"lifting\" operation which substitutes coercions for type
+-- variables in a type to produce a coercion.
+--
+-- For the inverse operation, see 'liftCoMatch'
+liftCoSubst :: CvSubst -> Type -> Coercion
+-- The CvSubst maps TyVar -> Type (mainly for cloning foralls)
+-- TyVar -> Coercion (this is the payload)
+-- The unusual thing is that the *coercion* substitution maps
+-- some *type* variables. That's the whole point of this function!
+liftCoSubst subst ty | isEmptyCvSubst subst = Refl ty
+ | otherwise = ty_co_subst subst ty
+
+ty_co_subst :: CvSubst -> Type -> Coercion
+ty_co_subst subst ty
+ = go ty
where
- leftProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
- where
- (ty1,ty2) = fst (splitCoercionKindOf co)
+ go (TyVarTy tv) = liftCoSubstTyVar subst tv `orElse` Refl (TyVarTy tv)
+ go (AppTy ty1 ty2) = mkAppCo (go ty1) (go ty2)
+ go (TyConApp tc tys) = mkTyConAppCo tc (map go tys)
+ go (FunTy ty1 ty2) = mkFunCo (go ty1) (go ty2)
+ go (ForAllTy v ty) = mkForAllCo v' $! (ty_co_subst subst' ty)
+ where
+ (subst', v') = liftCoSubstTyVarBndr subst v
+ go (PredTy p) = mkPredCo (go <$> p)
-rightCoercionTyCon =
- mkCoercionTyCon rightCoercionTyConName 1 (mkKindingFun rightProjectCoercionKindOf)
+liftCoSubstTyVar :: CvSubst -> TyVar -> Maybe Coercion
+liftCoSubstTyVar subst@(CvSubst _ tenv cenv) tv
+ = case (lookupVarEnv tenv tv, lookupVarEnv cenv tv) of
+ (Nothing, Nothing) -> Nothing
+ (Just ty, Nothing) -> Just (Refl ty)
+ (Nothing, Just co) -> Just co
+ (Just {}, Just {}) -> pprPanic "ty_co_subst" (ppr tv $$ ppr subst)
+
+liftCoSubstTyVarBndr :: CvSubst -> TyVar -> (CvSubst, TyVar)
+liftCoSubstTyVarBndr (CvSubst in_scope tenv cenv) old_var
+ = (CvSubst (in_scope `extendInScopeSet` new_var)
+ new_tenv
+ (delVarEnv cenv old_var) -- See Note [Lifting substitutions]
+ , new_var)
where
- rightProjectCoercionKindOf (co:rest) = (ty1, ty2, rest)
- where
- (ty1,ty2) = snd (splitCoercionKindOf co)
+ new_tenv | no_change = delVarEnv tenv old_var
+ | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
-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))
-
-instCoercionTyCon
- = mkCoercionTyCon instCoercionTyConName 2 (mkKindingFun instCoercionKind)
+ no_change = new_var == old_var
+ new_var = uniqAway in_scope old_var
+\end{code}
+
+Note [Lifting substitutions]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider liftCoSubstWith [a] [co] (a, forall a. a)
+Then we want to substitute for the free 'a', but obviously not for
+the bound 'a'. hence the (delVarEnv cent old_var) in liftCoSubstTyVarBndr.
+
+This also why we need a full CvSubst when doing lifting substitutions.
+
+\begin{code}
+-- | 'liftCoMatch' is sort of inverse to 'liftCoSubst'. In particular, if
+-- @liftCoMatch vars ty co == Just s@, then @tyCoSubst s ty == co@.
+-- That is, it matches a type against a coercion of the same
+-- "shape", and returns a lifting substitution which could have been
+-- used to produce the given coercion from the given type.
+liftCoMatch :: TyVarSet -> Type -> Coercion -> Maybe CvSubst
+liftCoMatch tmpls ty co
+ = case ty_co_match menv (emptyVarEnv, emptyVarEnv) ty co of
+ Just (tv_env, cv_env) -> Just (CvSubst in_scope tv_env cv_env)
+ Nothing -> Nothing
where
- instantiateCo t s =
- let Just (tv, ty) = splitForAllTy_maybe t in
- substTyWith [tv] [s] ty
+ menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope }
+ in_scope = mkInScopeSet (tmpls `unionVarSet` tyCoVarsOfCo co)
+ -- Like tcMatchTy, assume all the interesting variables
+ -- in ty are in tmpls
- instCoercionKind (co1:ty:rest) = (instantiateCo t1 ty, instantiateCo t2 ty, rest)
- where (t1, t2) = coercionKind co1
+type TyCoSubstEnv = (TvSubstEnv, CvSubstEnv)
+ -- Used locally inside ty_co_match only
-unsafeCoercionTyCon
- = mkCoercionTyCon unsafeCoercionTyConName 2 (mkKindingFun unsafeCoercionKind)
+-- | 'ty_co_match' does all the actual work for 'liftCoMatch'.
+ty_co_match :: MatchEnv -> TyCoSubstEnv -> Type -> Coercion -> Maybe TyCoSubstEnv
+ty_co_match menv subst ty co | Just ty' <- coreView ty = ty_co_match menv subst ty' co
+
+ -- Deal with the Refl case by delegating to type matching
+ty_co_match menv (tenv, cenv) ty co
+ | Just ty' <- isReflCo_maybe co
+ = case ruleMatchTyX ty_menv tenv ty ty' of
+ Just tenv' -> Just (tenv', cenv)
+ Nothing -> Nothing
where
- unsafeCoercionKind (ty1:ty2:rest) = (ty1,ty2,rest)
-
---------------------------------------
--- ...and their names
+ ty_menv = menv { me_tmpls = me_tmpls menv `minusUFM` cenv }
+ -- Remove from the template set any variables already bound to non-refl coercions
-mkCoConName occ key coCon = mkWiredInName gHC_PRIM (mkOccNameFS tcName occ)
- key Nothing (ATyCon coCon) BuiltInSyntax
+ -- Match a type variable against a non-refl coercion
+ty_co_match menv subst@(tenv, cenv) (TyVarTy tv1) co
+ | Just {} <- lookupVarEnv tenv tv1' -- tv1' is already bound to (Refl ty)
+ = Nothing -- The coercion 'co' is not Refl
-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
+ | Just co1' <- lookupVarEnv cenv tv1' -- tv1' is already bound to co1
+ = if coreEqCoercion2 (nukeRnEnvL rn_env) co1' co
+ then Just subst
+ else Nothing -- no match since tv1 matches two different coercions
+ | tv1' `elemVarSet` me_tmpls menv -- tv1' is a template var
+ = if any (inRnEnvR rn_env) (varSetElems (tyCoVarsOfCo co))
+ then Nothing -- occurs check failed
+ else return (tenv, extendVarEnv cenv tv1' co)
+ -- BAY: I don't think we need to do any kind matching here yet
+ -- (compare 'match'), but we probably will when moving to SHE.
+ | otherwise -- tv1 is not a template ty var, so the only thing it
+ -- can match is a reflexivity coercion for itself.
+ -- But that case is dealt with already
+ = 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
-splitNewTypeRepCo_maybe ty
- | Just ty' <- coreView ty = splitNewTypeRepCo_maybe ty'
-splitNewTypeRepCo_maybe (TyConApp tc tys)
- | isNewTyCon 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 tc)
-splitNewTypeRepCo_maybe other = Nothing
+ rn_env = me_env menv
+ tv1' = rnOccL rn_env tv1
+
+ty_co_match menv subst (AppTy ty1 ty2) co
+ | Just (co1, co2) <- splitAppCo_maybe co -- c.f. Unify.match on AppTy
+ = do { subst' <- ty_co_match menv subst ty1 co1
+ ; ty_co_match menv subst' ty2 co2 }
+
+ty_co_match menv subst (TyConApp tc1 tys) (TyConAppCo tc2 cos)
+ | tc1 == tc2 = ty_co_matches menv subst tys cos
+
+ty_co_match menv subst (FunTy ty1 ty2) (TyConAppCo tc cos)
+ | tc == funTyCon = ty_co_matches menv subst [ty1,ty2] cos
+
+ty_co_match menv subst (ForAllTy tv1 ty) (ForAllCo tv2 co)
+ = ty_co_match menv' subst ty co
+ where
+ menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 }
+
+ty_co_match _ _ _ _ = Nothing
+
+ty_co_matches :: MatchEnv -> TyCoSubstEnv -> [Type] -> [Coercion] -> Maybe TyCoSubstEnv
+ty_co_matches menv = matchList (ty_co_match menv)
+\end{code}
+
+%************************************************************************
+%* *
+ Sequencing on coercions
+%* *
+%************************************************************************
+
+\begin{code}
+seqCo :: Coercion -> ()
+seqCo (Refl ty) = seqType ty
+seqCo (TyConAppCo tc cos) = tc `seq` seqCos cos
+seqCo (AppCo co1 co2) = seqCo co1 `seq` seqCo co2
+seqCo (ForAllCo tv co) = tv `seq` seqCo co
+seqCo (CoVarCo cv) = cv `seq` ()
+seqCo (AxiomInstCo con cos) = con `seq` seqCos cos
+seqCo (UnsafeCo ty1 ty2) = seqType ty1 `seq` seqType ty2
+seqCo (SymCo co) = seqCo co
+seqCo (TransCo co1 co2) = seqCo co1 `seq` seqCo co2
+seqCo (NthCo _ co) = seqCo co
+seqCo (InstCo co ty) = seqCo co `seq` seqType ty
+
+seqCos :: [Coercion] -> ()
+seqCos [] = ()
+seqCos (co:cos) = seqCo co `seq` seqCos cos
+\end{code}
+
+
+%************************************************************************
+%* *
+ The kind of a type, and of a coercion
+%* *
+%************************************************************************
+
+\begin{code}
+coercionType :: Coercion -> Type
+coercionType co = case coercionKind co of
+ Pair ty1 ty2 -> mkCoType ty1 ty2
+
+------------------
+-- | If it is the case that
+--
+-- > c :: (t1 ~ t2)
+--
+-- i.e. the kind of @c@ relates @t1@ and @t2@, then @coercionKind c = Pair t1 t2@.
+coercionKind :: Coercion -> Pair Type
+coercionKind (Refl ty) = Pair ty ty
+coercionKind (TyConAppCo tc cos) = mkTyConApp tc <$> (sequenceA $ map coercionKind cos)
+coercionKind (AppCo co1 co2) = mkAppTy <$> coercionKind co1 <*> coercionKind co2
+coercionKind (ForAllCo tv co) = mkForAllTy tv <$> coercionKind co
+coercionKind (CoVarCo cv) = ASSERT( isCoVar cv ) toPair $ coVarKind cv
+coercionKind (AxiomInstCo ax cos) = let Pair tys1 tys2 = coercionKinds cos
+ in Pair (substTyWith (co_ax_tvs ax) tys1 (co_ax_lhs ax))
+ (substTyWith (co_ax_tvs ax) tys2 (co_ax_rhs ax))
+coercionKind (UnsafeCo ty1 ty2) = Pair ty1 ty2
+coercionKind (SymCo co) = swap $ coercionKind co
+coercionKind (TransCo co1 co2) = Pair (pFst $ coercionKind co1) (pSnd $ coercionKind co2)
+coercionKind (NthCo d co) = getNth d <$> coercionKind co
+coercionKind co@(InstCo aco ty) | Just ks <- splitForAllTy_maybe `traverse` coercionKind aco
+ = (\(tv, body) -> substTyWith [tv] [ty] body) <$> ks
+ | otherwise = pprPanic "coercionKind" (ppr co)
+
+-- | Apply 'coercionKind' to multiple 'Coercion's
+coercionKinds :: [Coercion] -> Pair [Type]
+coercionKinds tys = sequenceA $ map coercionKind tys
+
+getNth :: Int -> Type -> Type
+getNth n ty | Just (_, tys) <- splitTyConApp_maybe ty
+ = ASSERT2( n < length tys, ppr n <+> ppr tys ) tys !! n
+getNth n ty = pprPanic "getNth" (ppr n <+> ppr ty)
\end{code}
+
+\begin{code}
+applyCo :: Type -> Coercion -> Type
+-- Gives the type of (e co) where e :: (a~b) => ty
+applyCo ty co | Just ty' <- coreView ty = applyCo ty' co
+applyCo (FunTy _ ty) _ = ty
+applyCo _ _ = panic "applyCo"
+\end{code}
\ No newline at end of file
projects / ghc-hetmet.git / blobdiff