--- /dev/null
+%
+% (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
+%
+
+%************************************************************************
+%* *
+ Type refinement for GADTs
+%* *
+%************************************************************************
+
+\begin{code}
+module TcGadt (
+ Refinement, emptyRefinement, gadtRefine,
+ refineType, refineResType,
+ dataConCanMatch,
+ tcUnifyTys, BindFlag(..)
+ ) where
+
+import HsSyn ( ExprCoFn(..), idCoercion, isIdCoercion )
+import Coercion ( Coercion, mkSymCoercion, mkTransCoercion, mkUnsafeCoercion,
+ mkLeftCoercion, mkRightCoercion,
+ splitCoercionKind, decomposeCo )
+import TcType ( TvSubst(..), TvSubstEnv, substTy, mkTvSubst,
+ substTyVar, zipTopTvSubst, typeKind,
+ eqKind, isSubKind, repSplitAppTy_maybe,
+ tcView
+ )
+import Type ( Type, tyVarsOfType, tyVarsOfTypes )
+import TypeRep ( Type(..), PredType(..) )
+import DataCon ( DataCon, dataConUnivTyVars, dataConEqSpec )
+import Var ( CoVar, TyVar, tyVarKind )
+import VarEnv
+import VarSet
+import ErrUtils ( Message )
+import Maybes ( MaybeErr(..), isJust )
+import Control.Monad ( foldM )
+import Outputable
+
+#include "HsVersions.h"
+\end{code}
+
+
+%************************************************************************
+%* *
+ What a refinement is
+%* *
+%************************************************************************
+
+\begin{code}
+data Refinement = Reft InScopeSet TvSubstEnv CoSubstEnv
+type CoSubstEnv = TvSubstEnv -- Maps type variables to *coercions*
+-- INVARIANT: in the refinement (tsub, csub)
+-- forall a. (csub(a) :: a:=:tsub(a))
+
+instance Outputable Refinement where
+ ppr (Reft in_scope tv_env co_env)
+ = ptext SLIT("Refinment") <+>
+ braces (ppr tv_env $$ ppr co_env)
+
+emptyRefinement :: Refinement
+emptyRefinement = Reft emptyInScopeSet emptyVarEnv emptyVarEnv
+
+refineType :: Refinement -> Type -> (ExprCoFn, Type)
+-- Apply the refinement to the type.
+-- If (refineType r ty) = (co, ty')
+-- Then co :: ty:=:ty'
+refineType (Reft in_scope tv_env co_env) ty
+ | not (isEmptyVarEnv tv_env), -- Common case
+ any (`elemVarEnv` tv_env) (varSetElems (tyVarsOfType ty))
+ = (ExprCoFn (substTy co_subst ty), substTy tv_subst ty)
+ | otherwise
+ = (idCoercion, ty) -- The type doesn't mention any refined type variables
+ where
+ tv_subst = mkTvSubst in_scope tv_env
+ co_subst = mkTvSubst in_scope co_env
+
+refineResType :: Refinement -> Type -> (ExprCoFn, Type)
+-- Like refineType, but returns the 'sym' coercion
+-- If (refineResType r ty) = (co, ty')
+-- Then co :: ty':=:ty
+refineResType reft ty
+ = case refineType reft ty of
+ (ExprCoFn co, ty1) -> (ExprCoFn (mkSymCoercion co), ty1)
+ (id_co, ty1) -> ASSERT( isIdCoercion id_co )
+ (idCoercion, ty1)
+\end{code}
+
+
+%************************************************************************
+%* *
+ Generating a type refinement
+%* *
+%************************************************************************
+
+\begin{code}
+gadtRefine :: Refinement
+ -> [TyVar] -- Bind these by preference
+ -> [CoVar]
+ -> MaybeErr Message Refinement
+\end{code}
+
+(gadtRefine cvs) takes a list of coercion variables, and returns a
+list of coercions, obtained by unifying the types equated by the
+incoming coercions. The returned coercions all have kinds of form
+(a:=:ty), where a is a rigid type variable.
+
+Example:
+ gadtRefine [c :: (a,Int):=:(Bool,b)]
+ = [ right (left c) :: a:=:Bool,
+ sym (right c) :: b:=:Int ]
+
+That is, given evidence 'c' that (a,Int)=(Bool,b), it returns derived
+evidence in easy-to-use form. In particular, given any e::ty, we know
+that:
+ e `cast` ty[right (left c)/a, sym (right c)/b]
+ :: ty [Bool/a, Int/b]
+
+Two refinements:
+
+- It can fail, if the coercion is unsatisfiable.
+
+- It's biased, by being given a set of type variables to bind
+ when there is a choice. Example:
+ MkT :: forall a. a -> T [a]
+ f :: forall b. T [b] -> b
+ f x = let v = case x of { MkT y -> y }
+ in ...
+ Here we want to bind [a->b], not the other way round, because
+ in this example the return type is wobbly, and we want the
+ program to typecheck
+
+
+-- E.g. (a, Bool, right (left c))
+-- INVARIANT: in the triple (tv, ty, co), we have (co :: tv:=:ty)
+-- The result is idempotent: the
+
+\begin{code}
+gadtRefine (Reft in_scope tv_env1 co_env1)
+ ex_tvs co_vars
+-- Precondition: fvs( co_vars ) # tv_env1
+-- That is, the kinds of the co_vars are a
+-- fixed point of the incoming refinement
+
+ = initUM (tryToBind tv_set) $
+ do { -- Run the unifier, starting with an empty env
+ ; env2 <- foldM do_one emptyInternalReft co_vars
+
+ -- Find the fixed point of the resulting
+ -- non-idempotent substitution
+ ; let tv_env2 = tv_env1 `plusVarEnv` mapVarEnv snd env2
+ co_env2 = co_env1 `plusVarEnv` mapVarEnv fst env2
+
+ ; return (Reft in_scope' (fixTvSubstEnv in_scope' tv_env2)
+ (fixTvSubstEnv in_scope' co_env2)) }
+ where
+ tv_set = mkVarSet ex_tvs
+ in_scope' = foldr extend in_scope co_vars
+ extend co_var in_scope
+ = extendInScopeSetSet (extendInScopeSet in_scope co_var)
+ (tyVarsOfType (tyVarKind co_var))
+
+ do_one reft co_var = unify reft (TyVarTy co_var) ty1 ty2
+ where
+ (ty1,ty2) = splitCoercionKind (tyVarKind co_var)
+\end{code}
+
+%************************************************************************
+%* *
+ Unification
+%* *
+%************************************************************************
+
+\begin{code}
+tcUnifyTys :: (TyVar -> BindFlag)
+ -> [Type] -> [Type]
+ -> Maybe TvSubst -- A regular one-shot substitution
+-- The two types may have common type variables, and indeed do so in the
+-- second call to tcUnifyTys in FunDeps.checkClsFD
+--
+-- We implement tcUnifyTys using the evidence-generating 'unify' function
+-- in this module, even though we don't need to generate any evidence.
+-- This is simply to avoid replicating all all the code for unify
+tcUnifyTys bind_fn tys1 tys2
+ = maybeErrToMaybe $ initUM bind_fn $
+ do { reft <- unifyList emptyInternalReft cos tys1 tys2
+
+ -- Find the fixed point of the resulting non-idempotent substitution
+ ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2)
+ tv_env = fixTvSubstEnv in_scope (mapVarEnv snd reft)
+
+ ; return (mkTvSubst in_scope tv_env) }
+ where
+ tvs1 = tyVarsOfTypes tys1
+ tvs2 = tyVarsOfTypes tys2
+ cos = zipWith mkUnsafeCoercion tys1 tys2
+
+
+----------------------------
+fixTvSubstEnv :: InScopeSet -> TvSubstEnv -> TvSubstEnv
+ -- Find the fixed point of a TvSubstEnv
+ -- (assuming it has no loops!)
+fixTvSubstEnv in_scope env
+ = fixpt
+ where
+ fixpt = mapVarEnv (substTy (mkTvSubst in_scope fixpt)) env
+
+----------------------------
+dataConCanMatch :: DataCon -> [Type] -> Bool
+-- Returns True iff the data con can match a scrutinee of type (T tys)
+-- where T is the type constructor for the data con
+--
+-- Instantiate the equations and try to unify them
+dataConCanMatch con tys
+ = isJust (tcUnifyTys (\tv -> BindMe)
+ (map (substTyVar subst . fst) eq_spec)
+ (map snd eq_spec))
+ where
+ dc_tvs = dataConUnivTyVars con
+ eq_spec = dataConEqSpec con
+ subst = zipTopTvSubst dc_tvs tys
+
+----------------------------
+tryToBind :: TyVarSet -> TyVar -> BindFlag
+tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe
+ | otherwise = AvoidMe
+\end{code}
+
+
+%************************************************************************
+%* *
+ The workhorse
+%* *
+%************************************************************************
+
+\begin{code}
+type InternalReft = TyVarEnv (Coercion, Type)
+
+-- INVARIANT: a->(co,ty) then co :: (a:=:ty)
+-- Not necessarily idemopotent
+
+emptyInternalReft :: InternalReft
+emptyInternalReft = emptyVarEnv
+
+unify :: InternalReft -- An existing substitution to extend
+ -> Coercion -- Witness of their equality
+ -> Type -> Type -- Types to be unified, and witness of their equality
+ -> UM InternalReft -- Just the extended substitution,
+ -- Nothing if unification failed
+-- We do not require the incoming substitution to be idempotent,
+-- nor guarantee that the outgoing one is. That's fixed up by
+-- the wrappers.
+
+-- PRE-CONDITION: in the call (unify r co ty1 ty2), we know that
+-- co :: (ty1:=:ty2)
+
+-- Respects newtypes, PredTypes
+
+unify subst co ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $
+ unify_ subst co ty1 ty2
+
+-- in unify_, any NewTcApps/Preds should be taken at face value
+unify_ subst co (TyVarTy tv1) ty2 = uVar False subst co tv1 ty2
+unify_ subst co ty1 (TyVarTy tv2) = uVar True subst co tv2 ty1
+
+unify_ subst co ty1 ty2 | Just ty1' <- tcView ty1 = unify subst co ty1' ty2
+unify_ subst co ty1 ty2 | Just ty2' <- tcView ty2 = unify subst co ty1 ty2'
+
+unify_ subst co (PredTy p1) (PredTy p2) = unify_pred subst co p1 p2
+
+unify_ subst co t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2)
+ | tyc1 == tyc2 = unify_tys subst co tys1 tys2
+
+unify_ subst co (FunTy ty1a ty1b) (FunTy ty2a ty2b)
+ = do { let [co1,co2] = decomposeCo 2 co
+ ; subst' <- unify subst co1 ty1a ty2a
+ ; unify subst' co2 ty1b ty2b }
+
+ -- Applications need a bit of care!
+ -- They can match FunTy and TyConApp, so use splitAppTy_maybe
+ -- NB: we've already dealt with type variables and Notes,
+ -- so if one type is an App the other one jolly well better be too
+unify_ subst co (AppTy ty1a ty1b) ty2
+ | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
+ = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
+ ; unify subst' (mkRightCoercion co) ty1b ty2b }
+
+unify_ subst co ty1 (AppTy ty2a ty2b)
+ | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1
+ = do { subst' <- unify subst (mkLeftCoercion co) ty1a ty2a
+ ; unify subst' (mkRightCoercion co) ty1b ty2b }
+
+unify_ subst co ty1 ty2 = failWith (misMatch ty1 ty2)
+ -- ForAlls??
+
+
+------------------------------
+unify_pred subst co (ClassP c1 tys1) (ClassP c2 tys2)
+ | c1 == c2 = unify_tys subst co tys1 tys2
+unify_pred subst co (IParam n1 t1) (IParam n2 t2)
+ | n1 == n2 = unify subst co t1 t2
+unify_pred subst co p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
+
+------------------------------
+unify_tys :: InternalReft -> Coercion -> [Type] -> [Type] -> UM InternalReft
+unify_tys subst co xs ys
+ = unifyList subst (decomposeCo (length xs) co) xs ys
+
+unifyList :: InternalReft -> [Coercion] -> [Type] -> [Type] -> UM InternalReft
+unifyList subst orig_cos orig_xs orig_ys
+ = go subst orig_cos orig_xs orig_ys
+ where
+ go subst _ [] [] = return subst
+ go subst (co:cos) (x:xs) (y:ys) = do { subst' <- unify subst co x y
+ ; go subst' cos xs ys }
+ go subst _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
+
+---------------------------------
+uVar :: Bool -- Swapped
+ -> InternalReft -- An existing substitution to extend
+ -> Coercion
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> UM InternalReft
+
+-- PRE-CONDITION: in the call (uVar swap r co tv1 ty), we know that
+-- if swap=False co :: (tv1:=:ty)
+-- if swap=True co :: (ty:=:tv1)
+
+uVar swap subst co tv1 ty
+ = -- Check to see whether tv1 is refined by the substitution
+ case (lookupVarEnv subst tv1) of
+
+ -- Yes, call back into unify'
+ Just (co',ty') -- co' :: (tv1:=:ty')
+ | swap -- co :: (ty:=:tv1)
+ -> unify subst (mkTransCoercion co co') ty ty'
+ | otherwise -- co :: (tv1:=:ty)
+ -> unify subst (mkTransCoercion (mkSymCoercion co') co) ty' ty
+
+ -- No, continue
+ Nothing -> uUnrefined subst (if swap then mkSymCoercion co else co)
+ tv1 ty ty
+
+
+uUnrefined :: InternalReft -- An existing substitution to extend
+ -> Coercion
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> Type -- (de-noted version)
+ -> UM InternalReft
+
+-- We know that tv1 isn't refined
+-- PRE-CONDITION: in the call (uUnrefined r co tv ty ty'), we know that
+-- co :: tv:=:ty
+
+uUnrefined subst co tv1 ty2 ty2'
+ | Just ty2'' <- tcView ty2'
+ = uUnrefined subst co tv1 ty2 ty2'' -- Unwrap synonyms
+ -- This is essential, in case we have
+ -- type Foo a = a
+ -- and then unify a :=: Foo a
+
+uUnrefined subst co tv1 ty2 (TyVarTy tv2)
+ | tv1 == tv2 -- Same type variable
+ = return subst
+
+ -- Check to see whether tv2 is refined
+ | Just (co',ty') <- lookupVarEnv subst tv2
+ = uUnrefined subst (mkTransCoercion co co') tv1 ty' ty'
+
+ -- So both are unrefined; next, see if the kinds force the direction
+ | eqKind k1 k2 -- Can update either; so check the bind-flags
+ = do { b1 <- tvBindFlag tv1
+ ; b2 <- tvBindFlag tv2
+ ; case (b1,b2) of
+ (BindMe, _) -> bind tv1 ty2
+
+ (AvoidMe, BindMe) -> bind tv2 ty1
+ (AvoidMe, _) -> bind tv1 ty2
+
+ (WildCard, WildCard) -> return subst
+ (WildCard, Skolem) -> return subst
+ (WildCard, _) -> bind tv2 ty1
+
+ (Skolem, WildCard) -> return subst
+ (Skolem, Skolem) -> failWith (misMatch ty1 ty2)
+ (Skolem, _) -> bind tv2 ty1
+ }
+
+ | k1 `isSubKind` k2 = bindTv subst co tv2 ty1 -- Must update tv2
+ | k2 `isSubKind` k1 = bindTv subst co tv1 ty2 -- Must update tv1
+
+ | otherwise = failWith (kindMisMatch tv1 ty2)
+ where
+ ty1 = TyVarTy tv1
+ k1 = tyVarKind tv1
+ k2 = tyVarKind tv2
+ bind tv ty = return (extendVarEnv subst tv (co,ty))
+
+uUnrefined subst co tv1 ty2 ty2' -- ty2 is not a type variable
+ | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2')
+ = failWith (occursCheck tv1 ty2) -- Occurs check
+ | not (k2 `isSubKind` k1)
+ = failWith (kindMisMatch tv1 ty2) -- Kind check
+ | otherwise
+ = bindTv subst co tv1 ty2 -- Bind tyvar to the synonym if poss
+ where
+ k1 = tyVarKind tv1
+ k2 = typeKind ty2'
+
+substTvSet :: InternalReft -> TyVarSet -> TyVarSet
+-- Apply the non-idempotent substitution to a set of type variables,
+-- remembering that the substitution isn't necessarily idempotent
+substTvSet subst tvs
+ = foldVarSet (unionVarSet . get) emptyVarSet tvs
+ where
+ get tv = case lookupVarEnv subst tv of
+ Nothing -> unitVarSet tv
+ Just (_,ty) -> substTvSet subst (tyVarsOfType ty)
+
+bindTv subst co tv ty -- ty is not a type variable
+ = do { b <- tvBindFlag tv
+ ; case b of
+ Skolem -> failWith (misMatch (TyVarTy tv) ty)
+ WildCard -> return subst
+ other -> return (extendVarEnv subst tv (co,ty))
+ }
+\end{code}
+
+%************************************************************************
+%* *
+ Unification monad
+%* *
+%************************************************************************
+
+\begin{code}
+data BindFlag
+ = BindMe -- A regular type variable
+ | AvoidMe -- Like BindMe but, given the choice, avoid binding it
+
+ | Skolem -- This type variable is a skolem constant
+ -- Don't bind it; it only matches itself
+
+ | WildCard -- This type variable matches anything,
+ -- and does not affect the substitution
+
+newtype UM a = UM { unUM :: (TyVar -> BindFlag)
+ -> MaybeErr Message a }
+
+instance Monad UM where
+ return a = UM (\tvs -> Succeeded a)
+ fail s = UM (\tvs -> Failed (text s))
+ m >>= k = UM (\tvs -> case unUM m tvs of
+ Failed err -> Failed err
+ Succeeded v -> unUM (k v) tvs)
+
+initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a
+initUM badtvs um = unUM um badtvs
+
+tvBindFlag :: TyVar -> UM BindFlag
+tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv))
+
+failWith :: Message -> UM a
+failWith msg = UM (\tv_fn -> Failed msg)
+
+maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ
+maybeErrToMaybe (Succeeded a) = Just a
+maybeErrToMaybe (Failed m) = Nothing
+\end{code}
+
+
+%************************************************************************
+%* *
+ Error reporting
+ We go to a lot more trouble to tidy the types
+ in TcUnify. Maybe we'll end up having to do that
+ here too, but I'll leave it for now.
+%* *
+%************************************************************************
+
+\begin{code}
+misMatch t1 t2
+ = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+>
+ ptext SLIT("and") <+> quotes (ppr t2)
+
+lengthMisMatch tys1 tys2
+ = sep [ptext SLIT("Can't match unequal length lists"),
+ nest 2 (ppr tys1), nest 2 (ppr tys2) ]
+
+kindMisMatch tv1 t2
+ = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+>
+ ptext SLIT("and") <+> quotes (ppr (typeKind t2)),
+ ptext SLIT("when matching") <+> quotes (ppr tv1) <+>
+ ptext SLIT("with") <+> quotes (ppr t2)]
+
+occursCheck tv ty
+ = hang (ptext SLIT("Can't construct the infinite type"))
+ 2 (ppr tv <+> equals <+> ppr ty)
+\end{code}
\ No newline at end of file
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