From c4ec8f2a77894af1c6160c4e8ad5625ab62f0bea Mon Sep 17 00:00:00 2001 From: Manuel M T Chakravarty Date: Sun, 7 Sep 2008 11:21:28 +0000 Subject: [PATCH 1/1] Type families: new algorithm to solve equalities - This adds the new equational solver based on the notion of normalised equalities. - The new algorithm is conceptually much simpler and will eventually enable us to implement a fully integrated solver that solves equality and dictionary constraints together. - More details are at - The code is there, but it is not being used yet. --- compiler/typecheck/Inst.lhs | 158 ++++++-- compiler/typecheck/TcRnTypes.lhs | 33 +- compiler/typecheck/TcTyFuns.lhs | 790 +++++++++++++++++++++++++++++++++++++- compiler/types/Type.lhs | 8 +- 4 files changed, 927 insertions(+), 62 deletions(-) diff --git a/compiler/typecheck/Inst.lhs b/compiler/typecheck/Inst.lhs index f863028..17dce30 100644 --- a/compiler/typecheck/Inst.lhs +++ b/compiler/typecheck/Inst.lhs @@ -7,7 +7,7 @@ The @Inst@ type: dictionaries or method instances \begin{code} module Inst ( - Inst, + Inst, pprInstances, pprDictsTheta, pprDictsInFull, -- User error messages showLIE, pprInst, pprInsts, pprInstInFull, -- Debugging messages @@ -40,9 +40,10 @@ module Inst ( InstOrigin(..), InstLoc, pprInstLoc, mkWantedCo, mkGivenCo, - fromWantedCo, fromGivenCo, - eitherEqInst, mkEqInst, mkEqInsts, mkWantedEqInst, - finalizeEqInst, writeWantedCoercion, + isWantedCo, fromWantedCo, fromGivenCo, eqInstCoType, + mkIdEqInstCo, mkSymEqInstCo, mkLeftTransEqInstCo, + mkRightTransEqInstCo, mkAppEqInstCo, + eitherEqInst, mkEqInst, mkEqInsts, mkWantedEqInst, finalizeEqInst, eqInstType, updateEqInstCoercion, eqInstCoercion, eqInstTys ) where @@ -92,6 +93,7 @@ import Control.Monad \end{code} + Selection ~~~~~~~~~ \begin{code} @@ -935,21 +937,99 @@ syntaxNameCtxt name orig ty tidy_env = do %* * %************************************************************************ +Operations on EqInstCo. + \begin{code} -mkGivenCo :: Coercion -> Either TcTyVar Coercion +mkGivenCo :: Coercion -> EqInstCo mkGivenCo = Right -mkWantedCo :: TcTyVar -> Either TcTyVar Coercion +mkWantedCo :: TcTyVar -> EqInstCo mkWantedCo = Left -fromGivenCo :: Either TcTyVar Coercion -> Coercion +isWantedCo :: EqInstCo -> Bool +isWantedCo (Left _) = True +isWantedCo _ = False + +fromGivenCo :: EqInstCo -> Coercion fromGivenCo (Right co) = co fromGivenCo _ = panic "fromGivenCo: not a wanted coercion" -fromWantedCo :: String -> Either TcTyVar Coercion -> TcTyVar +fromWantedCo :: String -> EqInstCo -> TcTyVar fromWantedCo _ (Left covar) = covar -fromWantedCo msg _ = panic ("fromWantedCo: not a wanted coercion: " ++ msg) +fromWantedCo msg _ = + panic ("fromWantedCo: not a wanted coercion: " ++ msg) + +eqInstCoType :: EqInstCo -> TcType +eqInstCoType (Left cotv) = mkTyVarTy cotv +eqInstCoType (Right co) = co +\end{code} + +Coercion transformations on EqInstCo. These transformations work differently +depending on whether a EqInstCo is for a wanted or local equality: + + Local : apply the inverse of the specified coercion + Wanted: obtain a fresh coercion hole (meta tyvar) and update the old hole + to be the specified coercion applied to the new coercion hole + +\begin{code} +-- Coercion transformation: co = id +-- +mkIdEqInstCo :: EqInstCo -> Type -> TcM () +mkIdEqInstCo (Left cotv) t + = writeMetaTyVar cotv t +mkIdEqInstCo (Right _) _ + = return () + +-- Coercion transformation: co = sym co' +-- +mkSymEqInstCo :: EqInstCo -> (Type, Type) -> TcM EqInstCo +mkSymEqInstCo (Left cotv) (ty1, ty2) + = do { cotv' <- newMetaCoVar ty1 ty2 + ; writeMetaTyVar cotv (mkSymCoercion (TyVarTy cotv')) + ; return $ Left cotv' + } +mkSymEqInstCo (Right co) _ + = return $ Right (mkSymCoercion co) + +-- Coercion transformation: co = co' |> given_co +-- +mkLeftTransEqInstCo :: EqInstCo -> Coercion -> (Type, Type) -> TcM EqInstCo +mkLeftTransEqInstCo (Left cotv) given_co (ty1, ty2) + = do { cotv' <- newMetaCoVar ty1 ty2 + ; writeMetaTyVar cotv (TyVarTy cotv' `mkTransCoercion` given_co) + ; return $ Left cotv' + } +mkLeftTransEqInstCo (Right co) given_co _ + = return $ Right (co `mkTransCoercion` mkSymCoercion given_co) + +-- Coercion transformation: co = given_co |> co' +-- +mkRightTransEqInstCo :: EqInstCo -> Coercion -> (Type, Type) -> TcM EqInstCo +mkRightTransEqInstCo (Left cotv) given_co (ty1, ty2) + = do { cotv' <- newMetaCoVar ty1 ty2 + ; writeMetaTyVar cotv (given_co `mkTransCoercion` TyVarTy cotv') + ; return $ Left cotv' + } +mkRightTransEqInstCo (Right co) given_co _ + = return $ Right (mkSymCoercion given_co `mkTransCoercion` co) + +-- Coercion transformation: co = col cor +-- +mkAppEqInstCo :: EqInstCo -> (Type, Type) -> (Type, Type) + -> TcM (EqInstCo, EqInstCo) +mkAppEqInstCo (Left cotv) (ty1_l, ty2_l) (ty1_r, ty2_r) + = do { cotv_l <- newMetaCoVar ty1_l ty2_l + ; cotv_r <- newMetaCoVar ty1_r ty2_r + ; writeMetaTyVar cotv (mkAppCoercion (TyVarTy cotv_l) (TyVarTy cotv_r)) + ; return (Left cotv_l, Left cotv_r) + } +mkAppEqInstCo (Right co) _ _ + = return (Right $ mkLeftCoercion co, Right $ mkRightCoercion co) +\end{code} + +Operations on entire EqInst. +\begin{code} eitherEqInst :: Inst -- given or wanted EqInst -> (TcTyVar -> a) -- result if wanted -> (Coercion -> a) -- result if given @@ -960,20 +1040,26 @@ eitherEqInst (EqInst {tci_co = either_co}) withWanted withGiven Right co -> withGiven co eitherEqInst i _ _ = pprPanic "eitherEqInst" (ppr i) -mkEqInsts :: [PredType] -> [Either TcTyVar Coercion] -> TcM [Inst] +mkEqInsts :: [PredType] -> [EqInstCo] -> TcM [Inst] mkEqInsts preds cos = zipWithM mkEqInst preds cos -mkEqInst :: PredType -> Either TcTyVar Coercion -> TcM Inst +mkEqInst :: PredType -> EqInstCo -> TcM Inst mkEqInst (EqPred ty1 ty2) co = do { uniq <- newUnique ; src_span <- getSrcSpanM ; err_ctxt <- getErrCtxt ; let loc = InstLoc EqOrigin src_span err_ctxt name = mkName uniq src_span - inst = EqInst {tci_left = ty1, tci_right = ty2, tci_co = co, tci_loc = loc, tci_name = name} + inst = EqInst { tci_left = ty1 + , tci_right = ty2 + , tci_co = co + , tci_loc = loc + , tci_name = name + } ; return inst } - where mkName uniq src_span = mkInternalName uniq (mkVarOcc "co") src_span + where + mkName uniq src_span = mkInternalName uniq (mkVarOcc "co") src_span mkEqInst pred _ = pprPanic "mkEqInst" (ppr pred) mkWantedEqInst :: PredType -> TcM Inst @@ -983,40 +1069,36 @@ mkWantedEqInst pred@(EqPred ty1 ty2) } mkWantedEqInst pred = pprPanic "mkWantedEqInst" (ppr pred) --- type inference: --- We want to promote the wanted EqInst to a given EqInst --- in the signature context. --- This means we have to give the coercion a name --- and fill it in as its own name. -finalizeEqInst - :: Inst -- wanted - -> TcM Inst -- given -finalizeEqInst wanted@(EqInst {tci_left = ty1, tci_right = ty2, tci_name = name}) - = do { let var = Var.mkCoVar name (PredTy $ EqPred ty1 ty2) - ; writeWantedCoercion wanted (TyVarTy var) - ; let given = wanted { tci_co = mkGivenCo $ TyVarTy var } - ; return given - } -finalizeEqInst i = pprPanic "finalizeEqInst" (ppr i) +-- Turn a wanted into a local EqInst (needed during type inference for +-- signatures) +-- +-- * Give it a name and change the coercion around. +-- +finalizeEqInst :: Inst -- wanted + -> TcM Inst -- given +finalizeEqInst wanted@(EqInst{tci_left = ty1, tci_right = ty2, tci_name = name}) + = do { let var = Var.mkCoVar name (PredTy $ EqPred ty1 ty2) + + -- fill the coercion hole + ; let cotv = fromWantedCo "writeWantedCoercion" $ tci_co wanted + ; writeMetaTyVar cotv (TyVarTy var) + + -- set the new coercion + ; let given = wanted { tci_co = mkGivenCo $ TyVarTy var } + ; return given + } -writeWantedCoercion - :: Inst -- wanted EqInst - -> Coercion -- coercion to fill the hole with - -> TcM () -writeWantedCoercion wanted co - = do { let cotv = fromWantedCo "writeWantedCoercion" $ tci_co wanted - ; writeMetaTyVar cotv co - } +finalizeEqInst i = pprPanic "finalizeEqInst" (ppr i) eqInstType :: Inst -> TcType eqInstType inst = eitherEqInst inst mkTyVarTy id -eqInstCoercion :: Inst -> Either TcTyVar Coercion +eqInstCoercion :: Inst -> EqInstCo eqInstCoercion = tci_co eqInstTys :: Inst -> (TcType, TcType) eqInstTys inst = (tci_left inst, tci_right inst) -updateEqInstCoercion :: (Either TcTyVar Coercion -> Either TcTyVar Coercion) -> Inst -> Inst +updateEqInstCoercion :: (EqInstCo -> EqInstCo) -> Inst -> Inst updateEqInstCoercion f inst = inst {tci_co = f $ tci_co inst} \end{code} diff --git a/compiler/typecheck/TcRnTypes.lhs b/compiler/typecheck/TcRnTypes.lhs index ebf4101..3d9bb60 100644 --- a/compiler/typecheck/TcRnTypes.lhs +++ b/compiler/typecheck/TcRnTypes.lhs @@ -28,7 +28,7 @@ module TcRnTypes( ArrowCtxt(NoArrowCtxt), newArrowScope, escapeArrowScope, -- Insts - Inst(..), InstOrigin(..), InstLoc(..), + Inst(..), EqInstCo, InstOrigin(..), InstLoc(..), pprInstLoc, pprInstArising, instLocSpan, instLocOrigin, LIE, emptyLIE, unitLIE, plusLIE, consLIE, instLoc, instSpan, plusLIEs, mkLIE, isEmptyLIE, lieToList, listToLIE, @@ -700,27 +700,26 @@ data Inst -- co :: ty1 ~ ty2 tci_left :: TcType, -- ty1 -- both types are... tci_right :: TcType, -- ty2 -- ...free of boxes - tci_co :: Either -- co - TcTyVar -- - a wanted equation, with a hole, to be - -- filled with a witness for the equality; - -- for equation arising from deferring - -- unification, 'ty1' is the actual and - -- 'ty2' the expected type - Coercion, -- - a given equation, with a coercion - -- witnessing the equality; - -- a coercion that originates from a - -- signature or a GADT is a CoVar, but - -- after normalisation of coercions, they - -- can be arbitrary Coercions involving - -- constructors and pseudo-constructors - -- like sym and trans. + tci_co :: EqInstCo, -- co tci_loc :: InstLoc, tci_name :: Name -- Debugging help only: this makes it easier to -- follow where a constraint is used in a morass - -- of trace messages! Unlike other Insts, it has - -- no semantic significance whatsoever. + -- of trace messages! Unlike other Insts, it + -- has no semantic significance whatsoever. } + +type EqInstCo = Either -- Distinguish between given and wanted coercions + TcTyVar -- - a wanted equation, with a hole, to be filled + -- with a witness for the equality; for equation + -- arising from deferring unification, 'ty1' is + -- the actual and 'ty2' the expected type + Coercion -- - a given equation, with a coercion witnessing + -- the equality; a coercion that originates + -- from a signature or a GADT is a CoVar, but + -- after normalisation of coercions, they can + -- be arbitrary Coercions involving constructors + -- and pseudo-constructors like sym and trans. \end{code} @Insts@ are ordered by their class/type info, rather than by their diff --git a/compiler/typecheck/TcTyFuns.lhs b/compiler/typecheck/TcTyFuns.lhs index 4c5be1c..188a29e 100644 --- a/compiler/typecheck/TcTyFuns.lhs +++ b/compiler/typecheck/TcTyFuns.lhs @@ -3,13 +3,20 @@ normalisation and entailment checking of equality constraints. \begin{code} module TcTyFuns ( - tcNormaliseFamInst, + -- type normalisation wrt to toplevel equalities only + tcNormaliseFamInst, - normaliseGivenEqs, normaliseGivenDicts, - normaliseWantedEqs, normaliseWantedDicts, + -- normalisation and solving of equalities + EqConfig, + normaliseEqs, propagateEqs, finaliseEqs, normaliseDicts, + + -- errors + misMatchMsg, failWithMisMatch, + + -- DEPRECATED: interface for the ICFP'08 algorithm + normaliseGivenEqs, normaliseGivenDicts, + normaliseWantedEqs, normaliseWantedDicts, - -- errors - misMatchMsg, failWithMisMatch ) where @@ -29,6 +36,7 @@ import TypeRep ( Type(..) ) import TyCon import HsSyn import VarEnv +import VarSet import Var import Name import Bag @@ -45,7 +53,7 @@ import Control.Monad %************************************************************************ %* * - Normalisation of types + Normalisation of types wrt toplevel equality schemata %* * %************************************************************************ @@ -91,6 +99,10 @@ possible (ie, we treat family instances as a TRS). Also zonk meta variables. then co : ty ~ ty' \begin{code} +-- |Normalise the given type as far as possible with toplevel equalities. +-- This results in a coercion witnessing the type equality, in addition to the +-- normalised type. +-- tcNormaliseFamInst :: TcType -> TcM (CoercionI, TcType) tcNormaliseFamInst = tcGenericNormaliseFamInst tcUnfoldSynFamInst @@ -98,6 +110,772 @@ tcNormaliseFamInstPred :: TcPredType -> TcM (CoercionI, TcPredType) tcNormaliseFamInstPred = tcGenericNormaliseFamInstPred tcUnfoldSynFamInst \end{code} +%************************************************************************ +%* * + Equality Configurations +%* * +%************************************************************************ + +We maintain normalised equalities together with the skolems introduced as +intermediates during flattening of equalities. + +!!!TODO: Do we really need to keep track of the skolem variables? They are at +the moment not used in instantiateAndExtract, but it is hard to say until we +know exactly how finalisation will fianlly look like. + +\begin{code} +-- |Configuration of normalised equalities used during solving. +-- +data EqConfig = EqConfig { eqs :: [RewriteInst] + , skolems :: TyVarSet + } + +addSkolems :: EqConfig -> TyVarSet -> EqConfig +addSkolems eqCfg newSkolems + = eqCfg {skolems = skolems eqCfg `unionVarSet` newSkolems} + +addEq :: EqConfig -> RewriteInst -> EqConfig +addEq eqCfg eq = eqCfg {eqs = eq : eqs eqCfg} +\end{code} + +The set of operations on an equality configuration. We obtain the initialise +configuration by normalisation ('normaliseEqs'), solve the equalities by +propagation ('propagateEqs'), and eventually finalise the configuration when +no further propoagation is possible. + +!!!TODO: Eventually, normalisation of dictionaries and dictionary +simplification should be included in propagation. + +\begin{code} +-- |Turn a set of equalities into an equality configuration for solving. +-- +-- Precondition: The Insts are zonked. +-- +normaliseEqs :: [Inst] -> TcM EqConfig +normaliseEqs eqs + = do { (eqss, skolemss) <- mapAndUnzipM normEqInst eqs + ; return $ EqConfig { eqs = concat eqss + , skolems = unionVarSets skolemss + } + } + +-- |Solves the equalities as far as possible by applying propagation rules. +-- +propagateEqs :: EqConfig -> TcM EqConfig +propagateEqs eqCfg@(EqConfig {eqs = todoEqs}) + = propagate todoEqs (eqCfg {eqs = []}) + +-- |Finalise a set of equalities after propagation. The Boolean value is +-- `True' iff any flexible variables, except those introduced by flattening +-- (i.e., those in the `skolems' component of the argument) where instantiated. +-- The returned set of instances are all residual wanteds. +-- +finaliseEqs :: EqConfig -> TcM ([Inst], Bool) +finaliseEqs (EqConfig {eqs = eqs, skolems = skolems}) + = do { eqs' <- substitute eqs + ; instantiateAndExtract eqs' skolems + } + +-- |Normalise a set of class instances under a given equality configuration. +-- Both the class instances and the equality configuration may change. The +-- function returns 'Nothing' if neither changes. +-- +normaliseDicts :: EqConfig -> [Inst] -> TcM (Maybe (EqConfig, [Inst])) +normaliseDicts = error "TcTyFuns.normaliseDicts" +\end{code} + + +%************************************************************************ +%* * + Normalisation of equalities +%* * +%************************************************************************ + +A normal equality is a properly oriented equality with associated coercion +that contains at most one family equality (in its left-hand side) is oriented +such that it may be used as a reqrite rule. It has one of the following two +forms: + +(1) co :: F t1..tn ~ t (family equalities) +(2) co :: x ~ t (variable equalities) + +Variable equalities fall again in two classes: + +(2a) co :: x ~ t, where t is *not* a variable, or +(2b) co :: x ~ y, where x > y. + +The types t, t1, ..., tn may not contain any occurrences of synonym +families. Moreover, in Forms (2) & (3), the left-hand side may not occur in +the right-hand side, and the relation x > y is an arbitrary, but total order +on type variables + +!!!TODO: We may need to keep track of swapping for error messages (and to +re-orient on finilisation). + +\begin{code} +data RewriteInst + = RewriteVar -- Form (2) above + { rwi_var :: TyVar -- may be rigid or flexible + , rwi_right :: TcType -- contains no synonym family applications + , rwi_co :: EqInstCo -- the wanted or given coercion + , rwi_loc :: InstLoc + , rwi_name :: Name -- no semantic significance (cf. TcRnTypes.EqInst) + } + | RewriteFam -- Forms (1) above + { rwi_fam :: TyCon -- synonym family tycon + , rwi_args :: [Type] -- contain no synonym family applications + , rwi_right :: TcType -- contains no synonym family applications + , rwi_co :: EqInstCo -- the wanted or given coercion + , rwi_loc :: InstLoc + , rwi_name :: Name -- no semantic significance (cf. TcRnTypes.EqInst) + } + +isWantedRewriteInst :: RewriteInst -> Bool +isWantedRewriteInst = isWantedCo . rwi_co + +rewriteInstToInst :: RewriteInst -> Inst +rewriteInstToInst eq@(RewriteVar {rwi_var = tv}) + = EqInst + { tci_left = mkTyVarTy tv + , tci_right = rwi_right eq + , tci_co = rwi_co eq + , tci_loc = rwi_loc eq + , tci_name = rwi_name eq + } +rewriteInstToInst eq@(RewriteFam {rwi_fam = fam, rwi_args = args}) + = EqInst + { tci_left = mkTyConApp fam args + , tci_right = rwi_right eq + , tci_co = rwi_co eq + , tci_loc = rwi_loc eq + , tci_name = rwi_name eq + } +\end{code} + +The following functions turn an arbitrary equality into a set of normal +equalities. + +\begin{code} +normEqInst :: Inst -> TcM ([RewriteInst], TyVarSet) +normEqInst inst + = ASSERT( isEqInst inst ) + go ty1 ty2 (eqInstCoercion inst) + where + (ty1, ty2) = eqInstTys inst + + -- look through synonyms + go ty1 ty2 co | Just ty1' <- tcView ty1 = go ty1' ty2 co + go ty1 ty2 co | Just ty2' <- tcView ty2 = go ty1 ty2' co + + -- left-to-right rule with type family head + go (TyConApp con args) ty2 co + | isOpenSynTyCon con + = mkRewriteFam con args ty2 co + + -- right-to-left rule with type family head + go ty1 ty2@(TyConApp con args) co + | isOpenSynTyCon con + = do { co' <- mkSymEqInstCo co (ty2, ty1) + ; mkRewriteFam con args ty1 co' + } + + -- no outermost family + go ty1 ty2 co + = do { (ty1', co1, ty1_eqs, ty1_skolems) <- flattenType inst ty1 + ; (ty2', co2, ty2_eqs, ty2_skolems) <- flattenType inst ty2 + ; let ty12_eqs = ty1_eqs ++ ty2_eqs + rewriteCo = co1 `mkTransCoercion` mkSymCoercion co2 + eqTys = (ty1', ty2') + ; (co', ty12_eqs') <- adjustCoercions co rewriteCo eqTys ty12_eqs + ; eqs <- checkOrientation ty1' ty2' co' inst + ; return $ (eqs ++ ty12_eqs', + ty1_skolems `unionVarSet` ty2_skolems) + } + + mkRewriteFam con args ty2 co + = do { (args', cargs, args_eqss, args_skolemss) + <- mapAndUnzip4M (flattenType inst) args + ; (ty2', co2, ty2_eqs, ty2_skolems) <- flattenType inst ty2 + ; let rewriteCo = mkTyConApp con cargs `mkTransCoercion` + mkSymCoercion co2 + all_eqs = concat args_eqss ++ ty2_eqs + eqTys = (mkTyConApp con args', ty2') + ; (co', all_eqs') <- adjustCoercions co rewriteCo eqTys all_eqs + ; let thisRewriteFam = RewriteFam + { rwi_fam = con + , rwi_args = args' + , rwi_right = ty2' + , rwi_co = co' + , rwi_loc = tci_loc inst + , rwi_name = tci_name inst + } + ; return $ (thisRewriteFam : all_eqs', + unionVarSets (ty2_skolems:args_skolemss)) + } + +checkOrientation :: Type -> Type -> EqInstCo -> Inst -> TcM [RewriteInst] +-- Performs the occurs check, decomposition, and proper orientation +-- (returns a singleton, or an empty list in case of a trivial equality) +-- NB: We cannot assume that the two types already have outermost type +-- synonyms expanded due to the recursion in the case of type applications. +checkOrientation ty1 ty2 co inst + = go ty1 ty2 + where + -- look through synonyms + go ty1 ty2 | Just ty1' <- tcView ty1 = go ty1' ty2 + go ty1 ty2 | Just ty2' <- tcView ty2 = go ty1 ty2' + + -- identical types => trivial + go ty1 ty2 + | ty1 `tcEqType` ty2 + = do { mkIdEqInstCo co ty1 + ; return [] + } + + -- two tvs, left greater => unchanged + go ty1@(TyVarTy tv1) ty2@(TyVarTy tv2) + | tv1 > tv2 + = mkRewriteVar tv1 ty2 co + + -- two tvs, right greater => swap + | otherwise + = do { co' <- mkSymEqInstCo co (ty2, ty1) + ; mkRewriteVar tv2 ty1 co' + } + + -- only lhs is a tv => unchanged + go ty1@(TyVarTy tv1) ty2 + | ty1 `tcPartOfType` ty2 -- occurs check! + = occurCheckErr ty1 ty2 + | otherwise + = mkRewriteVar tv1 ty2 co + + -- only rhs is a tv => swap + go ty1 ty2@(TyVarTy tv2) + | ty2 `tcPartOfType` ty1 -- occurs check! + = occurCheckErr ty2 ty1 + | otherwise + = do { co' <- mkSymEqInstCo co (ty2, ty1) + ; mkRewriteVar tv2 ty1 co' + } + + -- type applications => decompose + go ty1 ty2 + | Just (ty1_l, ty1_r) <- repSplitAppTy_maybe ty1 -- won't split fam apps + , Just (ty2_l, ty2_r) <- repSplitAppTy_maybe ty2 + = do { (co_l, co_r) <- mkAppEqInstCo co (ty1_l, ty2_l) (ty1_r, ty2_r) + ; eqs_l <- checkOrientation ty1_l ty2_l co_l inst + ; eqs_r <- checkOrientation ty1_r ty2_r co_r inst + ; return $ eqs_l ++ eqs_r + } +-- !!!TODO: would be more efficient to handle the FunApp and the data +-- constructor application explicitly. + + -- inconsistency => type error + go ty1 ty2 + = ASSERT( (not . isForAllTy $ ty1) && (not . isForAllTy $ ty2) ) + eqInstMisMatch inst + + mkRewriteVar tv ty co = return [RewriteVar + { rwi_var = tv + , rwi_right = ty + , rwi_co = co + , rwi_loc = tci_loc inst + , rwi_name = tci_name inst + }] + +flattenType :: Inst -- context to get location & name + -> Type -- the type to flatten + -> TcM (Type, -- the flattened type + Coercion, -- coercion witness of flattening wanteds + [RewriteInst], -- extra equalities + TyVarSet) -- new intermediate skolems +-- Removes all family synonyms from a type by moving them into extra equalities +flattenType inst ty + = go ty + where + -- look through synonyms + go ty | Just ty' <- tcView ty = go ty' + + -- type family application => flatten to "id :: F t1'..tn' ~ alpha" + go ty@(TyConApp con args) + | isOpenSynTyCon con + = do { (args', cargs, args_eqss, args_skolemss) <- mapAndUnzip4M go args + ; alpha <- newFlexiTyVar (typeKind ty) + ; let alphaTy = mkTyVarTy alpha + ; cotv <- newMetaCoVar (mkTyConApp con args') alphaTy + ; let thisRewriteFam = RewriteFam + { rwi_fam = con + , rwi_args = args' + , rwi_right = alphaTy + , rwi_co = mkWantedCo cotv + , rwi_loc = tci_loc inst + , rwi_name = tci_name inst + } + ; return (alphaTy, + mkTyConApp con cargs `mkTransCoercion` mkTyVarTy cotv, + thisRewriteFam : concat args_eqss, + unionVarSets args_skolemss `extendVarSet` alpha) + } -- adding new unflatten var inst + + -- data constructor application => flatten subtypes + -- NB: Special cased for efficiency - could be handled as type application + go (TyConApp con args) + = do { (args', cargs, args_eqss, args_skolemss) <- mapAndUnzip4M go args + ; return (mkTyConApp con args', + mkTyConApp con cargs, + concat args_eqss, + unionVarSets args_skolemss) + } + + -- function type => flatten subtypes + -- NB: Special cased for efficiency - could be handled as type application + go (FunTy ty_l ty_r) + = do { (ty_l', co_l, eqs_l, skolems_l) <- go ty_l + ; (ty_r', co_r, eqs_r, skolems_r) <- go ty_r + ; return (mkFunTy ty_l' ty_r', + mkFunTy co_l co_r, + eqs_l ++ eqs_r, + skolems_l `unionVarSet` skolems_r) + } + + -- type application => flatten subtypes + go (AppTy ty_l ty_r) +-- | Just (ty_l, ty_r) <- repSplitAppTy_maybe ty + = do { (ty_l', co_l, eqs_l, skolems_l) <- go ty_l + ; (ty_r', co_r, eqs_r, skolems_r) <- go ty_r + ; return (mkAppTy ty_l' ty_r', + mkAppTy co_l co_r, + eqs_l ++ eqs_r, + skolems_l `unionVarSet` skolems_r) + } + + -- free of type families => leave as is + go ty + = ASSERT( not . isForAllTy $ ty ) + return (ty, ty, [] , emptyVarSet) + +adjustCoercions :: EqInstCo -- coercion of original equality + -> Coercion -- coercion witnessing the rewrite + -> (Type, Type) -- type sof flattened equality + -> [RewriteInst] -- equalities from flattening + -> TcM (EqInstCo, -- coercion for flattened equality + [RewriteInst]) -- final equalities from flattening +-- Depending on whether we flattened a local or wanted equality, that equality's +-- coercion and that of the new ones are adjusted +adjustCoercions co rewriteCo eqTys all_eqs + | isWantedCo co + = do { co' <- mkRightTransEqInstCo co rewriteCo eqTys + ; return (co', all_eqs) + } + | otherwise + = return (co, map wantedToLocal all_eqs) + where + wantedToLocal eq = eq {rwi_co = mkGivenCo (rwi_right eq)} +\end{code} + + +%************************************************************************ +%* * + Propagation of equalities +%* * +%************************************************************************ + +Apply the propagation rules exhaustively. + +\begin{code} +propagate :: [RewriteInst] -> EqConfig -> TcM EqConfig +propagate [] eqCfg = return eqCfg +propagate (eq:eqs) eqCfg + = do { optEqs <- applyTop eq + ; case optEqs of + + -- Top applied to 'eq' => retry with new equalities + Just (eqs2, skolems2) + -> propagate (eqs2 ++ eqs) (eqCfg `addSkolems` skolems2) + + -- Top doesn't apply => try subst rules with all other + -- equalities, after that 'eq' can go into the residual list + Nothing + -> do { (eqs', eqCfg') <- applySubstRules eq eqs eqCfg + ; propagate eqs' (eqCfg' `addEq` eq) + } + } + +applySubstRules :: RewriteInst -- currently considered eq + -> [RewriteInst] -- todo eqs list + -> EqConfig -- residual + -> TcM ([RewriteInst], EqConfig) -- new todo & residual +applySubstRules eq todoEqs (eqConfig@EqConfig {eqs = resEqs}) + = do { (newEqs_t, unchangedEqs_t, skolems_t) <- mapSubstRules eq todoEqs + ; (newEqs_r, unchangedEqs_r, skolems_r) <- mapSubstRules eq resEqs + ; return (newEqs_t ++ newEqs_r ++ unchangedEqs_t, + eqConfig {eqs = unchangedEqs_r} + `addSkolems` (skolems_t `unionVarSet` skolems_r)) + } + +mapSubstRules :: RewriteInst -- try substituting this equality + -> [RewriteInst] -- into these equalities + -> TcM ([RewriteInst], [RewriteInst], TyVarSet) +mapSubstRules eq eqs + = do { (newEqss, unchangedEqss, skolemss) <- mapAndUnzip3M (substRules eq) eqs + ; return (concat newEqss, concat unchangedEqss, unionVarSets skolemss) + } + where + substRules eq1 eq2 + = do { -- try the SubstFam rule + optEqs <- applySubstFam eq1 eq2 + ; case optEqs of + Just (eqs, skolems) -> return (eqs, [], skolems) + Nothing -> do + { -- try the SubstVarVar rule + optEqs <- applySubstVarVar eq1 eq2 + ; case optEqs of + Just (eqs, skolems) -> return (eqs, [], skolems) + Nothing -> do + { -- try the SubstVarFam rule + optEqs <- applySubstVarFam eq1 eq2 + ; case optEqs of + Just eq -> return ([eq], [], emptyVarSet) + Nothing -> return ([], [eq2], emptyVarSet) + -- if no rule matches, we return the equlity we tried to + -- substitute into unchanged + }}} +\end{code} + +Attempt to apply the Top rule. The rule is + + co :: F t1..tn ~ t + =(Top)=> + co' :: [s1/x1, .., sm/xm]s ~ t with co = g s1..sm |> co' + +where g :: forall x1..xm. F u1..um ~ s and [s1/x1, .., sm/xm]u1 == t1. + +Returns Nothing if the rule could not be applied. Otherwise, the resulting +equality is normalised and a list of the normal equalities is returned. + +\begin{code} +applyTop :: RewriteInst -> TcM (Maybe ([RewriteInst], TyVarSet)) + +applyTop eq@(RewriteFam {rwi_fam = fam, rwi_args = args}) + = do { optTyCo <- tcUnfoldSynFamInst (TyConApp fam args) + ; case optTyCo of + Nothing -> return Nothing + Just (lhs, rewrite_co) + -> do { co' <- mkRightTransEqInstCo co rewrite_co (lhs, rhs) + ; let eq' = EqInst + { tci_left = lhs + , tci_right = rhs + , tci_co = co' + , tci_loc = rwi_loc eq + , tci_name = rwi_name eq + } + ; liftM Just $ normEqInst eq' + } + } + where + co = rwi_co eq + rhs = rwi_right eq + +applyTop _ = return Nothing +\end{code} + +Attempt to apply the SubstFam rule. The rule is + + co1 :: F t1..tn ~ t & co2 :: F t1..tn ~ s + =(SubstFam)=> + co1 :: F t1..tn ~ t & co2' :: t ~ s with co2 = co1 |> co2' + +where co1 may be a wanted only if co2 is a wanted, too. + +Returns Nothing if the rule could not be applied. Otherwise, the equality +co2' is normalised and a list of the normal equalities is returned. (The +equality co1 is not returned as it remain unaltered.) + +\begin{code} +applySubstFam :: RewriteInst + -> RewriteInst + -> TcM (Maybe ([RewriteInst], TyVarSet)) +applySubstFam eq1@(RewriteFam {rwi_fam = fam1, rwi_args = args1}) + eq2@(RewriteFam {rwi_fam = fam2, rwi_args = args2}) + | fam1 == fam2 && tcEqTypes args1 args2 && + (isWantedRewriteInst eq2 || not (isWantedRewriteInst eq1)) +-- !!!TODO: tcEqTypes is insufficient as it does not look through type synonyms +-- !!!Check whether anything breaks by making tcEqTypes look through synonyms. +-- !!!Should be ok and we don't want three type equalities. + = do { co2' <- mkRightTransEqInstCo co2 co1 (lhs, rhs) + ; let eq2' = EqInst + { tci_left = lhs + , tci_right = rhs + , tci_co = co2' + , tci_loc = rwi_loc eq2 + , tci_name = rwi_name eq2 + } + ; liftM Just $ normEqInst eq2' + } + where + lhs = rwi_right eq1 + rhs = rwi_right eq2 + co1 = eqInstCoType (rwi_co eq1) + co2 = rwi_co eq2 +applySubstFam _ _ = return Nothing +\end{code} + +Attempt to apply the SubstVarVar rule. The rule is + + co1 :: x ~ t & co2 :: x ~ s + =(SubstVarVar)=> + co1 :: x ~ t & co2' :: t ~ s with co2 = co1 |> co2' + +where co1 may be a wanted only if co2 is a wanted, too. + +Returns Nothing if the rule could not be applied. Otherwise, the equality +co2' is normalised and a list of the normal equalities is returned. (The +equality co1 is not returned as it remain unaltered.) + +\begin{code} +applySubstVarVar :: RewriteInst + -> RewriteInst + -> TcM (Maybe ([RewriteInst], TyVarSet)) +applySubstVarVar eq1@(RewriteVar {rwi_var = tv1}) + eq2@(RewriteVar {rwi_var = tv2}) + | tv1 == tv2 && + (isWantedRewriteInst eq2 || not (isWantedRewriteInst eq1)) + = do { co2' <- mkRightTransEqInstCo co2 co1 (lhs, rhs) + ; let eq2' = EqInst + { tci_left = lhs + , tci_right = rhs + , tci_co = co2' + , tci_loc = rwi_loc eq2 + , tci_name = rwi_name eq2 + } + ; liftM Just $ normEqInst eq2' + } + where + lhs = rwi_right eq1 + rhs = rwi_right eq2 + co1 = eqInstCoType (rwi_co eq1) + co2 = rwi_co eq2 +applySubstVarVar _ _ = return Nothing +\end{code} + +Attempt to apply the SubstVarFam rule. The rule is + + co1 :: x ~ t & co2 :: F s1..sn ~ s + =(SubstVarFam)=> + co1 :: x ~ t & co2' :: [t/x](F s1..sn) ~ s + with co2 = [co1/x](F s1..sn) |> co2' + +where x occurs in F s1..sn. (co1 may be local or wanted.) + +Returns Nothing if the rule could not be applied. Otherwise, the equality +co2' is returned. (The equality co1 is not returned as it remain unaltered.) + +\begin{code} +applySubstVarFam :: RewriteInst -> RewriteInst -> TcM (Maybe RewriteInst) +applySubstVarFam eq1@(RewriteVar {rwi_var = tv1}) + eq2@(RewriteFam {rwi_fam = fam2, rwi_args = args2}) + | tv1 `elemVarSet` tyVarsOfTypes args2 + = do { let co1Subst = substTyWith [tv1] [co1] (mkTyConApp fam2 args2) + args2' = substTysWith [tv1] [rhs1] args2 + lhs2 = mkTyConApp fam2 args2' + ; co2' <- mkRightTransEqInstCo co2 co1Subst (lhs2, rhs2) + ; return $ Just (eq2 {rwi_args = args2', rwi_co = co2'}) + } + where + rhs1 = rwi_right eq1 + rhs2 = rwi_right eq2 + co1 = eqInstCoType (rwi_co eq1) + co2 = rwi_co eq2 +applySubstVarFam _ _ = return Nothing +\end{code} + + +%************************************************************************ +%* * + Finalisation of equalities +%* * +%************************************************************************ + +Exhaustive substitution of all variable equalities of the form co :: x ~ t +(both local and wanted) into the left-hand sides all other equalities. This +may lead to recursive equalities; i.e., (1) we need to apply the substitution +implied by one variable equality exhaustively before turning to the next and +(2) we need an occurs check. + +NB: Gievn that we apply the substitution corresponding to a single equality +exhaustively, before turning to the next, and because we eliminate recursive +eqaulities, all opportunities for subtitution will have been exhausted after +we have considered each equality once. + +\begin{code} +substitute :: [RewriteInst] -> TcM [RewriteInst] +substitute eqs = subst eqs [] + where + subst [] res = return res + subst (eq:eqs) res + = do { eqs' <- mapM (substOne eq) eqs + ; res' <- mapM (substOne eq) res + ; subst eqs' (eq:res') + } + + -- apply [ty/tv] to left-hand side of eq2 + substOne (RewriteVar {rwi_var = tv, rwi_right = ty, rwi_co = co}) eq2 + = do { let co1Subst = mkSymCoercion $ + substTyWith [tv] [eqInstCoType co] (rwi_right eq2) + right2' = substTyWith [tv] [ty] (rwi_right eq2) + left2 = case eq2 of + RewriteVar {rwi_var = tv2} -> mkTyVarTy tv2 + RewriteFam {rwi_fam = fam, + rwi_args = args} ->mkTyConApp fam args + ; co2' <- mkLeftTransEqInstCo (rwi_co eq2) co1Subst (left2, right2') + ; case eq2 of + RewriteVar {rwi_var = tv2} | tv2 `elemVarSet` tyVarsOfType ty + -> occurCheckErr left2 right2' + _ -> return $ eq2 {rwi_right = right2', rwi_co = co2'} + } + + -- changed + substOne _ eq2 + = return eq2 +\end{code} + +For any *wanted* variable equality of the form co :: alpha ~ t or co :: a ~ +alpha, we instantiate alpha with t or a, respectively, and set co := id. +Return all remaining wanted equalities. The Boolean result component is True +if at least one instantiation of a flexible was performed. + +\begin{code} +instantiateAndExtract :: [RewriteInst] -> TyVarSet -> TcM ([Inst], Bool) +instantiateAndExtract eqs _skolems + = do { let wanteds = filter (isWantedCo . rwi_co) eqs + ; wanteds' <- mapM inst wanteds + ; let residuals = catMaybes wanteds' + improved = length wanteds /= length residuals + ; return (map rewriteInstToInst residuals, improved) + } + where + inst eq@(RewriteVar {rwi_var = tv1, rwi_right = ty2, rwi_co = co}) + + -- co :: alpha ~ t + | isMetaTyVar tv1 + = doInst tv1 ty2 co eq + + -- co :: a ~ alpha + | Just tv2 <- tcGetTyVar_maybe ty2 + , isMetaTyVar tv2 + = doInst tv2 (mkTyVarTy tv1) co eq + + inst eq = return $ Just eq + + doInst _ _ (Right ty) _eq = pprPanic "TcTyFuns.doInst: local eq: " + (ppr ty) + doInst tv ty (Left cotv) eq = do { lookupTV <- lookupTcTyVar tv + ; uMeta False tv lookupTV ty cotv + } + where + -- meta variable has been filled already + -- => panic (all equalities should have been zonked on normalisation) + uMeta _swapped _tv (IndirectTv _) _ty _cotv + = panic "TcTyFuns.uMeta: expected zonked equalities" + + -- type variable meets type variable + -- => check that tv2 hasn't been updated yet and choose which to update + uMeta swapped tv1 (DoneTv details1) (TyVarTy tv2) cotv + | tv1 == tv2 + = panic "TcTyFuns.uMeta: normalisation shouldn't allow x ~ x" + + | otherwise + = do { lookupTV2 <- lookupTcTyVar tv2 + ; case lookupTV2 of + IndirectTv ty -> + uMeta swapped tv1 (DoneTv details1) ty cotv + DoneTv details2 -> + uMetaVar swapped tv1 details1 tv2 details2 cotv + } + + ------ Beyond this point we know that ty2 is not a type variable + + -- signature skolem meets non-variable type + -- => cannot update (retain the equality)! + uMeta _swapped _tv (DoneTv (MetaTv (SigTv _) _)) _non_tv_ty _cotv + = return $ Just eq + + -- updatable meta variable meets non-variable type + -- => occurs check, monotype check, and kinds match check, then update + uMeta swapped tv (DoneTv (MetaTv _ ref)) non_tv_ty cotv + = do { -- occurs + monotype check + ; mb_ty' <- checkTauTvUpdate tv non_tv_ty + + ; case mb_ty' of + Nothing -> + -- normalisation shouldn't leave families in non_tv_ty + panic "TcTyFuns.uMeta: unexpected synonym family" + Just ty' -> + do { checkUpdateMeta swapped tv ref ty' -- update meta var + ; writeMetaTyVar cotv ty' -- update co var + ; return Nothing + } + } + + uMeta _ _ _ _ _ = panic "TcTyFuns.uMeta" + + -- uMetaVar: unify two type variables + -- meta variable meets skolem + -- => just update + uMetaVar swapped tv1 (MetaTv _ ref) tv2 (SkolemTv _) cotv + = do { checkUpdateMeta swapped tv1 ref (mkTyVarTy tv2) + ; writeMetaTyVar cotv (mkTyVarTy tv2) + ; return Nothing + } + + -- meta variable meets meta variable + -- => be clever about which of the two to update + -- (from TcUnify.uUnfilledVars minus boxy stuff) + uMetaVar swapped tv1 (MetaTv info1 ref1) tv2 (MetaTv info2 ref2) cotv + = do { case (info1, info2) of + -- Avoid SigTvs if poss + (SigTv _, _ ) | k1_sub_k2 -> update_tv2 + (_, SigTv _) | k2_sub_k1 -> update_tv1 + + (_, _) | k1_sub_k2 -> if k2_sub_k1 && nicer_to_update_tv1 + then update_tv1 -- Same kinds + else update_tv2 + | k2_sub_k1 -> update_tv1 + | otherwise -> kind_err + -- Update the variable with least kind info + -- See notes on type inference in Kind.lhs + -- The "nicer to" part only applies if the two kinds are the same, + -- so we can choose which to do. + + ; writeMetaTyVar cotv (mkTyVarTy tv2) + ; return Nothing + } + where + -- Kinds should be guaranteed ok at this point + update_tv1 = updateMeta tv1 ref1 (mkTyVarTy tv2) + update_tv2 = updateMeta tv2 ref2 (mkTyVarTy tv1) + + kind_err = addErrCtxtM (unifyKindCtxt swapped tv1 (mkTyVarTy tv2)) $ + unifyKindMisMatch k1 k2 + + k1 = tyVarKind tv1 + k2 = tyVarKind tv2 + k1_sub_k2 = k1 `isSubKind` k2 + k2_sub_k1 = k2 `isSubKind` k1 + + nicer_to_update_tv1 = isSystemName (Var.varName tv1) + -- Try to update sys-y type variables in preference to ones + -- gotten (say) by instantiating a polymorphic function with + -- a user-written type sig + + uMetaVar _ _ _ _ _ _ = panic "uMetaVar" +\end{code} + + + +==================== CODE FOR THE OLD ICFP'08 ALGORITHM ====================== + An elementary rewrite is a properly oriented equality with associated coercion that has one of the following two forms: diff --git a/compiler/types/Type.lhs b/compiler/types/Type.lhs index 7163079..d80bd52 100644 --- a/compiler/types/Type.lhs +++ b/compiler/types/Type.lhs @@ -128,7 +128,7 @@ module Type ( isEmptyTvSubst, -- ** Performing substitution on types - substTy, substTys, substTyWith, substTheta, + substTy, substTys, substTyWith, substTysWith, substTheta, substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar, -- * Pretty-printing @@ -1514,6 +1514,12 @@ substTyWith :: [TyVar] -> [Type] -> Type -> Type substTyWith tvs tys = ASSERT( length tvs == length tys ) substTy (zipOpenTvSubst tvs tys) +-- | Type substitution making use of an 'TvSubst' that +-- is assumed to be open, see 'zipOpenTvSubst' +substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type] +substTysWith tvs tys = ASSERT( length tvs == length tys ) + substTys (zipOpenTvSubst tvs tys) + -- | Substitute within a 'Type' substTy :: TvSubst -> Type -> Type substTy subst ty | isEmptyTvSubst subst = ty -- 1.7.10.4