X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=ghc%2Fcompiler%2Ftypecheck%2FTcTyDecls.lhs;h=4ce5fed3f3987e2f0d5869e08fb31cdba2e8cf43;hb=28a464a75e14cece5db40f2765a29348273ff2d2;hp=5ef86a3cc71bc804f54676af7c39e2b06340b742;hpb=9af77fa423926fbda946b31e174173d0ec5ebac8;p=ghc-hetmet.git diff --git a/ghc/compiler/typecheck/TcTyDecls.lhs b/ghc/compiler/typecheck/TcTyDecls.lhs index 5ef86a3..4ce5fed 100644 --- a/ghc/compiler/typecheck/TcTyDecls.lhs +++ b/ghc/compiler/typecheck/TcTyDecls.lhs @@ -1,196 +1,473 @@ % -% (c) The AQUA Project, Glasgow University, 1996-1998 +% (c) The GRASP/AQUA Project, Glasgow University, 1992-1999 % -\section[TcTyDecls]{Typecheck type declarations} + +Analysis functions over data types. Specficially + a) detecting recursive types + b) computing argument variances + +This stuff is only used for source-code decls; it's recorded in interface +files for imported data types. + \begin{code} -module TcTyDecls ( tcTyDecl, kcConDetails ) where +module TcTyDecls( + calcTyConArgVrcs, + calcRecFlags, + calcClassCycles, calcSynCycles + ) where #include "HsVersions.h" -import HsSyn ( TyClDecl(..), ConDecl(..), HsConDetails(..), BangType, - getBangType, getBangStrictness, conDetailsTys - ) -import RnHsSyn ( RenamedTyClDecl, RenamedConDecl, RenamedContext ) -import BasicTypes ( NewOrData(..) ) - -import TcMonoType ( tcHsTyVars, tcHsTheta, tcHsType, - kcHsContext, kcHsSigType, kcHsLiftedSigType - ) -import TcEnv ( tcExtendTyVarEnv, tcLookupTyCon, TyThingDetails(..) ) -import TcType ( tyVarsOfTypes, tyVarsOfPred, ThetaType ) -import RnEnv ( lookupSysName ) -import TcRnMonad - -import DataCon ( DataCon, mkDataCon, dataConFieldLabels ) -import FieldLabel ( fieldLabelName, fieldLabelType, allFieldLabelTags, mkFieldLabel ) -import MkId ( mkDataConId, mkDataConWrapId, mkRecordSelId ) -import Var ( TyVar ) -import Name ( Name ) -import OccName ( mkWorkerOcc, mkGenOcc1, mkGenOcc2 ) +import TypeRep ( Type(..), TyNote(..), PredType(..) ) -- friend +import HsSyn ( TyClDecl(..), HsPred(..), LTyClDecl, isClassDecl ) +import RnHsSyn ( extractHsTyNames ) +import Type ( predTypeRep, tcView ) +import HscTypes ( TyThing(..), ModDetails(..) ) +import TyCon ( TyCon, ArgVrcs, tyConArity, tyConDataCons, tyConTyVars, + synTyConDefn, isSynTyCon, isAlgTyCon, + tyConName, isNewTyCon, isProductTyCon, tyConArgVrcs, newTyConRhs ) +import Class ( classTyCon ) +import DataCon ( dataConOrigArgTys ) +import Var ( TyVar ) +import VarSet +import Name ( Name, isTyVarName ) +import NameEnv +import NameSet +import Digraph ( SCC(..), stronglyConnComp, stronglyConnCompR ) +import BasicTypes ( RecFlag(..) ) +import SrcLoc ( Located(..), unLoc ) import Outputable -import TyCon ( TyCon, DataConDetails(..), visibleDataCons, - tyConTyVars, tyConName ) -import VarSet ( intersectVarSet, isEmptyVarSet ) -import Generics ( mkTyConGenInfo ) -import CmdLineOpts ( DynFlag(..) ) -import List ( nubBy ) \end{code} + %************************************************************************ %* * -\subsection{Type checking} + Cycles in class and type synonym declarations %* * %************************************************************************ +Checking for class-decl loops is easy, because we don't allow class decls +in interface files. + +We allow type synonyms in hi-boot files, but we *trust* hi-boot files, +so we don't check for loops that involve them. So we only look for synonym +loops in the module being compiled. + +We check for type synonym and class cycles on the *source* code. +Main reasons: + + a) Otherwise we'd need a special function to extract type-synonym tycons + from a type, whereas we have extractHsTyNames already + + b) If we checked for type synonym loops after building the TyCon, we + can't do a hoistForAllTys on the type synonym rhs, (else we fall into + a black hole) which seems unclean. Apart from anything else, it'd mean + that a type-synonym rhs could have for-alls to the right of an arrow, + which means adding new cases to the validity checker + + Indeed, in general, checking for cycles beforehand means we need to + be less careful about black holes through synonym cycles. + +The main disadvantage is that a cycle that goes via a type synonym in an +.hi-boot file can lead the compiler into a loop, because it assumes that cycles +only occur entirely within the source code of the module being compiled. +But hi-boot files are trusted anyway, so this isn't much worse than (say) +a kind error. + +[ NOTE ---------------------------------------------- +If we reverse this decision, this comment came from tcTyDecl1, and should + go back there + -- dsHsType, not tcHsKindedType, to avoid a loop. tcHsKindedType does hoisting, + -- which requires looking through synonyms... and therefore goes into a loop + -- on (erroneously) recursive synonyms. + -- Solution: do not hoist synonyms, because they'll be hoisted soon enough + -- when they are substituted + +We'd also need to add back in this definition + +synTyConsOfType :: Type -> [TyCon] +-- Does not look through type synonyms at all +-- Return a list of synonym tycons +synTyConsOfType ty + = nameEnvElts (go ty) + where + go :: Type -> NameEnv TyCon -- The NameEnv does duplicate elim + go (TyVarTy v) = emptyNameEnv + go (TyConApp tc tys) = go_tc tc tys + go (AppTy a b) = go a `plusNameEnv` go b + go (FunTy a b) = go a `plusNameEnv` go b + go (PredTy (IParam _ ty)) = go ty + go (PredTy (ClassP cls tys)) = go_s tys -- Ignore class + go (NoteTy _ ty) = go ty + go (ForAllTy _ ty) = go ty + + go_tc tc tys | isSynTyCon tc = extendNameEnv (go_s tys) (tyConName tc) tc + | otherwise = go_s tys + go_s tys = foldr (plusNameEnv . go) emptyNameEnv tys +---------------------------------------- END NOTE ] + \begin{code} -tcTyDecl :: RenamedTyClDecl -> TcM (Name, TyThingDetails) -tcTyDecl (TySynonym {tcdName = tycon_name, tcdSynRhs = rhs}) - = tcLookupTyCon tycon_name `thenM` \ tycon -> - tcExtendTyVarEnv (tyConTyVars tycon) $ - tcHsType rhs `thenM` \ rhs_ty -> - returnM (tycon_name, SynTyDetails rhs_ty) - -tcTyDecl (TyData {tcdND = new_or_data, tcdCtxt = context, - tcdName = tycon_name, tcdCons = con_decls, - tcdGeneric = generic}) - = tcLookupTyCon tycon_name `thenM` \ tycon -> - let - tyvars = tyConTyVars tycon - in - tcExtendTyVarEnv tyvars $ - tcHsTheta context `thenM` \ ctxt -> - tcConDecls new_or_data tycon tyvars ctxt con_decls `thenM` \ data_cons -> - let - sel_ids = mkRecordSelectors tycon data_cons - in - tcGenericInfo tycon generic `thenM` \ gen_info -> - returnM (tycon_name, DataTyDetails ctxt data_cons sel_ids gen_info) - -tcTyDecl (ForeignType {tcdName = tycon_name}) - = returnM (tycon_name, ForeignTyDetails) - - -tcGenericInfo tycon generics -- Source code decl: consult the flag - = do_we_want generics `thenM` \ want_generics -> - if want_generics then - mapM (lookupSysName (tyConName tycon)) - [mkGenOcc1, mkGenOcc2] `thenM` \ gen_sys_names -> - returnM (mkTyConGenInfo tycon gen_sys_names) - else - returnM Nothing +calcSynCycles :: [LTyClDecl Name] -> [SCC (LTyClDecl Name)] +calcSynCycles decls + = stronglyConnComp syn_edges where - do_we_want (Just g) = returnM g -- Interface file decl - -- so look at decl - do_we_want Nothing = doptM Opt_Generics -- Source code decl - -- so look at flag - -mkRecordSelectors tycon data_cons - = -- We'll check later that fields with the same name - -- from different constructors have the same type. - [ mkRecordSelId tycon field - | field <- nubBy eq_name fields ] + syn_edges = [ (ldecl, unLoc (tcdLName decl), + mk_syn_edges (tcdSynRhs decl)) + | ldecl@(L _ decl) <- decls ] + + mk_syn_edges rhs = [ tc | tc <- nameSetToList (extractHsTyNames rhs), + not (isTyVarName tc) ] + + +calcClassCycles :: [LTyClDecl Name] -> [[LTyClDecl Name]] +calcClassCycles decls + = [decls | CyclicSCC decls <- stronglyConnComp cls_edges] where - fields = [ field | con <- visibleDataCons data_cons, - field <- dataConFieldLabels con ] - eq_name field1 field2 = fieldLabelName field1 == fieldLabelName field2 + cls_edges = [ (ldecl, unLoc (tcdLName decl), + mk_cls_edges (unLoc (tcdCtxt decl))) + | ldecl@(L _ decl) <- decls, isClassDecl decl ] + + mk_cls_edges ctxt = [ cls | L _ (HsClassP cls _) <- ctxt ] \end{code} %************************************************************************ %* * -\subsection{Kind and type check constructors} + Deciding which type constructors are recursive %* * %************************************************************************ +For newtypes, we label some as "recursive" such that + + INVARIANT: there is no cycle of non-recursive newtypes + +In any loop, only one newtype need be marked as recursive; it is +a "loop breaker". Labelling more than necessary as recursive is OK, +provided the invariant is maintained. + +A newtype M.T is defined to be "recursive" iff + (a) it is declared in an hi-boot file (see RdrHsSyn.hsIfaceDecl) + (b) it is declared in a source file, but that source file has a + companion hi-boot file which declares the type + or (c) one can get from T's rhs to T via type + synonyms, or non-recursive newtypes *in M* + e.g. newtype T = MkT (T -> Int) + +(a) is conservative; declarations in hi-boot files are always + made loop breakers. That's why in (b) we can restrict attention + to tycons in M, because any loops through newtypes outside M + will be broken by those newtypes +(b) ensures that a newtype is not treated as a loop breaker in one place +and later as a non-loop-breaker. This matters in GHCi particularly, when +a newtype T might be embedded in many types in the environment, and then +T's source module is compiled. We don't want T's recursiveness to change. + +The "recursive" flag for algebraic data types is irrelevant (never consulted) +for types with more than one constructor. + +An algebraic data type M.T is "recursive" iff + it has just one constructor, and + (a) it is declared in an hi-boot file (see RdrHsSyn.hsIfaceDecl) + (b) it is declared in a source file, but that source file has a + companion hi-boot file which declares the type + or (c) one can get from its arg types to T via type synonyms, + or by non-recursive newtypes or non-recursive product types in M + e.g. data T = MkT (T -> Int) Bool +Just like newtype in fact + +A type synonym is recursive if one can get from its +right hand side back to it via type synonyms. (This is +reported as an error.) + +A class is recursive if one can get from its superclasses +back to it. (This is an error too.) + +Hi-boot types +~~~~~~~~~~~~~ +A data type read from an hi-boot file will have an AbstractTyCon as its AlgTyConRhs +and will respond True to isHiBootTyCon. The idea is that we treat these as if one +could get from these types to anywhere. So when we see + + module Baz where + import {-# SOURCE #-} Foo( T ) + newtype S = MkS T + +then we mark S as recursive, just in case. What that means is that if we see + + import Baz( S ) + newtype R = MkR S + +then we don't need to look inside S to compute R's recursiveness. Since S is imported +(not from an hi-boot file), one cannot get from R back to S except via an hi-boot file, +and that means that some data type will be marked recursive along the way. So R is +unconditionly non-recursive (i.e. there'll be a loop breaker elsewhere if necessary) + +This in turn means that we grovel through fewer interface files when computing +recursiveness, because we need only look at the type decls in the module being +compiled, plus the outer structure of directly-mentioned types. + \begin{code} -kcConDetails :: NewOrData -> RenamedContext - -> HsConDetails Name (BangType Name) -> TcM () -kcConDetails new_or_data ex_ctxt details - = kcHsContext ex_ctxt `thenM_` - mappM_ kc_sig_type (conDetailsTys details) - where - kc_sig_type = case new_or_data of - DataType -> kcHsSigType - NewType -> kcHsLiftedSigType - -- Can't allow an unlifted type here, because we're effectively - -- going to remove the constructor while coercing it to a lifted type. - - -tcConDecls :: NewOrData -> TyCon -> [TyVar] -> ThetaType - -> DataConDetails RenamedConDecl -> TcM (DataConDetails DataCon) - -tcConDecls new_or_data tycon tyvars ctxt con_decls - = case con_decls of - Unknown -> returnM Unknown - HasCons n -> returnM (HasCons n) - DataCons cs -> mappM tc_con_decl cs `thenM` \ data_cons -> - returnM (DataCons data_cons) +calcRecFlags :: ModDetails -> [TyThing] -> (Name -> RecFlag) +-- The 'boot_names' are the things declared in M.hi-boot, if M is the current module. +-- Any type constructors in boot_names are automatically considered loop breakers +calcRecFlags boot_details tyclss + = is_rec where - tc_con_decl (ConDecl name ex_tvs ex_ctxt details src_loc) - = addSrcLoc src_loc $ - tcHsTyVars ex_tvs (kcConDetails new_or_data ex_ctxt details) $ \ ex_tyvars -> - tcHsTheta ex_ctxt `thenM` \ ex_theta -> - case details of - PrefixCon btys -> tc_datacon ex_tyvars ex_theta btys - InfixCon bty1 bty2 -> tc_datacon ex_tyvars ex_theta [bty1,bty2] - RecCon fields -> tc_rec_con ex_tyvars ex_theta fields - where + is_rec n | n `elemNameSet` rec_names = Recursive + | otherwise = NonRecursive + + boot_name_set = md_exports boot_details + rec_names = boot_name_set `unionNameSets` + nt_loop_breakers `unionNameSets` + prod_loop_breakers + + all_tycons = [ tc | tycls <- tyclss, + -- Recursion of newtypes/data types can happen via + -- the class TyCon, so tyclss includes the class tycons + let tc = getTyCon tycls, + not (tyConName tc `elemNameSet` boot_name_set) ] + -- Remove the boot_name_set because they are going + -- to be loop breakers regardless. + + ------------------------------------------------- + -- NOTE + -- These edge-construction loops rely on + -- every loop going via tyclss, the types and classes + -- in the module being compiled. Stuff in interface + -- files should be correctly marked. If not (e.g. a + -- type synonym in a hi-boot file) we can get an infinite + -- loop. We could program round this, but it'd make the code + -- rather less nice, so I'm not going to do that yet. + + --------------- Newtypes ---------------------- + new_tycons = filter isNewTyCon all_tycons + nt_loop_breakers = mkNameSet (findLoopBreakers nt_edges) + is_rec_nt tc = tyConName tc `elemNameSet` nt_loop_breakers + -- is_rec_nt is a locally-used helper function + + nt_edges = [(t, mk_nt_edges t) | t <- new_tycons] + + mk_nt_edges nt -- Invariant: nt is a newtype + = concatMap (mk_nt_edges1 nt) (tcTyConsOfType (new_tc_rhs nt)) + -- tyConsOfType looks through synonyms + + mk_nt_edges1 nt tc + | tc `elem` new_tycons = [tc] -- Loop + -- At this point we know that either it's a local *data* type, + -- or it's imported. Either way, it can't form part of a newtype cycle + | otherwise = [] + + --------------- Product types ---------------------- + -- The "prod_tycons" are the non-newtype products + prod_tycons = [tc | tc <- all_tycons, + not (isNewTyCon tc), isProductTyCon tc] + prod_loop_breakers = mkNameSet (findLoopBreakers prod_edges) + + prod_edges = [(tc, mk_prod_edges tc) | tc <- prod_tycons] - tc_datacon ex_tyvars ex_theta btys - = mappM tcHsType (map getBangType btys) `thenM` \ arg_tys -> - mk_data_con ex_tyvars ex_theta (map getBangStrictness btys) arg_tys [] - - tc_rec_con ex_tyvars ex_theta fields - = checkTc (null ex_tyvars) (exRecConErr name) `thenM_` - mappM tc_field (fields `zip` allFieldLabelTags) `thenM` \ field_labels -> - let - arg_stricts = [str | (n, bty) <- fields, - let str = getBangStrictness bty - ] - in - mk_data_con ex_tyvars ex_theta arg_stricts - (map fieldLabelType field_labels) field_labels - - tc_field ((field_label_name, bty), tag) - = tcHsType (getBangType bty) `thenM` \ field_ty -> - returnM (mkFieldLabel field_label_name tycon field_ty tag) - - mk_data_con ex_tyvars ex_theta arg_stricts arg_tys fields - = lookupSysName name mkWorkerOcc `thenM` \ wkr_name -> - let - data_con = mkDataCon name arg_stricts fields - tyvars (thinContext arg_tys ctxt) - ex_tyvars ex_theta - arg_tys - tycon data_con_id data_con_wrap_id - - data_con_id = mkDataConId wkr_name data_con - data_con_wrap_id = mkDataConWrapId data_con - in - returnM data_con - --- The context for a data constructor should be limited to --- the type variables mentioned in the arg_tys -thinContext arg_tys ctxt - = filter in_arg_tys ctxt + mk_prod_edges tc -- Invariant: tc is a product tycon + = concatMap (mk_prod_edges1 tc) (dataConOrigArgTys (head (tyConDataCons tc))) + + mk_prod_edges1 ptc ty = concatMap (mk_prod_edges2 ptc) (tcTyConsOfType ty) + + mk_prod_edges2 ptc tc + | tc `elem` prod_tycons = [tc] -- Local product + | tc `elem` new_tycons = if is_rec_nt tc -- Local newtype + then [] + else mk_prod_edges1 ptc (new_tc_rhs tc) + -- At this point we know that either it's a local non-product data type, + -- or it's imported. Either way, it can't form part of a cycle + | otherwise = [] + +new_tc_rhs tc = snd (newTyConRhs tc) -- Ignore the type variables + +getTyCon (ATyCon tc) = tc +getTyCon (AClass cl) = classTyCon cl + +findLoopBreakers :: [(TyCon, [TyCon])] -> [Name] +-- Finds a set of tycons that cut all loops +findLoopBreakers deps + = go [(tc,tc,ds) | (tc,ds) <- deps] + where + go edges = [ name + | CyclicSCC ((tc,_,_) : edges') <- stronglyConnCompR edges, + name <- tyConName tc : go edges'] +\end{code} + +These two functions know about type representations, so they could be +in Type or TcType -- but they are very specialised to this module, so +I've chosen to put them here. + +\begin{code} +tcTyConsOfType :: Type -> [TyCon] +-- tcTyConsOfType looks through all synonyms, but not through any newtypes. +-- When it finds a Class, it returns the class TyCon. The reaons it's here +-- (not in Type.lhs) is because it is newtype-aware. +tcTyConsOfType ty + = nameEnvElts (go ty) where - arg_tyvars = tyVarsOfTypes arg_tys - in_arg_tys pred = not $ isEmptyVarSet $ - tyVarsOfPred pred `intersectVarSet` arg_tyvars + go :: Type -> NameEnv TyCon -- The NameEnv does duplicate elim + go ty | Just ty' <- tcView ty = go ty' + go (TyVarTy v) = emptyNameEnv + go (TyConApp tc tys) = go_tc tc tys + go (AppTy a b) = go a `plusNameEnv` go b + go (FunTy a b) = go a `plusNameEnv` go b + go (PredTy (IParam _ ty)) = go ty + go (PredTy (ClassP cls tys)) = go_tc (classTyCon cls) tys + go (ForAllTy _ ty) = go ty + + go_tc tc tys = extendNameEnv (go_s tys) (tyConName tc) tc + go_s tys = foldr (plusNameEnv . go) emptyNameEnv tys \end{code} %************************************************************************ %* * -\subsection{Errors and contexts} + Compuing TyCon argument variances %* * %************************************************************************ +Computing the tyConArgVrcs info +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +@tyConArgVrcs@ gives a list of (occPos,occNeg) flags, one for each +tyvar. For @AlgTyCon@s and @SynTyCon@s, this info must be precomputed +separately. Note that this is information about occurrences of type +variables, not usages of term variables. + +The function @calcTyConArgVrcs@ must be passed a list of *algebraic or +syntycons only* such that all tycons referred to (by mutual recursion) +appear in the list. The fixpointing will be done on this set of +tycons as a whole. It returns a list of @tyconVrcInfo@ data, ready to +be (knot-tyingly?) stuck back into the appropriate fields. \begin{code} -exRecConErr name - = ptext SLIT("Can't combine named fields with locally-quantified type variables") - $$ - (ptext SLIT("In the declaration of data constructor") <+> ppr name) +calcTyConArgVrcs :: [TyThing] -> Name -> ArgVrcs +-- Gives arg variances for TyCons, +-- including the class TyCon of a class +calcTyConArgVrcs tyclss + = get_vrc + where + tycons = map getTyCon tyclss + + -- We should only look up things that are in the map + get_vrc n = case lookupNameEnv final_oi n of + Just (_, pms) -> pms + Nothing -> pprPanic "calcVrcs" (ppr n) + + -- We are going to fold over this map, + -- so we need the TyCon in the range + final_oi :: NameEnv (TyCon, ArgVrcs) + final_oi = tcaoFix initial_oi + + initial_oi :: NameEnv (TyCon, ArgVrcs) + initial_oi = mkNameEnv [(tyConName tc, (tc, initial tc)) + | tc <- tycons] + initial tc = replicate (tyConArity tc) (False,False) + + tcaoFix :: NameEnv (TyCon, ArgVrcs) -- initial ArgVrcs per tycon + -> NameEnv (TyCon, ArgVrcs) -- fixpointed ArgVrcs per tycon + tcaoFix oi + | changed = tcaoFix oi' + | otherwise = oi' + where + (changed,oi') = foldNameEnv iterate (False,oi) oi + + iterate (tc, pms) (changed,oi') + = (changed || (pms /= pms'), + extendNameEnv oi' (tyConName tc) (tc, pms')) + where + pms' = tcaoIter oi' tc -- seq not simult + + tcaoIter :: NameEnv (TyCon, ArgVrcs) -- reference ArgVrcs (initial) + -> TyCon -- tycon to update + -> ArgVrcs -- new ArgVrcs for tycon + + tcaoIter oi tc | isAlgTyCon tc + = map (\v -> anyVrc (vrcInTy (lookup oi) v) argtys) vs + where + data_cons = tyConDataCons tc + vs = tyConTyVars tc + argtys = concatMap dataConOrigArgTys data_cons -- Rep? or Orig? + + tcaoIter oi tc | isSynTyCon tc + = let (tyvs,ty) = synTyConDefn tc + -- we use the already-computed result for tycons not in this SCC + in map (\v -> vrcInTy (lookup oi) v ty) tyvs + + lookup oi tc = case lookupNameEnv oi (tyConName tc) of + Just (_, pms) -> pms + Nothing -> tyConArgVrcs tc + -- We use the already-computed result for tycons not in this SCC +\end{code} + + +Variance of tyvars in a type +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A general variance-check function. We pass a function for determining +the @ArgVrc@s of a tycon; when fixpointing this refers to the current +value; otherwise this should be looked up from the tycon's own +tyConArgVrcs. Again, it knows the representation of Types. + +\begin{code} +vrcInTy :: (TyCon -> ArgVrcs) -- function to get argVrcs of a tycon (break out of recursion) + -> TyVar -- tyvar to check Vrcs of + -> Type -- type to check for occ in + -> (Bool,Bool) -- (occurs positively, occurs negatively) + +vrcInTy fao v (NoteTy (FTVNote ftv) ty) = if elemVarSet v ftv + then vrcInTy fao v ty + else (False,False) + -- note that ftv cannot be calculated as occPos||occNeg, + -- since if a tyvar occurs only as unused tyconarg, + -- occPos==occNeg==False, but ftv=True + +vrcInTy fao v (TyVarTy v') = if v==v' + then (True,False) + else (False,False) + +vrcInTy fao v (AppTy ty1 ty2) = if vrcInTy fao v ty2 /= (False,False) + then (True,True) + else vrcInTy fao v ty1 + -- ty1 is probably unknown (or it would have been beta-reduced); + -- hence if v occurs in ty2 at all then it could occur with + -- either variance. Otherwise it occurs as it does in ty1. + +vrcInTy fao v (FunTy ty1 ty2) = negVrc (vrcInTy fao v ty1) + `orVrc` + vrcInTy fao v ty2 + +vrcInTy fao v (ForAllTy v' ty) = if v==v' + then (False,False) + else vrcInTy fao v ty + +vrcInTy fao v (TyConApp tc tys) = let pms1 = map (vrcInTy fao v) tys + pms2 = fao tc + in orVrcs (zipWith timesVrc pms1 pms2) + +vrcInTy fao v (PredTy st) = vrcInTy fao v (predTypeRep st) +\end{code} + +Variance algebra +~~~~~~~~~~~~~~~~ + +\begin{code} +orVrc :: (Bool,Bool) -> (Bool,Bool) -> (Bool,Bool) +orVrc (p1,m1) (p2,m2) = (p1||p2,m1||m2) + +orVrcs :: [(Bool,Bool)] -> (Bool,Bool) +orVrcs = foldl orVrc (False,False) + +negVrc :: (Bool,Bool) -> (Bool,Bool) +negVrc (p1,m1) = (m1,p1) + +anyVrc :: (a -> (Bool,Bool)) -> [a] -> (Bool,Bool) +anyVrc p as = foldl (\ pm a -> pm `orVrc` p a) + (False,False) as + +timesVrc :: (Bool,Bool) -> (Bool,Bool) -> (Bool,Bool) +timesVrc (p1,m1) (p2,m2) = (p1 && p2 || m1 && m2, + p1 && m2 || m1 && p2) \end{code}