typecheck/TcType.lhs

% % (c) The University of Glasgow 2006 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 % \section[TcType]{Types used in the typechecker} This module provides the Type interface for front-end parts of the compiler. These parts * treat "source types" as opaque: newtypes, and predicates are meaningful. * look through usage types The "tc" prefix is for "TypeChecker", because the type checker is the principal client. \begin{code}

    module TcType (
      --------------------------------
      -- Types
      TcType, TcSigmaType, TcRhoType, TcTauType, TcPredType, TcThetaType,
      TcTyVar, TcTyVarSet, TcKind, TcCoVar,

      -- Untouchables
      Untouchables(..), noUntouchables, pushUntouchables, isTouchable,

      --------------------------------
      -- MetaDetails
      UserTypeCtxt(..), pprUserTypeCtxt,
      TcTyVarDetails(..), pprTcTyVarDetails, vanillaSkolemTv, superSkolemTv,
      MetaDetails(Flexi, Indirect), MetaInfo(..),
      isImmutableTyVar, isSkolemTyVar, isMetaTyVar,  isMetaTyVarTy, isTyVarTy,
      isSigTyVar, isOverlappableTyVar,  isTyConableTyVar, isFlatSkolTyVar,
      isAmbiguousTyVar, metaTvRef, metaTyVarInfo,
      isFlexi, isIndirect, isRuntimeUnkSkol,
      isTypeVar, isKindVar,
      metaTyVarUntouchables, setMetaTyVarUntouchables,
      isTouchableMetaTyVar, isFloatedTouchableMetaTyVar,

      --------------------------------
      -- Builders
      mkPhiTy, mkSigmaTy, mkTcEqPred,

      --------------------------------
      -- Splitters
      -- These are important because they do not look through newtypes
      tcView,
      tcSplitForAllTys, tcSplitPhiTy, tcSplitPredFunTy_maybe,
      tcSplitFunTy_maybe, tcSplitFunTys, tcFunArgTy, tcFunResultTy, tcSplitFunTysN,
      tcSplitTyConApp, tcSplitTyConApp_maybe, tcTyConAppTyCon, tcTyConAppArgs,
      tcSplitAppTy_maybe, tcSplitAppTy, tcSplitAppTys, repSplitAppTy_maybe,
      tcInstHeadTyNotSynonym, tcInstHeadTyAppAllTyVars,
      tcGetTyVar_maybe, tcGetTyVar,
      tcSplitSigmaTy, tcDeepSplitSigmaTy_maybe,

      ---------------------------------
      -- Predicates.
      -- Again, newtypes are opaque
      eqType, eqTypes, eqPred, cmpType, cmpTypes, cmpPred, eqTypeX,
      pickyEqType, tcEqType, tcEqKind,
      isSigmaTy, isOverloadedTy,
      isDoubleTy, isFloatTy, isIntTy, isWordTy, isStringTy,
      isIntegerTy, isBoolTy, isUnitTy, isCharTy,
      isTauTy, isTauTyCon, tcIsTyVarTy, tcIsForAllTy,
      isSynFamilyTyConApp,
      isPredTy, isTyVarClassPred,

      ---------------------------------
      -- Misc type manipulators
      deNoteType, occurCheckExpand, OccCheckResult(..),
      orphNamesOfType, orphNamesOfDFunHead, orphNamesOfCo,
      orphNamesOfTypes, orphNamesOfCoCon,
      getDFunTyKey,
      evVarPred_maybe, evVarPred,

      ---------------------------------
      -- Predicate types
      mkMinimalBySCs, transSuperClasses, immSuperClasses,

      -- * Finding type instances
      tcTyFamInsts,

      -- * Finding "exact" (non-dead) type variables
      exactTyVarsOfType, exactTyVarsOfTypes,

      ---------------------------------
      -- Foreign import and export
      isFFIArgumentTy,     -- :: DynFlags -> Safety -> Type -> Bool
      isFFIImportResultTy, -- :: DynFlags -> Type -> Bool
      isFFIExportResultTy, -- :: Type -> Bool
      isFFIExternalTy,     -- :: Type -> Bool
      isFFIDynTy,          -- :: Type -> Type -> Bool
      isFFIPrimArgumentTy, -- :: DynFlags -> Type -> Bool
      isFFIPrimResultTy,   -- :: DynFlags -> Type -> Bool
      isFFILabelTy,        -- :: Type -> Bool
      isFFIDotnetTy,       -- :: DynFlags -> Type -> Bool
      isFFIDotnetObjTy,    -- :: Type -> Bool
      isFFITy,             -- :: Type -> Bool
      isFunPtrTy,          -- :: Type -> Bool
      tcSplitIOType_maybe, -- :: Type -> Maybe Type

      --------------------------------
      -- Rexported from Kind
      Kind, typeKind,
      unliftedTypeKind, liftedTypeKind,
      openTypeKind, constraintKind, mkArrowKind, mkArrowKinds,
      isLiftedTypeKind, isUnliftedTypeKind, isSubOpenTypeKind,
      tcIsSubKind, splitKindFunTys, defaultKind,

      --------------------------------
      -- Rexported from Type
      Type, PredType, ThetaType,
      mkForAllTy, mkForAllTys,
      mkFunTy, mkFunTys, zipFunTys,
      mkTyConApp, mkAppTy, mkAppTys, applyTy, applyTys,
      mkTyVarTy, mkTyVarTys, mkTyConTy,

      isClassPred, isEqPred, isIPPred,
      mkClassPred,
      isDictLikeTy,
      tcSplitDFunTy, tcSplitDFunHead,
      mkEqPred,

      -- Type substitutions
      TvSubst(..),  -- Representation visible to a few friends
      TvSubstEnv, emptyTvSubst,
      mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst,
      mkTopTvSubst, notElemTvSubst, unionTvSubst,
      getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
      Type.lookupTyVar, Type.extendTvSubst, Type.substTyVarBndr,
      extendTvSubstList, isInScope, mkTvSubst, zipTyEnv,
      Type.substTy, substTys, substTyWith, substTheta, substTyVar, substTyVars,

      isUnLiftedType,       -- Source types are always lifted
      isUnboxedTupleType,   -- Ditto
      isPrimitiveType,

      tyVarsOfType, tyVarsOfTypes, closeOverKinds,
      tcTyVarsOfType, tcTyVarsOfTypes,

      pprKind, pprParendKind, pprSigmaType,
      pprType, pprParendType, pprTypeApp, pprTyThingCategory,
      pprTheta, pprThetaArrowTy, pprClassPred

      ) where

    #include "HsVersions.h"

    -- friends:
    import Kind
    import TypeRep
    import Class
    import Var
    import ForeignCall
    import VarSet
    import Coercion
    import Type
    import TyCon
    import CoAxiom

    -- others:
    import DynFlags
    import Name -- hiding (varName)
                -- We use this to make dictionaries for type literals.
                -- Perhaps there's a better way to do this?
    import NameSet
    import VarEnv
    import PrelNames
    import TysWiredIn
    import BasicTypes
    import Util
    import Maybes
    import ListSetOps
    import Outputable
    import FastString

    import Data.IORef
    import Control.Monad (liftM, ap)
    import Control.Applicative (Applicative(..))

\end{code} %************************************************************************ %* * \subsection{Types} %* * %************************************************************************ The type checker divides the generic Type world into the following more structured beasts: sigma ::= forall tyvars. phi -- A sigma type is a qualified type -- -- Note that even if 'tyvars' is empty, theta -- may not be: e.g. (?x::Int) => Int -- Note that 'sigma' is in prenex form: -- all the foralls are at the front. -- A 'phi' type has no foralls to the right of -- an arrow phi :: theta => rho rho ::= sigma -> rho | tau -- A 'tau' type has no quantification anywhere -- Note that the args of a type constructor must be taus tau ::= tyvar | tycon tau_1 .. tau_n | tau_1 tau_2 | tau_1 -> tau_2 -- In all cases, a (saturated) type synonym application is legal, -- provided it expands to the required form. \begin{code}

    type TcTyVar = TyVar    -- Used only during type inference
    type TcCoVar = CoVar    -- Used only during type inference; mutable
    type TcType = Type      -- A TcType can have mutable type variables
            -- Invariant on ForAllTy in TcTypes:
            --      forall a. T
            -- a cannot occur inside a MutTyVar in T; that is,
            -- T is "flattened" before quantifying over a

    -- These types do not have boxy type variables in them
    type TcPredType     = PredType
    type TcThetaType    = ThetaType
    type TcSigmaType    = TcType
    type TcRhoType      = TcType
    type TcTauType      = TcType
    type TcKind         = Kind
    type TcTyVarSet     = TyVarSet

\end{code} %************************************************************************ %* * \subsection{TyVarDetails} %* * %************************************************************************ TyVarDetails gives extra info about type variables, used during type checking. It's attached to mutable type variables only. It's knot-tied back to Var.lhs. There is no reason in principle why Var.lhs shouldn't actually have the definition, but it "belongs" here. Note [Signature skolems] ~~~~~~~~~~~~~~~~~~~~~~~~ Consider this f :: forall a. [a] -> Int f (x::b : xs) = 3 Here 'b' is a lexically scoped type variable, but it turns out to be the same as the skolem 'a'. So we have a special kind of skolem constant, SigTv, which can unify with other SigTvs. They are used *only* for pattern type signatures. Similarly consider data T (a:k1) = MkT (S a) data S (b:k2) = MkS (T b) When doing kind inference on {S,T} we don't want *skolems* for k1,k2, because they end up unifying; we want those SigTvs again. \begin{code}

    -- A TyVarDetails is inside a TyVar
    data TcTyVarDetails
      = SkolemTv      -- A skolem
           Bool       -- True <=> this skolem type variable can be overlapped
                      --          when looking up instances
                      -- See Note [Binding when looking up instances] in InstEnv

      | RuntimeUnk    -- Stands for an as-yet-unknown type in the GHCi
                      -- interactive context

      | FlatSkol TcType
               -- The "skolem" obtained by flattening during
               -- constraint simplification

               -- In comments we will use the notation alpha[flat = ty]
               -- to represent a flattening skolem variable alpha
               -- identified with type ty.

      | MetaTv { mtv_info  :: MetaInfo
               , mtv_ref   :: IORef MetaDetails
               , mtv_untch :: Untouchables }  -- See Note [Untouchable type variables]

    vanillaSkolemTv, superSkolemTv :: TcTyVarDetails
    -- See Note [Binding when looking up instances] in InstEnv
    vanillaSkolemTv = SkolemTv False  -- Might be instantiated
    superSkolemTv   = SkolemTv True   -- Treat this as a completely distinct type

    -----------------------------
    data MetaDetails
      = Flexi  -- Flexi type variables unify to become Indirects
      | Indirect TcType

    instance Outputable MetaDetails where
      ppr Flexi         = ptext (sLit "Flexi")
      ppr (Indirect ty) = ptext (sLit "Indirect") <+> ppr ty

    data MetaInfo
       = TauTv         -- This MetaTv is an ordinary unification variable
                       -- A TauTv is always filled in with a tau-type, which
                       -- never contains any ForAlls

       | PolyTv        -- Like TauTv, but can unify with a sigma-type

       | SigTv         -- A variant of TauTv, except that it should not be
                       -- unified with a type, only with a type variable
                       -- SigTvs are only distinguished to improve error messages
                       --      see Note [Signature skolems]
                       --      The MetaDetails, if filled in, will
                       --      always be another SigTv or a SkolemTv

    -------------------------------------
    -- UserTypeCtxt describes the origin of the polymorphic type
    -- in the places where we need to an expression has that type

    data UserTypeCtxt
      = FunSigCtxt Name     -- Function type signature
                            -- Also used for types in SPECIALISE pragmas
      | InfSigCtxt Name     -- Inferred type for function
      | ExprSigCtxt         -- Expression type signature
      | ConArgCtxt Name     -- Data constructor argument
      | TySynCtxt Name      -- RHS of a type synonym decl
      | LamPatSigCtxt               -- Type sig in lambda pattern
                            --      f (x::t) = ...
      | BindPatSigCtxt      -- Type sig in pattern binding pattern
                            --      (x::t, y) = e
      | RuleSigCtxt Name    -- LHS of a RULE forall
                            --    RULE "foo" forall (x :: a -> a). f (Just x) = ...
      | ResSigCtxt          -- Result type sig
                            --      f x :: t = ....
      | ForSigCtxt Name     -- Foreign import or export signature
      | DefaultDeclCtxt     -- Types in a default declaration
      | InstDeclCtxt        -- An instance declaration
      | SpecInstCtxt        -- SPECIALISE instance pragma
      | ThBrackCtxt         -- Template Haskell type brackets [t| ... |]
      | GenSigCtxt          -- Higher-rank or impredicative situations
                            -- e.g. (f e) where f has a higher-rank type
                            -- We might want to elaborate this
      | GhciCtxt            -- GHCi command :kind <type>

      | ClassSCCtxt Name    -- Superclasses of a class
      | SigmaCtxt           -- Theta part of a normal for-all type
                            --      f :: <S> => a -> a
      | DataTyCtxt Name     -- Theta part of a data decl
                            --      data <S> => T a = MkT a

\end{code} -- Notes re TySynCtxt -- We allow type synonyms that aren't types; e.g. type List = [] -- -- If the RHS mentions tyvars that aren't in scope, we'll -- quantify over them: -- e.g. type T = a->a -- will become type T = forall a. a->a -- -- With gla-exts that's right, but for H98 we should complain. %************************************************************************ %* * Untoucable type variables %* * %************************************************************************ Note [Untouchable type variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Each unification variable (MetaTv) and each Implication has a level number (of type Untouchables) * INVARIANTS. In a tree of Implications, (ImplicInv) The level number of an Implication is STRICTLY GREATER THAN that of its parent (MetaTvInv) The level number of a unification variable is LESS THAN OR EQUAL TO that of its parent implication * A unification variable is *touchable* if its level number is EQUAL TO that of its immediate parent implication. * INVARIANT (GivenInv) The free variables of the ic_given of an implication are all untouchable; ie their level numbers are LESS THAN the ic_untch of the implication Note [Skolem escape prevention] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We only unify touchable unification variables. Because of (MetaTvInv), there can be no occurrences of he variable further out, so the unification can't cause the kolems to escape. Example: data T = forall a. MkT a (a->Int) f x (MkT v f) = length [v,x] We decide (x::alpha), and generate an implication like [1]forall a. (a ~ alpha[0]) But we must not unify alpha:=a, because the skolem would escape. For the cases where we DO want to unify, we rely on floating the equality. Example (with same T) g x (MkT v f) = x && True We decide (x::alpha), and generate an implication like [1]forall a. (Bool ~ alpha[0]) We do NOT unify directly, bur rather float out (if the constraint does not mention 'a') to get (Bool ~ alpha[0]) /\ [1]forall a.() and NOW we can unify alpha. The same idea of only unifying touchables solves another problem. Suppose we had (F Int ~ uf[0]) /\ [1](forall a. C a => F Int ~ beta[1]) In this example, beta is touchable inside the implication. The first solveInteract step leaves 'uf' un-unified. Then we move inside the implication where a new constraint uf ~ beta emerges. If we (wrongly) spontaneously solved it to get uf := beta, the whole implication disappears but when we pop out again we are left with (F Int ~ uf) which will be unified by our final solveCTyFunEqs stage and uf will get unified *once more* to (F Int). \begin{code}

    newtype Untouchables = Untouchables Int
      -- See Note [Untouchable type variables] for what this Int is

    noUntouchables :: Untouchables
    noUntouchables = Untouchables 0   -- 0 = outermost level

    pushUntouchables :: Untouchables -> Untouchables
    pushUntouchables (Untouchables us) = Untouchables (us+1)

    isFloatedTouchable :: Untouchables -> Untouchables -> Bool
    isFloatedTouchable (Untouchables ctxt_untch) (Untouchables tv_untch)
      = ctxt_untch < tv_untch

    isTouchable :: Untouchables -> Untouchables -> Bool
    isTouchable (Untouchables ctxt_untch) (Untouchables tv_untch)
      = ctxt_untch == tv_untch   -- NB: invariant ctxt_untch >= tv_untch
                                 --     So <= would be equivalent

    checkTouchableInvariant :: Untouchables -> Untouchables -> Bool
    -- Checks (MetaTvInv) from Note [Untouchable type variables]
    checkTouchableInvariant (Untouchables ctxt_untch) (Untouchables tv_untch)
      = ctxt_untch >= tv_untch

    instance Outputable Untouchables where
      ppr (Untouchables us) = ppr us

\end{code} %************************************************************************ %* * Pretty-printing %* * %************************************************************************ \begin{code}

    pprTcTyVarDetails :: TcTyVarDetails -> SDoc
    -- For debugging
    pprTcTyVarDetails (SkolemTv True)  = ptext (sLit "ssk")
    pprTcTyVarDetails (SkolemTv False) = ptext (sLit "sk")
    pprTcTyVarDetails (RuntimeUnk {})  = ptext (sLit "rt")
    pprTcTyVarDetails (FlatSkol {})    = ptext (sLit "fsk")
    pprTcTyVarDetails (MetaTv { mtv_info = info, mtv_untch = untch })
      = pp_info <> brackets (ppr untch)
      where
        pp_info = case info of
                    PolyTv -> ptext (sLit "poly")
                    TauTv  -> ptext (sLit "tau")
                    SigTv  -> ptext (sLit "sig")

    pprUserTypeCtxt :: UserTypeCtxt -> SDoc
    pprUserTypeCtxt (InfSigCtxt n)    = ptext (sLit "the inferred type for") <+> quotes (ppr n)
    pprUserTypeCtxt (FunSigCtxt n)    = ptext (sLit "the type signature for") <+> quotes (ppr n)
    pprUserTypeCtxt (RuleSigCtxt n)    = ptext (sLit "a RULE for") <+> quotes (ppr n)
    pprUserTypeCtxt ExprSigCtxt       = ptext (sLit "an expression type signature")
    pprUserTypeCtxt (ConArgCtxt c)    = ptext (sLit "the type of the constructor") <+> quotes (ppr c)
    pprUserTypeCtxt (TySynCtxt c)     = ptext (sLit "the RHS of the type synonym") <+> quotes (ppr c)
    pprUserTypeCtxt ThBrackCtxt       = ptext (sLit "a Template Haskell quotation [t|...|]")
    pprUserTypeCtxt LamPatSigCtxt     = ptext (sLit "a pattern type signature")
    pprUserTypeCtxt BindPatSigCtxt    = ptext (sLit "a pattern type signature")
    pprUserTypeCtxt ResSigCtxt        = ptext (sLit "a result type signature")
    pprUserTypeCtxt (ForSigCtxt n)    = ptext (sLit "the foreign declaration for") <+> quotes (ppr n)
    pprUserTypeCtxt DefaultDeclCtxt   = ptext (sLit "a type in a `default' declaration")
    pprUserTypeCtxt InstDeclCtxt      = ptext (sLit "an instance declaration")
    pprUserTypeCtxt SpecInstCtxt      = ptext (sLit "a SPECIALISE instance pragma")
    pprUserTypeCtxt GenSigCtxt        = ptext (sLit "a type expected by the context")
    pprUserTypeCtxt GhciCtxt          = ptext (sLit "a type in a GHCi command")
    pprUserTypeCtxt (ClassSCCtxt c)   = ptext (sLit "the super-classes of class") <+> quotes (ppr c)
    pprUserTypeCtxt SigmaCtxt         = ptext (sLit "the context of a polymorphic type")
    pprUserTypeCtxt (DataTyCtxt tc)   = ptext (sLit "the context of the data type declaration for") <+> quotes (ppr tc)

\end{code} %************************************************************************ %* * Finding type family instances %* * %************************************************************************ \begin{code}

    -- | Finds outermost type-family applications occuring in a type,
    -- after expanding synonyms.
    tcTyFamInsts :: Type -> [(TyCon, [Type])]
    tcTyFamInsts ty
      | Just exp_ty <- tcView ty    = tcTyFamInsts exp_ty
    tcTyFamInsts (TyVarTy _)        = []
    tcTyFamInsts (TyConApp tc tys)
      | isSynFamilyTyCon tc         = [(tc, tys)]
      | otherwise                   = concat (map tcTyFamInsts tys)
    tcTyFamInsts (LitTy {})         = []
    tcTyFamInsts (FunTy ty1 ty2)    = tcTyFamInsts ty1 ++ tcTyFamInsts ty2
    tcTyFamInsts (AppTy ty1 ty2)    = tcTyFamInsts ty1 ++ tcTyFamInsts ty2
    tcTyFamInsts (ForAllTy _ ty)    = tcTyFamInsts ty

\end{code} %************************************************************************ %* * The "exact" free variables of a type %* * %************************************************************************ Note [Silly type synonym] ~~~~~~~~~~~~~~~~~~~~~~~~~ Consider type T a = Int What are the free tyvars of (T x)? Empty, of course! Here's the example that Ralf Laemmel showed me: foo :: (forall a. C u a -> C u a) -> u mappend :: Monoid u => u -> u -> u bar :: Monoid u => u bar = foo (\t -> t `mappend` t) We have to generalise at the arg to f, and we don't want to capture the constraint (Monad (C u a)) because it appears to mention a. Pretty silly, but it was useful to him. exactTyVarsOfType is used by the type checker to figure out exactly which type variables are mentioned in a type. It's also used in the smart-app checking code --- see TcExpr.tcIdApp On the other hand, consider a *top-level* definition f = (\x -> x) :: T a -> T a If we don't abstract over 'a' it'll get fixed to GHC.Prim.Any, and then if we have an application like (f "x") we get a confusing error message involving Any. So the conclusion is this: when generalising - at top level use tyVarsOfType - in nested bindings use exactTyVarsOfType See Trac #1813 for example. \begin{code}

    exactTyVarsOfType :: Type -> TyVarSet
    -- Find the free type variables (of any kind)
    -- but *expand* type synonyms.  See Note [Silly type synonym] above.
    exactTyVarsOfType ty
      = go ty
      where
        go ty | Just ty' <- tcView ty = go ty'  -- This is the key line
        go (TyVarTy tv)         = unitVarSet tv
        go (TyConApp _ tys)     = exactTyVarsOfTypes tys
        go (LitTy {})           = emptyVarSet
        go (FunTy arg res)      = go arg `unionVarSet` go res
        go (AppTy fun arg)      = go fun `unionVarSet` go arg
        go (ForAllTy tyvar ty)  = delVarSet (go ty) tyvar

    exactTyVarsOfTypes :: [Type] -> TyVarSet
    exactTyVarsOfTypes tys = foldr (unionVarSet . exactTyVarsOfType) emptyVarSet tys

\end{code} %************************************************************************ %* * Predicates %* * %************************************************************************ \begin{code}

    isTouchableMetaTyVar :: Untouchables -> TcTyVar -> Bool
    isTouchableMetaTyVar ctxt_untch tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
          MetaTv { mtv_untch = tv_untch }
            -> ASSERT2( checkTouchableInvariant ctxt_untch tv_untch,
                        ppr tv $$ ppr tv_untch $$ ppr ctxt_untch )
               isTouchable ctxt_untch tv_untch
          _ -> False

    isFloatedTouchableMetaTyVar :: Untouchables -> TcTyVar -> Bool
    isFloatedTouchableMetaTyVar ctxt_untch tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
          MetaTv { mtv_untch = tv_untch } -> isFloatedTouchable ctxt_untch tv_untch
          _ -> False

    isImmutableTyVar :: TyVar -> Bool
    isImmutableTyVar tv
      | isTcTyVar tv = isSkolemTyVar tv
      | otherwise    = True

    isTyConableTyVar, isSkolemTyVar, isOverlappableTyVar,
      isMetaTyVar, isAmbiguousTyVar, isFlatSkolTyVar :: TcTyVar -> Bool

    isTyConableTyVar tv
            -- True of a meta-type variable that can be filled in
            -- with a type constructor application; in particular,
            -- not a SigTv
      = ASSERT( isTcTyVar tv)
        case tcTyVarDetails tv of
            MetaTv { mtv_info = SigTv } -> False
            _                           -> True

    isFlatSkolTyVar tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
            FlatSkol {} -> True
            _           -> False

    isSkolemTyVar tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
            SkolemTv {}   -> True
            FlatSkol {}   -> True
            RuntimeUnk {} -> True
            MetaTv {}     -> False

    isOverlappableTyVar tv
      = ASSERT( isTcTyVar tv )
        case tcTyVarDetails tv of
            SkolemTv overlappable -> overlappable
            _                     -> False

    isMetaTyVar tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
            MetaTv {} -> True
            _         -> False

    -- isAmbiguousTyVar is used only when reporting type errors
    -- It picks out variables that are unbound, namely meta
    -- type variables and the RuntimUnk variables created by
    -- RtClosureInspect.zonkRTTIType.  These are "ambiguous" in
    -- the sense that they stand for an as-yet-unknown type
    isAmbiguousTyVar tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
            MetaTv {}     -> True
            RuntimeUnk {} -> True
            _             -> False

    isMetaTyVarTy :: TcType -> Bool
    isMetaTyVarTy (TyVarTy tv) = isMetaTyVar tv
    isMetaTyVarTy _            = False

    metaTyVarInfo :: TcTyVar -> MetaInfo
    metaTyVarInfo tv
      = ASSERT( isTcTyVar tv )
        case tcTyVarDetails tv of
          MetaTv { mtv_info = info } -> info
          _ -> pprPanic "metaTyVarInfo" (ppr tv)

    metaTyVarUntouchables :: TcTyVar -> Untouchables
    metaTyVarUntouchables tv
      = ASSERT( isTcTyVar tv )
        case tcTyVarDetails tv of
          MetaTv { mtv_untch = untch } -> untch
          _ -> pprPanic "metaTyVarUntouchables" (ppr tv)

    setMetaTyVarUntouchables :: TcTyVar -> Untouchables -> TcTyVar
    setMetaTyVarUntouchables tv untch
      = ASSERT( isTcTyVar tv )
        case tcTyVarDetails tv of
          details@(MetaTv {}) -> setTcTyVarDetails tv (details { mtv_untch = untch })
          _ -> pprPanic "metaTyVarUntouchables" (ppr tv)

    isSigTyVar :: Var -> Bool
    isSigTyVar tv
      = ASSERT( isTcTyVar tv )
        case tcTyVarDetails tv of
            MetaTv { mtv_info = SigTv } -> True
            _                           -> False

    metaTvRef :: TyVar -> IORef MetaDetails
    metaTvRef tv
      = ASSERT2( isTcTyVar tv, ppr tv )
        case tcTyVarDetails tv of
            MetaTv { mtv_ref = ref } -> ref
            _ -> pprPanic "metaTvRef" (ppr tv)

    isFlexi, isIndirect :: MetaDetails -> Bool
    isFlexi Flexi = True
    isFlexi _     = False

    isIndirect (Indirect _) = True
    isIndirect _            = False

    isRuntimeUnkSkol :: TyVar -> Bool
    -- Called only in TcErrors; see Note [Runtime skolems] there
    isRuntimeUnkSkol x
      | isTcTyVar x, RuntimeUnk <- tcTyVarDetails x = True
      | otherwise                                   = False

\end{code} %************************************************************************ %* * \subsection{Tau, sigma and rho} %* * %************************************************************************ \begin{code}

    mkSigmaTy :: [TyVar] -> [PredType] -> Type -> Type
    mkSigmaTy tyvars theta tau = mkForAllTys tyvars (mkPhiTy theta tau)

    mkPhiTy :: [PredType] -> Type -> Type
    mkPhiTy theta ty = foldr mkFunTy ty theta

    mkTcEqPred :: TcType -> TcType -> Type
    -- During type checking we build equalities between
    -- type variables with OpenKind or ArgKind.  Ultimately
    -- they will all settle, but we want the equality predicate
    -- itself to have kind '*'.  I think.
    --
    -- But for now we call mkTyConApp, not mkEqPred, because the invariants
    -- of the latter might not be satisfied during type checking.
    -- Notably when we form an equalty   (a : OpenKind) ~ (Int : *)
    --
    -- But this is horribly delicate: what about type variables
    -- that turn out to be bound to Int#?
    mkTcEqPred ty1 ty2
      = mkTyConApp eqTyCon [k, ty1, ty2]
      where
        k = defaultKind (typeKind ty1)

\end{code} @isTauTy@ tests for nested for-alls. It should not be called on a boxy type. \begin{code}

    isTauTy :: Type -> Bool
    isTauTy ty | Just ty' <- tcView ty = isTauTy ty'
    isTauTy (TyVarTy _)       = True
    isTauTy (LitTy {})        = True
    isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc
    isTauTy (AppTy a b)       = isTauTy a && isTauTy b
    isTauTy (FunTy a b)       = isTauTy a && isTauTy b
    isTauTy (ForAllTy {})     = False

    isTauTyCon :: TyCon -> Bool
    -- Returns False for type synonyms whose expansion is a polytype
    isTauTyCon tc
      | Just (_, rhs) <- synTyConDefn_maybe tc = isTauTy rhs
      | otherwise                              = True

    ---------------
    getDFunTyKey :: Type -> OccName -- Get some string from a type, to be used to
                                    -- construct a dictionary function name
    getDFunTyKey ty | Just ty' <- tcView ty = getDFunTyKey ty'
    getDFunTyKey (TyVarTy tv)    = getOccName tv
    getDFunTyKey (TyConApp tc _) = getOccName tc
    getDFunTyKey (LitTy x)       = getDFunTyLitKey x
    getDFunTyKey (AppTy fun _)   = getDFunTyKey fun
    getDFunTyKey (FunTy _ _)     = getOccName funTyCon
    getDFunTyKey (ForAllTy _ t)  = getDFunTyKey t

    getDFunTyLitKey :: TyLit -> OccName
    getDFunTyLitKey (NumTyLit n) = mkOccName Name.varName (show n)
    getDFunTyLitKey (StrTyLit n) = mkOccName Name.varName (show n)  -- hm

\end{code} %************************************************************************ %* * \subsection{Expanding and splitting} %* * %************************************************************************ These tcSplit functions are like their non-Tc analogues, but *) they do not look through newtypes However, they are non-monadic and do not follow through mutable type variables. It's up to you to make sure this doesn't matter. \begin{code}

    tcSplitForAllTys :: Type -> ([TyVar], Type)
    tcSplitForAllTys ty = split ty ty []
       where
         split orig_ty ty tvs | Just ty' <- tcView ty = split orig_ty ty' tvs
         split _ (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
         split orig_ty _          tvs = (reverse tvs, orig_ty)

    tcIsForAllTy :: Type -> Bool
    tcIsForAllTy ty | Just ty' <- tcView ty = tcIsForAllTy ty'
    tcIsForAllTy (ForAllTy {}) = True
    tcIsForAllTy _             = False

    tcSplitPredFunTy_maybe :: Type -> Maybe (PredType, Type)
    -- Split off the first predicate argument from a type
    tcSplitPredFunTy_maybe ty
      | Just ty' <- tcView ty = tcSplitPredFunTy_maybe ty'
    tcSplitPredFunTy_maybe (FunTy arg res)
      | isPredTy arg = Just (arg, res)
    tcSplitPredFunTy_maybe _
      = Nothing

    tcSplitPhiTy :: Type -> (ThetaType, Type)
    tcSplitPhiTy ty
      = split ty []
      where
        split ty ts
          = case tcSplitPredFunTy_maybe ty of
              Just (pred, ty) -> split ty (pred:ts)
              Nothing         -> (reverse ts, ty)

    tcSplitSigmaTy :: Type -> ([TyVar], ThetaType, Type)
    tcSplitSigmaTy ty = case tcSplitForAllTys ty of
                            (tvs, rho) -> case tcSplitPhiTy rho of
                                            (theta, tau) -> (tvs, theta, tau)

    -----------------------
    tcDeepSplitSigmaTy_maybe
      :: TcSigmaType -> Maybe ([TcType], [TyVar], ThetaType, TcSigmaType)
    -- Looks for a *non-trivial* quantified type, under zero or more function arrows
    -- By "non-trivial" we mean either tyvars or constraints are non-empty

    tcDeepSplitSigmaTy_maybe ty
      | Just (arg_ty, res_ty)           <- tcSplitFunTy_maybe ty
      , Just (arg_tys, tvs, theta, rho) <- tcDeepSplitSigmaTy_maybe res_ty
      = Just (arg_ty:arg_tys, tvs, theta, rho)

      | (tvs, theta, rho) <- tcSplitSigmaTy ty
      , not (null tvs && null theta)
      = Just ([], tvs, theta, rho)

      | otherwise = Nothing

    -----------------------
    tcTyConAppTyCon :: Type -> TyCon
    tcTyConAppTyCon ty = case tcSplitTyConApp_maybe ty of
                            Just (tc, _) -> tc
                            Nothing      -> pprPanic "tcTyConAppTyCon" (pprType ty)

    tcTyConAppArgs :: Type -> [Type]
    tcTyConAppArgs ty = case tcSplitTyConApp_maybe ty of
                            Just (_, args) -> args
                            Nothing        -> pprPanic "tcTyConAppArgs" (pprType ty)

    tcSplitTyConApp :: Type -> (TyCon, [Type])
    tcSplitTyConApp ty = case tcSplitTyConApp_maybe ty of
                            Just stuff -> stuff
                            Nothing    -> pprPanic "tcSplitTyConApp" (pprType ty)

    tcSplitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty'
    tcSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
    tcSplitTyConApp_maybe (FunTy arg res)   = Just (funTyCon, [arg,res])
            -- Newtypes are opaque, so they may be split
            -- However, predicates are not treated
            -- as tycon applications by the type checker
    tcSplitTyConApp_maybe _                 = Nothing

    -----------------------
    tcSplitFunTys :: Type -> ([Type], Type)
    tcSplitFunTys ty = case tcSplitFunTy_maybe ty of
                            Nothing        -> ([], ty)
                            Just (arg,res) -> (arg:args, res')
                                           where
                                              (args,res') = tcSplitFunTys res

    tcSplitFunTy_maybe :: Type -> Maybe (Type, Type)
    tcSplitFunTy_maybe ty | Just ty' <- tcView ty           = tcSplitFunTy_maybe ty'
    tcSplitFunTy_maybe (FunTy arg res) | not (isPredTy arg) = Just (arg, res)
    tcSplitFunTy_maybe _                                    = Nothing
            -- Note the typeKind guard
            -- Consider     (?x::Int) => Bool
            -- We don't want to treat this as a function type!
            -- A concrete example is test tc230:
            --      f :: () -> (?p :: ()) => () -> ()
            --
            --      g = f () ()

    tcSplitFunTysN
            :: TcRhoType
            -> Arity                -- N: Number of desired args
            -> ([TcSigmaType],      -- Arg types (N or fewer)
                TcSigmaType)        -- The rest of the type

    tcSplitFunTysN ty n_args
      | n_args == 0
      = ([], ty)
      | Just (arg,res) <- tcSplitFunTy_maybe ty
      = case tcSplitFunTysN res (n_args - 1) of
            (args, res) -> (arg:args, res)
      | otherwise
      = ([], ty)

    tcSplitFunTy :: Type -> (Type, Type)
    tcSplitFunTy  ty = expectJust "tcSplitFunTy" (tcSplitFunTy_maybe ty)

    tcFunArgTy :: Type -> Type
    tcFunArgTy    ty = fst (tcSplitFunTy ty)

    tcFunResultTy :: Type -> Type
    tcFunResultTy ty = snd (tcSplitFunTy ty)

    -----------------------
    tcSplitAppTy_maybe :: Type -> Maybe (Type, Type)
    tcSplitAppTy_maybe ty | Just ty' <- tcView ty = tcSplitAppTy_maybe ty'
    tcSplitAppTy_maybe ty = repSplitAppTy_maybe ty

    tcSplitAppTy :: Type -> (Type, Type)
    tcSplitAppTy ty = case tcSplitAppTy_maybe ty of
                        Just stuff -> stuff
                        Nothing    -> pprPanic "tcSplitAppTy" (pprType ty)

    tcSplitAppTys :: Type -> (Type, [Type])
    tcSplitAppTys ty
      = go ty []
      where
        go ty args = case tcSplitAppTy_maybe ty of
                       Just (ty', arg) -> go ty' (arg:args)
                       Nothing         -> (ty,args)

    -----------------------
    tcGetTyVar_maybe :: Type -> Maybe TyVar
    tcGetTyVar_maybe ty | Just ty' <- tcView ty = tcGetTyVar_maybe ty'
    tcGetTyVar_maybe (TyVarTy tv)   = Just tv
    tcGetTyVar_maybe _              = Nothing

    tcGetTyVar :: String -> Type -> TyVar
    tcGetTyVar msg ty = expectJust msg (tcGetTyVar_maybe ty)

    tcIsTyVarTy :: Type -> Bool
    tcIsTyVarTy ty = maybeToBool (tcGetTyVar_maybe ty)

    -----------------------
    tcSplitDFunTy :: Type -> ([TyVar], [Type], Class, [Type])
    -- Split the type of a dictionary function
    -- We don't use tcSplitSigmaTy,  because a DFun may (with NDP)
    -- have non-Pred arguments, such as
    --     df :: forall m. (forall b. Eq b => Eq (m b)) -> C m
    --
    -- Also NB splitFunTys, not tcSplitFunTys;
    -- the latter  specifically stops at PredTy arguments,
    -- and we don't want to do that here
    tcSplitDFunTy ty
      = case tcSplitForAllTys ty   of { (tvs, rho)   ->
        case splitFunTys rho       of { (theta, tau) ->
        case tcSplitDFunHead tau   of { (clas, tys)  ->
        (tvs, theta, clas, tys) }}}

    tcSplitDFunHead :: Type -> (Class, [Type])
    tcSplitDFunHead = getClassPredTys

    tcInstHeadTyNotSynonym :: Type -> Bool
    -- Used in Haskell-98 mode, for the argument types of an instance head
    -- These must not be type synonyms, but everywhere else type synonyms
    -- are transparent, so we need a special function here
    tcInstHeadTyNotSynonym ty
      = case ty of
            TyConApp tc _ -> not (isSynTyCon tc)
            _ -> True

    tcInstHeadTyAppAllTyVars :: Type -> Bool
    -- Used in Haskell-98 mode, for the argument types of an instance head
    -- These must be a constructor applied to type variable arguments.
    -- But we allow kind instantiations.
    tcInstHeadTyAppAllTyVars ty
      | Just ty' <- tcView ty       -- Look through synonyms
      = tcInstHeadTyAppAllTyVars ty'
      | otherwise
      = case ty of
            TyConApp _ tys  -> ok (filter (not . isKind) tys)  -- avoid kinds
            FunTy arg res   -> ok [arg, res]
            _               -> False
      where
            -- Check that all the types are type variables,
            -- and that each is distinct
        ok tys = equalLength tvs tys && hasNoDups tvs
               where
                 tvs = mapCatMaybes get_tv tys

        get_tv (TyVarTy tv)  = Just tv      -- through synonyms
        get_tv _             = Nothing

\end{code} \begin{code}

    tcEqKind :: TcKind -> TcKind -> Bool
    tcEqKind = tcEqType

    tcEqType :: TcType -> TcType -> Bool
    -- tcEqType is a proper, sensible type-equality function, that does
    -- just what you'd expect The function Type.eqType (currently) has a
    -- grotesque hack that makes OpenKind = *, and that is NOT what we
    -- want in the type checker!  Otherwise, for example, TcCanonical.reOrient
    -- thinks the LHS and RHS have the same kinds, when they don't, and
    -- fails to re-orient.  That in turn caused Trac #8553.

    tcEqType ty1 ty2
      = go init_env ty1 ty2
      where
        init_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2))
        go env t1 t2 | Just t1' <- tcView t1 = go env t1' t2
                     | Just t2' <- tcView t2 = go env t1 t2'
        go env (TyVarTy tv1)       (TyVarTy tv2)     = rnOccL env tv1 == rnOccR env tv2
        go _   (LitTy lit1)        (LitTy lit2)      = lit1 == lit2
        go env (ForAllTy tv1 t1)   (ForAllTy tv2 t2) = go env (tyVarKind tv1) (tyVarKind tv2)
                                                    && go (rnBndr2 env tv1 tv2) t1 t2
        go env (AppTy s1 t1)       (AppTy s2 t2)     = go env s1 s2 && go env t1 t2
        go env (FunTy s1 t1)       (FunTy s2 t2)     = go env s1 s2 && go env t1 t2
        go env (TyConApp tc1 ts1) (TyConApp tc2 ts2) = (tc1 == tc2) && gos env ts1 ts2
        go _ _ _ = False

        gos _   []       []       = True
        gos env (t1:ts1) (t2:ts2) = go env t1 t2 && gos env ts1 ts2
        gos _ _ _ = False

    pickyEqType :: TcType -> TcType -> Bool
    -- Check when two types _look_ the same, _including_ synonyms.
    -- So (pickyEqType String [Char]) returns False
    pickyEqType ty1 ty2
      = go init_env ty1 ty2
      where
        init_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2))
        go env (TyVarTy tv1)       (TyVarTy tv2)     = rnOccL env tv1 == rnOccR env tv2
        go _   (LitTy lit1)        (LitTy lit2)      = lit1 == lit2
        go env (ForAllTy tv1 t1)   (ForAllTy tv2 t2) = go env (tyVarKind tv1) (tyVarKind tv2)
                                                    && go (rnBndr2 env tv1 tv2) t1 t2
        go env (AppTy s1 t1)       (AppTy s2 t2)     = go env s1 s2 && go env t1 t2
        go env (FunTy s1 t1)       (FunTy s2 t2)     = go env s1 s2 && go env t1 t2
        go env (TyConApp tc1 ts1) (TyConApp tc2 ts2) = (tc1 == tc2) && gos env ts1 ts2
        go _ _ _ = False

        gos _   []       []       = True
        gos env (t1:ts1) (t2:ts2) = go env t1 t2 && gos env ts1 ts2
        gos _ _ _ = False

\end{code} Note [Occurs check expansion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (occurCheckExpand tv xi) expands synonyms in xi just enough to get rid of occurrences of tv outside type function arguments, if that is possible; otherwise, it returns Nothing. For example, suppose we have type F a b = [a] Then occurCheckExpand b (F Int b) = Just [Int] but occurCheckExpand a (F a Int) = Nothing We don't promise to do the absolute minimum amount of expanding necessary, but we try not to do expansions we don't need to. We prefer doing inner expansions first. For example, type F a b = (a, Int, a, [a]) type G b = Char We have occurCheckExpand b (F (G b)) = F Char even though we could also expand F to get rid of b. See also Note [occurCheckExpand] in TcCanonical \begin{code}

    data OccCheckResult a
      = OC_OK a
      | OC_Forall
      | OC_NonTyVar
      | OC_Occurs

    instance Functor OccCheckResult where
          fmap = liftM

    instance Applicative OccCheckResult where
          pure = return
          (<*>) = ap

    instance Monad OccCheckResult where
      return x = OC_OK x
      OC_OK x     >>= k = k x
      OC_Forall   >>= _ = OC_Forall
      OC_NonTyVar >>= _ = OC_NonTyVar
      OC_Occurs   >>= _ = OC_Occurs

    occurCheckExpand :: DynFlags -> TcTyVar -> Type -> OccCheckResult Type
    -- See Note [Occurs check expansion]
    -- Check whether
    --   a) the given variable occurs in the given type.
    --   b) there is a forall in the type (unless we have -XImpredicativeTypes
    --                                     or it's a PolyTv
    --   c) if it's a SigTv, ty should be a tyvar
    --
    -- We may have needed to do some type synonym unfolding in order to
    -- get rid of the variable (or forall), so we also return the unfolded
    -- version of the type, which is guaranteed to be syntactically free
    -- of the given type variable.  If the type is already syntactically
    -- free of the variable, then the same type is returned.

    occurCheckExpand dflags tv ty
      | MetaTv { mtv_info = SigTv } <- details
                      = go_sig_tv ty
      | fast_check ty = return ty
      | otherwise     = go ty
      where
        details = ASSERT2( isTcTyVar tv, ppr tv ) tcTyVarDetails tv

        impredicative
          = case details of
              MetaTv { mtv_info = PolyTv } -> True
              MetaTv { mtv_info = SigTv }  -> False
              MetaTv { mtv_info = TauTv }  -> xopt Opt_ImpredicativeTypes dflags
                                           || isOpenTypeKind (tyVarKind tv)
                                              -- Note [OpenTypeKind accepts foralls]
                                              -- in TcUnify
              _other                       -> True
              -- We can have non-meta tyvars in given constraints

        -- Check 'ty' is a tyvar, or can be expanded into one
        go_sig_tv ty@(TyVarTy {})            = OC_OK ty
        go_sig_tv ty | Just ty' <- tcView ty = go_sig_tv ty'
        go_sig_tv _                          = OC_NonTyVar

        -- True => fine
        fast_check (LitTy {})        = True
        fast_check (TyVarTy tv')     = tv /= tv'
        fast_check (TyConApp _ tys)  = all fast_check tys
        fast_check (FunTy arg res)   = fast_check arg && fast_check res
        fast_check (AppTy fun arg)   = fast_check fun && fast_check arg
        fast_check (ForAllTy tv' ty) = impredicative
                                    && fast_check (tyVarKind tv')
                                    && (tv == tv' || fast_check ty)

        go t@(TyVarTy tv') | tv == tv' = OC_Occurs
                           | otherwise = return t
        go ty@(LitTy {}) = return ty
        go (AppTy ty1 ty2) = do { ty1' <- go ty1
                                ; ty2' <- go ty2
                                ; return (mkAppTy ty1' ty2') }
        go (FunTy ty1 ty2) = do { ty1' <- go ty1
                                ; ty2' <- go ty2
                                ; return (mkFunTy ty1' ty2') }
        go ty@(ForAllTy tv' body_ty)
           | not impredicative                = OC_Forall
           | not (fast_check (tyVarKind tv')) = OC_Occurs
               -- Can't expand away the kinds unless we create
               -- fresh variables which we don't want to do at this point.
               -- In principle fast_check might fail because of a for-all
               -- but we don't yet have poly-kinded tyvars so I'm not
               -- going to worry about that now
           | tv == tv' = return ty
           | otherwise = do { body' <- go body_ty
                            ; return (ForAllTy tv' body') }

        -- For a type constructor application, first try expanding away the
        -- offending variable from the arguments.  If that doesn't work, next
        -- see if the type constructor is a type synonym, and if so, expand
        -- it and try again.
        go ty@(TyConApp tc tys)
          = case do { tys <- mapM go tys; return (mkTyConApp tc tys) } of
              OC_OK ty -> return ty  -- First try to eliminate the tyvar from the args
              bad | Just ty' <- tcView ty -> go ty'
                  | otherwise             -> bad
                          -- Failing that, try to expand a synonym

\end{code} %************************************************************************ %* * \subsection{Predicate types} %* * %************************************************************************ Deconstructors and tests on predicate types \begin{code}

    isTyVarClassPred :: PredType -> Bool
    isTyVarClassPred ty = case getClassPredTys_maybe ty of
        Just (_, tys) -> all isTyVarTy tys
        _             -> False

    evVarPred_maybe :: EvVar -> Maybe PredType
    evVarPred_maybe v = if isPredTy ty then Just ty else Nothing
      where ty = varType v

    evVarPred :: EvVar -> PredType
    evVarPred var
     | debugIsOn
      = case evVarPred_maybe var of
          Just pred -> pred
          Nothing   -> pprPanic "tcEvVarPred" (ppr var <+> ppr (varType var))
     | otherwise
      = varType var

\end{code} Superclasses \begin{code}

    mkMinimalBySCs :: [PredType] -> [PredType]
    -- Remove predicates that can be deduced from others by superclasses
    mkMinimalBySCs ptys = [ ploc |  ploc <- ptys
                                 ,  ploc `not_in_preds` rec_scs ]
     where
       rec_scs = concatMap trans_super_classes ptys
       not_in_preds p ps = not (any (eqPred p) ps)

       trans_super_classes pred   -- Superclasses of pred, excluding pred itself
         = case classifyPredType pred of
             ClassPred cls tys -> transSuperClasses cls tys
             TuplePred ts      -> concatMap trans_super_classes ts
             _                 -> []

    transSuperClasses :: Class -> [Type] -> [PredType]
    transSuperClasses cls tys    -- Superclasses of (cls tys),
                                 -- excluding (cls tys) itself
      = concatMap trans_sc (immSuperClasses cls tys)
      where
        trans_sc :: PredType -> [PredType]
        -- (trans_sc p) returns (p : p's superclasses)
        trans_sc p = case classifyPredType p of
                       ClassPred cls tys -> p : transSuperClasses cls tys
                       TuplePred ps      -> concatMap trans_sc ps
                       _                 -> [p]

    immSuperClasses :: Class -> [Type] -> [PredType]
    immSuperClasses cls tys
      = substTheta (zipTopTvSubst tyvars tys) sc_theta
      where
        (tyvars,sc_theta,_,_) = classBigSig cls

\end{code} %************************************************************************ %* * \subsection{Predicates} %* * %************************************************************************ isSigmaTy returns true of any qualified type. It doesn't *necessarily* have any foralls. E.g. f :: (?x::Int) => Int -> Int \begin{code}

    isSigmaTy :: Type -> Bool
    isSigmaTy ty | Just ty' <- tcView ty = isSigmaTy ty'
    isSigmaTy (ForAllTy _ _) = True
    isSigmaTy (FunTy a _)    = isPredTy a
    isSigmaTy _              = False

    isOverloadedTy :: Type -> Bool
    -- Yes for a type of a function that might require evidence-passing
    -- Used only by bindLocalMethods
    isOverloadedTy ty | Just ty' <- tcView ty = isOverloadedTy ty'
    isOverloadedTy (ForAllTy _ ty) = isOverloadedTy ty
    isOverloadedTy (FunTy a _)     = isPredTy a
    isOverloadedTy _               = False

\end{code} \begin{code}

    isFloatTy, isDoubleTy, isIntegerTy, isIntTy, isWordTy, isBoolTy,
        isUnitTy, isCharTy, isAnyTy :: Type -> Bool
    isFloatTy      = is_tc floatTyConKey
    isDoubleTy     = is_tc doubleTyConKey
    isIntegerTy    = is_tc integerTyConKey
    isIntTy        = is_tc intTyConKey
    isWordTy       = is_tc wordTyConKey
    isBoolTy       = is_tc boolTyConKey
    isUnitTy       = is_tc unitTyConKey
    isCharTy       = is_tc charTyConKey
    isAnyTy        = is_tc anyTyConKey

    isStringTy :: Type -> Bool
    isStringTy ty
      = case tcSplitTyConApp_maybe ty of
          Just (tc, [arg_ty]) -> tc == listTyCon && isCharTy arg_ty
          _                   -> False

    is_tc :: Unique -> Type -> Bool
    -- Newtypes are opaque to this
    is_tc uniq ty = case tcSplitTyConApp_maybe ty of
                            Just (tc, _) -> uniq == getUnique tc
                            Nothing      -> False

\end{code} \begin{code}

    -- NB: Currently used in places where we have already expanded type synonyms;
    --     hence no 'coreView'.  This could, however, be changed without breaking
    --     any code.
    isSynFamilyTyConApp :: TcTauType -> Bool
    isSynFamilyTyConApp (TyConApp tc tys) = isSynFamilyTyCon tc &&
                                          length tys == tyConArity tc
    isSynFamilyTyConApp _other            = False

\end{code} %************************************************************************ %* * \subsection{Misc} %* * %************************************************************************ \begin{code}

    deNoteType :: Type -> Type
    -- Remove all *outermost* type synonyms and other notes
    deNoteType ty | Just ty' <- tcView ty = deNoteType ty'
    deNoteType ty = ty

    tcTyVarsOfType :: Type -> TcTyVarSet
    -- Just the *TcTyVars* free in the type
    -- (Types.tyVarsOfTypes finds all free TyVars)
    tcTyVarsOfType (TyVarTy tv)         = if isTcTyVar tv then unitVarSet tv
                                                          else emptyVarSet
    tcTyVarsOfType (TyConApp _ tys)     = tcTyVarsOfTypes tys
    tcTyVarsOfType (LitTy {})           = emptyVarSet
    tcTyVarsOfType (FunTy arg res)      = tcTyVarsOfType arg `unionVarSet` tcTyVarsOfType res
    tcTyVarsOfType (AppTy fun arg)      = tcTyVarsOfType fun `unionVarSet` tcTyVarsOfType arg
    tcTyVarsOfType (ForAllTy tyvar ty)  = tcTyVarsOfType ty `delVarSet` tyvar
            -- We do sometimes quantify over skolem TcTyVars

    tcTyVarsOfTypes :: [Type] -> TyVarSet
    tcTyVarsOfTypes tys = foldr (unionVarSet.tcTyVarsOfType) emptyVarSet tys

\end{code} Find the free tycons and classes of a type. This is used in the front end of the compiler. \begin{code}

    orphNamesOfTyCon :: TyCon -> NameSet
    orphNamesOfTyCon tycon = unitNameSet (getName tycon) `unionNameSets` case tyConClass_maybe tycon of
        Nothing  -> emptyNameSet
        Just cls -> unitNameSet (getName cls)

    orphNamesOfType :: Type -> NameSet
    orphNamesOfType ty | Just ty' <- tcView ty = orphNamesOfType ty'
                    -- Look through type synonyms (Trac #4912)
    orphNamesOfType (TyVarTy _)          = emptyNameSet
    orphNamesOfType (LitTy {})           = emptyNameSet
    orphNamesOfType (TyConApp tycon tys) = orphNamesOfTyCon tycon
                                           `unionNameSets` orphNamesOfTypes tys
    orphNamesOfType (FunTy arg res)      = orphNamesOfTyCon funTyCon   -- NB!  See Trac #8535
                                           `unionNameSets` orphNamesOfType arg
                                           `unionNameSets` orphNamesOfType res
    orphNamesOfType (AppTy fun arg)      = orphNamesOfType fun `unionNameSets` orphNamesOfType arg
    orphNamesOfType (ForAllTy _ ty)      = orphNamesOfType ty

    orphNamesOfThings :: (a -> NameSet) -> [a] -> NameSet
    orphNamesOfThings f = foldr (unionNameSets . f) emptyNameSet

    orphNamesOfTypes :: [Type] -> NameSet
    orphNamesOfTypes = orphNamesOfThings orphNamesOfType

    orphNamesOfDFunHead :: Type -> NameSet
    -- Find the free type constructors and classes
    -- of the head of the dfun instance type
    -- The 'dfun_head_type' is because of
    --      instance Foo a => Baz T where ...
    -- The decl is an orphan if Baz and T are both not locally defined,
    --      even if Foo *is* locally defined
    orphNamesOfDFunHead dfun_ty
      = case tcSplitSigmaTy dfun_ty of
            (_, _, head_ty) -> orphNamesOfType head_ty

    orphNamesOfCo :: Coercion -> NameSet
    orphNamesOfCo (Refl _ ty)           = orphNamesOfType ty
    orphNamesOfCo (TyConAppCo _ tc cos) = unitNameSet (getName tc) `unionNameSets` orphNamesOfCos cos
    orphNamesOfCo (AppCo co1 co2)       = orphNamesOfCo co1 `unionNameSets` orphNamesOfCo co2
    orphNamesOfCo (ForAllCo _ co)       = orphNamesOfCo co
    orphNamesOfCo (CoVarCo _)           = emptyNameSet
    orphNamesOfCo (AxiomInstCo con _ cos) = orphNamesOfCoCon con `unionNameSets` orphNamesOfCos cos
    orphNamesOfCo (UnivCo _ ty1 ty2)    = orphNamesOfType ty1 `unionNameSets` orphNamesOfType ty2
    orphNamesOfCo (SymCo co)            = orphNamesOfCo co
    orphNamesOfCo (TransCo co1 co2)     = orphNamesOfCo co1 `unionNameSets` orphNamesOfCo co2
    orphNamesOfCo (NthCo _ co)          = orphNamesOfCo co
    orphNamesOfCo (LRCo  _ co)          = orphNamesOfCo co
    orphNamesOfCo (InstCo co ty)        = orphNamesOfCo co `unionNameSets` orphNamesOfType ty
    orphNamesOfCo (SubCo co)            = orphNamesOfCo co
    orphNamesOfCo (AxiomRuleCo _ ts cs) = orphNamesOfTypes ts `unionNameSets`
                                          orphNamesOfCos cs

    orphNamesOfCos :: [Coercion] -> NameSet
    orphNamesOfCos = orphNamesOfThings orphNamesOfCo

    orphNamesOfCoCon :: CoAxiom br -> NameSet
    orphNamesOfCoCon (CoAxiom { co_ax_tc = tc, co_ax_branches = branches })
      = orphNamesOfTyCon tc `unionNameSets` orphNamesOfCoAxBranches branches

    orphNamesOfCoAxBranches :: BranchList CoAxBranch br -> NameSet
    orphNamesOfCoAxBranches = brListFoldr (unionNameSets . orphNamesOfCoAxBranch) emptyNameSet

    orphNamesOfCoAxBranch :: CoAxBranch -> NameSet
    orphNamesOfCoAxBranch (CoAxBranch { cab_lhs = lhs, cab_rhs = rhs })
      = orphNamesOfTypes lhs `unionNameSets` orphNamesOfType rhs

\end{code} %************************************************************************ %* * \subsection[TysWiredIn-ext-type]{External types} %* * %************************************************************************ The compiler's foreign function interface supports the passing of a restricted set of types as arguments and results (the restricting factor being the ) \begin{code}

    tcSplitIOType_maybe :: Type -> Maybe (TyCon, Type)
    -- (tcSplitIOType_maybe t) returns Just (IO,t',co)
    --              if co : t ~ IO t'
    --              returns Nothing otherwise
    tcSplitIOType_maybe ty
      = case tcSplitTyConApp_maybe ty of
            Just (io_tycon, [io_res_ty])
             | io_tycon `hasKey` ioTyConKey ->
                Just (io_tycon, io_res_ty)
            _ ->
                Nothing

    isFFITy :: Type -> Bool
    -- True for any TyCon that can possibly be an arg or result of an FFI call
    isFFITy ty = checkRepTyCon legalFFITyCon ty

    isFFIArgumentTy :: DynFlags -> Safety -> Type -> Bool
    -- Checks for valid argument type for a 'foreign import'
    isFFIArgumentTy dflags safety ty
       = checkRepTyCon (legalOutgoingTyCon dflags safety) ty

    isFFIExternalTy :: Type -> Bool
    -- Types that are allowed as arguments of a 'foreign export'
    isFFIExternalTy ty = checkRepTyCon legalFEArgTyCon ty

    isFFIImportResultTy :: DynFlags -> Type -> Bool
    isFFIImportResultTy dflags ty
      = checkRepTyCon (legalFIResultTyCon dflags) ty

    isFFIExportResultTy :: Type -> Bool
    isFFIExportResultTy ty = checkRepTyCon legalFEResultTyCon ty

    isFFIDynTy :: Type -> Type -> Bool
    -- The type in a foreign import dynamic must be Ptr, FunPtr, or a newtype of
    -- either, and the wrapped function type must be equal to the given type.
    -- We assume that all types have been run through normalizeFfiType, so we don't
    -- need to worry about expanding newtypes here.
    isFFIDynTy expected ty
        -- Note [Foreign import dynamic]
        -- In the example below, expected would be 'CInt -> IO ()', while ty would
        -- be 'FunPtr (CDouble -> IO ())'.
        | Just (tc, [ty']) <- splitTyConApp_maybe ty
        , tyConUnique tc `elem` [ptrTyConKey, funPtrTyConKey]
        , eqType ty' expected
        = True
        | otherwise
        = False

    isFFILabelTy :: Type -> Bool
    -- The type of a foreign label must be Ptr, FunPtr, or a newtype of either.
    isFFILabelTy = checkRepTyConKey [ptrTyConKey, funPtrTyConKey]

    isFFIPrimArgumentTy :: DynFlags -> Type -> Bool
    -- Checks for valid argument type for a 'foreign import prim'
    -- Currently they must all be simple unlifted types, or the well-known type
    -- Any, which can be used to pass the address to a Haskell object on the heap to
    -- the foreign function.
    isFFIPrimArgumentTy dflags ty
       = isAnyTy ty || checkRepTyCon (legalFIPrimArgTyCon dflags) ty

    isFFIPrimResultTy :: DynFlags -> Type -> Bool
    -- Checks for valid result type for a 'foreign import prim'
    -- Currently it must be an unlifted type, including unboxed tuples.
    isFFIPrimResultTy dflags ty
       = checkRepTyCon (legalFIPrimResultTyCon dflags) ty

    isFFIDotnetTy :: DynFlags -> Type -> Bool
    isFFIDotnetTy dflags ty
      = checkRepTyCon (\ tc -> (legalFIResultTyCon dflags tc ||
                               isFFIDotnetObjTy ty || isStringTy ty)) ty
            -- NB: isStringTy used to look through newtypes, but
            --     it no longer does so.  May need to adjust isFFIDotNetTy
            --     if we do want to look through newtypes.

    isFFIDotnetObjTy :: Type -> Bool
    isFFIDotnetObjTy ty
      = checkRepTyCon check_tc t_ty
      where
       (_, t_ty) = tcSplitForAllTys ty
       check_tc tc = getName tc == objectTyConName

    isFunPtrTy :: Type -> Bool
    isFunPtrTy = checkRepTyConKey [funPtrTyConKey]

    -- normaliseFfiType gets run before checkRepTyCon, so we don't
    -- need to worry about looking through newtypes or type functions
    -- here; that's already been taken care of.
    checkRepTyCon :: (TyCon -> Bool) -> Type -> Bool
    checkRepTyCon check_tc ty
        | Just (tc, _) <- splitTyConApp_maybe ty
        = check_tc tc
        | otherwise
        = False

    checkRepTyConKey :: [Unique] -> Type -> Bool
    -- Like checkRepTyCon, but just looks at the TyCon key
    checkRepTyConKey keys
      = checkRepTyCon (\tc -> tyConUnique tc `elem` keys)

\end{code} Note [Foreign import dynamic] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A dynamic stub must be of the form 'FunPtr ft -> ft' where ft is any foreign type. Similarly, a wrapper stub must be of the form 'ft -> IO (FunPtr ft)'. We use isFFIDynTy to check whether a signature is well-formed. For example, given a (illegal) declaration like: foreign import ccall "dynamic" foo :: FunPtr (CDouble -> IO ()) -> CInt -> IO () isFFIDynTy will compare the 'FunPtr' type 'CDouble -> IO ()' with the curried result type 'CInt -> IO ()', and return False, as they are not equal. ---------------------------------------------- These chaps do the work; they are not exported ---------------------------------------------- \begin{code}

    legalFEArgTyCon :: TyCon -> Bool
    legalFEArgTyCon tc
      -- It's illegal to make foreign exports that take unboxed
      -- arguments.  The RTS API currently can't invoke such things.  --SDM 7/2000
      = boxedMarshalableTyCon tc

    legalFIResultTyCon :: DynFlags -> TyCon -> Bool
    legalFIResultTyCon dflags tc
      | tc == unitTyCon         = True
      | otherwise               = marshalableTyCon dflags tc

    legalFEResultTyCon :: TyCon -> Bool
    legalFEResultTyCon tc
      | tc == unitTyCon         = True
      | otherwise               = boxedMarshalableTyCon tc

    legalOutgoingTyCon :: DynFlags -> Safety -> TyCon -> Bool
    -- Checks validity of types going from Haskell -> external world
    legalOutgoingTyCon dflags _ tc
      = marshalableTyCon dflags tc

    legalFFITyCon :: TyCon -> Bool
    -- True for any TyCon that can possibly be an arg or result of an FFI call
    legalFFITyCon tc
      = isUnLiftedTyCon tc || boxedMarshalableTyCon tc || tc == unitTyCon

    marshalableTyCon :: DynFlags -> TyCon -> Bool
    marshalableTyCon dflags tc
      =  (xopt Opt_UnliftedFFITypes dflags
          && isUnLiftedTyCon tc
          && not (isUnboxedTupleTyCon tc)
          && case tyConPrimRep tc of        -- Note [Marshalling VoidRep]
               VoidRep -> False
               _       -> True)
      || boxedMarshalableTyCon tc

    boxedMarshalableTyCon :: TyCon -> Bool
    boxedMarshalableTyCon tc
       = getUnique tc `elem` [ intTyConKey, int8TyConKey, int16TyConKey
                             , int32TyConKey, int64TyConKey
                             , wordTyConKey, word8TyConKey, word16TyConKey
                             , word32TyConKey, word64TyConKey
                             , floatTyConKey, doubleTyConKey
                             , ptrTyConKey, funPtrTyConKey
                             , charTyConKey
                             , stablePtrTyConKey
                             , boolTyConKey
                             ]

    legalFIPrimArgTyCon :: DynFlags -> TyCon -> Bool
    -- Check args of 'foreign import prim', only allow simple unlifted types.
    -- Strictly speaking it is unnecessary to ban unboxed tuples here since
    -- currently they're of the wrong kind to use in function args anyway.
    legalFIPrimArgTyCon dflags tc
      = xopt Opt_UnliftedFFITypes dflags
        && isUnLiftedTyCon tc
        && not (isUnboxedTupleTyCon tc)

    legalFIPrimResultTyCon :: DynFlags -> TyCon -> Bool
    -- Check result type of 'foreign import prim'. Allow simple unlifted
    -- types and also unboxed tuple result types '... -> (# , , #)'
    legalFIPrimResultTyCon dflags tc
      = xopt Opt_UnliftedFFITypes dflags
        && isUnLiftedTyCon tc
        && (isUnboxedTupleTyCon tc
            || case tyConPrimRep tc of      -- Note [Marshalling VoidRep]
               VoidRep -> False
               _       -> True)

\end{code} Note [Marshalling VoidRep] ~~~~~~~~~~~~~~~~~~~~~~~~~~ We don't treat State# (whose PrimRep is VoidRep) as marshalable. In turn that means you can't write foreign import foo :: Int -> State# RealWorld Reason: the back end falls over with panic "primRepHint:VoidRep"; and there is no compelling reason to permit it