content: {-
  (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.
  -}
  
  {-# LANGUAGE CPP #-}
  
  module Eta.TypeCheck.TcType (
    --------------------------------
    -- Types
    TcType, TcSigmaType, TcRhoType, TcTauType, TcPredType, TcThetaType,
    TcTyVar, TcTyVarSet, TcKind, TcCoVar,
  
    -- TcLevel
    TcLevel(..), topTcLevel, pushTcLevel,
    strictlyDeeperThan, sameDepthAs, fskTcLevel,
  
    --------------------------------
    -- MetaDetails
    UserTypeCtxt(..), pprUserTypeCtxt, pprSigCtxt,
    TcTyVarDetails(..), pprTcTyVarDetails, vanillaSkolemTv, superSkolemTv,
    MetaDetails(Flexi, Indirect), MetaInfo(..),
    isImmutableTyVar, isSkolemTyVar, isMetaTyVar,  isMetaTyVarTy, isTyVarTy,
    isSigTyVar, isOverlappableTyVar,  isTyConableTyVar,
    isFskTyVar, isFmvTyVar, isFlattenTyVar, isReturnTyVar,
    isAmbiguousTyVar, metaTvRef, metaTyVarInfo,
    isFlexi, isIndirect, isRuntimeUnkSkol,
    isTypeVar, isKindVar,
    metaTyVarTcLevel, setMetaTyVarTcLevel, metaTyVarTcLevel_maybe,
    isTouchableMetaTyVar, isTouchableOrFmv,
    isFloatedTouchableMetaTyVar,
    canUnifyWithPolyType,
  
    --------------------------------
    -- Builders
    mkPhiTy, mkSigmaTy, mkTcEqPred, mkTcReprEqPred, mkTcEqPredRole,
  
    --------------------------------
    -- 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, nextRole,
    tcSplitSigmaTy, tcDeepSplitSigmaTy_maybe,
  
    ---------------------------------
    -- Predicates.
    -- Again, newtypes are opaque
    eqType, eqTypes, eqPred, cmpType, cmpTypes, cmpPred, eqTypeX,
    pickyEqType, tcEqType, tcEqKind,
    isSigmaTy, isRhoTy, isOverloadedTy,
    isFloatingTy, isDoubleTy, isFloatTy, isIntTy, isWordTy, isStringTy,
    isIntegerTy, isBoolTy, isUnitTy, isCharTy, isCallStackTy, isCallStackPred,
    isTauTy, isTauTyCon, tcIsTyVarTy, tcIsForAllTy,
    isPredTy, isTyVarClassPred, isTyVarExposed, isTyVarUnderDatatype,
  
    ---------------------------------
    -- 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
    --isFFITy,             -- :: Type -> Bool
    isFunPtrTy,          -- :: Type -> Bool
    tcSplitIOType_maybe, -- :: Type -> Maybe Type
    tcSplitJavaType_maybe, -- :: Type -> Maybe Type
    tcSplitExtendsType_maybe, -- :: Type -> Maybe Type
    tcSplitExtendsType, -- :: Type -> Maybe Type
    extendsVars,
  
    --------------------------------
    -- 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,
    tyVarsOfTypeList, tyVarsOfTypesList,
    tcTyVarsOfType, tcTyVarsOfTypes,
  
    --------------------------------
    -- Transforming Types to TcTypes
    toTcType,    -- :: Type -> TcType
    toTcTyVar,   -- :: TyVar -> TcTyVar
    toTcTypeBag, -- :: Bag EvVar -> Bag EvVar
  
  
    pprKind, pprParendKind, pprSigmaType,
    pprType, pprParendType, pprTypeApp, pprTyThingCategory,
    pprTheta, pprThetaArrowTy, pprClassPred
  
    ) where
  
  #include "HsVersions.h"
  
  -- friends:
  import Eta.Types.Kind
  import Eta.Types.TypeRep
  import Eta.Types.Class
  import Eta.BasicTypes.Var
  import Eta.Prelude.ForeignCall
  import Eta.BasicTypes.VarSet
  import Eta.Types.Coercion
  import Eta.Types.Type
  import qualified Eta.Types.Type as Type
  import Eta.Types.TyCon
  import Eta.Types.CoAxiom
  import Eta.Utils.Bag
  -- others:
  import Eta.Main.DynFlags
  import Eta.BasicTypes.Name
  import qualified Eta.BasicTypes.Name as Name
    -- hiding (varName)
    -- We use this to make dictionaries for type literals.
    -- Perhaps there's a better way to do this?
  import Eta.BasicTypes.NameSet
  import Eta.BasicTypes.VarEnv
  import Eta.BasicTypes.DataCon
  import Eta.Prelude.PrelNames
  import Eta.Prelude.TysWiredIn
  import Eta.BasicTypes.BasicTypes
  import Eta.Utils.Util
  import Eta.Utils.Maybes
  import Eta.Utils.ListSetOps
  import Eta.Utils.Outputable
  import Eta.Utils.FastString
  import Eta.Main.ErrUtils( Validity(..), isValid )
  import Data.IORef
  import Control.Monad (liftM, ap)
  import qualified Eta.LanguageExtensions as LangExt
  
  {-
  ************************************************************************
  *                                                                      *
  \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.
  -}
  
  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  -- Note [TcRhoType]
  type TcTauType      = TcType
  type TcKind         = Kind
  type TcTyVarSet     = TyVarSet
  
  {-
  Note [TcRhoType]
  ~~~~~~~~~~~~~~~~
  A TcRhoType has no foralls or contexts at the top, or to the right of an arrow
    YES    (forall a. a->a) -> Int
    NO     forall a. a ->  Int
    NO     Eq a => a -> a
    NO     Int -> forall a. a -> Int
  
  
  ************************************************************************
  *                                                                      *
  \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.
  
  Note [ReturnTv]
  ~~~~~~~~~~~~~~~
  We sometimes want to convert a checking algorithm into an inference
  algorithm. An easy way to do this is to "check" that a term has a
  metavariable as a type. But, we must be careful to allow that metavariable
  to unify with *anything*. (Well, anything that doesn't fail an occurs-check.)
  This is what ReturnTv means.
  
  For example, if we have
  
    (undefined :: (forall a. TF1 a ~ TF2 a => a)) x
  
  we'll call (tcInfer . tcExpr) on the function expression. tcInfer will
  create a ReturnTv to represent the expression's type. We really need this
  ReturnTv to become set to (forall a. TF1 a ~ TF2 a => a) despite the fact
  that this type mentions type families and is a polytype.
  
  However, we must also be careful to make sure that the ReturnTvs really
  always do get unified with something -- we don't want these floating
  around in the solver. So, we check after running the checker to make
  sure the ReturnTv is filled. If it's not, we set it to a TauTv.
  
  We can't ASSERT that no ReturnTvs hit the solver, because they
  can if there's, say, a kind error that stops checkTauTvUpdate from
  working. This happens in test case typecheck/should_fail/T5570, for
  example.
  
  See also the commentary on #9404.
  -}
  
  -- 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
  
    | FlatSkol      -- A flatten-skolem.  It stands for the TcType, and zonking
         TcType     -- will replace it by that type.
                    -- See Note [The flattening story] in TcFlatten
  
    | RuntimeUnk    -- Stands for an as-yet-unknown type in the GHCi
                    -- interactive context
  
    | MetaTv { mtv_info  :: MetaInfo
             , mtv_ref   :: IORef MetaDetails
             , mtv_tclvl :: TcLevel }  -- See Note [TcLevel and 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 Bool    -- This MetaTv is an ordinary unification variable
                     -- A TauTv is always filled in with a tau-type, which
                     -- never contains any ForAlls.
                     -- The boolean is true when the meta var originates
                     -- from a wildcard.
  
     | ReturnTv      -- Can unify with *anything*. Used to convert a
                     -- type "checking" algorithm into a type inference algorithm.
                     -- See Note [ReturnTv]
  
     | 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
  
     | FlatMetaTv    -- A flatten meta-tyvar
                     -- It is a meta-tyvar, but it is always untouchable, with level 0
                     -- See Note [The flattening story] in TcFlatten
  
  -------------------------------------
  -- 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
    | PatSigCtxt          -- Type sig in pattern
                          --   eg  f (x::t) = ...
                          --   or  (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
  
  {-
  -- 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
  *                                                                      *
  ************************************************************************
  -}
  
  newtype TcLevel = TcLevel Int deriving( Eq )
    -- See Note [TcLevel and untouchable type variables] for what this Int is
  
  {-
  Note [TcLevel and untouchable type variables]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  * Each unification variable (MetaTv)
    and each Implication
    has a level number (of type TcLevel)
  
  * 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_tclvl of the implication
  
  
  Note [Skolem escape prevention]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We only unify touchable unification variables.  Because of
  (MetaTvInv), there can be no occurrences of the variable further out,
  so the unification can't cause the skolems 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 solveSimpleWanteds 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 zonking stage and
  uf will get unified *once more* to (F Int).
  -}
  
  fskTcLevel :: TcLevel
  fskTcLevel = TcLevel 0  -- 0 = Outside the outermost level:
                                    --     flatten skolems
  
  topTcLevel :: TcLevel
  topTcLevel = TcLevel 1   -- 1 = outermost level
  
  pushTcLevel :: TcLevel -> TcLevel
  pushTcLevel (TcLevel us) = TcLevel (us+1)
  
  strictlyDeeperThan :: TcLevel -> TcLevel -> Bool
  strictlyDeeperThan (TcLevel tv_tclvl) (TcLevel ctxt_tclvl)
    = tv_tclvl > ctxt_tclvl
  
  sameDepthAs :: TcLevel -> TcLevel -> Bool
  sameDepthAs (TcLevel ctxt_tclvl) (TcLevel tv_tclvl)
    = ctxt_tclvl == tv_tclvl   -- NB: invariant ctxt_tclvl >= tv_tclvl
                               --     So <= would be equivalent
  
  checkTcLevelInvariant :: TcLevel -> TcLevel -> Bool
  -- Checks (MetaTvInv) from Note [TcLevel and untouchable type variables]
  checkTcLevelInvariant (TcLevel ctxt_tclvl) (TcLevel tv_tclvl)
    = ctxt_tclvl >= tv_tclvl
  
  instance Outputable TcLevel where
    ppr (TcLevel us) = ppr us
  
  {-
  ************************************************************************
  *                                                                      *
                  Pretty-printing
  *                                                                      *
  ************************************************************************
  -}
  
  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_tclvl = tclvl })
    = pp_info <> colon <> ppr tclvl
    where
      pp_info = case info of
                  ReturnTv    -> ptext (sLit "ret")
                  TauTv True  -> ptext (sLit "twc")
                  TauTv False -> ptext (sLit "tau")
                  SigTv       -> ptext (sLit "sig")
                  FlatMetaTv  -> ptext (sLit "fuv")
  
  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 PatSigCtxt        = 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 Eta REPL 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)
  
  pprSigCtxt :: UserTypeCtxt -> SDoc -> SDoc -> SDoc
  -- (pprSigCtxt ctxt <extra> <type>)
  -- prints    In <extra> the type signature for 'f':
  --              f :: <type>
  -- The <extra> is either empty or "the ambiguity check for"
  pprSigCtxt ctxt extra pp_ty
    = sep [ ptext (sLit "In") <+> extra <+> pprUserTypeCtxt ctxt <> colon
          , nest 2 (pp_sig ctxt) ]
    where
      pp_sig (FunSigCtxt n)  = pp_n_colon n
      pp_sig (ConArgCtxt n)  = pp_n_colon n
      pp_sig (ForSigCtxt n)  = pp_n_colon n
      pp_sig _               = pp_ty
  
      pp_n_colon n = pprPrefixOcc n <+> dcolon <+> pp_ty
  
  {-
  ************************************************************************
  *                  *
      Finding type family instances
  *                  *
  ************************************************************************
  -}
  
  -- | 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)
    | isTypeFamilyTyCon 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
  
  {-
  ************************************************************************
  *                  *
            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.
  -}
  
  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 = mapUnionVarSet exactTyVarsOfType
  
  {-
  ************************************************************************
  *                                                                      *
                  Predicates
  *                                                                      *
  ************************************************************************
  -}
  
  isTouchableOrFmv :: TcLevel -> TcTyVar -> Bool
  isTouchableOrFmv ctxt_tclvl tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_tclvl = tv_tclvl, mtv_info = info }
          -> ASSERT2( checkTcLevelInvariant ctxt_tclvl tv_tclvl,
                      ppr tv $$ ppr tv_tclvl $$ ppr ctxt_tclvl )
             case info of
               FlatMetaTv -> True
               _          -> tv_tclvl `sameDepthAs` ctxt_tclvl
        _          -> False
  
  isTouchableMetaTyVar :: TcLevel -> TcTyVar -> Bool
  isTouchableMetaTyVar ctxt_tclvl tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_tclvl = tv_tclvl }
          -> ASSERT2( checkTcLevelInvariant ctxt_tclvl tv_tclvl,
                      ppr tv $$ ppr tv_tclvl $$ ppr ctxt_tclvl )
             tv_tclvl `sameDepthAs` ctxt_tclvl
        _ -> False
  
  isFloatedTouchableMetaTyVar :: TcLevel -> TcTyVar -> Bool
  isFloatedTouchableMetaTyVar ctxt_tclvl tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_tclvl = tv_tclvl } -> tv_tclvl `strictlyDeeperThan` ctxt_tclvl
        _ -> False
  
  isImmutableTyVar :: TyVar -> Bool
  isImmutableTyVar tv
    | isTcTyVar tv = isSkolemTyVar tv
    | otherwise    = True
  
  isTyConableTyVar, isSkolemTyVar, isOverlappableTyVar,
    isMetaTyVar, isAmbiguousTyVar,
    isFmvTyVar, isFskTyVar, isFlattenTyVar, isReturnTyVar :: 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
  
  isFmvTyVar tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
          MetaTv { mtv_info = FlatMetaTv } -> True
          _                                -> False
  
  -- | True of both given and wanted flatten-skolems (fak and usk)
  isFlattenTyVar tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
          FlatSkol {}                      -> True
          MetaTv { mtv_info = FlatMetaTv } -> True
          _                                -> False
  
  -- | True of FlatSkol skolems only
  isFskTyVar tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
          FlatSkol {} -> True
          _           -> False
  
  isSkolemTyVar tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
          MetaTv {} -> False
          _other    -> True
  
  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
  
  isReturnTyVar tv
    = ASSERT2( isTcTyVar tv, ppr tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_info = ReturnTv } -> 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)
  
  metaTyVarTcLevel :: TcTyVar -> TcLevel
  metaTyVarTcLevel tv
    = ASSERT( isTcTyVar tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_tclvl = tclvl } -> tclvl
        _ -> pprPanic "metaTyVarTcLevel" (ppr tv)
  
  metaTyVarTcLevel_maybe :: TcTyVar -> Maybe TcLevel
  metaTyVarTcLevel_maybe tv
    = ASSERT( isTcTyVar tv )
      case tcTyVarDetails tv of
        MetaTv { mtv_tclvl = tclvl } -> Just tclvl
        _                            -> Nothing
  
  setMetaTyVarTcLevel :: TcTyVar -> TcLevel -> TcTyVar
  setMetaTyVarTcLevel tv tclvl
    = ASSERT( isTcTyVar tv )
      case tcTyVarDetails tv of
        details@(MetaTv {}) -> setTcTyVarDetails tv (details { mtv_tclvl = tclvl })
        _ -> pprPanic "metaTyVarTcLevel" (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
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Tau, sigma and rho}
  *                                                                      *
  ************************************************************************
  -}
  
  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 = typeKind ty1
  
  -- | Make a representational equality predicate
  mkTcReprEqPred :: TcType -> TcType -> Type
  mkTcReprEqPred ty1 ty2
    = mkTyConApp coercibleTyCon [k, ty1, ty2]
    where
      k = typeKind ty1
  
  -- | Make an equality predicate at a given role. The role must not be Phantom.
  mkTcEqPredRole :: Role -> TcType -> TcType -> Type
  mkTcEqPredRole Nominal          = mkTcEqPred
  mkTcEqPredRole Representational = mkTcReprEqPred
  mkTcEqPredRole Phantom          = panic "mkTcEqPredRole Phantom"
  
  -- @isTauTy@ tests for nested for-alls.  It should not be called on a boxy type.
  
  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
  
  {-
  ************************************************************************
  *                                                                      *
  \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.
  -}
  
  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 = isJust (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 (isTypeSynonymTyCon 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 = mapMaybe get_tv tys
  
      get_tv (TyVarTy tv)  = Just tv      -- through synonyms
      get_tv _             = Nothing
  
  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
  
  {-
  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
  -}
  
  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 ReturnTv
  --   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 = canUnifyWithPolyType dflags details (tyVarKind tv)
  
      -- 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
  
  canUnifyWithPolyType :: DynFlags -> TcTyVarDetails -> TcKind -> Bool
  canUnifyWithPolyType dflags details kind
    = case details of
        MetaTv { mtv_info = ReturnTv } -> True      -- See Note [ReturnTv]
        MetaTv { mtv_info = SigTv }    -> False
        MetaTv { mtv_info = TauTv _ }  -> xopt LangExt.ImpredicativeTypes dflags
                                       || isOpenTypeKind kind
                                            -- Note [OpenTypeKind accepts foralls]
        _other                         -> True
            -- We can have non-meta tyvars in given constraints
  
  {-
  Note [OpenTypeKind accepts foralls]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Here is a common paradigm:
     foo :: (forall a. a -> a) -> Int
     foo = error "urk"
  To make this work we need to instantiate 'error' with a polytype.
  A similar case is
     bar :: Bool -> (forall a. a->a) -> Int
     bar True = \x. (x 3)
     bar False = error "urk"
  Here we need to instantiate 'error' with a polytype.
  
  But 'error' has an OpenTypeKind type variable, precisely so that
  we can instantiate it with Int#.  So we also allow such type variables
  to be instantiated with foralls.  It's a bit of a hack, but seems
  straightforward.
  
  ************************************************************************
  *                                                                      *
  \subsection{Predicate types}
  *                                                                      *
  ************************************************************************
  
  Deconstructors and tests on predicate types
  -}
  
  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
  
  -- Superclasses
  
  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
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Predicates}
  *                                                                      *
  ************************************************************************
  -}
  
  isSigmaTy :: TcType -> Bool
  -- isSigmaTy returns true of any qualified type.  It doesn't
  -- *necessarily* have any foralls.  E.g
  --        f :: (?x::Int) => Int -> Int
  isSigmaTy ty | Just ty' <- tcView ty = isSigmaTy ty'
  isSigmaTy (ForAllTy _ _) = True
  isSigmaTy (FunTy a _)    = isPredTy a
  isSigmaTy _              = False
  
  isRhoTy :: TcType -> Bool   -- True of TcRhoTypes; see Note [TcRhoType]
  isRhoTy ty | Just ty' <- tcView ty = isRhoTy ty'
  isRhoTy (ForAllTy {}) = False
  isRhoTy (FunTy a r)   = not (isPredTy a) && isRhoTy r
  isRhoTy _             = True
  
  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
  
  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
  
  -- | Does a type represent a floating-point number?
  isFloatingTy :: Type -> Bool
  isFloatingTy ty = isFloatTy ty || isDoubleTy ty
  
  -- | Is a type 'String'?
  isStringTy :: Type -> Bool
  isStringTy ty
    = case tcSplitTyConApp_maybe ty of
        Just (tc, [arg_ty]) -> tc == listTyCon && isCharTy arg_ty
        _                   -> False
  
  -- | Is a type a 'CallStack'?
  isCallStackTy :: Type -> Bool
  isCallStackTy ty
    | Just tc <- tyConAppTyCon_maybe ty
    = tc `hasKey` callStackTyConKey
    | otherwise
    = False
  
  -- | Is a 'PredType' a 'CallStack' implicit parameter?
  --
  -- If so, return the name of the parameter.
  isCallStackPred :: PredType -> Maybe FastString
  isCallStackPred pred
    | Just (str, ty) <- isIPPred_maybe pred
    , isCallStackTy ty
    = Just str
    | otherwise
    = Nothing
  
  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
  
  -- | Does the given tyvar appear in the given type outside of any
  -- non-newtypes? Assume we're looking for @a@. Says "yes" for
  -- @a@, @N a@, @b a@, @a b@, @b (N a)@. Says "no" for
  -- @[a]@, @Maybe a@, @T a@, where @N@ is a newtype and @T@ is a datatype.
  isTyVarExposed :: TcTyVar -> TcType -> Bool
  isTyVarExposed tv (TyVarTy tv')   = tv == tv'
  isTyVarExposed tv (TyConApp tc tys)
    | isNewTyCon tc                 = any (isTyVarExposed tv) tys
    | otherwise                     = False
  isTyVarExposed _  (LitTy {})      = False
  isTyVarExposed _  (FunTy {})      = False
  isTyVarExposed tv (AppTy fun arg) = isTyVarExposed tv fun
                                   || isTyVarExposed tv arg
  isTyVarExposed _  (ForAllTy {})   = False
  
  -- | Does the given tyvar appear under a type generative w.r.t.
  -- representational equality? See Note [Occurs check error] in
  -- TcCanonical for the motivation for this function.
  isTyVarUnderDatatype :: TcTyVar -> TcType -> Bool
  isTyVarUnderDatatype tv = go False
    where
      go under_dt ty | Just ty' <- tcView ty = go under_dt ty'
      go under_dt (TyVarTy tv') = under_dt && (tv == tv')
      go under_dt (TyConApp tc tys) = let under_dt' = under_dt ||
                                                      isGenerativeTyCon tc
                                                        Representational
                                      in any (go under_dt') tys
      go _        (LitTy {}) = False
      go _        (FunTy arg res) = go True arg || go True res
      go under_dt (AppTy fun arg) = go under_dt fun || go under_dt arg
      go under_dt (ForAllTy tv' inner_ty)
        | tv' == tv = False
        | otherwise = go under_dt inner_ty
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Misc}
  *                                                                      *
  ************************************************************************
  -}
  
  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 = mapUnionVarSet tcTyVarsOfType
  
  {-
  Find the free tycons and classes of a type.  This is used in the front
  end of the compiler.
  -}
  
  orphNamesOfTyCon :: TyCon -> NameSet
  orphNamesOfTyCon tycon = unitNameSet (getName tycon) `unionNameSet` 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
                                         `unionNameSet` orphNamesOfTypes tys
  orphNamesOfType (FunTy arg res)      = orphNamesOfTyCon funTyCon   -- NB!  See Trac #8535
                                         `unionNameSet` orphNamesOfType arg
                                         `unionNameSet` orphNamesOfType res
  orphNamesOfType (AppTy fun arg)      = orphNamesOfType fun `unionNameSet` orphNamesOfType arg
  orphNamesOfType (ForAllTy _ ty)      = orphNamesOfType ty
  
  orphNamesOfThings :: (a -> NameSet) -> [a] -> NameSet
  orphNamesOfThings f = foldr (unionNameSet . 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) `unionNameSet` orphNamesOfCos cos
  orphNamesOfCo (AppCo co1 co2)       = orphNamesOfCo co1 `unionNameSet` orphNamesOfCo co2
  orphNamesOfCo (ForAllCo _ co)       = orphNamesOfCo co
  orphNamesOfCo (CoVarCo _)           = emptyNameSet
  orphNamesOfCo (AxiomInstCo con _ cos) = orphNamesOfCoCon con `unionNameSet` orphNamesOfCos cos
  orphNamesOfCo (UnivCo _ _ ty1 ty2)  = orphNamesOfType ty1 `unionNameSet` orphNamesOfType ty2
  orphNamesOfCo (SymCo co)            = orphNamesOfCo co
  orphNamesOfCo (TransCo co1 co2)     = orphNamesOfCo co1 `unionNameSet` orphNamesOfCo co2
  orphNamesOfCo (NthCo _ co)          = orphNamesOfCo co
  orphNamesOfCo (LRCo  _ co)          = orphNamesOfCo co
  orphNamesOfCo (InstCo co ty)        = orphNamesOfCo co `unionNameSet` orphNamesOfType ty
  orphNamesOfCo (SubCo co)            = orphNamesOfCo co
  orphNamesOfCo (AxiomRuleCo _ ts cs) = orphNamesOfTypes ts `unionNameSet`
                                        orphNamesOfCos cs
  
  orphNamesOfCos :: [Coercion] -> NameSet
  orphNamesOfCos = orphNamesOfThings orphNamesOfCo
  
  orphNamesOfCoCon :: CoAxiom br -> NameSet
  orphNamesOfCoCon (CoAxiom { co_ax_tc = tc, co_ax_branches = branches })
    = orphNamesOfTyCon tc `unionNameSet` orphNamesOfCoAxBranches branches
  
  orphNamesOfCoAxBranches :: BranchList CoAxBranch br -> NameSet
  orphNamesOfCoAxBranches = brListFoldr (unionNameSet . orphNamesOfCoAxBranch) emptyNameSet
  
  orphNamesOfCoAxBranch :: CoAxBranch -> NameSet
  orphNamesOfCoAxBranch (CoAxBranch { cab_lhs = lhs, cab_rhs = rhs })
    = orphNamesOfTypes lhs `unionNameSet` orphNamesOfType rhs
  
  {-
  ************************************************************************
  *                                                                      *
  \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 )
  -}
  
  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
  
  tcSplitJavaType_maybe :: Type -> Maybe (TyCon, Type, Type)
  tcSplitJavaType_maybe ty
    = case tcSplitTyConApp_maybe ty of
          Just (javaTyCon, [javaTagType, javaResType])
           | javaTyCon `hasKey` javaTyConKey  ->
              Just (javaTyCon, javaTagType, javaResType)
          _ ->
              Nothing
  
  tcSplitExtendsType_maybe :: Type -> Maybe (Type, Type)
  tcSplitExtendsType_maybe ty
    = case tcSplitTyConApp_maybe ty of
          Just (extendsTyCon, [extendsVarType, extendsTagType])
           | extendsTyCon `hasKey` extendsClassKey  ->
              Just ( extendsVarType
                   , extendsTagType )
          _ ->
              Nothing
  
  tcSplitExtendsType :: Type -> (Type, Type)
  tcSplitExtendsType ty = expectJust "tcSplitExtendsType" $ tcSplitExtendsType_maybe ty
  
  extendsVars :: ThetaType -> VarSet
  extendsVars = mkVarSet . mapMaybe ( fmap ( getTyVar "extendsVars: Not type variable!"
                                           . fst) . tcSplitExtendsType_maybe )
  
  -- isFFITy :: Type -> Bool
  -- -- True for any TyCon that can possibly be an arg or result of an FFI call
  -- isFFITy ty = isValid (checkRepTyCon legalFFITyCon ty empty)
  
  isFFIArgumentTy :: DynFlags -> Safety -> VarSet -> Type -> Validity
  -- Checks for valid argument type for a 'foreign import'
  isFFIArgumentTy dflags safety vs ty
    | checkValidTyVar vs ty = IsValid
    | otherwise = checkRepTyCon (legalOutgoingTyCon dflags safety) ty empty
  
  isFFIExternalTy :: VarSet -> Type -> Validity
  -- Types that are allowed as arguments of a 'foreign export'
  isFFIExternalTy vs ty
    | checkValidTyVar vs ty = IsValid
    | otherwise = checkRepTyCon legalFEArgTyCon ty empty
  
  isFFIImportResultTy :: DynFlags -> Type -> Validity
  isFFIImportResultTy dflags = isFFIResultTy (legalFIResultTyCon dflags) 
  
  isFFIExportResultTy :: Type -> Validity
  isFFIExportResultTy = isFFIResultTy legalFEResultTyCon
  
  isFFIResultTy :: (TyCon -> Type -> Bool) -> Type -> Validity
  isFFIResultTy isLegalResultTyCon ty
    | isTyVarTy ty = IsValid
    | otherwise = checkRepTyCon isLegalResultTyCon ty empty
  
  -- isFFIDynTy :: Type -> Type -> Validity
  -- -- 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 normaliseFfiType, 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
  --     = IsValid
  --     | otherwise
  --     = NotValid (vcat [ ptext (sLit "Expected: Ptr/FunPtr") <+> pprParendType expected <> comma
  --                      , ptext (sLit "  Actual:") <+> ppr ty ])
  
  -- isFFILabelTy :: Type -> Validity
  -- -- The type of a foreign label must be Ptr, FunPtr, or a newtype of either.
  -- isFFILabelTy ty = checkRepTyCon ok ty extra
  --   where
  --     ok tc _ = tc `hasKey` funPtrTyConKey || tc `hasKey` ptrTyConKey
  --     extra = ptext (sLit "A foreign-imported address (via &foo) must have type (Ptr a) or (FunPtr a)")
  
  isFFIPrimArgumentTy :: DynFlags -> Type -> Validity
  -- 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 = IsValid
    | otherwise  = checkRepTyCon (legalFIPrimArgTyCon dflags) ty empty
  
  isFFIPrimResultTy :: DynFlags -> Type -> Validity
  -- 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 empty
  
  isFunPtrTy :: Type -> Bool
  isFunPtrTy ty = isValid (checkRepTyCon (\tc _ -> tc `hasKey` funPtrTyConKey) ty empty)
  
  -- 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 -> Type -> Bool) -> Type -> SDoc -> Validity
  checkRepTyCon checkTc ty extra
    = case splitTyConApp_maybe ty of
          Just (tc, tys)
            | isNewTyCon tc           -> NotValid (hang msg 2 (mk_nt_reason tc tys $$ nt_fix))
            | checkTc tc ty           -> IsValid
            | null (tyConDataCons tc) -> NotValid (nullDataConstructorMessage $$ extra)
            | otherwise               -> IsValid
          Nothing -> NotValid (quotes (ppr ty) <+> ptext (sLit "is not a data type") $$ extra)
    where
      msg = quotes (ppr ty) <+> ptext (sLit "cannot be marshalled in a foreign call")
      nullDataConstructorMessage =
        quotes (ppr ty) <+> ptext (sLit "cannot be marshalled in a foreign call, as it has no data constructors.")
      mk_nt_reason tc tys
       | null tys  = ptext (sLit "because its data construtor is not in scope")
       | otherwise = ptext (sLit "because the data construtor for")
                    <+> quotes (ppr tc) <+> ptext (sLit "is not in scope")
      nt_fix = ptext (sLit "Possible fix: import the data constructor to bring it into scope")
  
  checkValidTyVar :: VarSet -> Type -> Bool
  checkValidTyVar vs ty
    | Just var <- getTyVar_maybe ty
    , var `elemVarSet` vs
    = True
    | otherwise
    = False
  
  {-
  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
  ----------------------------------------------
  -}
  
  legalFEArgTyCon :: TyCon -> Type -> Bool
  legalFEArgTyCon tc ty
    -- 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 ty
  
  legalFIResultTyCon :: DynFlags -> TyCon -> Type -> Bool
  legalFIResultTyCon dflags tc ty
    | tc == unitTyCon         = True
    | otherwise               = marshalableTyCon dflags tc ty
  
  legalFEResultTyCon :: TyCon -> Type -> Bool
  legalFEResultTyCon tc ty
    | tc == unitTyCon         = True
    | otherwise               = boxedMarshalableTyCon tc ty
  
  legalOutgoingTyCon :: DynFlags -> Safety -> TyCon -> Type -> Bool
  -- Checks validity of types going from Haskell -> external world
  legalOutgoingTyCon dflags _ tc ty
    = marshalableTyCon dflags tc ty
  
  -- legalFFITyCon :: VarSet -> TyCon -> Type -> Bool
  -- -- True for any TyCon that can possibly be an arg or result of an FFI call
  -- legalFFITyCon vs tc ty
  --   | isUnLiftedTyCon tc = True
  --   | tc == unitTyCon    = True
  --   | otherwise          = boxedMarshalableTyCon vs tc ty
  
  marshalableTyCon :: DynFlags -> TyCon -> Type -> Bool
  marshalableTyCon dflags tc ty
    |  (xopt LangExt.UnliftedFFITypes dflags
        && isUnLiftedTyCon tc
        && not (isUnboxedTupleTyCon tc))
        -- && not (isVoidRep (typePrimRep ty)))
    = True
    | otherwise
    = boxedMarshalableTyCon tc ty
  
  boxedMarshalableTyCon :: TyCon -> Type -> Bool
  boxedMarshalableTyCon tc ty
     | getUnique tc `elem` [ intTyConKey, int8TyConKey, int16TyConKey
                           , int32TyConKey, int64TyConKey
                           , wordTyConKey, word8TyConKey, word16TyConKey
                           , word32TyConKey, word64TyConKey
                           , floatTyConKey, doubleTyConKey
                           , ptrTyConKey, funPtrTyConKey
                           , charTyConKey
                           , stablePtrTyConKey
                           , boolTyConKey
                           , maybeTyConKey
                           , listTyConKey ]
    = True
     -- TODO: Optimize this to add just raw key checks like above.
     --       Can be done once the GHC source in integrated.
    | Just (_, _, _, [primTy]) <- splitDataProductType_maybe ty
    , isPrimitiveType primTy
    = True
    | otherwise = False
  
  legalFIPrimArgTyCon :: DynFlags -> TyCon -> Type -> 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 LangExt.UnliftedFFITypes dflags
      && isUnLiftedTyCon tc
      && not (isUnboxedTupleTyCon tc)
    = True
    | otherwise
    = False
  
  legalFIPrimResultTyCon :: DynFlags -> TyCon -> Type -> Bool
  -- Check result type of 'foreign import prim'. Allow simple unlifted
  -- types and also unboxed tuple result types '... -> (# , , #)'
  legalFIPrimResultTyCon dflags tc _ty
    | xopt LangExt.UnliftedFFITypes dflags
      && isUnLiftedTyCon tc
    = True
    | otherwise
    = False
  
  {-
  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
  -}
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Transformation of Types to TcTypes}
  *                                                                      *
  ************************************************************************
  -}
  
  toTcType :: Type -> TcType
  toTcType ty = to_tc_type emptyVarSet ty
     where
      to_tc_type :: VarSet -> Type -> TcType
      -- The constraint solver expects EvVars to have TcType, in which the
      -- free type variables are TcTyVars. So we convert from Type to TcType here
      -- A bit tiresome; but one day I expect the two types to be entirely separate
      -- in which case we'll definitely need to do this
      to_tc_type forall_tvs (TyVarTy tv)
        | Just var <- lookupVarSet forall_tvs tv = TyVarTy var
        | otherwise = TyVarTy (toTcTyVar tv)
      to_tc_type  ftvs (FunTy t1 t2)     = FunTy (to_tc_type ftvs t1) (to_tc_type ftvs t2)
      to_tc_type  ftvs (AppTy t1 t2)     = AppTy (to_tc_type ftvs t1) (to_tc_type ftvs t2)
      to_tc_type  ftvs (TyConApp tc tys) = TyConApp tc (map (to_tc_type ftvs) tys)
      to_tc_type  ftvs (ForAllTy tv ty)  = let tv' = toTcTyVar tv
                                           in ForAllTy tv' (to_tc_type (ftvs `extendVarSet` tv') ty)
      to_tc_type _ftvs (LitTy l)         = LitTy l
  
  toTcTyVar :: TyVar -> TcTyVar
  toTcTyVar tv
    | isTcTyVar tv = setVarType tv (toTcType (tyVarKind tv))
    | isId tv      = pprPanic "toTcTyVar: Id:" (ppr tv)
    | otherwise    = mkTcTyVar (tyVarName tv) (toTcType (tyVarKind tv)) vanillaSkolemTv
  
  toTcTypeBag :: Bag EvVar -> Bag EvVar -- All TyVars are transformed to TcTyVars
  toTcTypeBag evvars = mapBag (\tv -> setTyVarKind tv (toTcType (tyVarKind tv))) evvars
  