types/TypeRep.lhs

| % % (c) The University of Glasgow 2006 % (c) The GRASP/AQUA Project, Glasgow University, 1998 % \section[TypeRep]{Type - friends' interface} Note [The Type-related module hierarchy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Class TyCon imports Class TypeRep TysPrim imports TypeRep ( including mkTyConTy ) Kind imports TysPrim ( mainly for primitive kinds ) Type imports Kind Coercion imports Type \begin{code}

    {-# OPTIONS -fno-warn-tabs #-}
    -- The above warning supression flag is a temporary kludge.
    -- While working on this module you are encouraged to remove it and
    -- detab the module (please do the detabbing in a separate patch). See
    --     http://ghc.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#TabsvsSpaces
    -- for details

    -- We expose the relevant stuff from this module via the Type module
    {-# OPTIONS_HADDOCK hide #-}
    {-# LANGUAGE DeriveDataTypeable, DeriveFunctor, DeriveFoldable, DeriveTraversable #-}
    module TypeRep (
    	TyThing(..),
    	Type(..),
            TyLit(..),
            KindOrType, Kind, SuperKind,
            PredType, ThetaType,      -- Synonyms

            -- Functions over types
            mkTyConTy, mkTyVarTy, mkTyVarTys,
            isLiftedTypeKind, isSuperKind, isTypeVar, isKindVar,

            -- Pretty-printing
    	pprType, pprParendType, pprTypeApp, pprTvBndr, pprTvBndrs,
    	pprTyThing, pprTyThingCategory, pprSigmaType,
    	pprEqPred, pprTheta, pprForAll, pprThetaArrowTy, pprClassPred,
            pprKind, pprParendKind, pprTyLit, suppressKinds,
    	Prec(..), maybeParen, pprTcApp,
            pprPrefixApp, pprArrowChain, ppr_type,

            -- Free variables
            tyVarsOfType, tyVarsOfTypes, closeOverKinds, varSetElemsKvsFirst,

            -- * Tidying type related things up for printing
            tidyType,      tidyTypes,
            tidyOpenType,  tidyOpenTypes,
            tidyOpenKind,
            tidyTyVarBndr, tidyTyVarBndrs, tidyFreeTyVars,
            tidyOpenTyVar, tidyOpenTyVars,
            tidyTyVarOcc,
            tidyTopType,
            tidyKind,

            -- Substitutions
            TvSubst(..), TvSubstEnv
        ) where

    #include "HsVersions.h"

    import {-# SOURCE #-} DataCon( dataConTyCon )
    import ConLike ( ConLike(..) )
    import {-# SOURCE #-} Type( noParenPred, isPredTy ) -- Transitively pulls in a LOT of stuff, better to break the loop

    -- friends:
    import Var
    import VarEnv
    import VarSet
    import Name
    import BasicTypes
    import TyCon
    import Class
    import CoAxiom

    -- others
    import PrelNames
    import Outputable
    import FastString
    import Pair
    import Util
    import DynFlags

    -- libraries
    import Data.List( mapAccumL, partition )
    import qualified Data.Data        as Data hiding ( TyCon )

\end{code} %************************************************************************ %* * \subsection{The data type} %* * %************************************************************************ \begin{code}

    -- | The key representation of types within the compiler

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    data Type
      = TyVarTy Var	-- ^ Vanilla type or kind variable (*never* a coercion variable)

      | AppTy         -- See Note [AppTy invariant]
    	Type
    	Type		-- ^ Type application to something other than a 'TyCon'. Parameters:
    	                --
                            --  1) Function: must /not/ be a 'TyConApp',
                            --     must be another 'AppTy', or 'TyVarTy'
    	                --
    	                --  2) Argument type

      | TyConApp      -- See Note [AppTy invariant]
    	TyCon
    	[KindOrType]	-- ^ Application of a 'TyCon', including newtypes /and/ synonyms.
    	                -- Invariant: saturated appliations of 'FunTyCon' must
    	                -- use 'FunTy' and saturated synonyms must use their own
                            -- constructors. However, /unsaturated/ 'FunTyCon's
                            -- do appear as 'TyConApp's.
    	                -- Parameters:
    	                --
    	                -- 1) Type constructor being applied to.
    	                --
                            -- 2) Type arguments. Might not have enough type arguments
                            --    here to saturate the constructor.
                            --    Even type synonyms are not necessarily saturated;
                            --    for example unsaturated type synonyms
    	                --    can appear as the right hand side of a type synonym.

      | FunTy
    	Type
    	Type		-- ^ Special case of 'TyConApp': @TyConApp FunTyCon [t1, t2]@
    			-- See Note [Equality-constrained types]

      | ForAllTy
    	Var         -- Type or kind variable
    	Type	        -- ^ A polymorphic type

      | LitTy TyLit     -- ^ Type literals are similar to type constructors.

      deriving (Data.Data, Data.Typeable)

    -- NOTE:  Other parts of the code assume that type literals do not contain
    -- types or type variables.
    data TyLit
      = NumTyLit Integer
      | StrTyLit FastString
      deriving (Eq, Ord, Data.Data, Data.Typeable)

    type KindOrType = Type -- See Note [Arguments to type constructors]

    -- | The key type representing kinds in the compiler.
    -- Invariant: a kind is always in one of these forms:
    --
    -- > FunTy k1 k2
    -- > TyConApp PrimTyCon [...]
    -- > TyVar kv   -- (during inference only)
    -- > ForAll ... -- (for top-level coercions)
    type Kind = Type

    -- | "Super kinds", used to help encode 'Kind's as types.
    -- Invariant: a super kind is always of this form:
    --
    -- > TyConApp SuperKindTyCon ...
    type SuperKind = Type

\end{code} Note [The kind invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~ The kinds # UnliftedTypeKind OpenKind super-kind of *, # can never appear under an arrow or type constructor in a kind; they can only be at the top level of a kind. It follows that primitive TyCons, which have a naughty pseudo-kind State# :: * -> # must always be saturated, so that we can never get a type whose kind has a UnliftedTypeKind or ArgTypeKind underneath an arrow. Nor can we abstract over a type variable with any of these kinds. k :: = kk | # | ArgKind | (#) | OpenKind kk :: = * | kk -> kk | T kk1 ... kkn So a type variable can only be abstracted kk. Note [Arguments to type constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Because of kind polymorphism, in addition to type application we now have kind instantiation. We reuse the same notations to do so. For example: Just (* -> *) Maybe Right * Nat Zero are represented by: TyConApp (PromotedDataCon Just) [* -> *, Maybe] TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)] Important note: Nat is used as a *kind* and not as a type. This can be confusing, since type-level Nat and kind-level Nat are identical. We use the kind of (PromotedDataCon Right) to know if its arguments are kinds or types. This kind instantiation only happens in TyConApp currently. Note [Equality-constrained types] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The type forall ab. (a ~ [b]) => blah is encoded like this: ForAllTy (a:*) $ ForAllTy (b:*) $ FunTy (TyConApp (~) [a, [b]]) $ blah ------------------------------------- Note [PredTy] \begin{code}

    -- | A type of the form @p@ of kind @Constraint@ represents a value whose type is
    -- the Haskell predicate @p@, where a predicate is what occurs before
    -- the @=>@ in a Haskell type.
    --
    -- We use 'PredType' as documentation to mark those types that we guarantee to have
    -- this kind.
    --
    -- It can be expanded into its representation, but:
    --
    -- * The type checker must treat it as opaque
    --
    -- * The rest of the compiler treats it as transparent
    --
    -- Consider these examples:
    --
    -- > f :: (Eq a) => a -> Int
    -- > g :: (?x :: Int -> Int) => a -> Int
    -- > h :: (r\l) => {r} => {l::Int | r}
    --
    -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\"
    type PredType = Type

    -- | A collection of 'PredType's
    type ThetaType = [PredType]

\end{code} (We don't support TREX records yet, but the setup is designed to expand to allow them.) A Haskell qualified type, such as that for f,g,h above, is represented using * a FunTy for the double arrow * with a type of kind Constraint as the function argument The predicate really does turn into a real extra argument to the function. If the argument has type (p :: Constraint) then the predicate p is represented by evidence of type p. %************************************************************************ %* * Simple constructors %* * %************************************************************************ These functions are here so that they can be used by TysPrim, which in turn is imported by Type \begin{code}

    mkTyVarTy  :: TyVar   -> Type
    mkTyVarTy  = TyVarTy

    mkTyVarTys :: [TyVar] -> [Type]
    mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy

    -- | Create the plain type constructor type which has been applied to no type arguments at all.
    mkTyConTy :: TyCon -> Type
    mkTyConTy tycon = TyConApp tycon []

\end{code} Some basic functions, put here to break loops eg with the pretty printer \begin{code}

    isLiftedTypeKind :: Kind -> Bool
    isLiftedTypeKind (TyConApp tc []) = tc `hasKey` liftedTypeKindTyConKey
    isLiftedTypeKind _                = False

    -- | Is this a super-kind (i.e. a type-of-kinds)?
    isSuperKind :: Type -> Bool
    isSuperKind (TyConApp skc []) = skc `hasKey` superKindTyConKey
    isSuperKind _                 = False

    isTypeVar :: Var -> Bool
    isTypeVar v = isTKVar v && not (isSuperKind (varType v))

    isKindVar :: Var -> Bool
    isKindVar v = isTKVar v && isSuperKind (varType v)

\end{code} %************************************************************************ %* * Free variables of types and coercions %* * %************************************************************************ \begin{code}

    tyVarsOfType :: Type -> VarSet
    -- ^ NB: for type synonyms tyVarsOfType does /not/ expand the synonym
    -- tyVarsOfType returns only the free variables of a type
    -- For example, tyVarsOfType (a::k) returns {a}, not including the
    -- kind variable {k}
    tyVarsOfType (TyVarTy v)         = unitVarSet v
    tyVarsOfType (TyConApp _ tys)    = tyVarsOfTypes tys
    tyVarsOfType (LitTy {})          = emptyVarSet
    tyVarsOfType (FunTy arg res)     = tyVarsOfType arg `unionVarSet` tyVarsOfType res
    tyVarsOfType (AppTy fun arg)     = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
    tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
                                       `unionVarSet` tyVarsOfType (tyVarKind tyvar)

    tyVarsOfTypes :: [Type] -> TyVarSet
    tyVarsOfTypes tys = foldr (unionVarSet . tyVarsOfType) emptyVarSet tys

    closeOverKinds :: TyVarSet -> TyVarSet
    -- Add the kind variables free in the kinds
    -- of the tyvars in the given set
    closeOverKinds tvs
      = foldVarSet (\tv ktvs -> tyVarsOfType (tyVarKind tv) `unionVarSet` ktvs)
                   tvs tvs

    varSetElemsKvsFirst :: VarSet -> [TyVar]
    -- {k1,a,k2,b} --> [k1,k2,a,b]
    varSetElemsKvsFirst set
      = kvs ++ tvs
      where
        (kvs, tvs) = partition isKindVar (varSetElems set)

\end{code} %************************************************************************ %* * TyThing %* * %************************************************************************ Despite the fact that DataCon has to be imported via a hi-boot route, this module seems the right place for TyThing, because it's needed for funTyCon and all the types in TysPrim. Note [ATyCon for classes] ~~~~~~~~~~~~~~~~~~~~~~~~~ Both classes and type constructors are represented in the type environment as ATyCon. You can tell the difference, and get to the class, with isClassTyCon :: TyCon -> Bool tyConClass_maybe :: TyCon -> Maybe Class The Class and its associated TyCon have the same Name. \begin{code}

    -- | A typecheckable-thing, essentially anything that has a name
    data TyThing
      = AnId     Id
      | AConLike ConLike
      | ATyCon   TyCon       -- TyCons and classes; see Note [ATyCon for classes]
      | ACoAxiom (CoAxiom Branched)
      deriving (Eq, Ord)

    instance Outputable TyThing where
      ppr = pprTyThing

    pprTyThing :: TyThing -> SDoc
    pprTyThing thing = pprTyThingCategory thing <+> quotes (ppr (getName thing))

    pprTyThingCategory :: TyThing -> SDoc
    pprTyThingCategory (ATyCon tc)
      | isClassTyCon tc = ptext (sLit "Class")
      | otherwise       = ptext (sLit "Type constructor")
    pprTyThingCategory (ACoAxiom _) = ptext (sLit "Coercion axiom")
    pprTyThingCategory (AnId   _)   = ptext (sLit "Identifier")
    pprTyThingCategory (AConLike (RealDataCon _)) = ptext (sLit "Data constructor")
    pprTyThingCategory (AConLike (PatSynCon _))  = ptext (sLit "Pattern synonym")

    instance NamedThing TyThing where	-- Can't put this with the type
      getName (AnId id)     = getName id	-- decl, because the DataCon instance
      getName (ATyCon tc)   = getName tc	-- isn't visible there
      getName (ACoAxiom cc) = getName cc
      getName (AConLike cl) = getName cl

\end{code} %************************************************************************ %* * Substitutions Data type defined here to avoid unnecessary mutual recursion %* * %************************************************************************ \begin{code}

    -- | Type substitution
    --
    -- #tvsubst_invariant#
    -- The following invariants must hold of a 'TvSubst':
    --
    -- 1. The in-scope set is needed /only/ to
    -- guide the generation of fresh uniques
    --
    -- 2. In particular, the /kind/ of the type variables in
    -- the in-scope set is not relevant
    --
    -- 3. The substition is only applied ONCE! This is because
    -- in general such application will not reached a fixed point.
    data TvSubst
      = TvSubst InScopeSet 	-- The in-scope type and kind variables
    	    TvSubstEnv  -- Substitutes both type and kind variables
    	-- See Note [Apply Once]
    	-- and Note [Extending the TvSubstEnv]

    -- | A substitition of 'Type's for 'TyVar's
    --                 and 'Kind's for 'KindVar's
    type TvSubstEnv = TyVarEnv Type
    	-- A TvSubstEnv is used both inside a TvSubst (with the apply-once
    	-- invariant discussed in Note [Apply Once]), and also independently
    	-- in the middle of matching, and unification (see Types.Unify)
    	-- So you have to look at the context to know if it's idempotent or
    	-- apply-once or whatever

\end{code} Note [Apply Once] ~~~~~~~~~~~~~~~~~ We use TvSubsts to instantiate things, and we might instantiate forall a b. ty \with the types [a, b], or [b, a]. So the substition might go [a->b, b->a]. A similar situation arises in Core when we find a beta redex like (/\ a /\ b -> e) b a Then we also end up with a substition that permutes type variables. Other variations happen to; for example [a -> (a, b)]. *************************************************** *** So a TvSubst must be applied precisely once *** *************************************************** A TvSubst is not idempotent, but, unlike the non-idempotent substitution we use during unifications, it must not be repeatedly applied. Note [Extending the TvSubst] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ See #tvsubst_invariant# for the invariants that must hold. This invariant allows a short-cut when the TvSubstEnv is empty: if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds --- then (substTy subst ty) does nothing. For example, consider: (/\a. /\b:(a~Int). ...b..) Int We substitute Int for 'a'. The Unique of 'b' does not change, but nevertheless we add 'b' to the TvSubstEnv, because b's kind does change This invariant has several crucial consequences: * In substTyVarBndr, we need extend the TvSubstEnv - if the unique has changed - or if the kind has changed * In substTyVar, we do not need to consult the in-scope set; the TvSubstEnv is enough * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty %************************************************************************ %* * Pretty-printing types Defined very early because of debug printing in assertions %* * %************************************************************************ @pprType@ is the standard @Type@ printer; the overloaded @ppr@ function is defined to use this. @pprParendType@ is the same, except it puts parens around the type, except for the atomic cases. @pprParendType@ works just by setting the initial context precedence very high. \begin{code}

    data Prec = TopPrec 	-- No parens
    	  | FunPrec 	-- Function args; no parens for tycon apps
    	  | TyConPrec 	-- Tycon args; no parens for atomic
    	  deriving( Eq, Ord )

    maybeParen :: Prec -> Prec -> SDoc -> SDoc
    maybeParen ctxt_prec inner_prec pretty
      | ctxt_prec < inner_prec = pretty
      | otherwise		   = parens pretty

    ------------------
    pprType, pprParendType :: Type -> SDoc
    pprType       ty = ppr_type TopPrec ty
    pprParendType ty = ppr_type TyConPrec ty

    pprTyLit :: TyLit -> SDoc
    pprTyLit = ppr_tylit TopPrec

    pprKind, pprParendKind :: Kind -> SDoc
    pprKind       = pprType
    pprParendKind = pprParendType

    ------------------
    pprEqPred :: Pair Type -> SDoc
    -- NB: Maybe move to Coercion? It's only called after coercionKind anyway.
    pprEqPred (Pair ty1 ty2)
      = sep [ ppr_type FunPrec ty1
            , nest 2 (ptext (sLit "~#"))
            , ppr_type FunPrec ty2]
        -- Precedence looks like (->) so that we get
        --    Maybe a ~ Bool
        --    (a->a) ~ Bool
        -- Note parens on the latter!

    ------------
    pprClassPred :: Class -> [Type] -> SDoc
    pprClassPred clas tys = pprTypeApp (classTyCon clas) tys

    ------------
    pprTheta :: ThetaType -> SDoc
    -- pprTheta [pred] = pprPred pred	 -- I'm in two minds about this
    pprTheta theta  = parens (sep (punctuate comma (map (ppr_type TopPrec) theta)))

    pprThetaArrowTy :: ThetaType -> SDoc
    pprThetaArrowTy []      = empty
    pprThetaArrowTy [pred]
          | noParenPred pred = ppr_type TopPrec pred <+> darrow
    pprThetaArrowTy preds   = parens (fsep (punctuate comma (map (ppr_type TopPrec) preds)))
                                <+> darrow
        -- Notice 'fsep' here rather that 'sep', so that
        -- type contexts don't get displayed in a giant column
        -- Rather than
        --  instance (Eq a,
        --            Eq b,
        --            Eq c,
        --            Eq d,
        --            Eq e,
        --            Eq f,
        --            Eq g,
        --            Eq h,
        --            Eq i,
        --            Eq j,
        --            Eq k,
        --            Eq l) =>
        --           Eq (a, b, c, d, e, f, g, h, i, j, k, l)
        -- we get
        --
        --  instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i,
        --            Eq j, Eq k, Eq l) =>
        --           Eq (a, b, c, d, e, f, g, h, i, j, k, l)

    ------------------
    instance Outputable Type where
        ppr ty = pprType ty

    instance Outputable TyLit where
       ppr = pprTyLit

    ------------------
    	-- OK, here's the main printer

    ppr_type :: Prec -> Type -> SDoc
    ppr_type _ (TyVarTy tv)	      = ppr_tvar tv

    ppr_type _ (TyConApp tc [LitTy (StrTyLit n),ty])
      | tc `hasKey` ipClassNameKey
      = char '?' <> ftext n <> ptext (sLit "::") <> ppr_type TopPrec ty

    ppr_type p (TyConApp tc tys)  = pprTyTcApp p tc tys

    ppr_type p (LitTy l)          = ppr_tylit p l
    ppr_type p ty@(ForAllTy {})   = ppr_forall_type p ty

    ppr_type p (AppTy t1 t2) = maybeParen p TyConPrec $
    			   ppr_type FunPrec t1 <+> ppr_type TyConPrec t2

    ppr_type p fun_ty@(FunTy ty1 ty2)
      | isPredTy ty1
      = ppr_forall_type p fun_ty
      | otherwise
      = pprArrowChain p (ppr_type FunPrec ty1 : ppr_fun_tail ty2)
      where
        -- We don't want to lose synonyms, so we mustn't use splitFunTys here.
        ppr_fun_tail (FunTy ty1 ty2)
          | not (isPredTy ty1) = ppr_type FunPrec ty1 : ppr_fun_tail ty2
        ppr_fun_tail other_ty = [ppr_type TopPrec other_ty]

    ppr_forall_type :: Prec -> Type -> SDoc
    ppr_forall_type p ty
      = maybeParen p FunPrec $ ppr_sigma_type True ty

    ppr_tvar :: TyVar -> SDoc
    ppr_tvar tv  -- Note [Infix type variables]
      = parenSymOcc (getOccName tv) (ppr tv)

    ppr_tylit :: Prec -> TyLit -> SDoc
    ppr_tylit _ tl =
      case tl of
        NumTyLit n -> integer n
        StrTyLit s -> text (show s)

    -------------------
    ppr_sigma_type :: Bool -> Type -> SDoc
    -- Bool <=> Show the foralls
    ppr_sigma_type show_foralls ty
      = sdocWithDynFlags $ \ dflags ->
        let filtered_tvs | gopt Opt_PrintExplicitKinds dflags
                         = tvs
                         | otherwise
                         = filterOut isKindVar tvs
        in sep [ ppWhen show_foralls (pprForAll filtered_tvs)
               , pprThetaArrowTy ctxt
               , pprType tau ]
      where
        (tvs,  rho) = split1 [] ty
        (ctxt, tau) = split2 [] rho

        split1 tvs (ForAllTy tv ty) = split1 (tv:tvs) ty
        split1 tvs ty          = (reverse tvs, ty)

        split2 ps (ty1 `FunTy` ty2) | isPredTy ty1 = split2 (ty1:ps) ty2
        split2 ps ty                               = (reverse ps, ty)

    pprSigmaType :: Type -> SDoc
    pprSigmaType ty = sdocWithDynFlags $ \dflags ->
                      ppr_sigma_type (gopt Opt_PrintExplicitForalls dflags) ty

    pprForAll :: [TyVar] -> SDoc
    pprForAll []  = empty
    pprForAll tvs = ptext (sLit "forall") <+> pprTvBndrs tvs <> dot

    pprTvBndrs :: [TyVar] -> SDoc
    pprTvBndrs tvs = sep (map pprTvBndr tvs)

    pprTvBndr :: TyVar -> SDoc
    pprTvBndr tv
      | isLiftedTypeKind kind = ppr_tvar tv
      | otherwise	          = parens (ppr_tvar tv <+> dcolon <+> pprKind kind)
    	     where
    	       kind = tyVarKind tv

\end{code} Note [Infix type variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ With TypeOperators you can say f :: (a ~> b) -> b and the (~>) is considered a type variable. However, the type pretty-printer in this module will just see (a ~> b) as App (App (TyVarTy "~>") (TyVarTy "a")) (TyVarTy "b") So it'll print the type in prefix form. To avoid confusion we must remember to parenthesise the operator, thus (~>) a b -> b See Trac #2766. \begin{code}

    pprTypeApp :: TyCon -> [Type] -> SDoc
    pprTypeApp tc tys = pprTyTcApp TopPrec tc tys
            -- We have to use ppr on the TyCon (not its name)
            -- so that we get promotion quotes in the right place

    pprTyTcApp :: Prec -> TyCon -> [Type] -> SDoc
    -- Used for types only; so that we can make a
    -- special case for type-level lists
    pprTyTcApp p tc tys
      | tc `hasKey` consDataConKey
      , [_kind,ty1,ty2] <- tys
      = sdocWithDynFlags $ \dflags ->
        if gopt Opt_PrintExplicitKinds dflags then pprTcApp  p ppr_type tc tys
                                       else pprTyList p ty1 ty2

      | otherwise
      = pprTcApp p ppr_type tc tys

    pprTcApp :: Prec -> (Prec -> a -> SDoc) -> TyCon -> [a] -> SDoc
    -- Used for both types and coercions, hence polymorphism
    pprTcApp _ pp tc [ty]
      | tc `hasKey` listTyConKey = pprPromotionQuote tc <> brackets   (pp TopPrec ty)
      | tc `hasKey` parrTyConKey = pprPromotionQuote tc <> paBrackets (pp TopPrec ty)

    pprTcApp p pp tc tys
      | isTupleTyCon tc && tyConArity tc == length tys
      = pprPromotionQuote tc <>
        tupleParens (tupleTyConSort tc) (sep (punctuate comma (map (pp TopPrec) tys)))

      | Just dc <- isPromotedDataCon_maybe tc
      , let dc_tc = dataConTyCon dc
      , isTupleTyCon dc_tc
      , let arity = tyConArity dc_tc    -- E.g. 3 for (,,) k1 k2 k3 t1 t2 t3
            ty_args = drop arity tys    -- Drop the kind args
      , ty_args `lengthIs` arity        -- Result is saturated
      = pprPromotionQuote tc <>
        (tupleParens (tupleTyConSort dc_tc) $
         sep (punctuate comma (map (pp TopPrec) ty_args)))

      | otherwise
      = sdocWithDynFlags (pprTcApp_help p pp tc tys)

    pprTcApp_help :: Prec -> (Prec -> a -> SDoc) -> TyCon -> [a] -> DynFlags -> SDoc
    -- This one has accss to the DynFlags
    pprTcApp_help p pp tc tys dflags
      | not (isSymOcc (nameOccName (tyConName tc)))
      = pprPrefixApp p (ppr tc) (map (pp TyConPrec) tys_wo_kinds)

      | [ty1,ty2] <- tys_wo_kinds  -- Infix, two arguments;
                                   -- we know nothing of precedence though
      = pprInfixApp p pp (ppr tc) ty1 ty2

      |  tc `hasKey` liftedTypeKindTyConKey
      || tc `hasKey` unliftedTypeKindTyConKey
      = ASSERT( null tys ) ppr tc   -- Do not wrap *, # in parens

      | otherwise
      = pprPrefixApp p (parens (ppr tc)) (map (pp TyConPrec) tys_wo_kinds)
      where
        tys_wo_kinds = suppressKinds dflags (tyConKind tc) tys

    ------------------
    suppressKinds :: DynFlags -> Kind -> [a] -> [a]
    -- Given the kind of a TyCon, and the args to which it is applied,
    -- suppress the args that are kind args
    suppressKinds dflags kind xs
      | gopt Opt_PrintExplicitKinds dflags = xs
      | otherwise                          = suppress kind xs
      where
        suppress (ForAllTy _ kind) (_ : xs) = suppress kind xs
        suppress (FunTy _ res)     (x:xs)   = x : suppress res xs
        suppress _                 xs       = xs

    ----------------
    pprTyList :: Prec -> Type -> Type -> SDoc
    -- Given a type-level list (t1 ': t2), see if we can print
    -- it in list notation [t1, ...].
    pprTyList p ty1 ty2
      = case gather ty2 of
          (arg_tys, Nothing) -> char '\'' <> brackets (fsep (punctuate comma
                                                (map (ppr_type TopPrec) (ty1:arg_tys))))
          (arg_tys, Just tl) -> maybeParen p FunPrec $
                                hang (ppr_type FunPrec ty1)
                                   2 (fsep [ colon <+> ppr_type FunPrec ty | ty <- arg_tys ++ [tl]])
      where
        gather :: Type -> ([Type], Maybe Type)
         -- (gather ty) = (tys, Nothing) means ty is a list [t1, .., tn]
         --             = (tys, Just tl) means ty is of form t1:t2:...tn:tl
        gather (TyConApp tc tys)
          | tc `hasKey` consDataConKey
          , [_kind, ty1,ty2] <- tys
          , (args, tl) <- gather ty2
          = (ty1:args, tl)
          | tc `hasKey` nilDataConKey
          = ([], Nothing)
        gather ty = ([], Just ty)

    ----------------
    pprInfixApp :: Prec -> (Prec -> a -> SDoc) -> SDoc -> a -> a -> SDoc
    pprInfixApp p pp pp_tc ty1 ty2
      = maybeParen p FunPrec $
        sep [pp FunPrec ty1, pprInfixVar True pp_tc <+> pp FunPrec ty2]

    pprPrefixApp :: Prec -> SDoc -> [SDoc] -> SDoc
    pprPrefixApp p pp_fun pp_tys
      | null pp_tys = pp_fun
      | otherwise   = maybeParen p TyConPrec $
                      hang pp_fun 2 (sep pp_tys)

    ----------------
    pprArrowChain :: Prec -> [SDoc] -> SDoc
    -- pprArrowChain p [a,b,c]  generates   a -> b -> c
    pprArrowChain _ []         = empty
    pprArrowChain p (arg:args) = maybeParen p FunPrec $
                                 sep [arg, sep (map (arrow <+>) args)]

\end{code} %************************************************************************ %* * \subsection{TidyType} %* * %************************************************************************ Tidying is here because it has a special case for FlatSkol \begin{code}

    -- | This tidies up a type for printing in an error message, or in
    -- an interface file.
    --
    -- It doesn't change the uniques at all, just the print names.
    tidyTyVarBndrs :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
    tidyTyVarBndrs env tvs = mapAccumL tidyTyVarBndr env tvs

    tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
    tidyTyVarBndr tidy_env@(occ_env, subst) tyvar
      = case tidyOccName occ_env occ1 of
          (tidy', occ') -> ((tidy', subst'), tyvar')
    	where
              subst' = extendVarEnv subst tyvar tyvar'
              tyvar' = setTyVarKind (setTyVarName tyvar name') kind'
              name'  = tidyNameOcc name occ'
              kind'  = tidyKind tidy_env (tyVarKind tyvar)
      where
        name = tyVarName tyvar
        occ  = getOccName name
        -- System Names are for unification variables;
        -- when we tidy them we give them a trailing "0" (or 1 etc)
        -- so that they don't take precedence for the un-modified name
        occ1 | isSystemName name = mkTyVarOcc (occNameString occ ++ "0")
             | otherwise         = occ

    ---------------
    tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
    -- ^ Add the free 'TyVar's to the env in tidy form,
    -- so that we can tidy the type they are free in
    tidyFreeTyVars (full_occ_env, var_env) tyvars
      = fst (tidyOpenTyVars (full_occ_env, var_env) (varSetElems tyvars))

            ---------------
    tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
    tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars

    ---------------
    tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
    -- ^ Treat a new 'TyVar' as a binder, and give it a fresh tidy name
    -- using the environment if one has not already been allocated. See
    -- also 'tidyTyVarBndr'
    tidyOpenTyVar env@(_, subst) tyvar
      = case lookupVarEnv subst tyvar of
    	Just tyvar' -> (env, tyvar')		-- Already substituted
    	Nothing	    -> tidyTyVarBndr env tyvar	-- Treat it as a binder

    ---------------
    tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
    tidyTyVarOcc (_, subst) tv
      = case lookupVarEnv subst tv of
    	Nothing  -> tv
    	Just tv' -> tv'

    ---------------
    tidyTypes :: TidyEnv -> [Type] -> [Type]
    tidyTypes env tys = map (tidyType env) tys

    ---------------
    tidyType :: TidyEnv -> Type -> Type
    tidyType _   (LitTy n)            = LitTy n
    tidyType env (TyVarTy tv)	  = TyVarTy (tidyTyVarOcc env tv)
    tidyType env (TyConApp tycon tys) = let args = tidyTypes env tys
     		                    in args `seqList` TyConApp tycon args
    tidyType env (AppTy fun arg)	  = (AppTy $! (tidyType env fun)) $! (tidyType env arg)
    tidyType env (FunTy fun arg)	  = (FunTy $! (tidyType env fun)) $! (tidyType env arg)
    tidyType env (ForAllTy tv ty)	  = ForAllTy tvp $! (tidyType envp ty)
    			          where
    			            (envp, tvp) = tidyTyVarBndr env tv

    ---------------
    -- | Grabs the free type variables, tidies them
    -- and then uses 'tidyType' to work over the type itself
    tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
    tidyOpenType env ty
      = (env', tidyType (trimmed_occ_env, var_env) ty)
      where
        (env'@(_, var_env), tvs') = tidyOpenTyVars env (varSetElems (tyVarsOfType ty))
        trimmed_occ_env = initTidyOccEnv (map getOccName tvs')
          -- The idea here was that we restrict the new TidyEnv to the
          -- _free_ vars of the type, so that we don't gratuitously rename
          -- the _bound_ variables of the type.

    ---------------
    tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
    tidyOpenTypes env tys = mapAccumL tidyOpenType env tys

    ---------------
    -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
    tidyTopType :: Type -> Type
    tidyTopType ty = tidyType emptyTidyEnv ty

    ---------------
    tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
    tidyOpenKind = tidyOpenType

    tidyKind :: TidyEnv -> Kind -> Kind
    tidyKind = tidyType

\end{code}