types/Kind.lhs

% % (c) The University of Glasgow 2006-2012 % \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

    module Kind (
            -- * Main data type
            SuperKind, Kind, typeKind,

    	-- Kinds
    	anyKind, liftedTypeKind, unliftedTypeKind, openTypeKind, constraintKind,
            mkArrowKind, mkArrowKinds,

            -- Kind constructors...
            anyKindTyCon, liftedTypeKindTyCon, openTypeKindTyCon,
            unliftedTypeKindTyCon, constraintKindTyCon,

            -- Super Kinds
    	superKind, superKindTyCon,

    	pprKind, pprParendKind,

            -- ** Deconstructing Kinds
            kindAppResult, synTyConResKind,
            splitKindFunTys, splitKindFunTysN, splitKindFunTy_maybe,

            -- ** Predicates on Kinds
            isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
            isConstraintKind, isConstraintOrLiftedKind, returnsConstraintKind,
            isKind, isKindVar,
            isSuperKind, isSuperKindTyCon,
            isLiftedTypeKindCon, isConstraintKindCon,
            isAnyKind, isAnyKindCon,
            okArrowArgKind, okArrowResultKind,

            isSubOpenTypeKind, isSubOpenTypeKindKey,
            isSubKind, isSubKindCon,
            tcIsSubKind, tcIsSubKindCon,
            defaultKind, defaultKind_maybe,

            -- ** Functions on variables
            kiVarsOfKind, kiVarsOfKinds

           ) where

    #include "HsVersions.h"

    import {-# SOURCE #-} Type      ( typeKind, substKiWith, eqKind )

    import TypeRep
    import TysPrim
    import TyCon
    import VarSet
    import PrelNames
    import Outputable
    import Maybes( orElse )
    import Util

\end{code} %************************************************************************ %* * Functions over Kinds %* * %************************************************************************ Note [Kind Constraint and kind *] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The kind Constraint is the kind of classes and other type constraints. The special thing about types of kind Constraint is that * They are displayed with double arrow: f :: Ord a => a -> a * They are implicitly instantiated at call sites; so the type inference engine inserts an extra argument of type (Ord a) at every call site to f. However, once type inference is over, there is *no* distinction between Constraint and *. Indeed we can have coercions between the two. Consider class C a where op :: a -> a For this single-method class we may generate a newtype, which in turn generates an axiom witnessing Ord a ~ (a -> a) so on the left we have Constraint, and on the right we have *. See Trac #7451. Bottom line: although '*' and 'Constraint' are distinct TyCons, with distinct uniques, they are treated as equal at all times except during type inference. Hence cmpTc treats them as equal. \begin{code}

    -- | Essentially 'funResultTy' on kinds handling pi-types too
    kindFunResult :: Kind -> KindOrType -> Kind
    kindFunResult (FunTy _ res) _ = res
    kindFunResult (ForAllTy kv res) arg = substKiWith [kv] [arg] res
    kindFunResult k _ = pprPanic "kindFunResult" (ppr k)

    kindAppResult :: Kind -> [Type] -> Kind
    kindAppResult k []     = k
    kindAppResult k (a:as) = kindAppResult (kindFunResult k a) as

    -- | Essentially 'splitFunTys' on kinds
    splitKindFunTys :: Kind -> ([Kind],Kind)
    splitKindFunTys (FunTy a r) = case splitKindFunTys r of
                                  (as, k) -> (a:as, k)
    splitKindFunTys k = ([], k)

    splitKindFunTy_maybe :: Kind -> Maybe (Kind,Kind)
    splitKindFunTy_maybe (FunTy a r) = Just (a,r)
    splitKindFunTy_maybe _           = Nothing

    -- | Essentially 'splitFunTysN' on kinds
    splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
    splitKindFunTysN 0 k           = ([], k)
    splitKindFunTysN n (FunTy a r) = case splitKindFunTysN (n-1) r of
                                       (as, k) -> (a:as, k)
    splitKindFunTysN n k = pprPanic "splitKindFunTysN" (ppr n <+> ppr k)

    -- | Find the result 'Kind' of a type synonym,
    -- after applying it to its 'arity' number of type variables
    -- Actually this function works fine on data types too,
    -- but they'd always return '*', so we never need to ask
    synTyConResKind :: TyCon -> Kind
    synTyConResKind tycon = kindAppResult (tyConKind tycon) (map mkTyVarTy (tyConTyVars tycon))

    -- | See "Type#kind_subtyping" for details of the distinction between these 'Kind's
    isOpenTypeKind, isUnliftedTypeKind,
      isConstraintKind, isAnyKind, isConstraintOrLiftedKind :: Kind -> Bool

    isOpenTypeKindCon, isUnliftedTypeKindCon,
      isSubOpenTypeKindCon, isConstraintKindCon,
      isLiftedTypeKindCon, isAnyKindCon, isSuperKindTyCon :: TyCon -> Bool

    isLiftedTypeKindCon   tc = tyConUnique tc == liftedTypeKindTyConKey
    isAnyKindCon          tc = tyConUnique tc == anyKindTyConKey
    isOpenTypeKindCon     tc = tyConUnique tc == openTypeKindTyConKey
    isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
    isConstraintKindCon   tc = tyConUnique tc == constraintKindTyConKey
    isSuperKindTyCon      tc = tyConUnique tc == superKindTyConKey

    isAnyKind (TyConApp tc _) = isAnyKindCon tc
    isAnyKind _               = False

    isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
    isOpenTypeKind _               = False

    isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
    isUnliftedTypeKind _               = False

    isConstraintKind (TyConApp tc _) = isConstraintKindCon tc
    isConstraintKind _               = False

    isConstraintOrLiftedKind (TyConApp tc _)
      = isConstraintKindCon tc || isLiftedTypeKindCon tc
    isConstraintOrLiftedKind _ = False

    returnsConstraintKind :: Kind -> Bool
    returnsConstraintKind (ForAllTy _ k)  = returnsConstraintKind k
    returnsConstraintKind (FunTy _ k)     = returnsConstraintKind k
    returnsConstraintKind (TyConApp tc _) = isConstraintKindCon tc
    returnsConstraintKind _               = False

    --------------------------------------------
    --            Kinding for arrow (->)
    -- Says when a kind is acceptable on lhs or rhs of an arrow
    --     arg -> res

    okArrowArgKindCon, okArrowResultKindCon :: TyCon -> Bool
    okArrowArgKindCon    = isSubOpenTypeKindCon
    okArrowResultKindCon = isSubOpenTypeKindCon

    okArrowArgKind, okArrowResultKind :: Kind -> Bool
    okArrowArgKind    (TyConApp kc []) = okArrowArgKindCon kc
    okArrowArgKind    _                = False

    okArrowResultKind (TyConApp kc []) = okArrowResultKindCon kc
    okArrowResultKind _                = False

    -----------------------------------------
    --              Subkinding
    -- The tc variants are used during type-checking, where we don't want the
    -- Constraint kind to be a subkind of anything
    -- After type-checking (in core), Constraint is a subkind of openTypeKind

    isSubOpenTypeKind :: Kind -> Bool
    -- ^ True of any sub-kind of OpenTypeKind
    isSubOpenTypeKind (TyConApp kc []) = isSubOpenTypeKindCon kc
    isSubOpenTypeKind _                = False

    isSubOpenTypeKindCon kc = isSubOpenTypeKindKey (tyConUnique kc)

    isSubOpenTypeKindKey :: Unique -> Bool
    isSubOpenTypeKindKey uniq
      =  uniq == openTypeKindTyConKey
      || uniq == unliftedTypeKindTyConKey
      || uniq == liftedTypeKindTyConKey
      || uniq == constraintKindTyConKey  -- Needed for error (Num a) "blah"
                                         -- and so that (Ord a -> Eq a) is well-kinded
                                         -- and so that (# Eq a, Ord b #) is well-kinded
                                  	     -- See Note [Kind Constraint and kind *]

    -- | Is this a kind (i.e. a type-of-types)?
    isKind :: Kind -> Bool
    isKind k = isSuperKind (typeKind k)

    isSubKind :: Kind -> Kind -> Bool
    -- ^ @k1 \`isSubKind\` k2@ checks that @k1@ <: @k2@
    -- Sub-kinding is extremely simple and does not look
    -- under arrrows or type constructors

    -- If you edit this function, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    isSubKind k1@(TyConApp kc1 k1s) k2@(TyConApp kc2 k2s)
      | isPromotedTyCon kc1 || isPromotedTyCon kc2
        -- handles promoted kinds (List *, Nat, etc.)
      = eqKind k1 k2

      | otherwise -- handles usual kinds (*, #, (#), etc.)
      = ASSERT2( null k1s && null k2s, ppr k1 <+> ppr k2 )
        kc1 `isSubKindCon` kc2

    isSubKind k1 k2 = eqKind k1 k2

    isSubKindCon :: TyCon -> TyCon -> Bool
    -- ^ @kc1 \`isSubKindCon\` kc2@ checks that @kc1@ <: @kc2@

    -- If you edit this function, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    isSubKindCon kc1 kc2
      | kc1 == kc2              = True
      | isOpenTypeKindCon kc2   = isSubOpenTypeKindCon kc1
      | isConstraintKindCon kc1 = isLiftedTypeKindCon kc2
      | isLiftedTypeKindCon kc1 = isConstraintKindCon kc2
        -- See Note [Kind Constraint and kind *]
      | otherwise               = False

    -------------------------
    -- Hack alert: we need a tiny variant for the typechecker
    -- Reason:     f :: Int -> (a~b)
    --             g :: forall (c::Constraint). Int -> c
    --             h :: Int => Int
    -- We want to reject these, even though Constraint is
    -- a sub-kind of OpenTypeKind.  It must be a sub-kind of OpenTypeKind
    -- *after* the typechecker
    --   a) So that (Ord a -> Eq a) is a legal type
    --   b) So that the simplifer can generate (error (Eq a) "urk")
    -- Moreover, after the type checker, Constraint and *
    -- are identical; see Note [Kind Constraint and kind *]
    --
    -- Easiest way to reject is simply to make Constraint a compliete
    -- below OpenTypeKind when type checking

    tcIsSubKind :: Kind -> Kind -> Bool
    tcIsSubKind k1 k2
      | isConstraintKind k1 = isConstraintKind k2
      | isConstraintKind k2 = isConstraintKind k1
      | otherwise           = isSubKind k1 k2

    tcIsSubKindCon :: TyCon -> TyCon -> Bool
    tcIsSubKindCon kc1 kc2
      | isConstraintKindCon kc1 = isConstraintKindCon kc2
      | isConstraintKindCon kc2 = isConstraintKindCon kc1
      | otherwise               = isSubKindCon kc1 kc2

    -------------------------
    defaultKind       :: Kind -> Kind
    defaultKind_maybe :: Kind -> Maybe Kind
    -- ^ Used when generalising: default OpenKind and ArgKind to *.
    -- See "Type#kind_subtyping" for more information on what that means

    -- When we generalise, we make generic type variables whose kind is
    -- simple (* or *->* etc).  So generic type variables (other than
    -- built-in constants like 'error') always have simple kinds.  This is important;
    -- consider
    --	f x = True
    -- We want f to get type
    --	f :: forall (a::*). a -> Bool
    -- Not
    --	f :: forall (a::ArgKind). a -> Bool
    -- because that would allow a call like (f 3#) as well as (f True),
    -- and the calling conventions differ.
    -- This defaulting is done in TcMType.zonkTcTyVarBndr.
    --
    -- The test is really whether the kind is strictly above '*'
    defaultKind_maybe (TyConApp kc _args)
      | isOpenTypeKindCon kc = ASSERT( null _args ) Just liftedTypeKind
    defaultKind_maybe _      = Nothing

    defaultKind k = defaultKind_maybe k `orElse` k

    -- Returns the free kind variables in a kind
    kiVarsOfKind :: Kind -> VarSet
    kiVarsOfKind = tyVarsOfType

    kiVarsOfKinds :: [Kind] -> VarSet
    kiVarsOfKinds = tyVarsOfTypes

\end{code}