TcValidity.hs

{-
(c) The University of Glasgow 2006
(c) The GRASP/AQUA Project, Glasgow University, 1992-1998
-}

{-# LANGUAGE CPP, TupleSections, ViewPatterns #-}

module TcValidity (
  Rank, UserTypeCtxt(..), checkValidType, checkValidMonoType,
  ContextKind(..), expectedKindInCtxt,
  checkValidTheta, checkValidFamPats,
  checkValidInstance, validDerivPred,
  checkInstTermination, checkTySynRhs,
  ClsInstInfo, checkValidCoAxiom, checkValidCoAxBranch,
  checkValidTyFamEqn,
  arityErr, badATErr,
  checkValidTelescope, checkZonkValidTelescope, checkValidInferredKinds,
  allDistinctTyVars
  ) where

#include "HsVersions.h"

import Maybes

-- friends:
import TcUnify    ( tcSubType_NC )
import TcSimplify ( simplifyAmbiguityCheck )
import TyCoRep
import TcType hiding ( sizeType, sizeTypes )
import TcMType
import PrelNames
import Type
import Coercion
import Kind
import CoAxiom
import Class
import TyCon

-- others:
import HsSyn            -- HsType
import TcRnMonad        -- TcType, amongst others
import TcEnv       ( tcGetInstEnvs )
import FunDeps
import InstEnv     ( InstMatch, lookupInstEnv )
import FamInstEnv  ( isDominatedBy, injectiveBranches,
                     InjectivityCheckResult(..) )
import FamInst     ( makeInjectivityErrors )
import Name
import VarEnv
import VarSet
import UniqSet
import Var         ( TyVarBndr(..), mkTyVar )
import ErrUtils
import DynFlags
import Util
import ListSetOps
import SrcLoc
import Outputable
import Module
import Unique      ( mkAlphaTyVarUnique )
import qualified GHC.LanguageExtensions as LangExt

import Control.Monad
import Data.List        ( (\\) )

{-
************************************************************************
*                                                                      *
          Checking for ambiguity
*                                                                      *
************************************************************************

Note [The ambiguity check for type signatures]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
checkAmbiguity is a check on *user-supplied type signatures*.  It is
*purely* there to report functions that cannot possibly be called.  So for
example we want to reject:
   f :: C a => Int
The idea is there can be no legal calls to 'f' because every call will
give rise to an ambiguous constraint.  We could soundly omit the
ambiguity check on type signatures entirely, at the expense of
delaying ambiguity errors to call sites.  Indeed, the flag
-XAllowAmbiguousTypes switches off the ambiguity check.

What about things like this:
   class D a b | a -> b where ..
   h :: D Int b => Int
The Int may well fix 'b' at the call site, so that signature should
not be rejected.  Moreover, using *visible* fundeps is too
conservative.  Consider
   class X a b where ...
   class D a b | a -> b where ...
   instance D a b => X [a] b where...
   h :: X a b => a -> a
Here h's type looks ambiguous in 'b', but here's a legal call:
   ...(h [True])...
That gives rise to a (X [Bool] beta) constraint, and using the
instance means we need (D Bool beta) and that fixes 'beta' via D's
fundep!

Behind all these special cases there is a simple guiding principle.
Consider

  f :: <type>
  f = ...blah...

  g :: <type>
  g = f

You would think that the definition of g would surely typecheck!
After all f has exactly the same type, and g=f. But in fact f's type
is instantiated and the instantiated constraints are solved against
the originals, so in the case an ambiguous type it won't work.
Consider our earlier example f :: C a => Int.  Then in g's definition,
we'll instantiate to (C alpha) and try to deduce (C alpha) from (C a),
and fail.

So in fact we use this as our *definition* of ambiguity.  We use a
very similar test for *inferred* types, to ensure that they are
unambiguous. See Note [Impedance matching] in TcBinds.

This test is very conveniently implemented by calling
    tcSubType <type> <type>
This neatly takes account of the functional dependecy stuff above,
and implicit parameter (see Note [Implicit parameters and ambiguity]).
And this is what checkAmbiguity does.

What about this, though?
   g :: C [a] => Int
Is every call to 'g' ambiguous?  After all, we might have
   instance C [a] where ...
at the call site.  So maybe that type is ok!  Indeed even f's
quintessentially ambiguous type might, just possibly be callable:
with -XFlexibleInstances we could have
  instance C a where ...
and now a call could be legal after all!  Well, we'll reject this
unless the instance is available *here*.

Note [When to call checkAmbiguity]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We call checkAmbiguity
   (a) on user-specified type signatures
   (b) in checkValidType

Conncerning (b), you might wonder about nested foralls.  What about
    f :: forall b. (forall a. Eq a => b) -> b
The nested forall is ambiguous.  Originally we called checkAmbiguity
in the forall case of check_type, but that had two bad consequences:
  * We got two error messages about (Eq b) in a nested forall like this:
       g :: forall a. Eq a => forall b. Eq b => a -> a
  * If we try to check for ambiguity of an nested forall like
    (forall a. Eq a => b), the implication constraint doesn't bind
    all the skolems, which results in "No skolem info" in error
    messages (see Trac #10432).

To avoid this, we call checkAmbiguity once, at the top, in checkValidType.
(I'm still a bit worried about unbound skolems when the type mentions
in-scope type variables.)

In fact, because of the co/contra-variance implemented in tcSubType,
this *does* catch function f above. too.

Concerning (a) the ambiguity check is only used for *user* types, not
for types coming from inteface files.  The latter can legitimately
have ambiguous types. Example

   class S a where s :: a -> (Int,Int)
   instance S Char where s _ = (1,1)
   f:: S a => [a] -> Int -> (Int,Int)
   f (_::[a]) x = (a*x,b)
        where (a,b) = s (undefined::a)

Here the worker for f gets the type
        fw :: forall a. S a => Int -> (# Int, Int #)


Note [Implicit parameters and ambiguity]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Only a *class* predicate can give rise to ambiguity
An *implicit parameter* cannot.  For example:
        foo :: (?x :: [a]) => Int
        foo = length ?x
is fine.  The call site will supply a particular 'x'

Furthermore, the type variables fixed by an implicit parameter
propagate to the others.  E.g.
        foo :: (Show a, ?x::[a]) => Int
        foo = show (?x++?x)
The type of foo looks ambiguous.  But it isn't, because at a call site
we might have
        let ?x = 5::Int in foo
and all is well.  In effect, implicit parameters are, well, parameters,
so we can take their type variables into account as part of the
"tau-tvs" stuff.  This is done in the function 'FunDeps.grow'.
-}

checkAmbiguity :: UserTypeCtxt -> Type -> TcM ()
checkAmbiguity ctxt ty
  | wantAmbiguityCheck ctxt
  = do { traceTc "Ambiguity check for" (ppr ty)
         -- Solve the constraints eagerly because an ambiguous type
         -- can cause a cascade of further errors.  Since the free
         -- tyvars are skolemised, we can safely use tcSimplifyTop
       ; allow_ambiguous <- xoptM LangExt.AllowAmbiguousTypes
       ; (_wrap, wanted) <- addErrCtxt (mk_msg allow_ambiguous) $
                            captureConstraints $
                            tcSubType_NC ctxt ty ty
       ; simplifyAmbiguityCheck ty wanted

       ; traceTc "Done ambiguity check for" (ppr ty) }

  | otherwise
  = return ()
 where
   mk_msg allow_ambiguous
     = vcat [ text "In the ambiguity check for" <+> what
            , ppUnless allow_ambiguous ambig_msg ]
   ambig_msg = text "To defer the ambiguity check to use sites, enable AllowAmbiguousTypes"
   what | Just n <- isSigMaybe ctxt = quotes (ppr n)
        | otherwise                 = pprUserTypeCtxt ctxt

wantAmbiguityCheck :: UserTypeCtxt -> Bool
wantAmbiguityCheck ctxt
  = case ctxt of  -- See Note [When we don't check for ambiguity]
      GhciCtxt     -> False
      TySynCtxt {} -> False
      _            -> True

checkUserTypeError :: Type -> TcM ()
-- Check to see if the type signature mentions "TypeError blah"
-- anywhere in it, and fail if so.
--
-- Very unsatisfactorily (Trac #11144) we need to tidy the type
-- because it may have come from an /inferred/ signature, not a
-- user-supplied one.  This is really only a half-baked fix;
-- the other errors in checkValidType don't do tidying, and so
-- may give bad error messages when given an inferred type.
checkUserTypeError = check
  where
  check ty
    | Just msg     <- userTypeError_maybe ty  = fail_with msg
    | Just (_,ts)  <- splitTyConApp_maybe ty  = mapM_ check ts
    | Just (t1,t2) <- splitAppTy_maybe ty     = check t1 >> check t2
    | Just (_,t1)  <- splitForAllTy_maybe ty  = check t1
    | otherwise                               = return ()

  fail_with msg = do { env0 <- tcInitTidyEnv
                     ; let (env1, tidy_msg) = tidyOpenType env0 msg
                     ; failWithTcM (env1, pprUserTypeErrorTy tidy_msg) }


{- Note [When we don't check for ambiguity]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In a few places we do not want to check a user-specified type for ambiguity

* GhciCtxt: Allow ambiguous types in GHCi's :kind command
  E.g.   type family T a :: *  -- T :: forall k. k -> *
  Then :k T should work in GHCi, not complain that
  (T k) is ambiguous!

* TySynCtxt: type T a b = C a b => blah
  It may be that when we /use/ T, we'll give an 'a' or 'b' that somehow
  cure the ambiguity.  So we defer the ambiguity check to the use site.

  There is also an implementation reason (Trac #11608).  In the RHS of
  a type synonym we don't (currently) instantiate 'a' and 'b' with
  TcTyVars before calling checkValidType, so we get asertion failures
  from doing an ambiguity check on a type with TyVars in it.  Fixing this
  would not be hard, but let's wait till there's a reason.


************************************************************************
*                                                                      *
          Checking validity of a user-defined type
*                                                                      *
************************************************************************

When dealing with a user-written type, we first translate it from an HsType
to a Type, performing kind checking, and then check various things that should
be true about it.  We don't want to perform these checks at the same time
as the initial translation because (a) they are unnecessary for interface-file
types and (b) when checking a mutually recursive group of type and class decls,
we can't "look" at the tycons/classes yet.  Also, the checks are rather
diverse, and used to really mess up the other code.

One thing we check for is 'rank'.

        Rank 0:         monotypes (no foralls)
        Rank 1:         foralls at the front only, Rank 0 inside
        Rank 2:         foralls at the front, Rank 1 on left of fn arrow,

        basic ::= tyvar | T basic ... basic

        r2  ::= forall tvs. cxt => r2a
        r2a ::= r1 -> r2a | basic
        r1  ::= forall tvs. cxt => r0
        r0  ::= r0 -> r0 | basic

Another thing is to check that type synonyms are saturated.
This might not necessarily show up in kind checking.
        type A i = i
        data T k = MkT (k Int)
        f :: T A        -- BAD!
-}

checkValidType :: UserTypeCtxt -> Type -> TcM ()
-- Checks that a user-written type is valid for the given context
-- Assumes argument is fully zonked
-- Not used for instance decls; checkValidInstance instead
checkValidType ctxt ty
  = do { traceTc "checkValidType" (ppr ty <+> text "::" <+> ppr (typeKind ty))
       ; rankn_flag  <- xoptM LangExt.RankNTypes
       ; impred_flag <- xoptM LangExt.ImpredicativeTypes
       ; let gen_rank :: Rank -> Rank
             gen_rank r | rankn_flag = ArbitraryRank
                        | otherwise  = r

             rank1 = gen_rank r1
             rank0 = gen_rank r0

             r0 = rankZeroMonoType
             r1 = LimitedRank True r0

             rank
               = case ctxt of
                 DefaultDeclCtxt-> MustBeMonoType
                 ResSigCtxt     -> MustBeMonoType
                 PatSigCtxt     -> rank0
                 RuleSigCtxt _  -> rank1
                 TySynCtxt _    -> rank0

                 ExprSigCtxt    -> rank1
                 TypeAppCtxt | impred_flag -> ArbitraryRank
                             | otherwise   -> tyConArgMonoType
                    -- Normally, ImpredicativeTypes is handled in check_arg_type,
                    -- but visible type applications don't go through there.
                    -- So we do this check here.

                 FunSigCtxt {}  -> rank1
                 InfSigCtxt _   -> ArbitraryRank        -- Inferred type
                 ConArgCtxt _   -> rank1 -- We are given the type of the entire
                                         -- constructor, hence rank 1
                 PatSynCtxt _   -> rank1

                 ForSigCtxt _   -> rank1
                 SpecInstCtxt   -> rank1
                 ThBrackCtxt    -> rank1
                 GhciCtxt       -> ArbitraryRank
                 _              -> panic "checkValidType"
                                          -- Can't happen; not used for *user* sigs

       ; env <- tcInitOpenTidyEnv (tyCoVarsOfTypeList ty)

        -- Check the internal validity of the type itself
       ; check_type env ctxt rank ty

       ; checkUserTypeError ty

       -- Check for ambiguous types.  See Note [When to call checkAmbiguity]
       -- NB: this will happen even for monotypes, but that should be cheap;
       --     and there may be nested foralls for the subtype test to examine
       ; checkAmbiguity ctxt ty

       ; traceTc "checkValidType done" (ppr ty <+> text "::" <+> ppr (typeKind ty)) }

checkValidMonoType :: Type -> TcM ()
-- Assumes argument is fully zonked
checkValidMonoType ty
  = do { env <- tcInitOpenTidyEnv (tyCoVarsOfTypeList ty)
       ; check_type env SigmaCtxt MustBeMonoType ty }

checkTySynRhs :: UserTypeCtxt -> TcType -> TcM ()
checkTySynRhs ctxt ty
  | returnsConstraintKind actual_kind
  = do { ck <- xoptM LangExt.ConstraintKinds
       ; if ck
         then  when (isConstraintKind actual_kind)
                    (do { dflags <- getDynFlags
                        ; check_pred_ty emptyTidyEnv dflags ctxt ty })
         else addErrTcM (constraintSynErr emptyTidyEnv actual_kind) }

  | otherwise
  = return ()
  where
    actual_kind = typeKind ty

-- | The kind expected in a certain context.
data ContextKind = TheKind Kind   -- ^ a specific kind
                 | AnythingKind   -- ^ any kind will do
                 | OpenKind       -- ^ something of the form @TYPE _@

-- Depending on the context, we might accept any kind (for instance, in a TH
-- splice), or only certain kinds (like in type signatures).
expectedKindInCtxt :: UserTypeCtxt -> ContextKind
expectedKindInCtxt (TySynCtxt _)   = AnythingKind
expectedKindInCtxt ThBrackCtxt     = AnythingKind
expectedKindInCtxt GhciCtxt        = AnythingKind
-- The types in a 'default' decl can have varying kinds
-- See Note [Extended defaults]" in TcEnv
expectedKindInCtxt DefaultDeclCtxt = AnythingKind
expectedKindInCtxt TypeAppCtxt     = AnythingKind
expectedKindInCtxt (ForSigCtxt _)  = TheKind liftedTypeKind
expectedKindInCtxt InstDeclCtxt    = TheKind constraintKind
expectedKindInCtxt SpecInstCtxt    = TheKind constraintKind
expectedKindInCtxt _               = OpenKind

{-
Note [Higher rank types]
~~~~~~~~~~~~~~~~~~~~~~~~
Technically
            Int -> forall a. a->a
is still a rank-1 type, but it's not Haskell 98 (Trac #5957).  So the
validity checker allow a forall after an arrow only if we allow it
before -- that is, with Rank2Types or RankNTypes
-}

data Rank = ArbitraryRank         -- Any rank ok

          | LimitedRank   -- Note [Higher rank types]
                 Bool     -- Forall ok at top
                 Rank     -- Use for function arguments

          | MonoType SDoc   -- Monotype, with a suggestion of how it could be a polytype

          | MustBeMonoType  -- Monotype regardless of flags


rankZeroMonoType, tyConArgMonoType, synArgMonoType, constraintMonoType :: Rank
rankZeroMonoType   = MonoType (text "Perhaps you intended to use RankNTypes or Rank2Types")
tyConArgMonoType   = MonoType (text "GHC doesn't yet support impredicative polymorphism")
synArgMonoType     = MonoType (text "Perhaps you intended to use LiberalTypeSynonyms")
constraintMonoType = MonoType (text "A constraint must be a monotype")

funArgResRank :: Rank -> (Rank, Rank)             -- Function argument and result
funArgResRank (LimitedRank _ arg_rank) = (arg_rank, LimitedRank (forAllAllowed arg_rank) arg_rank)
funArgResRank other_rank               = (other_rank, other_rank)

forAllAllowed :: Rank -> Bool
forAllAllowed ArbitraryRank             = True
forAllAllowed (LimitedRank forall_ok _) = forall_ok
forAllAllowed _                         = False

----------------------------------------
check_type :: TidyEnv -> UserTypeCtxt -> Rank -> Type -> TcM ()
-- The args say what the *type context* requires, independent
-- of *flag* settings.  You test the flag settings at usage sites.
--
-- Rank is allowed rank for function args
-- Rank 0 means no for-alls anywhere

check_type env ctxt rank ty
  | not (null tvs && null theta)
  = do  { traceTc "check_type" (ppr ty $$ ppr (forAllAllowed rank))
        ; checkTcM (forAllAllowed rank) (forAllTyErr env rank ty)
                -- Reject e.g. (Maybe (?x::Int => Int)),
                -- with a decent error message

        ; check_valid_theta env' SigmaCtxt theta
                -- Allow     type T = ?x::Int => Int -> Int
                -- but not   type T = ?x::Int

        ; check_type env' ctxt rank tau      -- Allow foralls to right of arrow
        ; checkTcM (not (any (`elemVarSet` tyCoVarsOfType phi_kind) tvs))
                   (forAllEscapeErr env' ty tau_kind)
        }
  where
    (tvs, theta, tau) = tcSplitSigmaTy ty
    tau_kind          = typeKind tau
    (env', _)         = tidyTyCoVarBndrs env tvs

    phi_kind | null theta = tau_kind
             | otherwise  = liftedTypeKind
        -- If there are any constraints, the kind is *. (#11405)

check_type _ _ _ (TyVarTy _) = return ()

check_type env ctxt rank (FunTy arg_ty res_ty)
  = do  { check_type env ctxt arg_rank arg_ty
        ; check_type env ctxt res_rank res_ty }
  where
    (arg_rank, res_rank) = funArgResRank rank

check_type env ctxt rank (AppTy ty1 ty2)
  = do  { check_arg_type env ctxt rank ty1
        ; check_arg_type env ctxt rank ty2 }

check_type env ctxt rank ty@(TyConApp tc tys)
  | isTypeSynonymTyCon tc || isTypeFamilyTyCon tc
  = check_syn_tc_app env ctxt rank ty tc tys
  | isUnboxedTupleTyCon tc = check_ubx_tuple  env ctxt      ty    tys
  | otherwise              = mapM_ (check_arg_type env ctxt rank) tys

check_type _ _ _ (LitTy {}) = return ()

check_type env ctxt rank (CastTy ty _) = check_type env ctxt rank ty

check_type _ _ _ ty = pprPanic "check_type" (ppr ty)

----------------------------------------
check_syn_tc_app :: TidyEnv -> UserTypeCtxt -> Rank -> KindOrType
                 -> TyCon -> [KindOrType] -> TcM ()
-- Used for type synonyms and type synonym families,
-- which must be saturated,
-- but not data families, which need not be saturated
check_syn_tc_app env ctxt rank ty tc tys
  | tys `lengthAtLeast` tc_arity   -- Saturated
       -- Check that the synonym has enough args
       -- This applies equally to open and closed synonyms
       -- It's OK to have an *over-applied* type synonym
       --      data Tree a b = ...
       --      type Foo a = Tree [a]
       --      f :: Foo a b -> ...
  = do  { -- See Note [Liberal type synonyms]
        ; liberal <- xoptM LangExt.LiberalTypeSynonyms
        ; if not liberal || isTypeFamilyTyCon tc then
                -- For H98 and synonym families, do check the type args
                mapM_ check_arg tys

          else  -- In the liberal case (only for closed syns), expand then check
          case tcView ty of
             Just ty' -> check_type env ctxt rank ty'
             Nothing  -> pprPanic "check_tau_type" (ppr ty)  }

  | GhciCtxt <- ctxt  -- Accept under-saturated type synonyms in
                      -- GHCi :kind commands; see Trac #7586
  = mapM_ check_arg tys

  | otherwise
  = failWithTc (tyConArityErr tc tys)
  where
    tc_arity  = tyConArity tc
    check_arg | isTypeFamilyTyCon tc = check_arg_type  env ctxt rank
              | otherwise            = check_type      env ctxt synArgMonoType

----------------------------------------
check_ubx_tuple :: TidyEnv -> UserTypeCtxt -> KindOrType
                -> [KindOrType] -> TcM ()
check_ubx_tuple env ctxt ty tys
  = do  { ub_tuples_allowed <- xoptM LangExt.UnboxedTuples
        ; checkTcM ub_tuples_allowed (ubxArgTyErr env ty)

        ; impred <- xoptM LangExt.ImpredicativeTypes
        ; let rank' = if impred then ArbitraryRank else tyConArgMonoType
                -- c.f. check_arg_type
                -- However, args are allowed to be unlifted, or
                -- more unboxed tuples, so can't use check_arg_ty
        ; mapM_ (check_type env ctxt rank') tys }

----------------------------------------
check_arg_type :: TidyEnv -> UserTypeCtxt -> Rank -> KindOrType -> TcM ()
-- The sort of type that can instantiate a type variable,
-- or be the argument of a type constructor.
-- Not an unboxed tuple, but now *can* be a forall (since impredicativity)
-- Other unboxed types are very occasionally allowed as type
-- arguments depending on the kind of the type constructor
--
-- For example, we want to reject things like:
--
--      instance Ord a => Ord (forall s. T s a)
-- and
--      g :: T s (forall b.b)
--
-- NB: unboxed tuples can have polymorphic or unboxed args.
--     This happens in the workers for functions returning
--     product types with polymorphic components.
--     But not in user code.
-- Anyway, they are dealt with by a special case in check_tau_type

check_arg_type _ _ _ (CoercionTy {}) = return ()

check_arg_type env ctxt rank ty
  = do  { impred <- xoptM LangExt.ImpredicativeTypes
        ; let rank' = case rank of          -- Predictive => must be monotype
                        MustBeMonoType     -> MustBeMonoType  -- Monotype, regardless
                        _other | impred    -> ArbitraryRank
                               | otherwise -> tyConArgMonoType
                        -- Make sure that MustBeMonoType is propagated,
                        -- so that we don't suggest -XImpredicativeTypes in
                        --    (Ord (forall a.a)) => a -> a
                        -- and so that if it Must be a monotype, we check that it is!

        ; check_type env ctxt rank' ty }

----------------------------------------
forAllTyErr :: TidyEnv -> Rank -> Type -> (TidyEnv, SDoc)
forAllTyErr env rank ty
   = ( env
     , vcat [ hang herald 2 (ppr_tidy env ty)
            , suggestion ] )
  where
    (tvs, _theta, _tau) = tcSplitSigmaTy ty
    herald | null tvs  = text "Illegal qualified type:"
           | otherwise = text "Illegal polymorphic type:"
    suggestion = case rank of
                   LimitedRank {} -> text "Perhaps you intended to use RankNTypes or Rank2Types"
                   MonoType d     -> d
                   _              -> Outputable.empty -- Polytype is always illegal

forAllEscapeErr :: TidyEnv -> Type -> Kind -> (TidyEnv, SDoc)
forAllEscapeErr env ty tau_kind
  = ( env
    , hang (vcat [ text "Quantified type's kind mentions quantified type variable"
                 , text "(skolem escape)" ])
         2 (vcat [ text "   type:" <+> ppr_tidy env ty
                 , text "of kind:" <+> ppr_tidy env tau_kind ]) )

ubxArgTyErr :: TidyEnv -> Type -> (TidyEnv, SDoc)
ubxArgTyErr env ty = (env, sep [text "Illegal unboxed tuple type as function argument:", ppr_tidy env ty])

{-
Note [Liberal type synonyms]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If -XLiberalTypeSynonyms is on, expand closed type synonyms *before*
doing validity checking.  This allows us to instantiate a synonym defn
with a for-all type, or with a partially-applied type synonym.
        e.g.   type T a b = a
               type S m   = m ()
               f :: S (T Int)
Here, T is partially applied, so it's illegal in H98.  But if you
expand S first, then T we get just
               f :: Int
which is fine.

IMPORTANT: suppose T is a type synonym.  Then we must do validity
checking on an appliation (T ty1 ty2)

        *either* before expansion (i.e. check ty1, ty2)
        *or* after expansion (i.e. expand T ty1 ty2, and then check)
        BUT NOT BOTH

If we do both, we get exponential behaviour!!

  data TIACons1 i r c = c i ::: r c
  type TIACons2 t x = TIACons1 t (TIACons1 t x)
  type TIACons3 t x = TIACons2 t (TIACons1 t x)
  type TIACons4 t x = TIACons2 t (TIACons2 t x)
  type TIACons7 t x = TIACons4 t (TIACons3 t x)


************************************************************************
*                                                                      *
\subsection{Checking a theta or source type}
*                                                                      *
************************************************************************

Note [Implicit parameters in instance decls]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Implicit parameters _only_ allowed in type signatures; not in instance
decls, superclasses etc. The reason for not allowing implicit params in
instances is a bit subtle.  If we allowed
  instance (?x::Int, Eq a) => Foo [a] where ...
then when we saw
     (e :: (?x::Int) => t)
it would be unclear how to discharge all the potential uses of the ?x
in e.  For example, a constraint Foo [Int] might come out of e, and
applying the instance decl would show up two uses of ?x.  Trac #8912.
-}

checkValidTheta :: UserTypeCtxt -> ThetaType -> TcM ()
-- Assumes argument is fully zonked
checkValidTheta ctxt theta
  = do { env <- tcInitOpenTidyEnv (tyCoVarsOfTypesList theta)
       ; addErrCtxtM (checkThetaCtxt ctxt theta) $
         check_valid_theta env ctxt theta }

-------------------------
check_valid_theta :: TidyEnv -> UserTypeCtxt -> [PredType] -> TcM ()
check_valid_theta _ _ []
  = return ()
check_valid_theta env ctxt theta
  = do { dflags <- getDynFlags
       ; warnTcM (Reason Opt_WarnDuplicateConstraints)
                 (wopt Opt_WarnDuplicateConstraints dflags && notNull dups)
                 (dupPredWarn env dups)
       ; traceTc "check_valid_theta" (ppr theta)
       ; mapM_ (check_pred_ty env dflags ctxt) theta }
  where
    (_,dups) = removeDups nonDetCmpType theta
    -- It's OK to use nonDetCmpType because dups only appears in the
    -- warning

-------------------------
{- Note [Validity checking for constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We look through constraint synonyms so that we can see the underlying
constraint(s).  For example
   type Foo = ?x::Int
   instance Foo => C T
We should reject the instance because it has an implicit parameter in
the context.

But we record, in 'under_syn', whether we have looked under a synonym
to avoid requiring language extensions at the use site.  Main example
(Trac #9838):

   {-# LANGUAGE ConstraintKinds #-}
   module A where
      type EqShow a = (Eq a, Show a)

   module B where
      import A
      foo :: EqShow a => a -> String

We don't want to require ConstraintKinds in module B.
-}

check_pred_ty :: TidyEnv -> DynFlags -> UserTypeCtxt -> PredType -> TcM ()
-- Check the validity of a predicate in a signature
-- See Note [Validity checking for constraints]
check_pred_ty env dflags ctxt pred
  = do { check_type env SigmaCtxt constraintMonoType pred
       ; check_pred_help False env dflags ctxt pred }

check_pred_help :: Bool    -- True <=> under a type synonym
                -> TidyEnv
                -> DynFlags -> UserTypeCtxt
                -> PredType -> TcM ()
check_pred_help under_syn env dflags ctxt pred
  | Just pred' <- tcView pred  -- Switch on under_syn when going under a
                                 -- synonym (Trac #9838, yuk)
  = check_pred_help True env dflags ctxt pred'
  | otherwise
  = case splitTyConApp_maybe pred of
      Just (tc, tys)
        | isTupleTyCon tc
        -> check_tuple_pred under_syn env dflags ctxt pred tys
           -- NB: this equality check must come first, because (~) is a class,
           -- too.
        | tc `hasKey` heqTyConKey ||
          tc `hasKey` eqTyConKey ||
          tc `hasKey` eqPrimTyConKey
        -> check_eq_pred env dflags pred tc tys
        | Just cls <- tyConClass_maybe tc
        -> check_class_pred env dflags ctxt pred cls tys  -- Includes Coercible
      _ -> check_irred_pred under_syn env dflags ctxt pred

check_eq_pred :: TidyEnv -> DynFlags -> PredType -> TyCon -> [TcType] -> TcM ()
check_eq_pred env dflags pred tc tys
  =         -- Equational constraints are valid in all contexts if type
            -- families are permitted
    do { checkTc (tys `lengthIs` tyConArity tc) (tyConArityErr tc tys)
       ; checkTcM (xopt LangExt.TypeFamilies dflags
                   || xopt LangExt.GADTs dflags)
                  (eqPredTyErr env pred) }

check_tuple_pred :: Bool -> TidyEnv -> DynFlags -> UserTypeCtxt -> PredType -> [PredType] -> TcM ()
check_tuple_pred under_syn env dflags ctxt pred ts
  = do { -- See Note [ConstraintKinds in predicates]
         checkTcM (under_syn || xopt LangExt.ConstraintKinds dflags)
                  (predTupleErr env pred)
       ; mapM_ (check_pred_help under_syn env dflags ctxt) ts }
    -- This case will not normally be executed because without
    -- -XConstraintKinds tuple types are only kind-checked as *

check_irred_pred :: Bool -> TidyEnv -> DynFlags -> UserTypeCtxt -> PredType -> TcM ()
check_irred_pred under_syn env dflags ctxt pred
    -- The predicate looks like (X t1 t2) or (x t1 t2) :: Constraint
    -- where X is a type function
  = do { -- If it looks like (x t1 t2), require ConstraintKinds
         --   see Note [ConstraintKinds in predicates]
         -- But (X t1 t2) is always ok because we just require ConstraintKinds
         -- at the definition site (Trac #9838)
        failIfTcM (not under_syn && not (xopt LangExt.ConstraintKinds dflags)
                                && hasTyVarHead pred)
                  (predIrredErr env pred)

         -- Make sure it is OK to have an irred pred in this context
         -- See Note [Irreducible predicates in superclasses]
       ; failIfTcM (is_superclass ctxt
                    && not (xopt LangExt.UndecidableInstances dflags)
                    && has_tyfun_head pred)
                   (predSuperClassErr env pred) }
  where
    is_superclass ctxt = case ctxt of { ClassSCCtxt _ -> True; _ -> False }
    has_tyfun_head ty
      = case tcSplitTyConApp_maybe ty of
          Just (tc, _) -> isTypeFamilyTyCon tc
          Nothing      -> False

{- Note [ConstraintKinds in predicates]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Don't check for -XConstraintKinds under a type synonym, because that
was done at the type synonym definition site; see Trac #9838
e.g.   module A where
          type C a = (Eq a, Ix a)   -- Needs -XConstraintKinds
       module B where
          import A
          f :: C a => a -> a        -- Does *not* need -XConstraintKinds

Note [Irreducible predicates in superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Allowing type-family calls in class superclasses is somewhat dangerous
because we can write:

 type family Fooish x :: * -> Constraint
 type instance Fooish () = Foo
 class Fooish () a => Foo a where

This will cause the constraint simplifier to loop because every time we canonicalise a
(Foo a) class constraint we add a (Fooish () a) constraint which will be immediately
solved to add+canonicalise another (Foo a) constraint.  -}

-------------------------
check_class_pred :: TidyEnv -> DynFlags -> UserTypeCtxt -> PredType -> Class -> [TcType] -> TcM ()
check_class_pred env dflags ctxt pred cls tys
  | isIPClass cls
  = do { check_arity
       ; checkTcM (okIPCtxt ctxt) (badIPPred env pred) }

  | otherwise
  = do { check_arity
       ; warn_simp <- woptM Opt_WarnSimplifiableClassConstraints
       ; when warn_simp check_simplifiable_class_constraint
       ; checkTcM arg_tys_ok (predTyVarErr env pred) }
  where
    check_arity = checkTc (tys `lengthIs` classArity cls)
                          (tyConArityErr (classTyCon cls) tys)

    -- Check the arguments of a class constraint
    flexible_contexts = xopt LangExt.FlexibleContexts     dflags
    undecidable_ok    = xopt LangExt.UndecidableInstances dflags
    arg_tys_ok = case ctxt of
        SpecInstCtxt -> True    -- {-# SPECIALISE instance Eq (T Int) #-} is fine
        InstDeclCtxt -> checkValidClsArgs (flexible_contexts || undecidable_ok) cls tys
                                -- Further checks on head and theta
                                -- in checkInstTermination
        _            -> checkValidClsArgs flexible_contexts cls tys

    -- See Note [Simplifiable given constraints]
    check_simplifiable_class_constraint
       | xopt LangExt.MonoLocalBinds dflags
       = return ()
       | DataTyCtxt {} <- ctxt   -- Don't do this check for the "stupid theta"
       = return ()               -- of a data type declaration
       | otherwise
       = do { envs <- tcGetInstEnvs
            ; case lookupInstEnv False envs cls tys of
                 ([m], [], _) -> addWarnTc (Reason Opt_WarnSimplifiableClassConstraints)
                                           (simplifiable_constraint_warn m)
                 _ -> return () }

    simplifiable_constraint_warn :: InstMatch -> SDoc
    simplifiable_constraint_warn (match, _)
     = vcat [ hang (text "The constraint" <+> quotes (ppr (tidyType env pred)))
                 2 (text "matches an instance declaration")
            , ppr match
            , hang (text "This makes type inference for inner bindings fragile;")
                 2 (text "either use MonoLocalBinds, or simplify it using the instance") ]

{- Note [Simplifiable given constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A type signature like
   f :: Eq [(a,b)] => a -> b
is very fragile, for reasons described at length in TcInteract
Note [Instance and Given overlap].  As that Note discusses, for the
most part the clever stuff in TcInteract means that we don't use a
top-level instance if a local Given might fire, so there is no
fragility. But if we /infer/ the type of a local let-binding, things
can go wrong (Trac #11948 is an example, discussed in the Note).

So this warning is switched on only if we have NoMonoLocalBinds; in
that case the warning discourages users from writing simplifiable
class constraints.

The warning only fires if the constraint in the signature
matches the top-level instances in only one way, and with no
unifiers -- that is, under the same circumstances that
TcInteract.matchInstEnv fires an interaction with the top
level instances.  For example (Trac #13526), consider

  instance {-# OVERLAPPABLE #-} Eq (T a) where ...
  instance                   Eq (T Char) where ..
  f :: Eq (T a) => ...

We don't want to complain about this, even though the context
(Eq (T a)) matches an instance, because the user may be
deliberately deferring the choice so that the Eq (T Char)
has a chance to fire when 'f' is called.  And the fragility
only matters when there's a risk that the instance might
fire instead of the local 'given'; and there is no such
risk in this case.  Just use the same rules as for instance
firing!
-}

-------------------------
okIPCtxt :: UserTypeCtxt -> Bool
  -- See Note [Implicit parameters in instance decls]
okIPCtxt (FunSigCtxt {})        = True
okIPCtxt (InfSigCtxt {})        = True
okIPCtxt ExprSigCtxt            = True
okIPCtxt TypeAppCtxt            = True
okIPCtxt PatSigCtxt             = True
okIPCtxt ResSigCtxt             = True
okIPCtxt GenSigCtxt             = True
okIPCtxt (ConArgCtxt {})        = True
okIPCtxt (ForSigCtxt {})        = True  -- ??
okIPCtxt ThBrackCtxt            = True
okIPCtxt GhciCtxt               = True
okIPCtxt SigmaCtxt              = True
okIPCtxt (DataTyCtxt {})        = True
okIPCtxt (PatSynCtxt {})        = True
okIPCtxt (TySynCtxt {})         = True   -- e.g.   type Blah = ?x::Int
                                         -- Trac #11466

okIPCtxt (ClassSCCtxt {})  = False
okIPCtxt (InstDeclCtxt {}) = False
okIPCtxt (SpecInstCtxt {}) = False
okIPCtxt (RuleSigCtxt {})  = False
okIPCtxt DefaultDeclCtxt   = False

{-
Note [Kind polymorphic type classes]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MultiParam check:

    class C f where...   -- C :: forall k. k -> Constraint
    instance C Maybe where...

  The dictionary gets type [C * Maybe] even if it's not a MultiParam
  type class.

Flexibility check:

    class C f where...   -- C :: forall k. k -> Constraint
    data D a = D a
    instance C D where

  The dictionary gets type [C * (D *)]. IA0_TODO it should be
  generalized actually.
-}

checkThetaCtxt :: UserTypeCtxt -> ThetaType -> TidyEnv -> TcM (TidyEnv, SDoc)
checkThetaCtxt ctxt theta env
  = return ( env
           , vcat [ text "In the context:" <+> pprTheta (tidyTypes env theta)
                  , text "While checking" <+> pprUserTypeCtxt ctxt ] )

eqPredTyErr, predTupleErr, predIrredErr, predSuperClassErr :: TidyEnv -> PredType -> (TidyEnv, SDoc)
eqPredTyErr  env pred
  = ( env
    , text "Illegal equational constraint" <+> ppr_tidy env pred $$
      parens (text "Use GADTs or TypeFamilies to permit this") )
predTupleErr env pred
  = ( env
    , hang (text "Illegal tuple constraint:" <+> ppr_tidy env pred)
         2 (parens constraintKindsMsg) )
predIrredErr env pred
  = ( env
    , hang (text "Illegal constraint:" <+> ppr_tidy env pred)
         2 (parens constraintKindsMsg) )
predSuperClassErr env pred
  = ( env
    , hang (text "Illegal constraint" <+> quotes (ppr_tidy env pred)
            <+> text "in a superclass context")
         2 (parens undecidableMsg) )

predTyVarErr :: TidyEnv -> PredType -> (TidyEnv, SDoc)
predTyVarErr env pred
  = (env
    , vcat [ hang (text "Non type-variable argument")
                2 (text "in the constraint:" <+> ppr_tidy env pred)
           , parens (text "Use FlexibleContexts to permit this") ])

badIPPred :: TidyEnv -> PredType -> (TidyEnv, SDoc)
badIPPred env pred
  = ( env
    , text "Illegal implicit parameter" <+> quotes (ppr_tidy env pred) )

constraintSynErr :: TidyEnv -> Type -> (TidyEnv, SDoc)
constraintSynErr env kind
  = ( env
    , hang (text "Illegal constraint synonym of kind:" <+> quotes (ppr_tidy env kind))
         2 (parens constraintKindsMsg) )

dupPredWarn :: TidyEnv -> [[PredType]] -> (TidyEnv, SDoc)
dupPredWarn env dups
  = ( env
    , text "Duplicate constraint" <> plural primaryDups <> text ":"
      <+> pprWithCommas (ppr_tidy env) primaryDups )
  where
    primaryDups = map head dups

tyConArityErr :: TyCon -> [TcType] -> SDoc
-- For type-constructor arity errors, be careful to report
-- the number of /visible/ arguments required and supplied,
-- ignoring the /invisible/ arguments, which the user does not see.
-- (e.g. Trac #10516)
tyConArityErr tc tks
  = arityErr (ppr (tyConFlavour tc)) (tyConName tc)
             tc_type_arity tc_type_args
  where
    vis_tks = filterOutInvisibleTypes tc tks

    -- tc_type_arity = number of *type* args expected
    -- tc_type_args  = number of *type* args encountered
    tc_type_arity = count isVisibleTyConBinder (tyConBinders tc)
    tc_type_args  = length vis_tks

arityErr :: Outputable a => SDoc -> a -> Int -> Int -> SDoc
arityErr what name n m
  = hsep [ text "The" <+> what, quotes (ppr name), text "should have",
           n_arguments <> comma, text "but has been given",
           if m==0 then text "none" else int m]
    where