A bunch more simplification and refactoring to the constraint solver

[ghc.git] / compiler / typecheck / TcSimplify.lhs

\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://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#TabsvsSpaces
-- for details

module TcSimplify( 
       simplifyInfer, simplifyAmbiguityCheck,
       simplifyDefault, simplifyDeriv, 
       simplifyRule, simplifyTop, simplifyInteractive
  ) where

#include "HsVersions.h"

import TcRnTypes
import TcRnMonad
import TcErrors
import TcMType
import TcType 
import TcSMonad 
import TcInteract 
import Inst
import Unify    ( niFixTvSubst, niSubstTvSet )
import Type     ( classifyPredType, PredTree(..), getClassPredTys_maybe )
import Class    ( Class )
import Var
import Unique
import VarSet
import VarEnv 
import TcEvidence
import TypeRep
import Name
import Bag
import ListSetOps
import Util
import PrelInfo
import PrelNames
import Class            ( classKey )
import BasicTypes       ( RuleName )
import Control.Monad    ( when )
import Outputable
import FastString
import TrieMap () -- DV: for now
import DynFlags
\end{code}


*********************************************************************************
*                                                                               * 
*                           External interface                                  *
*                                                                               *
*********************************************************************************


\begin{code}


simplifyTop :: WantedConstraints -> TcM (Bag EvBind)
-- Simplify top-level constraints
-- Usually these will be implications,
-- but when there is nothing to quantify we don't wrap
-- in a degenerate implication, so we do that here instead
simplifyTop wanteds 
  = do { ev_binds_var <- newTcEvBinds
                         
       ; zonked_wanteds <- zonkWC wanteds

       ; traceTc "simplifyTop {" $ text "zonked_wc =" <+> ppr zonked_wanteds

       ; wc_first_go <- solveWantedsWithEvBinds ev_binds_var zonked_wanteds
       ; cts <- applyTyVarDefaulting wc_first_go 
                -- See Note [Top-level Defaulting Plan]
                
       ; let wc_for_loop = wc_first_go { wc_flat = wc_flat wc_first_go `unionBags` cts }
                           
       ; traceTc "simpl_top_loop" $ text "wc_for_loop =" <+> ppr wc_for_loop
       ; simpl_top_loop ev_binds_var wc_for_loop }
    
  where simpl_top_loop ev_binds_var wc
          | isEmptyWC wc 
          = do { traceTc "simpl_top_loop }" empty
               ; TcRnMonad.getTcEvBinds ev_binds_var }
          | otherwise
          = do { wc_residual <- solveWantedsWithEvBinds ev_binds_var wc
               ; let wc_flat_approximate = approximateWC wc_residual
               ; (dflt_eqs,_unused_bind) <- runTcS $
                                            applyDefaultingRules wc_flat_approximate
                                            -- See Note [Top-level Defaulting Plan]
               ; if isEmptyBag dflt_eqs then 
                   do { traceTc "End simplifyTop }" empty
                      ; report_and_finish ev_binds_var wc_residual }
                 else
                   simpl_top_loop ev_binds_var $ 
                   wc_residual { wc_flat = wc_flat wc_residual `unionBags` dflt_eqs } }

        report_and_finish ev_binds_var wc_residual 
          = do { eb1 <- TcRnMonad.getTcEvBinds ev_binds_var
               ; traceTc "reportUnsolved {" empty
                   -- See Note [Deferring coercion errors to runtime]
               ; runtimeCoercionErrors <- doptM Opt_DeferTypeErrors
               ; eb2 <- reportUnsolved runtimeCoercionErrors wc_residual
               ; traceTc "reportUnsolved }" empty
               ; return (eb1 `unionBags` eb2) }
\end{code}

Note [Top-level Defaulting Plan]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We have considered two design choices for where/when to apply defaulting.   
   (i) Do it in SimplCheck mode only /whenever/ you try to solve some 
       flat constraints, maybe deep inside the context of implications.
       This used to be the case in GHC 7.4.1.
   (ii) Do it in a tight loop at simplifyTop, once all other constraint has 
        finished. This is the current story.

Option (i) had many disadvantages: 
   a) First it was deep inside the actual solver, 
   b) Second it was dependent on the context (Infer a type signature, 
      or Check a type signature, or Interactive) since we did not want 
      to always start defaulting when inferring (though there is an exception to  
      this see Note [Default while Inferring])
   c) It plainly did not work. Consider typecheck/should_compile/DfltProb2.hs:
          f :: Int -> Bool
          f x = const True (\y -> let w :: a -> a
                                      w a = const a (y+1)
                                  in w y)
      We will get an implication constraint (for beta the type of y):
               [untch=beta] forall a. 0 => Num beta
      which we really cannot default /while solving/ the implication, since beta is
      untouchable.

Instead our new defaulting story is to pull defaulting out of the solver loop and
go with option (i), implemented at SimplifyTop. Namely:
     - First have a go at solving the residual constraint of the whole program
     - Try to approximate it with a flat constraint
     - Figure out derived defaulting equations for that flat constraint
     - Go round the loop again if you did manage to get some equations

Now, that has to do with class defaulting. However there exists type variable /kind/
defaulting. Again this is done at the top-level and the plan is:
     - At the top-level, once you had a go at solving the constraint, do 
       figure out /all/ the touchable unification variables of the wanted contraints.
     - Apply defaulting to their kinds

More details in Note [DefaultTyVar].

\begin{code}

------------------
simplifyAmbiguityCheck :: Name -> WantedConstraints -> TcM (Bag EvBind)
simplifyAmbiguityCheck name wanteds
  = traceTc "simplifyAmbiguityCheck" (text "name =" <+> ppr name) >> 
    simplifyTop wanteds  -- NB: must be simplifyTop not simplifyCheck, so that we
                         --     do ambiguity resolution.  
                         -- See Note [Impedence matching] in TcBinds.
 
------------------
simplifyInteractive :: WantedConstraints -> TcM (Bag EvBind)
simplifyInteractive wanteds 
  = traceTc "simplifyInteractive" empty >>
    simplifyTop wanteds 

------------------
simplifyDefault :: ThetaType    -- Wanted; has no type variables in it
                -> TcM ()       -- Succeeds iff the constraint is soluble
simplifyDefault theta
  = do { traceTc "simplifyInteractive" empty
       ; wanted <- newFlatWanteds DefaultOrigin theta
       ; _ignored_ev_binds <- simplifyCheck (mkFlatWC wanted)
       ; return () }
\end{code}


***********************************************************************************
*                                                                                 * 
*                            Deriving                                             *
*                                                                                 *
***********************************************************************************

\begin{code}
simplifyDeriv :: CtOrigin
              -> PredType
              -> [TyVar]        
              -> ThetaType              -- Wanted
              -> TcM ThetaType  -- Needed
-- Given  instance (wanted) => C inst_ty 
-- Simplify 'wanted' as much as possibles
-- Fail if not possible
simplifyDeriv orig pred tvs theta 
  = do { (skol_subst, tvs_skols) <- tcInstSkolTyVars tvs -- Skolemize
                -- The constraint solving machinery 
                -- expects *TcTyVars* not TyVars.  
                -- We use *non-overlappable* (vanilla) skolems
                -- See Note [Overlap and deriving]

       ; let subst_skol = zipTopTvSubst tvs_skols $ map mkTyVarTy tvs
             skol_set   = mkVarSet tvs_skols
             doc = ptext (sLit "deriving") <+> parens (ppr pred)

       ; wanted <- newFlatWanteds orig (substTheta skol_subst theta)

       ; traceTc "simplifyDeriv" $ 
         vcat [ pprTvBndrs tvs $$ ppr theta $$ ppr wanted, doc ]
       ; (residual_wanted, _ev_binds1)
             <- solveWanteds (mkFlatWC wanted)

       ; let (good, bad) = partitionBagWith get_good (wc_flat residual_wanted)
                         -- See Note [Exotic derived instance contexts]
             get_good :: Ct -> Either PredType Ct
             get_good ct | validDerivPred skol_set p 
                         , isWantedCt ct  = Left p 
                         -- NB: residual_wanted may contain unsolved
                         -- Derived and we stick them into the bad set
                         -- so that reportUnsolved may decide what to do with them
                         | otherwise = Right ct
                         where p = ctPred ct

       -- We never want to defer these errors because they are errors in the
       -- compiler! Hence the `False` below
       ; _ev_binds2 <- reportUnsolved False (residual_wanted { wc_flat = bad })

       ; let min_theta = mkMinimalBySCs (bagToList good)
       ; return (substTheta subst_skol min_theta) }
\end{code}

Note [Overlap and deriving]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider some overlapping instances:
  data Show a => Show [a] where ..
  data Show [Char] where ...

Now a data type with deriving:
  data T a = MkT [a] deriving( Show )

We want to get the derived instance
  instance Show [a] => Show (T a) where...
and NOT
  instance Show a => Show (T a) where...
so that the (Show (T Char)) instance does the Right Thing

It's very like the situation when we're inferring the type
of a function
   f x = show [x]
and we want to infer
   f :: Show [a] => a -> String

BOTTOM LINE: use vanilla, non-overlappable skolems when inferring
             the context for the derived instance. 
             Hence tcInstSkolTyVars not tcInstSuperSkolTyVars

Note [Exotic derived instance contexts]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In a 'derived' instance declaration, we *infer* the context.  It's a
bit unclear what rules we should apply for this; the Haskell report is
silent.  Obviously, constraints like (Eq a) are fine, but what about
        data T f a = MkT (f a) deriving( Eq )
where we'd get an Eq (f a) constraint.  That's probably fine too.

One could go further: consider
        data T a b c = MkT (Foo a b c) deriving( Eq )
        instance (C Int a, Eq b, Eq c) => Eq (Foo a b c)

Notice that this instance (just) satisfies the Paterson termination 
conditions.  Then we *could* derive an instance decl like this:

        instance (C Int a, Eq b, Eq c) => Eq (T a b c) 
even though there is no instance for (C Int a), because there just
*might* be an instance for, say, (C Int Bool) at a site where we
need the equality instance for T's.  

However, this seems pretty exotic, and it's quite tricky to allow
this, and yet give sensible error messages in the (much more common)
case where we really want that instance decl for C.

So for now we simply require that the derived instance context
should have only type-variable constraints.

Here is another example:
        data Fix f = In (f (Fix f)) deriving( Eq )
Here, if we are prepared to allow -XUndecidableInstances we
could derive the instance
        instance Eq (f (Fix f)) => Eq (Fix f)
but this is so delicate that I don't think it should happen inside
'deriving'. If you want this, write it yourself!

NB: if you want to lift this condition, make sure you still meet the
termination conditions!  If not, the deriving mechanism generates
larger and larger constraints.  Example:
  data Succ a = S a
  data Seq a = Cons a (Seq (Succ a)) | Nil deriving Show

Note the lack of a Show instance for Succ.  First we'll generate
  instance (Show (Succ a), Show a) => Show (Seq a)
and then
  instance (Show (Succ (Succ a)), Show (Succ a), Show a) => Show (Seq a)
and so on.  Instead we want to complain of no instance for (Show (Succ a)).

The bottom line
~~~~~~~~~~~~~~~
Allow constraints which consist only of type variables, with no repeats.

*********************************************************************************
*                                                                                 * 
*                            Inference
*                                                                                 *
***********************************************************************************

Note [Which variables to quantify]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose the inferred type of a function is
   T kappa (alpha:kappa) -> Int
where alpha is a type unification variable and 
      kappa is a kind unification variable
Then we want to quantify over *both* alpha and kappa.  But notice that
kappa appears "at top level" of the type, as well as inside the kind
of alpha.  So it should be fine to just look for the "top level"
kind/type variables of the type, without looking transitively into the
kinds of those type variables.

\begin{code}
simplifyInfer :: Bool
              -> Bool                  -- Apply monomorphism restriction
              -> [(Name, TcTauType)]   -- Variables to be generalised,
                                       -- and their tau-types
              -> WantedConstraints
              -> TcM ([TcTyVar],    -- Quantify over these type variables
                      [EvVar],      -- ... and these constraints
                      Bool,         -- The monomorphism restriction did something
                                    --   so the results type is not as general as
                                    --   it could be
                      TcEvBinds)    -- ... binding these evidence variables
simplifyInfer _top_lvl apply_mr name_taus wanteds
  | isEmptyWC wanteds
  = do { gbl_tvs     <- tcGetGlobalTyVars            -- Already zonked
       ; zonked_taus <- zonkTcTypes (map snd name_taus)
       ; let tvs_to_quantify = varSetElems (tyVarsOfTypes zonked_taus `minusVarSet` gbl_tvs)
                               -- tvs_to_quantify can contain both kind and type vars
                               -- See Note [Which variables to quantify]
       ; qtvs <- zonkQuantifiedTyVars tvs_to_quantify
       ; return (qtvs, [], False, emptyTcEvBinds) }

  | otherwise
  = do { runtimeCoercionErrors <- doptM Opt_DeferTypeErrors
       ; gbl_tvs        <- tcGetGlobalTyVars
       ; zonked_tau_tvs <- zonkTyVarsAndFV (tyVarsOfTypes (map snd name_taus))
       ; zonked_wanteds <- zonkWC wanteds

       ; traceTc "simplifyInfer {"  $ vcat
             [ ptext (sLit "names =") <+> ppr (map fst name_taus)
             , ptext (sLit "taus =") <+> ppr (map snd name_taus)
             , ptext (sLit "tau_tvs (zonked) =") <+> ppr zonked_tau_tvs
             , ptext (sLit "gbl_tvs =") <+> ppr gbl_tvs
             , ptext (sLit "closed =") <+> ppr _top_lvl
             , ptext (sLit "apply_mr =") <+> ppr apply_mr
             , ptext (sLit "wanted =") <+> ppr zonked_wanteds
             ]

              -- Historical note: Before step 2 we used to have a
              -- HORRIBLE HACK described in Note [Avoid unecessary
              -- constraint simplification] but, as described in Trac
              -- #4361, we have taken in out now.  That's why we start
              -- with step 2!

              -- Step 2) First try full-blown solving 

              -- NB: we must gather up all the bindings from doing
              -- this solving; hence (runTcSWithEvBinds ev_binds_var).
              -- And note that since there are nested implications,
              -- calling solveWanteds will side-effect their evidence
              -- bindings, so we can't just revert to the input
              -- constraint.
       ; ev_binds_var <- newTcEvBinds
       ; wanted_transformed <- solveWantedsWithEvBinds ev_binds_var zonked_wanteds

              -- Step 3) Fail fast if there is an insoluble constraint,
              -- unless we are deferring errors to runtime
       ; when (not runtimeCoercionErrors && insolubleWC wanted_transformed) $ 
         do { _ev_binds <- reportUnsolved False wanted_transformed; failM }

              -- Step 4) Candidates for quantification are an approximation of wanted_transformed
       ; let quant_candidates = approximateWC wanted_transformed               
              -- NB: Already the fixpoint of any unifications that may have happened                                
              -- NB: We do not do any defaulting when inferring a type, this can lead
              -- to less polymorphic types, see Note [Default while Inferring]
              -- NB: quant_candidates here are wanted or derived, we filter the wanteds later, anyway
 
              -- Step 5) Minimize the quantification candidates                             
       ; (quant_candidates_transformed, _extra_binds)   
             <- solveWanteds $ WC { wc_flat  = quant_candidates
                                  , wc_impl  = emptyBag
                                  , wc_insol = emptyBag }

              -- Step 6) Final candidates for quantification                
       ; let final_quant_candidates :: [PredType]
             final_quant_candidates = map ctPred $ bagToList $
                                      wc_flat quant_candidates_transformed
             -- NB: Already the fixpoint of any unifications that may have happened
                  
       ; gbl_tvs        <- tcGetGlobalTyVars -- TODO: can we just use untch instead of gbl_tvs?
       ; zonked_tau_tvs <- zonkTyVarsAndFV zonked_tau_tvs
       
       ; traceTc "simplifyWithApprox" $
         vcat [ ptext (sLit "final_quant_candidates =") <+> ppr final_quant_candidates
              , ptext (sLit "gbl_tvs=") <+> ppr gbl_tvs
              , ptext (sLit "zonked_tau_tvs=") <+> ppr zonked_tau_tvs ]
         
       ; let init_tvs  = zonked_tau_tvs `minusVarSet` gbl_tvs
             poly_qtvs = growThetaTyVars final_quant_candidates init_tvs 
                         `minusVarSet` gbl_tvs
             pbound    = filter (quantifyPred poly_qtvs) final_quant_candidates
             
       ; traceTc "simplifyWithApprox" $
         vcat [ ptext (sLit "pbound =") <+> ppr pbound
              , ptext (sLit "init_qtvs =") <+> ppr init_tvs 
              , ptext (sLit "poly_qtvs =") <+> ppr poly_qtvs ]
         
             -- Monomorphism restriction
       ; let mr_qtvs         = init_tvs `minusVarSet` constrained_tvs
             constrained_tvs = tyVarsOfTypes final_quant_candidates
             mr_bites        = apply_mr && not (null pbound)

             (qtvs, bound)
                | mr_bites  = (mr_qtvs,   [])
                | otherwise = (poly_qtvs, pbound)
             

       ; if isEmptyVarSet qtvs && null bound
         then do { traceTc "} simplifyInfer/no quantification" empty                   
                 ; emitConstraints wanted_transformed
                    -- Includes insolubles (if -fdefer-type-errors)
                    -- as well as flats and implications
                 ; return ([], [], mr_bites, TcEvBinds ev_binds_var) }
         else do

       { traceTc "simplifyApprox" $ 
         ptext (sLit "bound are =") <+> ppr bound 
         
            -- Step 4, zonk quantified variables 
       ; let minimal_flat_preds = mkMinimalBySCs bound
             skol_info = InferSkol [ (name, mkSigmaTy [] minimal_flat_preds ty)
                                   | (name, ty) <- name_taus ]
                        -- Don't add the quantified variables here, because
                        -- they are also bound in ic_skols and we want them to be
                        -- tidied uniformly

       ; qtvs_to_return <- zonkQuantifiedTyVars (varSetElems qtvs)

            -- Step 7) Emit an implication
       ; minimal_bound_ev_vars <- mapM TcMType.newEvVar minimal_flat_preds
       ; lcl_env <- getLclTypeEnv
       ; gloc <- getCtLoc skol_info
       ; untch <- TcRnMonad.getUntouchables
       ; uniq  <- TcRnMonad.newUnique
       ; let implic = Implic { ic_untch    = pushUntouchables uniq untch 
                             , ic_env      = lcl_env
                             , ic_skols    = qtvs_to_return
                             , ic_fsks     = []  -- wanted_tansformed arose only from solveWanteds
                                                 -- hence no flatten-skolems (which come from givens)
                             , ic_given    = minimal_bound_ev_vars
                             , ic_wanted   = wanted_transformed 
                             , ic_insol    = False
                             , ic_binds    = ev_binds_var
                             , ic_loc      = gloc }
       ; emitImplication implic
         
       ; traceTc "} simplifyInfer/produced residual implication for quantification" $
             vcat [ ptext (sLit "implic =") <+> ppr implic
                       -- ic_skols, ic_given give rest of result
                  , ptext (sLit "qtvs =") <+> ppr qtvs_to_return
                  , ptext (sLit "spb =") <+> ppr final_quant_candidates
                  , ptext (sLit "bound =") <+> ppr bound ]

       ; return ( qtvs_to_return, minimal_bound_ev_vars
                , mr_bites,  TcEvBinds ev_binds_var) } }
    where 
\end{code}


Note [Default while Inferring]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Our current plan is that defaulting only happens at simplifyTop and
not simplifyInfer.  This may lead to some insoluble deferred constraints
Example:

instance D g => C g Int b 

constraint inferred = (forall b. 0 => C gamma alpha b) /\ Num alpha
type inferred       = gamma -> gamma 

Now, if we try to default (alpha := Int) we will be able to refine the implication to 
  (forall b. 0 => C gamma Int b) 
which can then be simplified further to 
  (forall b. 0 => D gamma)
Finally we /can/ approximate this implication with (D gamma) and infer the quantified
type:  forall g. D g => g -> g

Instead what will currently happen is that we will get a quantified type 
(forall g. g -> g) and an implication:
       forall g. 0 => (forall b. 0 => C g alpha b) /\ Num alpha

which, even if the simplifyTop defaults (alpha := Int) we will still be left with an 
unsolvable implication:
       forall g. 0 => (forall b. 0 => D g)

The concrete example would be: 
       h :: C g a s => g -> a -> ST s a
       f (x::gamma) = (\_ -> x) (runST (h x (undefined::alpha)) + 1)

But it is quite tedious to do defaulting and resolve the implication constraints and
we have not observed code breaking because of the lack of defaulting in inference so 
we don't do it for now.



Note [Minimize by Superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
When we quantify over a constraint, in simplifyInfer we need to
quantify over a constraint that is minimal in some sense: For
instance, if the final wanted constraint is (Eq alpha, Ord alpha),
we'd like to quantify over Ord alpha, because we can just get Eq alpha
from superclass selection from Ord alpha. This minimization is what
mkMinimalBySCs does. Then, simplifyInfer uses the minimal constraint
to check the original wanted.

\begin{code}
approximateWC :: WantedConstraints -> Cts
-- Postcondition: Wanted or Derived Cts 
approximateWC wc = float_wc emptyVarSet wc
  where 
    float_wc :: TcTyVarSet -> WantedConstraints -> Cts
    float_wc skols (WC { wc_flat = flat, wc_impl = implic }) = floats1 `unionBags` floats2
      where floats1 = do_bag (float_flat skols) flat
            floats2 = do_bag (float_implic skols) implic
                                 
    float_implic :: TcTyVarSet -> Implication -> Cts
    float_implic skols imp
      = float_wc skols' (ic_wanted imp)
      where
        skols' = skols `extendVarSetList` ic_skols imp `extendVarSetList` ic_fsks imp
            
    float_flat :: TcTyVarSet -> Ct -> Cts
    float_flat skols ct
      | tyVarsOfCt ct `disjointVarSet` skols 
      = singleCt ct
      | otherwise = emptyCts
        
    do_bag :: (a -> Bag c) -> Bag a -> Bag c
    do_bag f = foldrBag (unionBags.f) emptyBag
\end{code}

Note [Avoid unecessary constraint simplification]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -------- NB NB NB (Jun 12) ------------- 
    This note not longer applies; see the notes with Trac #4361.
    But I'm leaving it in here so we remember the issue.)
    ----------------------------------------
When inferring the type of a let-binding, with simplifyInfer,
try to avoid unnecessarily simplifying class constraints.
Doing so aids sharing, but it also helps with delicate 
situations like

   instance C t => C [t] where ..

   f :: C [t] => ....
   f x = let g y = ...(constraint C [t])... 
         in ...
When inferring a type for 'g', we don't want to apply the
instance decl, because then we can't satisfy (C t).  So we
just notice that g isn't quantified over 't' and partition
the contraints before simplifying.

This only half-works, but then let-generalisation only half-works.


*********************************************************************************
*                                                                                 * 
*                             RULES                                               *
*                                                                                 *
***********************************************************************************

See note [Simplifying RULE consraints] in TcRule

Note [RULE quanfification over equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Decideing which equalities to quantify over is tricky:
 * We do not want to quantify over insoluble equalities (Int ~ Bool)
    (a) because we prefer to report a LHS type error
    (b) because if such things end up in 'givens' we get a bogus
        "inaccessible code" error

 * But we do want to quantify over things like (a ~ F b), where
   F is a type function.

The difficulty is that it's hard to tell what is insoluble!
So we see whether the simplificaiotn step yielded any type errors,
and if so refrain from quantifying over *any* equalites.

\begin{code}
simplifyRule :: RuleName 
             -> WantedConstraints       -- Constraints from LHS
             -> WantedConstraints       -- Constraints from RHS
             -> TcM ([EvVar], WantedConstraints)   -- LHS evidence varaibles
-- See Note [Simplifying RULE constraints] in TcRule
simplifyRule name lhs_wanted rhs_wanted
  = do { zonked_all <- zonkWC (lhs_wanted `andWC` rhs_wanted)
       ; let doc = ptext (sLit "LHS of rule") <+> doubleQuotes (ftext name)
             
                 -- We allow ourselves to unify environment 
                 -- variables: runTcS runs with NoUntouchables
       ; (resid_wanted, _) <- solveWanteds zonked_all

       ; zonked_lhs <- zonkWC lhs_wanted

       ; let (q_cts, non_q_cts) = partitionBag quantify_me (wc_flat zonked_lhs)
             quantify_me  -- Note [RULE quantification over equalities]
               | insolubleWC resid_wanted = quantify_insol
               | otherwise                = quantify_normal

             quantify_insol ct = not (isEqPred (ctPred ct))

             quantify_normal ct
               | EqPred t1 t2 <- classifyPredType (ctPred ct)
               = not (t1 `eqType` t2)
               | otherwise
               = True
             
       ; traceTc "simplifyRule" $
         vcat [ doc
              , text "zonked_lhs" <+> ppr zonked_lhs 
              , text "q_cts"      <+> ppr q_cts ]

       ; return ( map (ctEvId . ctEvidence) (bagToList q_cts)
                , zonked_lhs { wc_flat = non_q_cts }) }
\end{code}


*********************************************************************************
*                                                                                 * 
*                                 Main Simplifier                                 *
*                                                                                 *
***********************************************************************************

\begin{code}
simplifyCheck :: WantedConstraints      -- Wanted
              -> TcM (Bag EvBind)
-- Solve a single, top-level implication constraint
-- e.g. typically one created from a top-level type signature
--          f :: forall a. [a] -> [a]
--          f x = rhs
-- We do this even if the function has no polymorphism:
--          g :: Int -> Int

--          g y = rhs
-- (whereas for *nested* bindings we would not create
--  an implication constraint for g at all.)
--
-- Fails if can't solve something in the input wanteds
simplifyCheck wanteds
  = do { wanteds <- zonkWC wanteds

       ; traceTc "simplifyCheck {" (vcat
             [ ptext (sLit "wanted =") <+> ppr wanteds ])

       ; (unsolved, eb1) <- solveWanteds wanteds

       ; traceTc "simplifyCheck }" $ ptext (sLit "unsolved =") <+> ppr unsolved

       ; traceTc "reportUnsolved {" empty
       -- See Note [Deferring coercion errors to runtime]
       ; runtimeCoercionErrors <- doptM Opt_DeferTypeErrors
       ; eb2 <- reportUnsolved runtimeCoercionErrors unsolved 
       ; traceTc "reportUnsolved }" empty

       ; return (eb1 `unionBags` eb2) }
\end{code}

Note [Deferring coercion errors to runtime]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

While developing, sometimes it is desirable to allow compilation to succeed even
if there are type errors in the code. Consider the following case:

  module Main where

  a :: Int
  a = 'a'

  main = print "b"

Even though `a` is ill-typed, it is not used in the end, so if all that we're
interested in is `main` it is handy to be able to ignore the problems in `a`.

Since we treat type equalities as evidence, this is relatively simple. Whenever
we run into a type mismatch in TcUnify, we normally just emit an error. But it
is always safe to defer the mismatch to the main constraint solver. If we do
that, `a` will get transformed into

  co :: Int ~ Char
  co = ...

  a :: Int
  a = 'a' `cast` co

The constraint solver would realize that `co` is an insoluble constraint, and
emit an error with `reportUnsolved`. But we can also replace the right-hand side
of `co` with `error "Deferred type error: Int ~ Char"`. This allows the program
to compile, and it will run fine unless we evaluate `a`. This is what
`deferErrorsToRuntime` does.

It does this by keeping track of which errors correspond to which coercion
in TcErrors (with ErrEnv). TcErrors.reportTidyWanteds does not print the errors
and does not fail if -fwarn-type-errors is on, so that we can continue
compilation. The errors are turned into warnings in `reportUnsolved`.

\begin{code}

solveWanteds :: WantedConstraints -> TcM (WantedConstraints, Bag EvBind)
-- Return the evidence binds in the BagEvBinds result
-- Discards all Derived stuff in result
solveWanteds wanted 
  = runTcS $ do { wc <- solve_wanteds wanted 
                ; return (dropDerivedWC wc) }

solveWantedsWithEvBinds :: EvBindsVar -> WantedConstraints -> TcM WantedConstraints
-- Side-effect the EvBindsVar argument to add new bindings from solving
-- Discards all Derived stuff in result
solveWantedsWithEvBinds ev_binds_var wanted
  = runTcSWithEvBinds ev_binds_var $ 
    do { wc <- solve_wanteds wanted 
       ; return (dropDerivedWC wc) }

solve_wanteds :: WantedConstraints -> TcS WantedConstraints 
-- NB: wc_flats may be wanted /or/ derived now
solve_wanteds wanted@(WC { wc_flat = flats, wc_impl = implics, wc_insol = insols }) 
  = do { traceTcS "solveWanteds {" (ppr wanted)

         -- Try the flat bit, including insolubles. Solving insolubles a 
         -- second time round is a bit of a waste but the code is simple 
         -- and the program is wrong anyway, and we don't run the danger 
         -- of adding Derived insolubles twice; see 
         -- TcSMonad Note [Do not add duplicate derived insolubles] 
       ; traceTcS "solveFlats {" empty
       ; let all_flats = flats `unionBags` insols
       ; impls_from_flats <- solveInteract all_flats
       ; traceTcS "solveFlats end }" (ppr impls_from_flats)

       -- solve_wanteds iterates when it is able to float equalities 
       -- out of one or more of the implications. 
       ; unsolved_implics <- simpl_loop 1 (implics `unionBags` impls_from_flats)

       ; (unsolved_flats, insoluble_flats) <- getInertUnsolved

       ; wc <- unFlattenWC (WC { wc_flat  = unsolved_flats
                               , wc_impl  = unsolved_implics
                               , wc_insol = insoluble_flats })

       ; bb <- getTcEvBindsMap
       ; tb <- getTcSTyBindsMap
       ; traceTcS "solveWanteds }" $
                 vcat [ text "unsolved_flats   =" <+> ppr unsolved_flats
                      , text "unsolved_implics =" <+> ppr unsolved_implics
                      , text "current evbinds  =" <+> ppr (evBindMapBinds bb)
                      , text "current tybinds  =" <+> vcat (map ppr (varEnvElts tb))
                      , text "final wc =" <+> ppr wc ]

       ; return wc }

simpl_loop :: Int
           -> Bag Implication
           -> TcS (Bag Implication)
simpl_loop n implics
  | n > 10 
  = traceTcS "solveWanteds: loop!" empty >> return implics
  | otherwise 
  = do { (floated_eqs, unsolved_implics) <- solveNestedImplications implics
       ; if isEmptyBag floated_eqs 
         then return unsolved_implics 
         else 
    do {   -- Put floated_eqs into the current inert set before looping
         impls_from_eqs <- solveInteract floated_eqs
       ; simpl_loop (n+1) (unsolved_implics `unionBags` impls_from_eqs)} }


solveNestedImplications :: Bag Implication
                        -> TcS (Cts, Bag Implication)
-- Precondition: the TcS inerts may contain unsolved flats which have 
-- to be converted to givens before we go inside a nested implication.
solveNestedImplications implics
  | isEmptyBag implics
  = return (emptyBag, emptyBag)
  | otherwise 
  = do { inerts <- getTcSInerts
       ; let thinner_inerts = prepareInertsForImplications inerts
                 -- See Note [Preparing inert set for implications]
  
       ; traceTcS "solveNestedImplications starting {" $ 
         vcat [ text "original inerts = " <+> ppr inerts
              , text "thinner_inerts  = " <+> ppr thinner_inerts ]
         
       ; (floated_eqs, unsolved_implics)
           <- flatMapBagPairM (solveImplication thinner_inerts) implics

       -- ... and we are back in the original TcS inerts 
       -- Notice that the original includes the _insoluble_flats so it was safe to ignore
       -- them in the beginning of this function.
       ; traceTcS "solveNestedImplications end }" $
                  vcat [ text "all floated_eqs ="  <+> ppr floated_eqs
                       , text "unsolved_implics =" <+> ppr unsolved_implics ]

       ; return (floated_eqs, unsolved_implics) }

solveImplication :: InertSet
                 -> Implication    -- Wanted
                 -> TcS (Cts,      -- All wanted or derived floated equalities: var = type
                         Bag Implication) -- Unsolved rest (always empty or singleton)
-- Precondition: The TcS monad contains an empty worklist and given-only inerts 
-- which after trying to solve this implication we must restore to their original value
solveImplication inerts
     imp@(Implic { ic_untch  = untch
                 , ic_binds  = ev_binds
                 , ic_skols  = skols 
                 , ic_fsks   = old_fsks
                 , ic_given  = givens
                 , ic_wanted = wanteds
                 , ic_loc    = loc })
  = 
    do { traceTcS "solveImplication {" (ppr imp) 

         -- Solve the nested constraints
         -- NB: 'inerts' has empty inert_fsks
       ; (new_fsks, residual_wanted) 
            <- nestImplicTcS ev_binds untch inerts $
               do { solveInteractGiven loc old_fsks givens 
                  ; residual_wanted <- solve_wanteds wanteds
                  ; more_fsks <- getFlattenSkols
                  ; return (more_fsks ++ old_fsks, residual_wanted) }

       ; (floated_eqs, final_wanted)
             <- floatEqualities (skols ++ new_fsks) givens residual_wanted

       ; let res_implic | isEmptyWC final_wanted 
                        = emptyBag
                        | otherwise
                        = unitBag (imp { ic_fsks   = new_fsks
                                       , ic_wanted = dropDerivedWC final_wanted
                                       , ic_insol  = insolubleWC final_wanted })

       ; evbinds <- getTcEvBindsMap
       ; traceTcS "solveImplication end }" $ vcat
             [ text "floated_eqs =" <+> ppr floated_eqs
             , text "new_fsks =" <+> ppr new_fsks
             , text "res_implic =" <+> ppr res_implic
             , text "implication evbinds = " <+> ppr (evBindMapBinds evbinds) ]

       ; return (floated_eqs, res_implic) }
\end{code}


\begin{code}
floatEqualities :: [TcTyVar] -> [EvVar] -> WantedConstraints 
                -> TcS (Cts, WantedConstraints)
-- Post: The returned FlavoredEvVar's are only Wanted or Derived
-- and come from the input wanted ev vars or deriveds 
-- Also performs some unifications, adding to monadically-carried ty_binds
-- These will be used when processing floated_eqs later
floatEqualities skols can_given wanteds@(WC { wc_flat = flats })
  | hasEqualities can_given 
  = return (emptyBag, wanteds)   -- Note [Float Equalities out of Implications]
  | otherwise 
  = do { untch <- TcSMonad.getUntouchables
       ; mapM_ (promote_tv untch) (varSetElems (tyVarsOfCts float_eqs))
       ; ty_binds <- getTcSTyBindsMap
       ; traceTcS "floatEqualities" (vcat [ text "Ctxt untoucables =" <+> ppr untch
                                          , text "Floated eqs =" <+> ppr float_eqs
                                          , text "Ty binds =" <+> ppr ty_binds])
       ; return (float_eqs, wanteds { wc_flat = remaining_flats }) }
  where 
    (float_eqs, remaining_flats) = partitionBag is_floatable flats
    skol_set = growSkols wanteds (mkVarSet skols)

    is_floatable :: Ct -> Bool
    is_floatable ct
       = isEqPred pred && skol_set `disjointVarSet` tyVarsOfType pred
       where
         pred = ctPred ct

    promote_tv untch tv 
      | isFloatedTouchableMetaTyVar untch tv
      = do { cloned_tv <- TcSMonad.cloneMetaTyVar tv
           ; let rhs_tv = setMetaTyVarUntouchables cloned_tv untch
           ; setWantedTyBind tv (mkTyVarTy rhs_tv) }
      | otherwise
      = return ()

growSkols :: WantedConstraints -> VarSet -> VarSet
-- Find all the type variables that might possibly be unified
-- with a type that mentions a skolem.  This test is very conservative.
-- I don't *think* we need look inside the implications, because any 
-- relevant unification variables in there are untouchable.
growSkols (WC { wc_flat = flats }) skols
  = growThetaTyVars theta skols
  where
    theta = foldrBag ((:) . ctPred) [] flats
\end{code}

Note [Float Equalities out of Implications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
For ordinary pattern matches (including existentials) we float 
equalities out of implications, for instance: 
     data T where 
       MkT :: Eq a => a -> T 
     f x y = case x of MkT _ -> (y::Int)
We get the implication constraint (x::T) (y::alpha): 
     forall a. [untouchable=alpha] Eq a => alpha ~ Int
We want to float out the equality into a scope where alpha is no
longer untouchable, to solve the implication!  

But we cannot float equalities out of implications whose givens may
yield or contain equalities:

      data T a where 
        T1 :: T Int
        T2 :: T Bool
        T3 :: T a 
        
      h :: T a -> a -> Int
      
      f x y = case x of 
                T1 -> y::Int
                T2 -> y::Bool
                T3 -> h x y

We generate constraint, for (x::T alpha) and (y :: beta): 
   [untouchables = beta] (alpha ~ Int => beta ~ Int)   -- From 1st branch
   [untouchables = beta] (alpha ~ Bool => beta ~ Bool) -- From 2nd branch
   (alpha ~ beta)                                      -- From 3rd branch 

If we float the equality (beta ~ Int) outside of the first implication and 
the equality (beta ~ Bool) out of the second we get an insoluble constraint.
But if we just leave them inside the implications we unify alpha := beta and
solve everything.

Principle: 
    We do not want to float equalities out which may need the given *evidence*
    to become soluble.

Consequence: classes with functional dependencies don't matter (since there is 
no evidence for a fundep equality), but equality superclasses do matter (since 
they carry evidence).

Notice that, due to Note [Extra TcSTv Untouchables], the free unification variables 
of an equality that is floated out of an implication become effectively untouchables
for the leftover implication. This is absolutely necessary. Consider the following 
example. We start with two implications and a class with a functional dependency. 

    class C x y | x -> y
    instance C [a] [a]
          
    (I1)      [untch=beta]forall b. 0 => F Int ~ [beta]
    (I2)      [untch=beta]forall c. 0 => F Int ~ [[alpha]] /\ C beta [c]

We float (F Int ~ [beta]) out of I1, and we float (F Int ~ [[alpha]]) out of I2. 
They may react to yield that (beta := [alpha]) which can then be pushed inwards 
the leftover of I2 to get (C [alpha] [a]) which, using the FunDep, will mean that
(alpha := a). In the end we will have the skolem 'b' escaping in the untouchable
beta! Concrete example is in indexed_types/should_fail/ExtraTcsUntch.hs:

    class C x y | x -> y where 
     op :: x -> y -> ()

    instance C [a] [a]

    type family F a :: *

    h :: F Int -> ()
    h = undefined

    data TEx where 
      TEx :: a -> TEx 


    f (x::beta) = 
        let g1 :: forall b. b -> ()
            g1 _ = h [x]
            g2 z = case z of TEx y -> (h [[undefined]], op x [y])
        in (g1 '3', g2 undefined)

Note [Extra TcsTv untouchables]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Whenever we are solving a bunch of flat constraints, they may contain 
the following sorts of 'touchable' unification variables:
   
   (i)   Born-touchables in that scope
 
   (ii)  Simplifier-generated unification variables, such as unification 
         flatten variables

   (iii) Touchables that have been floated out from some nested 
         implications, see Note [Float Equalities out of Implications]. 

Now, once we are done with solving these flats and have to move inwards to 
the nested implications (perhaps for a second time), we must consider all the
extra variables (categories (ii) and (iii) above) as untouchables for the 
implication. Otherwise we have the danger or double unifications, as well
as the danger of not ``seeing'' some unification. Example (from Trac #4494):

   (F Int ~ uf)  /\  [untch=beta](forall a. C a => F Int ~ beta) 

In this example, beta is touchable inside the implication. The 
first solveInteract step leaves 'uf' ununified. Then we move inside 
the implication where a new constraint
       uf  ~  beta  
emerges. We may spontaneously solve it to get uf := beta, so the whole
implication disappears but when we pop out again we are left with (F
Int ~ uf) which will be unified by our final solveCTyFunEqs stage and
uf will get unified *once more* to (F Int).

The solution is to record the unification variables of the flats, 
and make them untouchables for the nested implication. In the 
example above uf would become untouchable, so beta would be forced 
to be unified as beta := uf.

\begin{code}
unFlattenWC :: WantedConstraints -> TcS WantedConstraints
unFlattenWC wc 
  = do { (subst, remaining_unsolved_flats) <- solveCTyFunEqs (wc_flat wc)
                -- See Note [Solving Family Equations]
                -- NB: remaining_flats has already had subst applied
       ; return $ 
         WC { wc_flat  = mapBag (substCt subst) remaining_unsolved_flats
            , wc_impl  = mapBag (substImplication subst) (wc_impl wc) 
            , wc_insol = mapBag (substCt subst) (wc_insol wc) }
       }
  where 
    solveCTyFunEqs :: Cts -> TcS (TvSubst, Cts)
    -- Default equalities (F xi ~ alpha) by setting (alpha := F xi), whenever possible
    -- See Note [Solving Family Equations]
    -- Returns: a bunch of unsolved constraints from the original Cts and implications
    --          where the newly generated equalities (alpha := F xi) have been substituted through.
    solveCTyFunEqs cts
     = do { untch   <- TcSMonad.getUntouchables 
          ; let (unsolved_can_cts, (ni_subst, cv_binds))
                    = getSolvableCTyFunEqs untch cts
          ; traceTcS "defaultCTyFunEqs" (vcat [ text "Trying to default family equations:"
                                              , text "untch" <+> ppr untch 
                                              , text "subst" <+> ppr ni_subst 
                                              , text "binds" <+> ppr cv_binds
                                              , ppr unsolved_can_cts
                                              ])
          ; mapM_ solve_one cv_binds

          ; return (niFixTvSubst ni_subst, unsolved_can_cts) }
      where
        solve_one (CtWanted { ctev_evar = cv }, tv, ty) 
          = setWantedTyBind tv ty >> setEvBind cv (EvCoercion (mkTcReflCo ty))
        solve_one (CtDerived {}, tv, ty)
          = setWantedTyBind tv ty
        solve_one arg
          = pprPanic "solveCTyFunEqs: can't solve a /given/ family equation!" $ ppr arg

------------
type FunEqBinds = (TvSubstEnv, [(CtEvidence, TcTyVar, TcType)])
  -- The TvSubstEnv is not idempotent, but is loop-free
  -- See Note [Non-idempotent substitution] in Unify
emptyFunEqBinds :: FunEqBinds
emptyFunEqBinds = (emptyVarEnv, [])

extendFunEqBinds :: FunEqBinds -> CtEvidence -> TcTyVar -> TcType -> FunEqBinds
extendFunEqBinds (tv_subst, cv_binds) fl tv ty
  = (extendVarEnv tv_subst tv ty, (fl, tv, ty):cv_binds)

------------
getSolvableCTyFunEqs :: Untouchables
                     -> Cts                -- Precondition: all Wanteds or Derived!
                     -> (Cts, FunEqBinds)  -- Postcondition: returns the unsolvables
getSolvableCTyFunEqs untch cts
  = Bag.foldlBag dflt_funeq (emptyCts, emptyFunEqBinds) cts
  where
    dflt_funeq :: (Cts, FunEqBinds) -> Ct
               -> (Cts, FunEqBinds)
    dflt_funeq (cts_in, feb@(tv_subst, _))
               (CFunEqCan { cc_ev = fl
                          , cc_fun = tc
                          , cc_tyargs = xis
                          , cc_rhs = xi })
      | Just tv <- tcGetTyVar_maybe xi      -- RHS is a type variable

      , isTouchableMetaTyVar untch tv
           -- And it's a *touchable* unification variable

      , typeKind xi `tcIsSubKind` tyVarKind tv
         -- Must do a small kind check since TcCanonical invariants 
         -- on family equations only impose compatibility, not subkinding

      , not (tv `elemVarEnv` tv_subst)
           -- Check not in extra_binds
           -- See Note [Solving Family Equations], Point 1

      , not (tv `elemVarSet` niSubstTvSet tv_subst (tyVarsOfTypes xis))
           -- Occurs check: see Note [Solving Family Equations], Point 2
      = ASSERT ( not (isGiven fl) )
        (cts_in, extendFunEqBinds feb fl tv (mkTyConApp tc xis))

    dflt_funeq (cts_in, fun_eq_binds) ct
      = (cts_in `extendCts` ct, fun_eq_binds)
\end{code}

Note [Solving Family Equations] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
After we are done with simplification we may be left with constraints of the form:
     [Wanted] F xis ~ beta 
If 'beta' is a touchable unification variable not already bound in the TyBinds 
then we'd like to create a binding for it, effectively "defaulting" it to be 'F xis'.

When is it ok to do so? 
    1) 'beta' must not already be defaulted to something. Example: 

           [Wanted] F Int  ~ beta   <~ Will default [beta := F Int]
           [Wanted] F Char ~ beta   <~ Already defaulted, can't default again. We 
                                       have to report this as unsolved.

    2) However, we must still do an occurs check when defaulting (F xis ~ beta), to 
       set [beta := F xis] only if beta is not among the free variables of xis.

    3) Notice that 'beta' can't be bound in ty binds already because we rewrite RHS 
       of type family equations. See Inert Set invariants in TcInteract. 


*********************************************************************************
*                                                                               * 
*                          Defaulting and disamgiguation                        *
*                                                                               *
*********************************************************************************
\begin{code}
applyDefaultingRules :: Cts      -- Wanteds or Deriveds
                     -> TcS Cts  -- Derived equalities 
-- Return some extra derived equalities, which express the
-- type-class default choice. 
applyDefaultingRules wanteds
  | isEmptyBag wanteds 
  = return emptyBag
  | otherwise
  = do { traceTcS "applyDefaultingRules { " $ 
                  text "wanteds =" <+> ppr wanteds
                  
       ; info@(default_tys, _) <- getDefaultInfo
       ; let groups = findDefaultableGroups info wanteds
       ; traceTcS "findDefaultableGroups" $ vcat [ text "groups=" <+> ppr groups
                                                 , text "info=" <+> ppr info ]
       ; deflt_cts <- mapM (disambigGroup default_tys) groups

       ; traceTcS "applyDefaultingRules }" $ 
                  vcat [ text "Type defaults =" <+> ppr deflt_cts]

       ; return (unionManyBags deflt_cts) }
\end{code}

Note [tryTcS in defaulting]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
defaultTyVar and disambigGroup create new evidence variables for
default equations, and hence update the EvVar cache. However, after
applyDefaultingRules we will try to solve these default equations
using solveInteractCts, which will consult the cache and solve those
EvVars from themselves! That's wrong.

To avoid this problem we guard defaulting under a @tryTcS@ which leaves
the original cache unmodified.

There is a second reason for @tryTcS@ in defaulting: disambGroup does
some constraint solving to determine if a default equation is
``useful'' in solving some wanted constraints, but we want to
discharge all evidence and unifications that may have happened during
this constraint solving.

Finally, @tryTcS@ importantly does not inherit the original cache from
the higher level but makes up a new cache, the reason is that disambigGroup
will call solveInteractCts so the new derived and the wanteds must not be 
in the cache!


\begin{code}
applyTyVarDefaulting :: WantedConstraints -> TcM Cts
applyTyVarDefaulting wc 
  = do { tv_cts <- mapM defaultTyVar $ 
                   varSetElems (tyVarsOfWC wc)
       ; return (unionManyBags tv_cts) }

defaultTyVar :: TcTyVar -> TcM Cts
-- Precondition: a touchable meta-variable
defaultTyVar the_tv
  | not (k `eqKind` default_k)
  = do { tv' <- TcMType.cloneMetaTyVar the_tv
       ; let rhs_ty = mkTyVarTy (setTyVarKind tv' default_k)
             loc = CtLoc DefaultOrigin (getSrcSpan the_tv) [] -- Yuk
             derived_pred = mkTcEqPred (mkTyVarTy the_tv) rhs_ty
             -- Why not directly derived_pred = mkTcEqPred k default_k? 
             -- See Note [DefaultTyVar]
             derived_cts = mkNonCanonical $
                           CtDerived { ctev_wloc = loc
                                     , ctev_pred = derived_pred } 
       
       ; return (unitBag derived_cts) }

  | otherwise = return emptyBag  -- The common case
  where
    k = tyVarKind the_tv
    default_k = defaultKind k
\end{code}

Note [DefaultTyVar]
~~~~~~~~~~~~~~~~~~~
defaultTyVar is used on any un-instantiated meta type variables to
default the kind of OpenKind and ArgKind etc to *.  This is important 
to ensure that instance declarations match.  For example consider

     instance Show (a->b)
     foo x = show (\_ -> True)

Then we'll get a constraint (Show (p ->q)) where p has kind ArgKind,
and that won't match the typeKind (*) in the instance decl.  See tests
tc217 and tc175.

We look only at touchable type variables. No further constraints
are going to affect these type variables, so it's time to do it by
hand.  However we aren't ready to default them fully to () or
whatever, because the type-class defaulting rules have yet to run.

An important point is that if the type variable tv has kind k and the
default is default_k we do not simply generate [D] (k ~ default_k) because:

   (1) k may be ArgKind and default_k may be * so we will fail

   (2) We need to rewrite all occurrences of the tv to be a type
       variable with the right kind and we choose to do this by rewriting 
       the type variable /itself/ by a new variable which does have the 
       right kind.

\begin{code}
findDefaultableGroups 
    :: ( [Type]
       , (Bool,Bool) )  -- (Overloaded strings, extended default rules)
    -> Cts              -- Unsolved (wanted or derived)
    -> [[(Ct,Class,TcTyVar)]]
findDefaultableGroups (default_tys, (ovl_strings, extended_defaults)) wanteds
  | null default_tys             = []
  | otherwise = filter is_defaultable_group (equivClasses cmp_tv unaries)
  where 
    unaries     :: [(Ct, Class, TcTyVar)]  -- (C tv) constraints
    non_unaries :: [Ct]             -- and *other* constraints
    
    (unaries, non_unaries) = partitionWith find_unary (bagToList wanteds)
        -- Finds unary type-class constraints
    find_unary cc 
        | Just (cls,[ty]) <- getClassPredTys_maybe (ctPred cc)
        , Just tv <- tcGetTyVar_maybe ty
        = Left (cc, cls, tv)
    find_unary cc = Right cc  -- Non unary or non dictionary 

    bad_tvs :: TcTyVarSet  -- TyVars mentioned by non-unaries 
    bad_tvs = foldr (unionVarSet . tyVarsOfCt) emptyVarSet non_unaries 

    cmp_tv (_,_,tv1) (_,_,tv2) = tv1 `compare` tv2

    is_defaultable_group ds@((_,_,tv):_)
        = let b1 = isTyConableTyVar tv  -- Note [Avoiding spurious errors]
              b2 = not (tv `elemVarSet` bad_tvs)
              b4 = defaultable_classes [cls | (_,cls,_) <- ds]
          in (b1 && b2 && b4)
    is_defaultable_group [] = panic "defaultable_group"

    defaultable_classes clss 
        | extended_defaults = any isInteractiveClass clss
        | otherwise         = all is_std_class clss && (any is_num_class clss)

    -- In interactive mode, or with -XExtendedDefaultRules,
    -- we default Show a to Show () to avoid graututious errors on "show []"
    isInteractiveClass cls 
        = is_num_class cls || (classKey cls `elem` [showClassKey, eqClassKey, ordClassKey])

    is_num_class cls = isNumericClass cls || (ovl_strings && (cls `hasKey` isStringClassKey))
    -- is_num_class adds IsString to the standard numeric classes, 
    -- when -foverloaded-strings is enabled

    is_std_class cls = isStandardClass cls || (ovl_strings && (cls `hasKey` isStringClassKey))
    -- Similarly is_std_class

------------------------------
disambigGroup :: [Type]                  -- The default types 
              -> [(Ct, Class, TcTyVar)]  -- All classes of the form (C a)
                                         --  sharing same type variable
              -> TcS Cts

disambigGroup []  _grp
  = return emptyBag
disambigGroup (default_ty:default_tys) group
  = do { traceTcS "disambigGroup" (ppr group $$ ppr default_ty)
       ; success <- tryTcS $ -- Why tryTcS? See Note [tryTcS in defaulting]
                    do { let derived_pred = mkTcEqPred (mkTyVarTy the_tv) default_ty
                             derived_cts = unitBag $ mkNonCanonical $
                                           CtDerived { ctev_wloc = the_loc
                                                     , ctev_pred = derived_pred }
                            
                       ; traceTcS "disambigGroup (solving) {" $
                         text "trying to solve constraints along with default equations ..."
                       ; implics_from_defaulting <- 
                                    solveInteract (derived_cts `unionBags` wanteds)
                       ; MASSERT (isEmptyBag implics_from_defaulting)
                           -- I am not certain if any implications can be generated
                           -- but I am letting this fail aggressively if this ever happens.
                                     
                       ; all_solved <- checkAllSolved
                       ; traceTcS "disambigGroup (solving) }" $
                         text "disambigGroup solved =" <+> ppr all_solved
                       ; if all_solved then
                             return (Just derived_cts) 
                         else 
                             return Nothing 
                       }
       ; case success of
           Just cts -> -- Success: record the type variable binding, and return
                    do { wrapWarnTcS $ warnDefaulting wanteds default_ty
                       ; traceTcS "disambigGroup succeeded" (ppr default_ty)
                       ; return cts }
           Nothing -> -- Failure: try with the next type
                    do { traceTcS "disambigGroup failed, will try other default types"
                                  (ppr default_ty)
                       ; disambigGroup default_tys group } }
  where
    ((the_ct,_,the_tv):_) = group
    the_fl                = cc_ev the_ct
    the_loc               = ctev_wloc the_fl
    wanteds               = listToBag (map fstOf3 group)
\end{code}

Note [Avoiding spurious errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When doing the unification for defaulting, we check for skolem
type variables, and simply don't default them.  For example:
   f = (*)      -- Monomorphic
   g :: Num a => a -> a
   g x = f x x
Here, we get a complaint when checking the type signature for g,
that g isn't polymorphic enough; but then we get another one when
dealing with the (Num a) context arising from f's definition;
we try to unify a with Int (to default it), but find that it's
already been unified with the rigid variable from g's type sig



*********************************************************************************
*                                                                               * 
*                   Utility functions
*                                                                               *
*********************************************************************************

\begin{code}
newFlatWanteds :: CtOrigin -> ThetaType -> TcM [Ct]
newFlatWanteds orig theta
  = do { loc <- getCtLoc orig
       ; mapM (inst_to_wanted loc) theta }
  where 
    inst_to_wanted loc pty 
          = do { v <- TcMType.newWantedEvVar pty 
               ; return $ mkNonCanonical $
                 CtWanted { ctev_evar = v
                          , ctev_wloc = loc
                          , ctev_pred = pty } }
\end{code}