TcSimplify.lhs 67.9 KB
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\begin{code}
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{-# 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

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module TcSimplify( 
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       simplifyInfer, simplifyAmbiguityCheck,
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       simplifyDefault, simplifyDeriv, 
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       simplifyRule, simplifyTop, simplifyInteractive
  ) where
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#include "HsVersions.h"
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import TcRnMonad
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import TcErrors
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import TcMType
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import TcType 
import TcSMonad 
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import TcInteract 
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import Inst
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import Unify	( niFixTvSubst, niSubstTvSet )
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import Type     ( classifyPredType, PredTree(..), isIPPred_maybe )
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import Var
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import Unique
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import VarSet
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import VarEnv 
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import TcEvidence
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import TypeRep
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import Name
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import Bag
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import ListSetOps
import Util
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import PrelInfo
import PrelNames
import Class		( classKey )
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import BasicTypes       ( RuleName )
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import Control.Monad    ( when )
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import Outputable
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import FastString
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import TrieMap () -- DV: for now
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import DynFlags
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import Data.Maybe ( mapMaybe )
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\end{code}


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*********************************************************************************
*                                                                               * 
*                           External interface                                  *
*                                                                               *
*********************************************************************************
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\begin{code}
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simplifyTop :: WantedConstraints -> TcM (Bag EvBind)
-- Simplify top-level constraints
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-- 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
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simplifyTop wanteds 
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  = do { ev_binds_var <- newTcEvBinds
                         
       ; zonked_wanteds <- zonkWC wanteds
       ; wc_first_go <- runTcSWithEvBinds ev_binds_var $ solveWanteds 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 "zonked_wc =" <+> ppr zonked_wanteds
       ; 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 <- runTcSWithEvBinds ev_binds_var $ solveWanteds 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 "simpl_top_loop }" 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}
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------------------
simplifyAmbiguityCheck :: Name -> WantedConstraints -> TcM (Bag EvBind)
simplifyAmbiguityCheck name wanteds
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  = traceTc "simplifyAmbiguityCheck" (text "name =" <+> ppr name) >> 
    simplifyCheck wanteds
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------------------
simplifyInteractive :: WantedConstraints -> TcM (Bag EvBind)
simplifyInteractive wanteds 
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  = traceTc "simplifyInteractive" empty >>
    simplifyTop wanteds 
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------------------
simplifyDefault :: ThetaType	-- Wanted; has no type variables in it
                -> TcM ()	-- Succeeds iff the constraint is soluble
simplifyDefault theta
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  = do { traceTc "simplifyInteractive" empty
       ; wanted <- newFlatWanteds DefaultOrigin theta
       ; _ignored_ev_binds <- simplifyCheck (mkFlatWC wanted)
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       ; return () }
\end{code}
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***********************************************************************************
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*                                                                                 * 
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*                            Deriving                                             *
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*                                                                                 *
***********************************************************************************
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\begin{code}
simplifyDeriv :: CtOrigin
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              -> PredType
	      -> [TyVar]	
	      -> ThetaType		-- Wanted
	      -> TcM ThetaType	-- Needed
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-- Given  instance (wanted) => C inst_ty 
-- Simplify 'wanted' as much as possibles
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-- Fail if not possible
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simplifyDeriv orig pred tvs theta 
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  = do { (skol_subst, tvs_skols) <- tcInstSkolTyVars tvs -- Skolemize
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      	 	-- The constraint solving machinery 
		-- expects *TcTyVars* not TyVars.  
		-- We use *non-overlappable* (vanilla) skolems
		-- See Note [Overlap and deriving]
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       ; let subst_skol = zipTopTvSubst tvs_skols $ map mkTyVarTy tvs
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             skol_set   = mkVarSet tvs_skols
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	     doc = ptext (sLit "deriving") <+> parens (ppr pred)
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       ; wanted <- newFlatWanteds orig (substTheta skol_subst theta)

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       ; traceTc "simplifyDeriv" $ 
         vcat [ pprTvBndrs tvs $$ ppr theta $$ ppr wanted, doc ]
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       ; (residual_wanted, _ev_binds1)
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             <- runTcS $ solveWanteds (mkFlatWC wanted)
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       ; let (good, bad) = partitionBagWith get_good (wc_flat residual_wanted)
                         -- See Note [Exotic derived instance contexts]
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             get_good :: Ct -> Either PredType Ct
             get_good ct | validDerivPred skol_set p = Left p
                         | otherwise                 = Right ct
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                         where p = ctPred ct
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       -- 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 })
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       ; let min_theta = mkMinimalBySCs (bagToList good)
       ; return (substTheta subst_skol min_theta) }
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\end{code}
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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

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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.
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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)
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Notice that this instance (just) satisfies the Paterson termination 
conditions.  Then we *could* derive an instance decl like this:
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	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.  
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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.
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So for now we simply require that the derived instance context
should have only type-variable constraints.
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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
*                                                                                 *
***********************************************************************************
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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.

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\begin{code}
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simplifyInfer :: Bool
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              -> Bool                  -- Apply monomorphism restriction
              -> [(Name, TcTauType)]   -- Variables to be generalised,
                                       -- and their tau-types
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              -> (Untouchables, WantedConstraints)
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              -> TcM ([TcTyVar],    -- Quantify over these type variables
                      [EvVar],      -- ... and these constraints
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		      Bool,	    -- The monomorphism restriction did something
		      		    --   so the results type is not as general as
				    --   it could be
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                      TcEvBinds)    -- ... binding these evidence variables
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simplifyInfer _top_lvl apply_mr name_taus (untch,wanteds)
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  | isEmptyWC wanteds
  = do { gbl_tvs     <- tcGetGlobalTyVars            -- Already zonked
       ; zonked_taus <- zonkTcTypes (map snd name_taus)
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       ; let tvs_to_quantify = varSetElems (tyVarsOfTypes zonked_taus `minusVarSet` gbl_tvs)
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       	     		       -- tvs_to_quantify can contain both kind and type vars
       	                       -- See Note [Which variables to quantify]
       ; qtvs <- zonkQuantifiedTyVars tvs_to_quantify
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       ; return (qtvs, [], False, emptyTcEvBinds) }
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  | otherwise
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  = do { runtimeCoercionErrors <- doptM Opt_DeferTypeErrors
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       ; gbl_tvs        <- tcGetGlobalTyVars
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       ; zonked_tau_tvs <- zonkTyVarsAndFV (tyVarsOfTypes (map snd name_taus))
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       ; zonked_wanteds <- zonkWC wanteds
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       ; traceTc "simplifyInfer {"  $ vcat
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             [ ptext (sLit "names =") <+> ppr (map fst name_taus)
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             , ptext (sLit "taus =") <+> ppr (map snd name_taus)
             , ptext (sLit "tau_tvs (zonked) =") <+> ppr zonked_tau_tvs
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             , ptext (sLit "gbl_tvs =") <+> ppr gbl_tvs
             , ptext (sLit "closed =") <+> ppr _top_lvl
             , ptext (sLit "apply_mr =") <+> ppr apply_mr
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             , ptext (sLit "untch =") <+> ppr untch
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             , ptext (sLit "wanted =") <+> ppr zonked_wanteds
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             ]

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              -- 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!
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              -- 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.
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       ; ev_binds_var <- newTcEvBinds
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       ; wanted_transformed <- runTcSWithEvBinds ev_binds_var $ 
                               solveWanteds zonked_wanteds

              -- Step 3) Fail fast if there is an insoluble constraint,
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              -- unless we are deferring errors to runtime
       ; when (not runtimeCoercionErrors && insolubleWC wanted_transformed) $ 
         do { _ev_binds <- reportUnsolved False wanted_transformed; failM }
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              -- Step 4) Candidates for quantification are an approximation of wanted_transformed
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       ; 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]
                                
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              -- Step 5) Minimize the quantification candidates                             
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       ; (quant_candidates_transformed, _extra_binds)   
             <- runTcS $ solveWanteds $ WC { wc_flat  = quant_candidates
                                           , wc_impl  = emptyBag
                                           , wc_insol = emptyBag }
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              -- Step 6) Final candidates for quantification                
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       ; let final_quant_candidates :: Bag PredType
             final_quant_candidates = mapBag ctPred $ 
                                      keepWanted (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?
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       ; zonked_tau_tvs <- zonkTyVarsAndFV zonked_tau_tvs
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       ; 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 ]
         
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       ; let init_tvs 	     = zonked_tau_tvs `minusVarSet` gbl_tvs
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             poly_qtvs       = growPreds gbl_tvs id final_quant_candidates init_tvs
             
             pbound          = filterBag (quantifyMe poly_qtvs id) final_quant_candidates
             
       ; traceTc "simplifyWithApprox" $
         vcat [ ptext (sLit "pbound =") <+> ppr pbound ]
         
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	     -- Monomorphism restriction
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       ; let mr_qtvs  	     = init_tvs `minusVarSet` constrained_tvs
             constrained_tvs = tyVarsOfBag tyVarsOfType final_quant_candidates
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	     mr_bites        = apply_mr && not (isEmptyBag pbound)

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

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

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       ; qtvs_to_return <- zonkQuantifiedTyVars (varSetElems qtvs)
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            -- Step 7) Emit an implication
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       ; minimal_bound_ev_vars <- mapM TcMType.newEvVar minimal_flat_preds
       ; lcl_env <- getLclTypeEnv
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       ; gloc <- getCtLoc skol_info
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       ; let implic = Implic { ic_untch    = untch 
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                             , ic_env      = lcl_env
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                             , ic_skols    = qtvs_to_return
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                             , ic_given    = minimal_bound_ev_vars
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                             , ic_wanted   = wanted_transformed 
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                             , ic_insol    = False
                             , ic_binds    = ev_binds_var
                             , ic_loc      = gloc }
       ; emitImplication implic
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       ; traceTc "} simplifyInfer/produced residual implication for quantification" $
             vcat [ ptext (sLit "implic =") <+> ppr implic
                       -- ic_skols, ic_given give rest of result
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                  , ptext (sLit "qtvs =") <+> ppr qtvs_to_return
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                  , ptext (sLit "spb =") <+> ppr final_quant_candidates
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                  , ptext (sLit "bound =") <+> ppr bound ]

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



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Note [Minimize by Superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
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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.
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\begin{code}
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approximateWC :: WantedConstraints -> Cts
approximateWC wc = float_wc emptyVarSet wc
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  where 
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    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
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    float_implic skols imp
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      = float_wc (skols `extendVarSetList` ic_skols imp) (ic_wanted imp)
            
    float_flat :: TcTyVarSet -> Ct -> Cts
    float_flat skols ct
      | tyVarsOfCt ct `disjointVarSet` skols 
      , isWantedCt ct = singleCt ct
      | otherwise = emptyCts
        
    do_bag :: (a -> Bag c) -> Bag a -> Bag c
    do_bag f = foldrBag (unionBags.f) emptyBag
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\end{code}
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\begin{code}
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growPreds :: TyVarSet -> (a -> PredType) -> Bag a -> TyVarSet -> TyVarSet
growPreds gbl_tvs get_pred items tvs
  = foldrBag extend tvs items
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  where
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    extend item tvs = tvs `unionVarSet`
                      (growPredTyVars (get_pred item) tvs `minusVarSet` gbl_tvs)
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--------------------
quantifyMe :: TyVarSet      -- Quantifying over these
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	   -> (a -> PredType)
	   -> a -> Bool	    -- True <=> quantify over this wanted
quantifyMe qtvs toPred ct
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  | isIPPred pred = True  -- Note [Inheriting implicit parameters]
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  | otherwise	  = tyVarsOfType pred `intersectsVarSet` qtvs
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  where
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    pred = toPred ct
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\end{code}
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Note [Avoid unecessary constraint simplification]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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    -------- 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.)
    ----------------------------------------
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When inferring the type of a let-binding, with simplifyInfer,
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try to avoid unnecessarily simplifying class constraints.
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Doing so aids sharing, but it also helps with delicate 
situations like
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   instance C t => C [t] where ..
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   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.


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Note [Inheriting implicit parameters]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Consider this:

	f x = (x::Int) + ?y
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where f is *not* a top-level binding.
From the RHS of f we'll get the constraint (?y::Int).
There are two types we might infer for f:
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	f :: Int -> Int

(so we get ?y from the context of f's definition), or
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	f :: (?y::Int) => Int -> Int

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At first you might think the first was better, becuase then
?y behaves like a free variable of the definition, rather than
having to be passed at each call site.  But of course, the WHOLE
IDEA is that ?y should be passed at each call site (that's what
dynamic binding means) so we'd better infer the second.

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BOTTOM LINE: when *inferring types* you *must* quantify 
over implicit parameters. See the predicate isFreeWhenInferring.
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*********************************************************************************
*                                                                                 * 
*                             RULES                                               *
*                                                                                 *
***********************************************************************************
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See note [Simplifying RULE consraints] in TcRule
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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.
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\begin{code}
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simplifyRule :: RuleName 
             -> WantedConstraints	-- Constraints from LHS
             -> WantedConstraints	-- Constraints from RHS
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             -> 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)
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             	 -- We allow ourselves to unify environment 
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		 -- variables: runTcS runs with NoUntouchables
       ; (resid_wanted, _) <- runTcS (solveWanteds zonked_all)
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       ; zonked_lhs <- zonkWC lhs_wanted

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       ; 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
             
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       ; traceTc "simplifyRule" $
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         vcat [ doc
              , text "zonked_lhs" <+> ppr zonked_lhs 
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              , text "q_cts"      <+> ppr q_cts ]

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


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*********************************************************************************
*                                                                                 * 
*                                 Main Simplifier                                 *
*                                                                                 *
***********************************************************************************
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\begin{code}
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simplifyCheck :: WantedConstraints	-- Wanted
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              -> 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
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simplifyCheck wanteds
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  = do { wanteds <- zonkWC wanteds
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       ; traceTc "simplifyCheck {" (vcat
             [ ptext (sLit "wanted =") <+> ppr wanteds ])

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       ; (unsolved, eb1) <- runTcS (solveWanteds wanteds)
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       ; traceTc "simplifyCheck }" $ ptext (sLit "unsolved =") <+> ppr unsolved

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

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       ; 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
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  a :: Int
  a = 'a'
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  main = print "b"
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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`.
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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 -> TcS WantedConstraints
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-- Returns: residual constraints, plus evidence bindings 
-- NB: When we are called from TcM there are no inerts to pass down to TcS
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solveWanteds wanted
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  = do { (_,wc_out) <- solve_wanteds wanted
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       ; let wc_ret = wc_out { wc_flat = keepWanted (wc_flat wc_out) } 
                      -- Discard Derived
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       ; return wc_ret }
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solve_wanteds :: WantedConstraints
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              -> TcS (TvSubst, WantedConstraints) 
              -- NB: wc_flats may be wanted *or* derived now
              -- Returns the flattening substitution as well in case we need to apply it
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solve_wanteds wanted@(WC { wc_flat = flats, wc_impl = implics, wc_insol = insols }) 
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  = do { traceTcS "solveWanteds {" (ppr wanted)

                 -- Try the flat bit
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                 -- Discard from insols all the derived/given constraints
                 -- because they will show up again when we try to solve
                 -- everything else.  Solving them a second time is a bit
                 -- of a waste, but the code is simple, and the program is
                 -- wrong anyway!
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                 -- DV: why only keepWanted? We make sure that we never float out
                 -- whatever constraints can yield equalities, including class 
                 -- constraints with functional dependencies and hence all the derived
                 -- that were potentially insoluble will be re-generated.
                 -- (It would not hurt though to just keep the wanted and the derived)
                 -- See Note [The HasEqualities Predicate] in Inst.lhs
         
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       ; let all_flats = flats `unionBags` keepWanted insols
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       ; impls_from_flats <- solveInteractCts $ bagToList all_flats
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       -- solve_wanteds iterates when it is able to float equalities 
       -- out of one or more of the implications. 
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       ; unsolved_implics <- simpl_loop 1 (implics `unionBags` impls_from_flats)
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       ; (insoluble_flats,unsolved_flats) <- extractUnsolvedTcS 

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

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       ; (subst, remaining_unsolved_flats) <- solveCTyFunEqs unsolved_flats
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                -- See Note [Solving Family Equations]
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                -- NB: remaining_flats has already had subst applied

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       ; traceTcS "solveWanteds finished with" $
                 vcat [ text "remaining_unsolved_flats =" <+> ppr remaining_unsolved_flats
                      , text "subst =" <+> ppr subst
                      ]

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       ; return $ 
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         (subst, WC { wc_flat  = mapBag (substCt subst) remaining_unsolved_flats
                    , wc_impl  = mapBag (substImplication subst) unsolved_implics
                    , wc_insol = mapBag (substCt subst) insoluble_flats })
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       }

simpl_loop :: Int
           -> Bag Implication
           -> TcS (Bag Implication)
simpl_loop n implics
  | n > 10 
  = traceTcS "solveWanteds: loop!" empty >> return implics
  | otherwise 
  = do { (implic_eqs, unsolved_implics) <- solveNestedImplications implics
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       ; inerts <- getTcSInerts
       ; let ((_,unsolved_flats),_) = extractUnsolved inerts
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       ; let improve_eqs = implic_eqs
             -- NB: improve_eqs used to contain defaulting equations HERE but 
             -- defaulting now happens only at simplifyTop and not deep inside 
             -- simpl_loop! See Note [Top-level Defaulting Plan]
             
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       ; traceTcS "solveWanteds: simpl_loop end" $
             vcat [ text "improve_eqs      =" <+> ppr improve_eqs
                  , text "unsolved_flats   =" <+> ppr unsolved_flats
                  , text "unsolved_implics =" <+> ppr unsolved_implics ]
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       ; if isEmptyBag improve_eqs then return unsolved_implics 
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         else do { impls_from_eqs <- solveInteractCts $ bagToList improve_eqs
                 ; simpl_loop (n+1) (unsolved_implics `unionBags` 
                                                 impls_from_eqs)} }
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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
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       ; traceTcS "solveNestedImplications starting, inerts are:" $ ppr inerts
         
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       ; let ((_insoluble_flats, unsolved_flats),thinner_inerts) = extractUnsolved inerts 
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       ; traceTcS "solveNestedImplications starting, more info:" $ 
         vcat [ text "inerts          = " <+> ppr inerts
              , text "insoluble_flats = " <+> ppr _insoluble_flats
              , text "unsolved_flats  = " <+> ppr unsolved_flats
              , text "thinner_inerts  = " <+> ppr thinner_inerts ]
         
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       ; (implic_eqs, unsolved_implics)
           <- doWithInert thinner_inerts $ 
              do { let pushed_givens = givens_from_wanteds unsolved_flats
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                       tcs_untouchables 
                         = foldr (unionVarSet . tyVarsOfCt) emptyVarSet pushed_givens
                                          -- Typically pushed_givens is very small, consists
                                          -- only of unsolved equalities, so no inefficiency 
                                          -- danger.
                                                                                    
                                          
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                 -- See Note [Preparing inert set for implications]
	         -- Push the unsolved wanteds inwards, but as givens
                 ; traceTcS "solveWanteds: preparing inerts for implications {" $ 
                   vcat [ppr tcs_untouchables, ppr pushed_givens]
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                 ; impls_from_givens <- solveInteractCts pushed_givens
                                        
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                 ; MASSERT (isEmptyBag impls_from_givens)
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                       -- impls_from_givens must be empty, since we are reacting givens
                       -- with givens, and they can never generate extra implications 
                       -- from decomposition of ForAll types. (Whereas wanteds can, see
                       -- TcCanonical, canEq ForAll-ForAll case)
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                 ; traceTcS "solveWanteds: } now doing nested implications {" empty
                 ; flatMapBagPairM (solveImplication tcs_untouchables) 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.
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       ; traceTcS "solveWanteds: done nested implications }" $
                  vcat [ text "implic_eqs ="       <+> ppr implic_eqs
                       , text "unsolved_implics =" <+> ppr unsolved_implics ]

       ; return (implic_eqs, unsolved_implics) }

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  where givens_from_wanteds = foldrBag get_wanted []
        get_wanted cc rest_givens
            | pushable_wanted cc
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            = let fl   = ctEvidence cc
                  gfl  = Given { ctev_gloc = setCtLocOrigin (ctev_wloc fl) UnkSkol
                               , ctev_evtm = EvId (ctev_evar fl)
                               , ctev_pred = ctev_pred fl }
                  this_given = cc { cc_ev = gfl }
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              in this_given : rest_givens
            | otherwise = rest_givens 

        pushable_wanted :: Ct -> Bool 
        pushable_wanted cc 
         | isWantedCt cc 
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         = isEqPred (ctPred cc) -- see Note [Preparing inert set for implications]
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         | otherwise = False 

solveImplication :: TcTyVarSet     -- Untouchable TcS unification variables
                 -> 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 tcs_untouchables
     imp@(Implic { ic_untch  = untch
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                 , ic_binds  = ev_binds
                 , ic_skols  = skols 
                 , ic_given  = givens
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                 , ic_wanted = wanteds
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                 , ic_loc    = loc })
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  = shadowIPs givens $    -- See Note [Shadowing of Implicit Parameters]
    nestImplicTcS ev_binds (untch, tcs_untouchables) $
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    recoverTcS (return (emptyBag, emptyBag)) $
       -- Recover from nested failures.  Even the top level is
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       -- just a bunch of implications, so failing at the first one is bad
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    do { traceTcS "solveImplication {" (ppr imp) 

         -- Solve flat givens
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       ; impls_from_givens <- solveInteractGiven loc givens 
       ; MASSERT (isEmptyBag impls_from_givens)
         
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         -- Simplify the wanteds
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       ; (_flat_subst, 
           WC { wc_flat = unsolved_flats
              , wc_impl = unsolved_implics
              , wc_insol = insols }) <- solve_wanteds wanteds
          -- NB: Not solveWanteds because we need the derived equalities,            
          -- which may not be solvable (due to touchability) in this implication
          -- but may become solvable by spontantenous unification outside. 
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       ; let (res_flat_free, res_flat_bound)
                 = floatEqualities skols givens unsolved_flats
             final_flat = keepWanted res_flat_bound
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       ; let res_wanted = WC { wc_flat  = final_flat
                             , wc_impl  = unsolved_implics
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                             , wc_insol = insols }
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             res_implic = unitImplication $
                          imp { ic_wanted = res_wanted
                              , ic_insol  = insolubleWC res_wanted }
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       ; evbinds <- getTcEvBindsMap

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       ; traceTcS "solveImplication end }" $ vcat
             [ text "res_flat_free =" <+> ppr res_flat_free
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             , text "implication evbinds = " <+> ppr (evBindMapBinds evbinds)
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             , text "res_implic =" <+> ppr res_implic ]
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       ; return (res_flat_free, res_implic) }
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    -- and we are back to the original inerts
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floatEqualities :: [TcTyVar] -> [EvVar] -> Cts -> (Cts, Cts)
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-- Post: The returned FlavoredEvVar's are only Wanted or Derived
-- and come from the input wanted ev vars or deriveds 
floatEqualities skols can_given wantders
  | hasEqualities can_given = (emptyBag, wantders)
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          -- Note [Float Equalities out of Implications]
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  | otherwise = partitionBag is_floatable wantders
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  where skol_set = mkVarSet skols
        is_floatable :: Ct -> Bool
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        is_floatable ct
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          | ct_predty <- ctPred ct
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          , isEqPred ct_predty
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          = skol_set `disjointVarSet` tvs_under_fsks ct_predty
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        is_floatable _ct = False
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        tvs_under_fsks :: Type -> TyVarSet
        -- ^ NB: for type synonyms tvs_under_fsks does /not/ expand the synonym
        tvs_under_fsks (TyVarTy tv)     
          | not (isTcTyVar tv)               = unitVarSet tv
          | FlatSkol ty <- tcTyVarDetails tv = tvs_under_fsks ty
          | otherwise                        = unitVarSet tv
        tvs_under_fsks (TyConApp _ tys) = unionVarSets (map tvs_under_fsks tys)
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        tvs_under_fsks (LitTy {})       = emptyVarSet
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        tvs_under_fsks (FunTy arg res)  = tvs_under_fsks arg `unionVarSet` tvs_under_fsks res
        tvs_under_fsks (AppTy fun arg)  = tvs_under_fsks fun `unionVarSet` tvs_under_fsks arg
        tvs_under_fsks (ForAllTy tv ty) -- The kind of a coercion binder 
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        	     	       	        -- can mention type variables!
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          | isTyVar tv		      = inner_tvs `delVarSet` tv
          | otherwise  {- Coercion -} = -- ASSERT( not (tv `elemVarSet` inner_tvs) )
                                        inner_tvs `unionVarSet` tvs_under_fsks (tyVarKind tv)
          where
            inner_tvs = tvs_under_fsks ty
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shadowIPs :: [EvVar] -> TcS a -> TcS a
shadowIPs gs m
  | null shadowed = m
  | otherwise     = do is <- getTcSInerts
                       doWithInert (purgeShadowed is) m
  where
  shadowed  = mapMaybe isIP gs

  isIP g    = do p <- evVarPred_maybe g
                 (x,_) <- isIPPred_maybe p
                 return x

  isShadowedCt ct = isShadowedEv (ctEvidence ct)
  isShadowedEv ev = case isIPPred_maybe (ctEvPred ev) of
                      Just (x,_) -> x `elem` shadowed
                      _          -> False

  purgeShadowed is = is { inert_cans = purgeCans (inert_cans is)
                        , inert_solved = purgeSolved (inert_solved is)
                        }

  purgeDicts    = snd . partitionCCanMap isShadowedCt
  purgeCans ics = ics { inert_dicts = purgeDicts (inert_dicts ics) }
  purgeSolved   = filterSolved (not . isShadowedEv)
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\end{code}
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Note [Preparing inert set for implications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Before solving the nested implications, we convert any unsolved flat wanteds
to givens, and add them to the inert set.  Reasons:
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  a) In checking mode, suppresses unnecessary errors.  We already have
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     on unsolved-wanted error; adding it to the givens prevents any 
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     consequential errors from showing up
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  b) More importantly, in inference mode, we are going to quantify over this
     constraint, and we *don't* want to quantify over any constraints that
     are deducible from it.

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