TcCanonical.hs 67.1 KB
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{-# LANGUAGE CPP #-}

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module TcCanonical( 
     canonicalize,
     unifyDerived,

     StopOrContinue(..), stopWith, continueWith
  ) where
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#include "HsVersions.h"

import TcRnTypes
import TcType
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import Type
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import Kind
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import TcFlatten
import TcSMonad
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import TcEvidence
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import Class
import TyCon
import TypeRep
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import Coercion
import FamInstEnv ( FamInstEnvs )
import FamInst ( tcTopNormaliseNewTypeTF_maybe )
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import Var
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import DataCon ( dataConName )
import Name( isSystemName, nameOccName )
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import OccName( OccName )
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import Outputable
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import DynFlags( DynFlags )
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import VarSet
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import RdrName
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import Pair
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import Util
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import MonadUtils ( zipWith3M, zipWith3M_ )
import Data.List  ( zip4 )
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import BasicTypes
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import Data.Maybe ( isJust )
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import FastString
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{-
************************************************************************
*                                                                      *
*                      The Canonicaliser                               *
*                                                                      *
************************************************************************
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Note [Canonicalization]
~~~~~~~~~~~~~~~~~~~~~~~
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Canonicalization converts a simple constraint to a canonical form. It is
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unary (i.e. treats individual constraints one at a time), does not do
any zonking, but lives in TcS monad because it needs to create fresh
variables (for flattening) and consult the inerts (for efficiency).
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The execution plan for canonicalization is the following:
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  1) Decomposition of equalities happens as necessary until we reach a
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     variable or type family in one side. There is no decomposition step
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     for other forms of constraints.
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  2) If, when we decompose, we discover a variable on the head then we
     look at inert_eqs from the current inert for a substitution for this
     variable and contine decomposing. Hence we lazily apply the inert
     substitution if it is needed.
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  3) If no more decomposition is possible, we deeply apply the substitution
     from the inert_eqs and continue with flattening.
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  4) During flattening, we examine whether we have already flattened some
     function application by looking at all the CTyFunEqs with the same
     function in the inert set. The reason for deeply applying the inert
     substitution at step (3) is to maximise our chances of matching an
     already flattened family application in the inert.
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The net result is that a constraint coming out of the canonicalization
phase cannot be rewritten any further from the inerts (but maybe /it/ can
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rewrite an inert or still interact with an inert in a further phase in the
simplifier.
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Note [Caching for canonicals]
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Our plan with pre-canonicalization is to be able to solve a constraint
really fast from existing bindings in TcEvBinds. So one may think that
the condition (isCNonCanonical) is not necessary.  However consider
the following setup:
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InertSet = { [W] d1 : Num t }
WorkList = { [W] d2 : Num t, [W] c : t ~ Int}
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Now, we prioritize equalities, but in our concrete example
(should_run/mc17.hs) the first (d2) constraint is dealt with first,
because (t ~ Int) is an equality that only later appears in the
worklist since it is pulled out from a nested implication
constraint. So, let's examine what happens:
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   - We encounter work item (d2 : Num t)

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   - Nothing is yet in EvBinds, so we reach the interaction with inerts
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     and set:
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              d2 := d1
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    and we discard d2 from the worklist. The inert set remains unaffected.

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   - Now the equation ([W] c : t ~ Int) is encountered and kicks-out
     (d1 : Num t) from the inerts.  Then that equation gets
     spontaneously solved, perhaps. We end up with:
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        InertSet : { [G] c : t ~ Int }
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        WorkList : { [W] d1 : Num t}
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   - Now we examine (d1), we observe that there is a binding for (Num
     t) in the evidence binds and we set:
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             d1 := d2
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     and end up in a loop!

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Now, the constraints that get kicked out from the inert set are always
Canonical, so by restricting the use of the pre-canonicalizer to
NonCanonical constraints we eliminate this danger. Moreover, for
canonical constraints we already have good caching mechanisms
(effectively the interaction solver) and we are interested in reducing
things like superclasses of the same non-canonical constraint being
generated hence I don't expect us to lose a lot by introducing the
(isCNonCanonical) restriction.
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A similar situation can arise in TcSimplify, at the end of the
solve_wanteds function, where constraints from the inert set are
returned as new work -- our substCt ensures however that if they are
not rewritten by subst, they remain canonical and hence we will not
attempt to solve them from the EvBinds. If on the other hand they did
get rewritten and are now non-canonical they will still not match the
EvBinds, so we are again good.
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-}
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-- Top-level canonicalization
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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canonicalize :: Ct -> TcS (StopOrContinue Ct)
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canonicalize ct@(CNonCanonical { cc_ev = ev })
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  = do { traceTcS "canonicalize (non-canonical)" (ppr ct)
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       ; {-# SCC "canEvVar" #-}
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         canEvNC ev }
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canonicalize (CDictCan { cc_ev = ev
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                       , cc_class  = cls
                       , cc_tyargs = xis })
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  = {-# SCC "canClass" #-}
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    canClass ev cls xis -- Do not add any superclasses
canonicalize (CTyEqCan { cc_ev = ev
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                       , cc_tyvar  = tv
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                       , cc_rhs    = xi
                       , cc_eq_rel = eq_rel })
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  = {-# SCC "canEqLeafTyVarEq" #-}
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    canEqTyVar ev eq_rel NotSwapped tv xi xi
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canonicalize (CFunEqCan { cc_ev = ev
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                        , cc_fun    = fn
                        , cc_tyargs = xis1
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                        , cc_fsk    = fsk })
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  = {-# SCC "canEqLeafFunEq" #-}
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    canCFunEqCan ev fn xis1 fsk
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canonicalize (CIrredEvCan { cc_ev = ev })
  = canIrred ev
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canonicalize (CHoleCan { cc_ev = ev, cc_occ = occ, cc_hole = hole })
  = canHole ev occ hole
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canEvNC :: CtEvidence -> TcS (StopOrContinue Ct)
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-- Called only for non-canonical EvVars
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canEvNC ev
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  = case classifyPredType (ctEvPred ev) of
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      ClassPred cls tys     -> do traceTcS "canEvNC:cls" (ppr cls <+> ppr tys)
                                  canClassNC ev cls tys
      EqPred eq_rel ty1 ty2 -> do traceTcS "canEvNC:eq" (ppr ty1 $$ ppr ty2)
                                  canEqNC    ev eq_rel ty1 ty2
      TuplePred tys         -> do traceTcS "canEvNC:tup" (ppr tys)
                                  canTuple   ev tys
      IrredPred {}          -> do traceTcS "canEvNC:irred" (ppr (ctEvPred ev))
                                  canIrred   ev
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{-
************************************************************************
*                                                                      *
*                      Tuple Canonicalization
*                                                                      *
************************************************************************
-}
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canTuple :: CtEvidence -> [PredType] -> TcS (StopOrContinue Ct)
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canTuple ev preds
  | CtWanted { ctev_evar = evar, ctev_loc = loc } <- ev
  = do { new_evars <- mapM (newWantedEvVar loc) preds
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       ; setWantedEvBind evar (EvTupleMk (map (ctEvTerm . fst) new_evars))
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       ; emitWorkNC (freshGoals new_evars)
         -- Note the "NC": these are fresh goals, not necessarily canonical
       ; stopWith ev "Decomposed tuple constraint" }

  | CtGiven { ctev_evtm = tm, ctev_loc = loc } <- ev
  = do { let mk_pr pred i = (pred, EvTupleSel tm i)
       ; given_evs <- newGivenEvVars loc (zipWith mk_pr preds [0..])
       ; emitWorkNC given_evs
       ; stopWith ev "Decomposed tuple constraint" }

  | CtDerived { ctev_loc = loc } <- ev
  = do { mapM_ (emitNewDerived loc) preds
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       ; stopWith ev "Decomposed tuple constraint" }
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  | otherwise = panic "canTuple"


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{-
************************************************************************
*                                                                      *
*                      Class Canonicalization
*                                                                      *
************************************************************************
-}
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canClass, canClassNC
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   :: CtEvidence
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   -> Class -> [Type] -> TcS (StopOrContinue Ct)
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-- Precondition: EvVar is class evidence
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-- The canClassNC version is used on non-canonical constraints
-- and adds superclasses.  The plain canClass version is used
-- for already-canonical class constraints (but which might have
-- been subsituted or somthing), and hence do not need superclasses

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canClassNC ev cls tys
  = canClass ev cls tys
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    `andWhenContinue` emitSuperclasses

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canClass ev cls tys
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  =   -- all classes do *nominal* matching
    ASSERT2( ctEvRole ev == Nominal, ppr ev $$ ppr cls $$ ppr tys )
    do { (xis, cos) <- flattenMany FM_FlattenAll ev (repeat Nominal) tys
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       ; let co = mkTcTyConAppCo Nominal (classTyCon cls) cos
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             xi = mkClassPred cls xis
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             mk_ct new_ev = CDictCan { cc_ev = new_ev
                                     , cc_tyargs = xis, cc_class = cls }
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       ; mb <- rewriteEvidence ev xi co
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       ; traceTcS "canClass" (vcat [ ppr ev <+> ppr cls <+> ppr tys
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                                   , ppr xi, ppr mb ])
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       ; return (fmap mk_ct mb) }
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emitSuperclasses :: Ct -> TcS (StopOrContinue Ct)
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emitSuperclasses ct@(CDictCan { cc_ev = ev , cc_tyargs = xis_new, cc_class = cls })
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            -- Add superclasses of this one here, See Note [Adding superclasses].
            -- But only if we are not simplifying the LHS of a rule.
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 = do { newSCWorkFromFlavored ev cls xis_new
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      -- Arguably we should "seq" the coercions if they are derived,
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      -- as we do below for emit_kind_constraint, to allow errors in
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      -- superclasses to be executed if deferred to runtime!
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      ; continueWith ct }
emitSuperclasses _ = panic "emit_superclasses of non-class!"
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{-
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Note [Adding superclasses]
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~~~~~~~~~~~~~~~~~~~~~~~~~~
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Since dictionaries are canonicalized only once in their lifetime, the
place to add their superclasses is canonicalisation.  See Note [Add
superclasses only during canonicalisation].  Here is what we do:

  Deriveds: Do nothing.

  Givens:   Add all their superclasses as Givens.

  Wanteds:  Add all their superclasses as Derived.
            Not as Wanted: we don't need a proof.
            Nor as Given: that leads to superclass loops.

We also want to ensure minimal constraints to quantify over.  For
instance, if our wanted constraint is (Eq a, Ord a) we'd only like to
quantify over Ord a.  But we deal with that completely independently
in TcSimplify. See Note [Minimize by SuperClasses] in TcSimplify.

Examples of how adding superclasses as Derived is useful

    --- Example 1
        class C a b | a -> b
    Suppose we want to solve
         [G] C a b
         [W] C a beta
    Then adding [D] beta~b will let us solve it.

    -- Example 2 (similar but using a type-equality superclass)
        class (F a ~ b) => C a b
    And try to sllve:
         [G] C a b
         [W] C a beta
    Follow the superclass rules to add
         [G] F a ~ b
         [D] F a ~ beta
    Now we we get [D] beta ~ b, and can solve that.

Example of why adding superclass of a Wanted as a Given would
be terrible, see Note [Do not add superclasses of solved dictionaries]
in TcSMonad, which has this example:
        class Ord a => C a where
        instance Ord [a] => C [a] where ...
Suppose we are trying to solve
  [G] d1 : Ord a
  [W] d2 : C [a]
If we (bogusly) added the superclass of d2 as Gievn we'd have
  [G] d1 : Ord a
  [W] d2 : C [a]
  [G] d3 : Ord [a]   -- Superclass of d2, bogus

Then we'll use the instance decl to give
  [G] d1 : Ord a     Solved: d2 : C [a] = $dfCList d4
  [G] d3 : Ord [a]   -- Superclass of d2, bogus
  [W] d4: Ord [a]

ANd now we could bogusly solve d4 from d3.


Note [Add superclasses only during canonicalisation]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We add superclasses only during canonicalisation, on the passage
from CNonCanonical to CDictCan.  A class constraint can be repeatedly
rewritten, and there's no point in repeatedly adding its superclasses.

Here's a serious, but now out-dated example, from Trac #4497:
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   class Num (RealOf t) => Normed t
   type family RealOf x

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Assume the generated wanted constraint is:
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   [W] RealOf e ~ e
   [W] Normed e

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If we were to be adding the superclasses during simplification we'd get:
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   [W] RealOf e ~ e
   [W] Normed e
   [D] RealOf e ~ fuv
   [D] Num fuv
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==>
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   e := fuv, Num fuv, Normed fuv, RealOf fuv ~ fuv
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While looks exactly like our original constraint. If we add the
superclass of (Normed fuv) again we'd loop.  By adding superclasses
definitely only once, during canonicalisation, this situation can't
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happen.
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Mind you, now that Wanteds cannot rewrite Derived, I think this particular
situation can't happen.
  -}
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newSCWorkFromFlavored :: CtEvidence -> Class -> [Xi] -> TcS ()
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-- Returns superclasses, see Note [Adding superclasses]
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newSCWorkFromFlavored flavor cls xis
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  | isDerived flavor
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  = return ()  -- Deriveds don't yield more superclasses because we will
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               -- add them transitively in the case of wanteds.

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  | CtGiven { ctev_evtm = ev_tm, ctev_loc = loc } <- flavor
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  = do { let sc_theta = immSuperClasses cls xis
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             mk_pr sc_pred i = (sc_pred, EvSuperClass ev_tm i)
       ; given_evs <- newGivenEvVars loc (zipWith mk_pr sc_theta [0..])
       ; emitWorkNC given_evs }
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  | isEmptyVarSet (tyVarsOfTypes xis)
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  = return () -- Wanteds with no variables yield no deriveds.
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              -- See Note [Improvement from Ground Wanteds]
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  | otherwise -- Wanted case, just add those SC that can lead to improvement.
  = do { let sc_rec_theta = transSuperClasses cls xis
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             impr_theta   = filter is_improvement_pty sc_rec_theta
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             loc          = ctEvLoc flavor
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       ; traceTcS "newSCWork/Derived" $ text "impr_theta =" <+> ppr impr_theta
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       ; mapM_ (emitNewDerived loc) impr_theta }
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is_improvement_pty :: PredType -> Bool
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-- Either it's an equality, or has some functional dependency
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is_improvement_pty ty = go (classifyPredType ty)
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  where
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    go (EqPred NomEq t1 t2) = not (t1 `tcEqType` t2)
    go (EqPred ReprEq _ _)  = False
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    go (ClassPred cls _tys) = not $ null fundeps
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                            where (_,fundeps) = classTvsFds cls
    go (TuplePred ts)       = any is_improvement_pty ts
    go (IrredPred {})       = True -- Might have equalities after reduction?
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{-
************************************************************************
*                                                                      *
*                      Irreducibles canonicalization
*                                                                      *
************************************************************************
-}
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canIrred :: CtEvidence -> TcS (StopOrContinue Ct)
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-- Precondition: ty not a tuple and no other evidence form
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canIrred old_ev
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  = do { let old_ty = ctEvPred old_ev
       ; traceTcS "can_pred" (text "IrredPred = " <+> ppr old_ty)
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       ; (xi,co) <- flatten FM_FlattenAll old_ev old_ty -- co :: xi ~ old_ty
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       ; rewriteEvidence old_ev xi co `andWhenContinue` \ new_ev ->
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    do { -- Re-classify, in case flattening has improved its shape
       ; case classifyPredType (ctEvPred new_ev) of
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           ClassPred cls tys     -> canClassNC new_ev cls tys
           TuplePred tys         -> canTuple   new_ev tys
           EqPred eq_rel ty1 ty2 -> canEqNC new_ev eq_rel ty1 ty2
           _                     -> continueWith $
                                    CIrredEvCan { cc_ev = new_ev } } }
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canHole :: CtEvidence -> OccName -> HoleSort -> TcS (StopOrContinue Ct)
canHole ev occ hole_sort
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  = do { let ty = ctEvPred ev
       ; (xi,co) <- flatten FM_SubstOnly ev ty -- co :: xi ~ ty
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       ; rewriteEvidence ev xi co `andWhenContinue` \ new_ev ->
    do { emitInsoluble (CHoleCan { cc_ev = new_ev
                                 , cc_occ = occ
                                 , cc_hole = hole_sort })
       ; stopWith new_ev "Emit insoluble hole" } }
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{-
************************************************************************
*                                                                      *
*        Equalities
*                                                                      *
************************************************************************
-}
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canEqNC :: CtEvidence -> EqRel -> Type -> Type -> TcS (StopOrContinue Ct)
canEqNC ev eq_rel ty1 ty2
  = can_eq_nc ev eq_rel ty1 ty1 ty2 ty2
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can_eq_nc
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   :: CtEvidence
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   -> EqRel
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   -> Type -> Type    -- LHS, after and before type-synonym expansion, resp
   -> Type -> Type    -- RHS, after and before type-synonym expansion, resp
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   -> TcS (StopOrContinue Ct)
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can_eq_nc ev eq_rel ty1 ps_ty1 ty2 ps_ty2
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  = do { traceTcS "can_eq_nc" $
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         vcat [ ppr ev, ppr eq_rel, ppr ty1, ppr ps_ty1, ppr ty2, ppr ps_ty2 ]
       ; rdr_env <- getGlobalRdrEnvTcS
       ; fam_insts <- getFamInstEnvs
       ; can_eq_nc' rdr_env fam_insts ev eq_rel ty1 ps_ty1 ty2 ps_ty2 }

can_eq_nc'
   :: GlobalRdrEnv   -- needed to see which newtypes are in scope
   -> FamInstEnvs    -- needed to unwrap data instances
   -> CtEvidence
   -> EqRel
   -> Type -> Type    -- LHS, after and before type-synonym expansion, resp
   -> Type -> Type    -- RHS, after and before type-synonym expansion, resp
   -> TcS (StopOrContinue Ct)
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-- Expand synonyms first; see Note [Type synonyms and canonicalization]
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can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 ty2 ps_ty2
  | Just ty1' <- tcView ty1 = can_eq_nc ev eq_rel ty1' ps_ty1 ty2  ps_ty2
  | Just ty2' <- tcView ty2 = can_eq_nc ev eq_rel ty1  ps_ty1 ty2' ps_ty2
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-- Type family on LHS or RHS take priority over tyvars,
-- so that  tv ~ F ty gets flattened
-- Otherwise  F a ~ F a  might not get solved!
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can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp fn1 tys1) _ ty2 ps_ty2
  | isTypeFamilyTyCon fn1
  = can_eq_fam_nc ev eq_rel NotSwapped fn1 tys1 ty2 ps_ty2
can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 (TyConApp fn2 tys2) _
  | isTypeFamilyTyCon fn2
  = can_eq_fam_nc ev eq_rel IsSwapped fn2 tys2 ty1 ps_ty1

-- When working with ReprEq, unwrap newtypes next.
-- Otherwise, a ~ Id a wouldn't get solved
can_eq_nc' rdr_env envs ev ReprEq ty1 _ ty2 ps_ty2
  | Just (co, ty1') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty1
  = can_eq_newtype_nc rdr_env ev NotSwapped co ty1 ty1' ty2 ps_ty2
can_eq_nc' rdr_env envs ev ReprEq ty1 ps_ty1 ty2 _
  | Just (co, ty2') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty2
  = can_eq_newtype_nc rdr_env ev IsSwapped  co ty2 ty2' ty1 ps_ty1
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-- Type variable on LHS or RHS are next
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can_eq_nc' _rdr_env _envs ev eq_rel (TyVarTy tv1) _ ty2 ps_ty2
  = canEqTyVar ev eq_rel NotSwapped tv1 ty2 ps_ty2
can_eq_nc' _rdr_env _envs ev eq_rel ty1 ps_ty1 (TyVarTy tv2) _
  = canEqTyVar ev eq_rel IsSwapped tv2 ty1 ps_ty1
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----------------------
-- Otherwise try to decompose
----------------------

-- Literals
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can_eq_nc' _rdr_env _envs ev eq_rel ty1@(LitTy l1) _ (LitTy l2) _
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 | l1 == l2
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  = do { setEvBindIfWanted ev (EvCoercion $
                               mkTcReflCo (eqRelRole eq_rel) ty1)
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       ; stopWith ev "Equal LitTy" }
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-- Decomposable type constructor applications
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-- Synonyms and type functions (which are not decomposable)
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-- have already been dealt with
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can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp tc1 tys1) _ (TyConApp tc2 tys2) _
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  | isDecomposableTyCon tc1
  , isDecomposableTyCon tc2
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  = canDecomposableTyConApp ev eq_rel tc1 tys1 tc2 tys2
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can_eq_nc' _rdr_env _envs ev eq_rel (TyConApp tc1 _) ps_ty1 (FunTy {}) ps_ty2
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  | isDecomposableTyCon tc1
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      -- The guard is important
      -- e.g.  (x -> y) ~ (F x y) where F has arity 1
      --       should not fail, but get the app/app case
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  = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
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can_eq_nc' _rdr_env _envs ev eq_rel (FunTy s1 t1) _ (FunTy s2 t2) _
  = do { canDecomposableTyConAppOK ev eq_rel funTyCon [s1,t1] [s2,t2]
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       ; stopWith ev "Decomposed FunTyCon" }

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can_eq_nc' _rdr_env _envs ev eq_rel (FunTy {}) ps_ty1 (TyConApp tc2 _) ps_ty2
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  | isDecomposableTyCon tc2
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  = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
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can_eq_nc' _rdr_env _envs ev eq_rel s1@(ForAllTy {}) _ s2@(ForAllTy {}) _
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 | CtWanted { ctev_loc = loc, ctev_evar = orig_ev } <- ev
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 = do { let (tvs1,body1) = tcSplitForAllTys s1
            (tvs2,body2) = tcSplitForAllTys s2
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      ; if not (equalLength tvs1 tvs2) then
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          canEqHardFailure ev eq_rel s1 s2
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        else
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          do { traceTcS "Creating implication for polytype equality" $ ppr ev
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             ; ev_term <- deferTcSForAllEq (eqRelRole eq_rel)
                                           loc (tvs1,body1) (tvs2,body2)
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             ; setWantedEvBind orig_ev ev_term
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             ; stopWith ev "Deferred polytype equality" } }
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 | otherwise
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 = do { traceTcS "Ommitting decomposition of given polytype equality" $
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        pprEq s1 s2    -- See Note [Do not decompose given polytype equalities]
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      ; stopWith ev "Discard given polytype equality" }
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can_eq_nc' _rdr_env _envs ev eq_rel (AppTy {}) ps_ty1 _ ps_ty2
  | isGiven ev = try_decompose_app ev eq_rel ps_ty1 ps_ty2
  | otherwise  = can_eq_wanted_app ev eq_rel ps_ty1 ps_ty2
can_eq_nc' _rdr_env _envs ev eq_rel _ ps_ty1 (AppTy {}) ps_ty2
  | isGiven ev = try_decompose_app ev eq_rel ps_ty1 ps_ty2
  | otherwise  = can_eq_wanted_app ev eq_rel ps_ty1 ps_ty2
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-- Everything else is a definite type error, eg LitTy ~ TyConApp
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can_eq_nc' _rdr_env _envs ev eq_rel _ ps_ty1 _ ps_ty2
  = canEqHardFailure ev eq_rel ps_ty1 ps_ty2
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------------
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can_eq_fam_nc :: CtEvidence -> EqRel -> SwapFlag
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              -> TyCon -> [TcType]
              -> TcType -> TcType
              -> TcS (StopOrContinue Ct)
-- Canonicalise a non-canonical equality of form (F tys ~ ty)
--   or the swapped version thereof
-- Flatten both sides and go round again
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can_eq_fam_nc ev eq_rel swapped fn tys rhs ps_rhs
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  = do { (xi_lhs, co_lhs) <- flattenFamApp FM_FlattenAll ev fn tys
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       ; rewriteEqEvidence ev eq_rel swapped xi_lhs rhs co_lhs
                           (mkTcReflCo (eqRelRole eq_rel) rhs)
         `andWhenContinue` \ new_ev ->
         can_eq_nc new_ev eq_rel xi_lhs xi_lhs rhs ps_rhs }
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{-
Note [Eager reflexivity check]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have

  newtype X = MkX (Int -> X)

and

  [W] X ~R X
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Naively, we would start unwrapping X and end up in a loop. Instead,
we do this eager reflexivity check. This is necessary only for representational
equality because the flattener technology deals with the similar case
(recursive type families) for nominal equality.

As an alternative, suppose we also have

  newtype Y = MkY (Int -> Y)

and now wish to prove

  [W] X ~R Y

This new Wanted will loop, expanding out the newtypes ever deeper looking
for a solid match or a solid discrepancy. Indeed, there is something
appropriate to this looping, because X and Y *do* have the same representation,
in the limit -- they're both (Fix ((->) Int)). However, no finitely-sized
coercion will ever witness it. This loop won't actually cause GHC to hang,
though, because of the stack-blowing check in can_eq_newtype_nc, along
with the fact that rewriteEqEvidence bumps the stack depth.

Note [AppTy reflexivity check]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider trying to prove (f a) ~R (f a). The AppTys in there can't
be decomposed, because representational equality isn't congruent with respect
to AppTy. So, when canonicalising the equality above, we get stuck and
would normally produce a CIrredEvCan. However, we really do want to
be able to solve (f a) ~R (f a). So, in the representational case only,
we do a reflexivity check.

(This would be sound in the nominal case, but unnecessary, and I [Richard
E.] am worried that it would slow down the common case.)
-}

------------------------
-- | We're able to unwrap a newtype. Update the bits accordingly.
can_eq_newtype_nc :: GlobalRdrEnv
                  -> CtEvidence           -- ^ :: ty1 ~ ty2
                  -> SwapFlag
                  -> TcCoercion           -- ^ :: ty1 ~ ty1'
                  -> TcType               -- ^ ty1
                  -> TcType               -- ^ ty1'
                  -> TcType               -- ^ ty2
                  -> TcType               -- ^ ty2, with type synonyms
                  -> TcS (StopOrContinue Ct)
can_eq_newtype_nc rdr_env ev swapped co ty1 ty1' ty2 ps_ty2
  = do { traceTcS "can_eq_newtype_nc" $
         vcat [ ppr ev, ppr swapped, ppr co, ppr ty1', ppr ty2 ]

         -- check for blowing our stack:
         -- See Note [Eager reflexivity check] for an example of
         -- when this is necessary
       ; dflags <- getDynFlags
       ; if isJust $ subGoalDepthExceeded (maxSubGoalDepth dflags)
                                          (ctLocDepth (ctEvLoc ev))
         then do { emitInsoluble (mkNonCanonical ev)
                 ; stopWith ev "unwrapping newtypes blew stack" }
         else do
       { if ty1 `eqType` ty2   -- See Note [Eager reflexivity check]
         then canEqReflexive ev ReprEq ty1
         else do
       { markDataConsAsUsed rdr_env (tyConAppTyCon ty1)
           -- we have actually used the newtype constructor here, so
           -- make sure we don't warn about importing it!

       ; rewriteEqEvidence ev ReprEq swapped ty1' ps_ty2
                           (mkTcSymCo co) (mkTcReflCo Representational ps_ty2)
         `andWhenContinue` \ new_ev ->
         can_eq_nc new_ev ReprEq ty1' ty1' ty2 ps_ty2 }}}

-- | Mark all the datacons of the given 'TyCon' as used in this module,
-- avoiding "redundant import" warnings.
markDataConsAsUsed :: GlobalRdrEnv -> TyCon -> TcS ()
markDataConsAsUsed rdr_env tc = addUsedRdrNamesTcS
  [ mkRdrQual (is_as (is_decl imp_spec)) occ
  | dc <- tyConDataCons tc
  , let dc_name = dataConName dc
        occ  = nameOccName dc_name
  , gre : _               <- return $ lookupGRE_Name rdr_env dc_name
  , Imported (imp_spec:_) <- return $ gre_prov gre ]

-------------------------------------------------
can_eq_wanted_app :: CtEvidence -> EqRel -> TcType -> TcType
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                  -> TcS (StopOrContinue Ct)
-- One or the other is an App; neither is a type variable
-- See Note [Canonicalising type applications]
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can_eq_wanted_app ev eq_rel ty1 ty2
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  = do { (xi1, co1) <- flatten FM_FlattenAll ev ty1
       ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
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        ; rewriteEqEvidence ev eq_rel NotSwapped xi1 xi2 co1 co2
          `andWhenContinue` \ new_ev ->
          try_decompose_app new_ev eq_rel xi1 xi2 }
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try_decompose_app :: CtEvidence -> EqRel
                  -> TcType -> TcType -> TcS (StopOrContinue Ct)
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-- Preconditions: neither is a type variable
--                so can't turn it into an application if it
--                   doesn't look like one already
-- See Note [Canonicalising type applications]
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try_decompose_app ev NomEq  ty1 ty2
  = try_decompose_nom_app ev ty1 ty2

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try_decompose_app ev ReprEq ty1 ty2
  | ty1 `eqType` ty2   -- See Note [AppTy reflexivity check]
  = canEqReflexive ev ReprEq ty1

  | otherwise
  = canEqFailure ev ReprEq ty1 ty2

try_decompose_nom_app :: CtEvidence
                      -> TcType -> TcType -> TcS (StopOrContinue Ct)
-- Preconditions: like try_decompose_app, but also
--                ev has a nominal role
-- See Note [Canonicalising type applications]
try_decompose_nom_app ev ty1 ty2
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   | AppTy s1 t1  <- ty1
   = case tcSplitAppTy_maybe ty2 of
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       Nothing      -> canEqHardFailure ev NomEq ty1 ty2
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       Just (s2,t2) -> do_decompose s1 t1 s2 t2

   | AppTy s2 t2 <- ty2
   = case tcSplitAppTy_maybe ty1 of
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       Nothing      -> canEqHardFailure ev NomEq ty1 ty2
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       Just (s1,t1) -> do_decompose s1 t1 s2 t2

   | otherwise  -- Neither is an AppTy
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   = canEqNC ev NomEq ty1 ty2
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   where
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     -- Recurses to try_decompose_nom_app to decompose a chain of AppTys
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     do_decompose s1 t1 s2 t2
       | CtDerived { ctev_loc = loc } <- ev
       = do { emitNewDerived loc (mkTcEqPred t1 t2)
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            ; canEqNC ev NomEq s1 s2 }
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       | CtWanted { ctev_evar = evar, ctev_loc = loc } <- ev
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       = do { ev_s <- newWantedEvVarNC loc (mkTcEqPred s1 s2)
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            ; co_t <- unifyWanted loc Nominal t1 t2
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            ; let co = mkTcAppCo (ctEvCoercion ev_s) co_t
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            ; setWantedEvBind evar (EvCoercion co)
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            ; canEqNC ev_s NomEq s1 s2 }
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       | CtGiven { ctev_evtm = ev_tm, ctev_loc = loc } <- ev
       = do { let co   = evTermCoercion ev_tm
                  co_s = mkTcLRCo CLeft  co
                  co_t = mkTcLRCo CRight co
            ; evar_s <- newGivenEvVar loc (mkTcEqPred s1 s2, EvCoercion co_s)
            ; evar_t <- newGivenEvVar loc (mkTcEqPred t1 t2, EvCoercion co_t)
            ; emitWorkNC [evar_t]
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            ; canEqNC evar_s NomEq s1 s2 }
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       | otherwise  -- Can't happen
       = error "try_decompose_app"
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------------------------
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canDecomposableTyConApp :: CtEvidence -> EqRel
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                        -> TyCon -> [TcType]
                        -> TyCon -> [TcType]
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                        -> TcS (StopOrContinue Ct)
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-- See Note [Decomposing TyConApps]
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canDecomposableTyConApp ev eq_rel tc1 tys1 tc2 tys2
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  | tc1 /= tc2 || length tys1 /= length tys2
    -- Fail straight away for better error messages
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  = let eq_failure
          | isDataFamilyTyCon tc1 || isDataFamilyTyCon tc2
                -- See Note [Use canEqFailure in canDecomposableTyConApp]
          = canEqFailure
          | otherwise
          = canEqHardFailure in
    eq_failure ev eq_rel (mkTyConApp tc1 tys1) (mkTyConApp tc2 tys2)

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  | otherwise
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  = do { traceTcS "canDecomposableTyConApp"
                  (ppr ev $$ ppr eq_rel $$ ppr tc1 $$ ppr tys1 $$ ppr tys2)
       ; canDecomposableTyConAppOK ev eq_rel tc1 tys1 tys2
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       ; stopWith ev "Decomposed TyConApp" }
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{-
Note [Use canEqFailure in canDecomposableTyConApp]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We must use canEqFailure, not canEqHardFailure here, because there is
the possibility of success if working with a representational equality.
Here is the case:

  type family TF a where TF Char = Bool
  data family DF a
  newtype instance DF Bool = MkDF Int

Suppose we are canonicalising (Int ~R DF (T a)), where we don't yet
know `a`. This is *not* a hard failure, because we might soon learn
that `a` is, in fact, Char, and then the equality succeeds.
-}

canDecomposableTyConAppOK :: CtEvidence -> EqRel
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                          -> TyCon -> [TcType] -> [TcType]
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                          -> TcS ()
-- Precondition: tys1 and tys2 are the same length, hence "OK"
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canDecomposableTyConAppOK ev eq_rel tc tys1 tys2
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  = case ev of
     CtDerived { ctev_loc = loc }
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        -> unifyDeriveds loc tc_roles tys1 tys2
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     CtWanted { ctev_evar = evar, ctev_loc = loc }
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        -> do { cos <- zipWith3M (unifyWanted loc) tc_roles tys1 tys2
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              ; setWantedEvBind evar (EvCoercion (mkTcTyConAppCo role tc cos)) }
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     CtGiven { ctev_evtm = ev_tm, ctev_loc = loc }
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        -> do { let ev_co = evTermCoercion ev_tm
              ; given_evs <- newGivenEvVars loc $
                             [ ( mkTcEqPredRole r ty1 ty2
                               , EvCoercion (mkTcNthCo i ev_co) )
                             | (r, ty1, ty2, i) <- zip4 tc_roles tys1 tys2 [0..]
                             , r /= Phantom ]
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              ; emitWorkNC given_evs }
  where
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    role     = eqRelRole eq_rel
    tc_roles = tyConRolesX role tc

-- | Call when canonicalizing an equality fails, but if the equality is
-- representational, there is some hope for the future.
-- Examples in Note [Flatten irreducible representational equalities]
canEqFailure :: CtEvidence -> EqRel
             -> TcType -> TcType -> TcS (StopOrContinue Ct)
canEqFailure ev ReprEq ty1 ty2
  = do { -- See Note [Flatten irreducible representational equalities]
         (xi1, co1) <- flatten FM_FlattenAll ev ty1
       ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
       ; traceTcS "canEqFailure with ReprEq" $
         vcat [ ppr ev, ppr ty1, ppr ty2, ppr xi1, ppr xi2 ]
       ; if xi1 `eqType` ty1 && xi2 `eqType` ty2
         then continueWith (CIrredEvCan { cc_ev = ev })  -- co1/2 must be refl
         else rewriteEqEvidence ev ReprEq NotSwapped xi1 xi2 co1 co2
              `andWhenContinue` \ new_ev ->
              can_eq_nc new_ev ReprEq xi1 xi1 xi2 xi2 }
canEqFailure ev NomEq ty1 ty2 = canEqHardFailure ev NomEq ty1 ty2

-- | Call when canonicalizing an equality fails with utterly no hope.
canEqHardFailure :: CtEvidence -> EqRel
                 -> TcType -> TcType -> TcS (StopOrContinue Ct)
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-- See Note [Make sure that insolubles are fully rewritten]
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canEqHardFailure ev eq_rel ty1 ty2
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  = do { (s1, co1) <- flatten FM_SubstOnly ev ty1
       ; (s2, co2) <- flatten FM_SubstOnly ev ty2
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       ; rewriteEqEvidence ev eq_rel NotSwapped s1 s2 co1 co2
         `andWhenContinue` \ new_ev ->
    do { emitInsoluble (mkNonCanonical new_ev)
       ; stopWith new_ev "Definitely not equal" }}
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{-
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Note [Flatten irreducible representational equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we can't make any progress with a representational equality, but
we haven't given up all hope, we must flatten before producing the
CIrredEvCan. There are two reasons to do this:

  * See case in Note [Use canEqFailure in canDecomposableTyConApp].
    Flattening here can expose that we know enough information to unwrap
    a newtype.

  * This case, which was encountered in the testsuite (T9117_3):

      work item: [W] c1: f a ~R g a
      inert set: [G] c2: g ~R f

    In can_eq_app, we try to flatten the LHS of c1. This causes no effect,
    because `f` cannot be rewritten. So, we go to can_eq_flat_app. Without
    flattening the RHS, the reflexivity check fails, and we give up. However,
    flattening the RHS rewrites `g` to `f`, the reflexivity check succeeds,
    and we go on to glory.

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Note [Decomposing TyConApps]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we see (T s1 t1 ~ T s2 t2), then we can just decompose to
  (s1 ~ s2, t1 ~ t2)
and push those back into the work list.  But if
  s1 = K k1    s2 = K k2
then we will jus decomopose s1~s2, and it might be better to
do so on the spot.  An important special case is where s1=s2,
and we get just Refl.

So canDecomposableTyCon is a fast-path decomposition that uses
unifyWanted etc to short-cut that work.

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Note [Canonicalising type applications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given (s1 t1) ~ ty2, how should we proceed?
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The simple things is to see if ty2 is of form (s2 t2), and
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decompose.  By this time s1 and s2 can't be saturated type
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function applications, because those have been dealt with
by an earlier equation in can_eq_nc, so it is always sound to
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decompose.

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However, over-eager decomposition gives bad error messages
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for things like
   a b ~ Maybe c
   e f ~ p -> q
Suppose (in the first example) we already know a~Array.  Then if we
decompose the application eagerly, yielding
   a ~ Maybe
   b ~ c
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we get an error        "Can't match Array ~ Maybe",
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but we'd prefer to get "Can't match Array b ~ Maybe c".

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So instead can_eq_wanted_app flattens the LHS and RHS before using
try_decompose_app to decompose it.
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Note [Make sure that insolubles are fully rewritten]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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When an equality fails, we still want to rewrite the equality
all the way down, so that it accurately reflects
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 (a) the mutable reference substitution in force at start of solving
 (b) any ty-binds in force at this point in solving
See Note [Kick out insolubles] in TcInteract.
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And if we don't do this there is a bad danger that
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TcSimplify.applyTyVarDefaulting will find a variable
that has in fact been substituted.

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Note [Do not decompose Given polytype equalities]
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider [G] (forall a. t1 ~ forall a. t2).  Can we decompose this?
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No -- what would the evidence look like?  So instead we simply discard
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this given evidence.
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Note [Combining insoluble constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As this point we have an insoluble constraint, like Int~Bool.

 * If it is Wanted, delete it from the cache, so that subsequent
   Int~Bool constraints give rise to separate error messages

 * But if it is Derived, DO NOT delete from cache.  A class constraint
   may get kicked out of the inert set, and then have its functional
   dependency Derived constraints generated a second time. In that
   case we don't want to get two (or more) error messages by
   generating two (or more) insoluble fundep constraints from the same
   class constraint.
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Note [No top-level newtypes on RHS of representational equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we're in this situation:

 work item:  [W] c1 : a ~R b
     inert:  [G] c2 : b ~R Id a

where
  newtype Id a = Id a

Further, suppose flattening `a` doesn't do anything. Then, we'll flatten the
RHS of c1 and have a new [W] c3 : a ~R Id a. If we just blindly proceed, we'll
fail in canEqTyVar2 with an occurs-check. What we really need to do is to
unwrap the `Id a` in the RHS. This is exactly analogous to the requirement for
no top-level type families on the RHS of a nominal equality. The only
annoyance is that the flattener doesn't do this work for us when flattening
the RHS, so we have to catch this case here and then go back to the beginning
of can_eq_nc. We know that this can't loop forever because we require that
flattening the RHS actually made progress. (If it didn't, then we really
*should* fail with an occurs-check!)

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-}
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canCFunEqCan :: CtEvidence
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             -> TyCon -> [TcType]   -- LHS
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             -> TcTyVar             -- RHS
             -> TcS (StopOrContinue Ct)
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-- ^ Canonicalise a CFunEqCan.  We know that
--     the arg types are already flat,
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-- and the RHS is a fsk, which we must *not* substitute.
-- So just substitute in the LHS
canCFunEqCan ev fn tys fsk
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  = do { (tys', cos) <- flattenMany FM_FlattenAll ev (repeat Nominal) tys
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                        -- cos :: tys' ~ tys
       ; let lhs_co  = mkTcTyConAppCo Nominal fn cos
                        -- :: F tys' ~ F tys
             new_lhs = mkTyConApp fn tys'
             fsk_ty  = mkTyVarTy fsk
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       ; rewriteEqEvidence ev NomEq NotSwapped new_lhs fsk_ty
                           lhs_co (mkTcNomReflCo fsk_ty)
         `andWhenContinue` \ ev' ->
    do { extendFlatCache fn tys' (ctEvCoercion ev', fsk_ty, ctEvFlavour ev')
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       ; continueWith (CFunEqCan { cc_ev = ev', cc_fun = fn
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                                 , cc_tyargs = tys', cc_fsk = fsk }) } }
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---------------------
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canEqTyVar :: CtEvidence -> EqRel -> SwapFlag
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           -> TcTyVar
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           -> TcType -> TcType
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           -> TcS (StopOrContinue Ct)
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-- A TyVar on LHS, but so far un-zonked
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canEqTyVar ev eq_rel swapped tv1 ty2 ps_ty2              -- ev :: tv ~ s2
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  = do { traceTcS "canEqTyVar" (ppr tv1 $$ ppr ty2 $$ ppr swapped)
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       ; let fmode = mkFlattenEnv FM_FlattenAll ev  -- the FM_ param is ignored
       ; mb_yes <- flattenTyVarOuter fmode tv1
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       ; case mb_yes of
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         { Right (ty1, co1) -> -- co1 :: ty1 ~ tv1
             do { traceTcS "canEqTyVar2"
                           (vcat [ ppr tv1, ppr ty2, ppr swapped
                                 , ppr ty1 , ppUnless (isDerived ev) (ppr co1)])
                ; rewriteEqEvidence ev eq_rel swapped ty1 ps_ty2
                                    co1 (mkTcReflCo (eqRelRole eq_rel) ps_ty2)
                  `andWhenContinue` \ new_ev ->
                  can_eq_nc new_ev eq_rel ty1 ty1 ty2 ps_ty2 }

         ; Left tv1' ->
    do { -- FM_Avoid commented out: see Note [Lazy flattening] in TcFlatten
         -- let fmode = FE { fe_ev = ev, fe_mode = FM_Avoid tv1' True }
         -- Flatten the RHS less vigorously, to avoid gratuitous flattening
         -- True <=> xi2 should not itself be a type-function application
       ; (xi2, co2) <- flatten FM_FlattenAll ev ps_ty2 -- co2 :: xi2 ~ ps_ty2
                      -- Use ps_ty2 to preserve type synonyms if poss
       ; traceTcS "canEqTyVar flat LHS"
           (vcat [ ppr tv1, ppr tv1', ppr ty2, ppr swapped, ppr xi2 ])
       ; dflags <- getDynFlags
       ; case eq_rel of
      -- See Note [No top-level newtypes on RHS of representational equalities]
           ReprEq
             | Just (tc2, _) <- tcSplitTyConApp_maybe xi2
             , isNewTyCon tc2
             , not (ps_ty2 `eqType` xi2)
             -> do { let xi1  = mkTyVarTy tv1'
                         role = eqRelRole eq_rel
                   ; traceTcS "canEqTyVar exposed newtype"
                       (vcat [ ppr tv1', ppr ps_ty2, ppr xi2, ppr tc2 ])
                   ; rewriteEqEvidence ev eq_rel swapped xi1 xi2
                                       (mkTcReflCo role xi1) co2
                     `andWhenContinue` \ new_ev ->
                     can_eq_nc new_ev eq_rel xi1 xi1 xi2 xi2 }
           _ -> canEqTyVar2 dflags ev eq_rel swapped tv1' xi2 co2 } } }
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canEqTyVar2 :: DynFlags
            -> CtEvidence   -- olhs ~ orhs (or, if swapped, orhs ~ olhs)
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            -> EqRel
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            -> SwapFlag
            -> TcTyVar      -- olhs
            -> TcType       -- nrhs
            -> TcCoercion   -- nrhs ~ orhs
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            -> TcS (StopOrContinue Ct)
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-- LHS is an inert type variable,
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-- and RHS is fully rewritten, but with type synonyms
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-- preserved as much as possible
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canEqTyVar2 dflags ev eq_rel swapped tv1 xi2 co2
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  | Just tv2 <- getTyVar_maybe xi2
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  = canEqTyVarTyVar ev eq_rel swapped tv1 tv2 co2
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  | OC_OK xi2' <- occurCheckExpand dflags tv1 xi2  -- No occurs check
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  = do { let k1 = tyVarKind tv1
             k2 = typeKind xi2'
       ; rewriteEqEvidence ev eq_rel swapped xi1 xi2' co1 co2
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                -- Ensure that the new goal has enough type synonyms