TcCanonical.hs 60.7 KB
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{-# LANGUAGE CPP #-}

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module TcCanonical(
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     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 Name( isSystemName )
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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 DataCon ( dataConName )
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import Pair
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import Util
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import Bag
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import MonadUtils ( zipWith3M, zipWith3M_ )
import Data.List  ( zip4 )
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import BasicTypes
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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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    canEqNC ev eq_rel (mkTyVarTy tv) xi
      -- NB: Don't use canEqTyVar because that expects flattened types,
      -- and tv and xi may not be flat w.r.t. an updated inert set
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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
      IrredPred {}          -> do traceTcS "canEvNC:irred" (ppr (ctEvPred ev))
                                  canIrred   ev
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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 )
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    do { (xis, cos) <- flattenManyNom ev 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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{- Note [Adding superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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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:

  Givens:   Add all their superclasses as Givens.
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            They may be needed to prove Wanteds

  Wanteds:  Do nothing.
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  Deriveds: Add all their superclasses as Derived.
            The sole reason is to expose functional dependencies
            in superclasses or equality superclasses.
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            We only do this in the improvement phase, if solving has
            not succeeded; see Note [The improvement story] in
            TcInteract
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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.

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---------- Historical note -----------
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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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  | CtGiven { ctev_evar = evar, ctev_loc = loc } <- flavor
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  = do { let size = sizePred (mkClassPred cls xis)
             loc' = case ctLocOrigin loc of
                       GivenOrigin InstSkol
                         -> loc { ctl_origin = GivenOrigin (InstSC size) }
                       GivenOrigin (InstSC n)
                         -> loc { ctl_origin = GivenOrigin (InstSC (n `max` size)) }
                       _ -> loc
                    -- See Note [Solving superclass constraints] in TcInstDcls
                    -- for explantation of loc'

       ; given_evs <- newGivenEvVars loc' (mkEvScSelectors (EvId evar) cls xis)
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       ; 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 -- Derived case, just add those SC that can lead to improvement.
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  = do { let sc_rec_theta = transSuperClasses cls xis
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             impr_theta   = filter isImprovementPred 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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       ; emitNewDeriveds loc impr_theta }
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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
           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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Note [Canonicalising equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In order to canonicalise an equality, we look at the structure of the
two types at hand, looking for similarities. A difficulty is that the
types may look dissimilar before flattening but similar after flattening.
However, we don't just want to jump in and flatten right away, because
this might be wasted effort. So, after looking for similarities and failing,
we flatten and then try again. Of course, we don't want to loop, so we
track whether or not we've already flattened.

It is conceivable to do a better job at tracking whether or not a type
is flattened, but this is left as future work. (Mar '15)
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-}
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canEqNC :: CtEvidence -> EqRel -> Type -> Type -> TcS (StopOrContinue Ct)
canEqNC ev eq_rel ty1 ty2
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  = can_eq_nc False ev eq_rel ty1 ty1 ty2 ty2
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can_eq_nc
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   :: Bool            -- True => both types are flat
   -> 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 flat 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
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       ; can_eq_nc' flat rdr_env fam_insts ev eq_rel ty1 ps_ty1 ty2 ps_ty2 }
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can_eq_nc'
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   :: Bool           -- True => both input types are flattened
   -> GlobalRdrEnv   -- needed to see which newtypes are in scope
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   -> 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' flat _rdr_env _envs ev eq_rel ty1 ps_ty1 ty2 ps_ty2
  | Just ty1' <- tcView ty1 = can_eq_nc flat ev eq_rel ty1' ps_ty1 ty2  ps_ty2
  | Just ty2' <- tcView ty2 = can_eq_nc flat ev eq_rel ty1  ps_ty1 ty2' ps_ty2

-- need to check for reflexivity in the ReprEq case.
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-- See Note [Eager reflexivity check]
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can_eq_nc' _flat _rdr_env _envs ev ReprEq ty1 _ ty2 _
  | ty1 `eqType` ty2
  = canEqReflexive ev ReprEq ty1

-- When working with ReprEq, unwrap newtypes.
can_eq_nc' _flat rdr_env envs ev ReprEq ty1 _ ty2 ps_ty2
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  | Just (co, ty1') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty1
  = can_eq_newtype_nc rdr_env ev NotSwapped co ty1 ty1' ty2 ps_ty2
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can_eq_nc' _flat rdr_env envs ev ReprEq ty1 ps_ty1 ty2 _
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  | 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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----------------------
-- Otherwise try to decompose
----------------------

-- Literals
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can_eq_nc' _flat _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' _flat _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' _flat _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' _flat _rdr_env _envs ev eq_rel (FunTy s1 t1) _ (FunTy s2 t2) _
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  = 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' _flat _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' _flat _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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-- See Note [Canonicalising type applications] about why we require flat types
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can_eq_nc' True _rdr_env _envs ev eq_rel (AppTy t1 s1) _ ty2 _
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  | Just (t2, s2) <- tcSplitAppTy_maybe ty2
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  = can_eq_app ev eq_rel t1 s1 t2 s2
can_eq_nc' True _rdr_env _envs ev eq_rel ty1 _ (AppTy t2 s2) _
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  | Just (t1, s1) <- tcSplitAppTy_maybe ty1
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  = can_eq_app ev eq_rel t1 s1 t2 s2
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-- No similarity in type structure detected. Flatten and try again!
can_eq_nc' False rdr_env envs ev eq_rel _ ps_ty1 _ ps_ty2
  = do { (xi1, co1) <- flatten FM_FlattenAll ev ps_ty1
       ; (xi2, co2) <- flatten FM_FlattenAll ev ps_ty2
       ; rewriteEqEvidence ev eq_rel NotSwapped xi1 xi2 co1 co2
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         `andWhenContinue` \ new_ev ->
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         can_eq_nc' True rdr_env envs new_ev eq_rel xi1 xi1 xi2 xi2 }

-- Type variable on LHS or RHS are last. We want only flat types sent
-- to canEqTyVar.
-- See also Note [No top-level newtypes on RHS of representational equalities]
can_eq_nc' True _rdr_env _envs ev eq_rel (TyVarTy tv1) _ _ ps_ty2
  = canEqTyVar ev eq_rel NotSwapped tv1 ps_ty2
can_eq_nc' True _rdr_env _envs ev eq_rel _ ps_ty1 (TyVarTy tv2) _
  = canEqTyVar ev eq_rel IsSwapped  tv2 ps_ty1

-- We've flattened and the types don't match. Give up.
can_eq_nc' True _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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Note [Newtypes can blow the stack]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have

  newtype X = MkX (Int -> X)
  newtype Y = MkY (Int -> Y)

and now wish to prove

  [W] X ~R Y

This 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 we check our depth when unwrapping newtypes.

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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.

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Note that this check does not catch all cases, but it will catch the cases
we're most worried about, types like X above that are actually inhabited.
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Here's another place where this reflexivity check is key:
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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:
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         -- See Note [Newtypes can blow the stack]
       ; checkReductionDepth (ctEvLoc ev) ty1
       ; markDataConsAsUsed rdr_env (tyConAppTyCon ty1)
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           -- 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 ->
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         can_eq_nc False new_ev ReprEq ty1' ty1' ty2 ps_ty2 }
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-- | 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
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  [ greUsedRdrName gre
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  | dc <- tyConDataCons tc
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  , gre : _  <- return $ lookupGRE_Name rdr_env (dataConName dc)
  , not (isLocalGRE gre) ]
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---------
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-- ^ Decompose a type application.
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-- All input types must be flat. See Note [Canonicalising type applications]
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can_eq_app :: CtEvidence       -- :: s1 t1 ~r s2 t2
           -> EqRel            -- r
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           -> Xi -> Xi         -- s1 t1
           -> Xi -> Xi         -- s2 t2
           -> TcS (StopOrContinue Ct)
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-- AppTys only decompose for nominal equality, so this case just leads
-- to an irreducible constraint
can_eq_app ev ReprEq _ _ _ _
  = do { traceTcS "failing to decompose representational AppTy equality" (ppr ev)
       ; continueWith (CIrredEvCan { cc_ev = ev }) }

can_eq_app ev NomEq s1 t1 s2 t2
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  | CtDerived { ctev_loc = loc } <- ev
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  = do { emitNewDerivedEq loc (mkTcEqPred t1 t2)
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       ; canEqNC ev NomEq s1 s2 }
  | CtWanted { ctev_evar = evar, ctev_loc = loc } <- ev
  = do { ev_s <- newWantedEvVarNC loc (mkTcEqPred s1 s2)
       ; co_t <- unifyWanted loc Nominal t1 t2
       ; let co = mkTcAppCo (ctEvCoercion ev_s) co_t
       ; setWantedEvBind evar (EvCoercion co)
       ; canEqNC ev_s NomEq s1 s2 }
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  | CtGiven { ctev_evar = evar, ctev_loc = loc } <- ev
  = do { let co   = mkTcCoVarCo evar
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             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]
       ; canEqNC evar_s NomEq s1 s2 }
  | otherwise  -- Can't happen
  = error "can_eq_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
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  , length tys1 == length tys2
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  = do { inerts <- getTcSInerts
       ; if    eq_rel == NomEq      -- NomEq doesn't care about newtype vs. data
            || isDistinctTyCon tc1  -- always good to decompose non-newtypes
            || (ctEvFlavour ev /= Given && isEmptyBag (matchableGivens loc pred inerts))
            -- See Note [Decomposing newtypes]
         then do { traceTcS "canDecomposableTyConApp"
                       (ppr ev $$ ppr eq_rel $$ ppr tc1 $$ ppr tys1 $$ ppr tys2)
                 ; canDecomposableTyConAppOK ev eq_rel tc1 tys1 tys2
                 ; stopWith ev "Decomposed TyConApp" }
         else canEqFailure ev eq_rel ty1 ty2 }
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  -- Fail straight away for better error messages
  -- See Note [Use canEqFailure in canDecomposableTyConApp]
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  | eq_rel == ReprEq && not (isDistinctTyCon tc1 && isDistinctTyCon tc2)
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  = canEqFailure ev eq_rel ty1 ty2
  | otherwise
  = canEqHardFailure ev eq_rel ty1 ty2
  where
    ty1 = mkTyConApp tc1 tys1
    ty2 = mkTyConApp tc2 tys2

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    loc  = ctEvLoc ev
    pred = ctEvPred ev

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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.
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Here is one case:
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  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.
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Here is another case:

  [G] Coercible Age Int

where Age's constructor is not in scope. We don't want to report
an "inaccessible code" error in the context of this Given!

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Note [Decomposing newtypes]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
As explained in Note [NthCo and newtypes] in Coercion, we can't use
NthCo on representational coercions over newtypes. So we avoid doing
so.

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But is it sensible to decompose *Wanted* constraints over newtypes? Yes, as
long as there are no Givens that might (later) influence Coercible solving.
(See Note [Instance and Given overlap] in TcInteract.) By the time we reach
canDecomposableTyConApp, we know that any newtypes that can be unwrapped have
been. So, without importing more constructors, say, we know there is no way
forward other than decomposition. So we take the one route we have available.
This *does* mean that importing a newtype's constructor might make code that
previously compiled fail to do so. (If that newtype is perversely recursive,
say.)
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-}

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_evar = evar, ctev_loc = loc }
        -> do { let ev_co = mkTcCoVarCo evar
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              ; 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.
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-- Examples in Note [Use canEqFailure in canDecomposableTyConApp]
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canEqFailure :: CtEvidence -> EqRel
             -> TcType -> TcType -> TcS (StopOrContinue Ct)
canEqFailure ev ReprEq ty1 ty2
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  = do { (xi1, co1) <- flatten FM_FlattenAll ev ty1
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       ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
       ; traceTcS "canEqFailure with ReprEq" $
         vcat [ ppr ev, ppr ty1, ppr ty2, ppr xi1, ppr xi2 ]
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       ; if isTcReflCo co1 && isTcReflCo co2
         then continueWith (CIrredEvCan { cc_ev = ev })
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         else rewriteEqEvidence ev ReprEq NotSwapped xi1 xi2 co1 co2
              `andWhenContinue` \ new_ev ->
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              can_eq_nc True new_ev ReprEq xi1 xi1 xi2 xi2 }
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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 [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, in the hope of
replacing (a b) by (Array b), 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

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We want to make sure canEqTyVar sees [W] a ~R a, after b is flattened
and the Id newtype is unwrapped. This is assured by requiring only flat
types in canEqTyVar *and* having the newtype-unwrapping check above
the tyvar check in can_eq_nc.
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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) <- flattenManyNom ev 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             -- already flat
           -> TcType              -- already flat
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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 ps_ty2              -- ev :: tv ~ s2
  = do { traceTcS "canEqTyVar" (ppr tv1 $$ ppr ps_ty2 $$ ppr swapped)
         -- FM_Avoid commented out: see Note [Lazy flattening] in TcFlatten
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         -- 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
       ; dflags <- getDynFlags
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       ; canEqTyVar2 dflags ev eq_rel swapped tv1 ps_ty2 }
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canEqTyVar2 :: DynFlags
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            -> CtEvidence   -- lhs ~ rhs (or, if swapped, orhs ~ olhs)
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            -> EqRel
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            -> SwapFlag
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            -> TcTyVar      -- lhs, flat
            -> TcType       -- rhs, flat
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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
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  | Just tv2 <- getTyVar_maybe xi2
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  = canEqTyVarTyVar ev eq_rel swapped tv1 tv2
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  | OC_OK xi2' <- occurCheckExpand dflags tv1 xi2  -- No occurs check
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     -- We use xi2' on the RHS of the new CTyEqCan, a ~ xi2'
     -- to establish the invariant that a does not appear in the
     -- rhs of the CTyEqCan. This is guaranteed by occurCheckExpand;
     -- see Note [Occurs check expansion] in TcType
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  = do { let k1 = tyVarKind tv1
             k2 = typeKind xi2'
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       ; rewriteEqEvidence ev eq_rel swapped xi1 xi2' co1 (mkTcReflCo role xi2')
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         `andWhenContinue` \ new_ev ->
         if k2 `isSubKind` k1
         then   -- Establish CTyEqCan kind invariant
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                -- Reorientation has done its best, but the kinds might
                -- simply be incompatible
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               continueWith (CTyEqCan { cc_ev = new_ev
                                      , cc_tyvar  = tv1, cc_rhs = xi2'
                                      , cc_eq_rel = eq_rel })
         else incompatibleKind new_ev xi1 k1 xi2' k2 }
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  | otherwise  -- Occurs check error
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  = rewriteEqEvidence ev eq_rel swapped xi1 xi2 co1 co2
    `andWhenContinue` \ new_ev ->
    case eq_rel of
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      NomEq  -> do { emitInsoluble (mkNonCanonical new_ev)
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              -- If we have a ~ [a], it is not canonical, and in particular
              -- we don't want to rewrite existing inerts with it, otherwise
              -- we'd risk divergence in the constraint solver
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                   ; stopWith new_ev "Occurs check" }

        -- A representational equality with an occurs-check problem isn't
        -- insoluble! For example:
        --   a ~R b a
        -- We might learn that b is the newtype Id.
        -- But, the occurs-check certainly prevents the equality from being
        -- canonical, and we might loop if we were to use it in rewriting.
      ReprEq -> do { traceTcS "Occurs-check in representational equality"
                              (ppr xi1 $$ ppr xi2)
                   ; continueWith (CIrredEvCan { cc_ev = new_ev }) }
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  where
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    role = eqRelRole eq_rel
    xi1  = mkTyVarTy tv1
    co1  = mkTcReflCo role xi1
    co2  = mkTcReflCo role xi2
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canEqTyVarTyVar :: CtEvidence           -- tv1 ~ rhs (or rhs ~ tv1, if swapped)
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                -> EqRel
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                -> SwapFlag
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                -> TcTyVar -> TcTyVar   -- tv1, tv2
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                -> TcS (StopOrContinue Ct)
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-- Both LHS and RHS rewrote to a type variable
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-- See Note [Canonical orientation for tyvar/tyvar equality constraints]
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canEqTyVarTyVar ev eq_rel swapped tv1 tv2
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  | tv1 == tv2
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  = do { setEvBindIfWanted ev (EvCoercion $ mkTcReflCo role xi1)
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       ; stopWith ev "Equal tyvars" }

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  | incompat_kind   = incompatibleKind ev xi1 k1 xi2 k2

-- We don't do this any more
-- See Note [Orientation of equalities with fmvs] in TcSMonad
--  | isFmvTyVar tv1  = do_fmv swapped            tv1 xi1 xi2 co1 co2
--  | isFmvTyVar tv2  = do_fmv (flipSwap swapped) tv2 xi2 xi1 co2 co1

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  | same_kind       = if swap_over then do_swap else no_swap
  | k1_sub_k2       = do_swap   -- Note [Kind orientation for CTyEqCan]
  | otherwise       = no_swap   -- k2_sub_k1
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  where
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    role = eqRelRole eq_rel
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    xi1 = mkTyVarTy tv1
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    co1 = mkTcReflCo role xi1
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    xi2 = mkTyVarTy tv2
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    co2 = mkTcReflCo role xi2
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    k1  = tyVarKind tv1
    k2  = tyVarKind tv2
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    k1_sub_k2     = k1 `isSubKind` k2
    k2_sub_k1     = k2 `isSubKind` k1
    same_kind     = k1_sub_k2 && k2_sub_k1
    incompat_kind = not (k1_sub_k2 || k2_sub_k1)

    no_swap = canon_eq swapped            tv1 xi1 xi2 co1 co2
    do_swap = canon_eq (flipSwap swapped) tv2 xi2 xi1 co2 co1

    canon_eq swapped tv1 xi1 xi2 co1 co2
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        -- ev  : tv1 ~ rhs  (not swapped) or   rhs ~ tv1   (swapped)
      = rewriteEqEvidence ev eq_rel swapped xi1 xi2 co1 co2
        `andWhenContinue` \ new_ev ->
        continueWith (CTyEqCan { cc_ev = new_ev, cc_tyvar = tv1
                               , cc_rhs = xi2, cc_eq_rel = eq_rel })
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{- We don't do this any more
   See Note [Orientation of equalities with fmvs] in TcSMonad
    -- tv1 is the flatten meta-var
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    do_fmv swapped tv1 xi1 xi2 co1 co2
      | same_kind
      = canon_eq swapped tv1 xi1 xi2 co1 co2
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      | otherwise  -- Presumably tv1 :: *, since it is a flatten meta-var,
                   -- at a kind that has some interesting sub-kind structure.
                   -- Since the two kinds are not the same, we must have
                   -- tv1 `subKind` tv2, which is the wrong way round
                   --   e.g.  (fmv::*) ~ (a::OpenKind)
                   -- So make a new meta-var and use that:
                   --         fmv ~ (beta::*)
                   --         (a::OpenKind) ~ (beta::*)
      = ASSERT2( k1_sub_k2,
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                 ppr tv1 <+> dcolon <+> ppr (tyVarKind tv1) $$
                 ppr xi2 <+> dcolon <+> ppr (typeKind xi2) )
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        ASSERT2( isWanted ev, ppr ev )  -- Only wanteds have flatten meta-vars
        do { tv_ty <- newFlexiTcSTy (tyVarKind tv1)
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           ; new_ev <- newWantedEvVarNC (ctEvLoc ev)
                                        (mkTcEqPredRole (eqRelRole eq_rel)
                                                        tv_ty xi2)
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           ; emitWorkNC [new_ev]
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           ; canon_eq swapped tv1 xi1 tv_ty co1 (ctEvCoercion new_ev) }
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-}
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    swap_over
      -- If tv1 is touchable, swap only if tv2 is also
      -- touchable and it's strictly better to update the latter
      -- But see Note [Avoid unnecessary swaps]
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      | Just lvl1 <- metaTyVarTcLevel_maybe tv1
      = case metaTyVarTcLevel_maybe tv2 of
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          Nothing   -> False
          Just lvl2 | lvl2 `strictlyDeeperThan` lvl1 -> True
                    | lvl1 `strictlyDeeperThan` lvl2 -> False
                    | otherwise                      -> nicer_to_update_tv2

      -- So tv1 is not a meta tyvar
      -- If only one is a meta tyvar, put it on the left
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      -- This is not because it'll be solved; but because
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      -- the floating step looks for meta tyvars on the left
      | isMetaTyVar tv2 = True

      -- So neither is a meta tyvar

      -- If only one is a flatten tyvar, put it on the left
      -- See Note [Eliminate flat-skols]
      | not (isFlattenTyVar tv1), isFlattenTyVar tv2 = True

      | otherwise = False

    nicer_to_update_tv2
      =  (isSigTyVar tv1                 && not (isSigTyVar tv2))
      || (isSystemName (Var.varName tv2) && not (isSystemName (Var.varName tv1)))

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-- | Solve a reflexive equality constraint
canEqReflexive :: CtEvidence    -- ty ~ ty
               -> EqRel
               -> TcType        -- ty
               -> TcS (StopOrContinue Ct)   -- always Stop
canEqReflexive ev eq_rel ty
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  = do { setEvBindIfWanted ev (EvCoercion $
                               mkTcReflCo (eqRelRole eq_rel) ty)
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       ; stopWith ev "Solved by reflexivity" }

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incompatibleKind :: CtEvidence         -- t1~t2
                 -> TcType -> TcKind
                 -> TcType -> TcKind   -- s1~s2, flattened and zonked
                 -> TcS (StopOrContinue Ct)
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-- LHS and RHS have incompatible kinds, so emit an "irreducible" constraint
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--       CIrredEvCan (NOT CTyEqCan or CFunEqCan)
-- for the type equality; and continue with the kind equality constraint.
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-- When the latter is solved, it'll kick out the irreducible equality for
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-- a second attempt at solving