{-# LANGUAGE CPP #-}

module TcCanonical(
     canonicalize,
     unifyDerived,

     StopOrContinue(..), stopWith, continueWith
  ) where

#include "HsVersions.h"

import TcRnTypes
import TcType
import Type
import Kind
import TcFlatten
import TcSMonad
import TcEvidence
import Class
import TyCon
import TypeRep
import Coercion
import FamInstEnv ( FamInstEnvs )
import FamInst ( tcTopNormaliseNewTypeTF_maybe )
import Var
import Name( isSystemName )
import OccName( OccName )
import Outputable
import DynFlags( DynFlags )
import VarSet
import RdrName

import Pair
import Util
import Bag
import MonadUtils ( zipWith3M, zipWith3M_ )
import Data.List  ( zip4 )
import BasicTypes
import FastString

{-
************************************************************************
*                                                                      *
*                      The Canonicaliser                               *
*                                                                      *
************************************************************************

Note [Canonicalization]
~~~~~~~~~~~~~~~~~~~~~~~

Canonicalization converts a simple constraint to a canonical form. It is
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).

The execution plan for canonicalization is the following:

  1) Decomposition of equalities happens as necessary until we reach a
     variable or type family in one side. There is no decomposition step
     for other forms of constraints.

  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.

  3) If no more decomposition is possible, we deeply apply the substitution
     from the inert_eqs and continue with flattening.

  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.

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
rewrite an inert or still interact with an inert in a further phase in the
simplifier.

Note [Caching for canonicals]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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:

InertSet = { [W] d1 : Num t }
WorkList = { [W] d2 : Num t, [W] c : t ~ Int}

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:

   - We encounter work item (d2 : Num t)

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

   - 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:
        InertSet : { [G] c : t ~ Int }
        WorkList : { [W] d1 : Num t}

   - Now we examine (d1), we observe that there is a binding for (Num
     t) in the evidence binds and we set:
             d1 := d2
     and end up in a loop!

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.

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.
-}

-- Top-level canonicalization
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

canonicalize :: Ct -> TcS (StopOrContinue Ct)
canonicalize ct@(CNonCanonical { cc_ev = ev })
  = do { traceTcS "canonicalize (non-canonical)" (ppr ct)
       ; {-# SCC "canEvVar" #-}
         canEvNC ev }

canonicalize (CDictCan { cc_ev = ev
                       , cc_class  = cls
                       , cc_tyargs = xis })
  = {-# SCC "canClass" #-}
    canClass ev cls xis -- Do not add any superclasses
canonicalize (CTyEqCan { cc_ev = ev
                       , cc_tyvar  = tv
                       , cc_rhs    = xi
                       , cc_eq_rel = eq_rel })
  = {-# SCC "canEqLeafTyVarEq" #-}
    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

canonicalize (CFunEqCan { cc_ev = ev
                        , cc_fun    = fn
                        , cc_tyargs = xis1
                        , cc_fsk    = fsk })
  = {-# SCC "canEqLeafFunEq" #-}
    canCFunEqCan ev fn xis1 fsk

canonicalize (CIrredEvCan { cc_ev = ev })
  = canIrred ev
canonicalize (CHoleCan { cc_ev = ev, cc_occ = occ, cc_hole = hole })
  = canHole ev occ hole

canEvNC :: CtEvidence -> TcS (StopOrContinue Ct)
-- Called only for non-canonical EvVars
canEvNC ev
  = case classifyPredType (ctEvPred ev) of
      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
{-
************************************************************************
*                                                                      *
*                      Class Canonicalization
*                                                                      *
************************************************************************
-}

canClass, canClassNC
   :: CtEvidence
   -> Class -> [Type] -> TcS (StopOrContinue Ct)
-- Precondition: EvVar is class evidence

-- 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

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

canClass ev cls tys
  =   -- all classes do *nominal* matching
    ASSERT2( ctEvRole ev == Nominal, ppr ev $$ ppr cls $$ ppr tys )
    do { (xis, cos) <- flattenManyNom ev tys
       ; let co = mkTcTyConAppCo Nominal (classTyCon cls) cos
             xi = mkClassPred cls xis
             mk_ct new_ev = CDictCan { cc_ev = new_ev
                                     , cc_tyargs = xis, cc_class = cls }
       ; mb <- rewriteEvidence ev xi co
       ; traceTcS "canClass" (vcat [ ppr ev <+> ppr cls <+> ppr tys
                                   , ppr xi, ppr mb ])
       ; return (fmap mk_ct mb) }

emitSuperclasses :: Ct -> TcS (StopOrContinue Ct)
emitSuperclasses ct@(CDictCan { cc_ev = ev , cc_tyargs = xis_new, cc_class = cls })
            -- Add superclasses of this one here, See Note [Adding superclasses].
            -- But only if we are not simplifying the LHS of a rule.
 = do { newSCWorkFromFlavored ev cls xis_new
      -- Arguably we should "seq" the coercions if they are derived,
      -- as we do below for emit_kind_constraint, to allow errors in
      -- superclasses to be executed if deferred to runtime!
      ; continueWith ct }
emitSuperclasses _ = panic "emit_superclasses of non-class!"

{- Note [Adding superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
            They may be needed to prove Wanteds.

  Wanteds/Derived:
            Add all their superclasses as Derived.
            The sole reason is to expose functional dependencies
            in superclasses or equality superclasses.

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 (tcfail138)
      class L a b | a -> b
      class (G a, L a b) => C a b

      instance C a b' => G (Maybe a)
      instance C a b  => C (Maybe a) a
      instance L (Maybe a) a

    When solving the superclasses of the (C (Maybe a) a) instance, we get
      [G] C a b, and hance by superclasses, [G] G a, [G] L a b
      [W] G (Maybe a)
    Use the instance decl to get
      [W] C a beta
    Generate its derived superclass
      [D] L a beta.  Now using fundeps, combine with [G] L a b to get
      [D] beta ~ b
    which is what we want.

---------- Historical note -----------
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 Given 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.
---------- End of historical note -----------

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:

   class Num (RealOf t) => Normed t
   type family RealOf x

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

If we were to be adding the superclasses during simplification we'd get:
   [W] RealOf e ~ e
   [W] Normed e
   [D] RealOf e ~ fuv
   [D] Num fuv
==>
   e := fuv, Num fuv, Normed fuv, RealOf fuv ~ fuv

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
happen.

Mind you, now that Wanteds cannot rewrite Derived, I think this particular
situation can't happen.
  -}

newSCWorkFromFlavored :: CtEvidence -> Class -> [Xi] -> TcS ()
-- Returns superclasses, see Note [Adding superclasses]
newSCWorkFromFlavored flavor cls xis
  | CtGiven { ctev_evar = evar, ctev_loc = loc } <- flavor
  = do { given_evs <- newGivenEvVars (mk_given_loc loc)
                                     (mkEvScSelectors (EvId evar) cls xis)
       ; emitWorkNC given_evs }

  | isEmptyVarSet (tyVarsOfTypes xis)
  = return () -- Wanteds with no variables yield no deriveds.
              -- See Note [Improvement from Ground Wanteds]

  | otherwise -- Wanted/Derived case, just add those SC that can lead to improvement.
  = do { let sc_rec_theta = transSuperClasses cls xis
             impr_theta   = filter isImprovementPred sc_rec_theta
             loc          = ctEvLoc flavor
       ; traceTcS "newSCWork/Derived" $ text "impr_theta =" <+> ppr impr_theta
       ; emitNewDeriveds loc impr_theta }

  where
    size = sizeTypes xis
    mk_given_loc loc
       | isCTupleClass cls
       = loc   -- For tuple predicates, just take them apart, without
               -- adding their (large) size into the chain.  When we
               -- get down to a base predicate, we'll include its size.
               -- Trac #10335

       | GivenOrigin skol_info <- ctLocOrigin loc
         -- See Note [Solving superclass constraints] in TcInstDcls
         -- for explantation of this transformation for givens
       = case skol_info of
            InstSkol -> loc { ctl_origin = GivenOrigin (InstSC size) }
            InstSC n -> loc { ctl_origin = GivenOrigin (InstSC (n `max` size)) }
            _        -> loc

       | otherwise  -- Probably doesn't happen, since this function
       = loc        -- is only used for Givens, but does no harm

{-
************************************************************************
*                                                                      *
*                      Irreducibles canonicalization
*                                                                      *
************************************************************************
-}

canIrred :: CtEvidence -> TcS (StopOrContinue Ct)
-- Precondition: ty not a tuple and no other evidence form
canIrred old_ev
  = do { let old_ty = ctEvPred old_ev
       ; traceTcS "can_pred" (text "IrredPred = " <+> ppr old_ty)
       ; (xi,co) <- flatten FM_FlattenAll old_ev old_ty -- co :: xi ~ old_ty
       ; rewriteEvidence old_ev xi co `andWhenContinue` \ new_ev ->
    do { -- Re-classify, in case flattening has improved its shape
       ; case classifyPredType (ctEvPred new_ev) of
           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 } } }

canHole :: CtEvidence -> OccName -> HoleSort -> TcS (StopOrContinue Ct)
canHole ev occ hole_sort
  = do { let ty = ctEvPred ev
       ; (xi,co) <- flatten FM_SubstOnly ev ty -- co :: xi ~ ty
       ; 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" } }

{-
************************************************************************
*                                                                      *
*        Equalities
*                                                                      *
************************************************************************

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)
-}

canEqNC :: CtEvidence -> EqRel -> Type -> Type -> TcS (StopOrContinue Ct)
canEqNC ev eq_rel ty1 ty2
  = can_eq_nc False ev eq_rel ty1 ty1 ty2 ty2

can_eq_nc
   :: Bool            -- True => both types are flat
   -> 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)
can_eq_nc flat ev eq_rel ty1 ps_ty1 ty2 ps_ty2
  = do { traceTcS "can_eq_nc" $
         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' flat rdr_env fam_insts ev eq_rel ty1 ps_ty1 ty2 ps_ty2 }

can_eq_nc'
   :: Bool           -- True => both input types are flattened
   -> 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)

-- Expand synonyms first; see Note [Type synonyms and canonicalization]
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.
-- See Note [Eager reflexivity check]
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
  | 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' _flat 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

----------------------
-- Otherwise try to decompose
----------------------

-- Literals
can_eq_nc' _flat _rdr_env _envs ev eq_rel ty1@(LitTy l1) _ (LitTy l2) _
 | l1 == l2
  = do { setEvBindIfWanted ev (EvCoercion $
                               mkTcReflCo (eqRelRole eq_rel) ty1)
       ; stopWith ev "Equal LitTy" }

-- Try to decompose type constructor applications
-- Including FunTy (s -> t)
can_eq_nc' _flat _rdr_env _envs ev eq_rel ty1 _ ty2 _
  | Just (tc1, tys1) <- tcSplitTyConApp_maybe ty1
  , Just (tc2, tys2) <- tcSplitTyConApp_maybe ty2
  , not (isTypeFamilyTyCon tc1)
  , not (isTypeFamilyTyCon tc2)
  = canTyConApp ev eq_rel tc1 tys1 tc2 tys2

can_eq_nc' _flat _rdr_env _envs ev eq_rel
           s1@(ForAllTy {}) _ s2@(ForAllTy {}) _
 | CtWanted { ctev_loc = loc, ctev_evar = orig_ev } <- ev
 = do { let (tvs1,body1) = tcSplitForAllTys s1
            (tvs2,body2) = tcSplitForAllTys s2
      ; if not (equalLength tvs1 tvs2) then
          canEqHardFailure ev eq_rel s1 s2
        else
          do { traceTcS "Creating implication for polytype equality" $ ppr ev
             ; ev_term <- deferTcSForAllEq (eqRelRole eq_rel)
                                           loc (tvs1,body1) (tvs2,body2)
             ; setWantedEvBind orig_ev ev_term
             ; stopWith ev "Deferred polytype equality" } }
 | otherwise
 = do { traceTcS "Ommitting decomposition of given polytype equality" $
        pprEq s1 s2    -- See Note [Do not decompose given polytype equalities]
      ; stopWith ev "Discard given polytype equality" }

-- See Note [Canonicalising type applications] about why we require flat types
can_eq_nc' True _rdr_env _envs ev eq_rel (AppTy t1 s1) _ ty2 _
  | Just (t2, s2) <- tcSplitAppTy_maybe ty2
  = can_eq_app ev eq_rel t1 s1 t2 s2
can_eq_nc' True _rdr_env _envs ev eq_rel ty1 _ (AppTy t2 s2) _
  | Just (t1, s1) <- tcSplitAppTy_maybe ty1
  = can_eq_app ev eq_rel t1 s1 t2 s2

-- 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
         `andWhenContinue` \ new_ev ->
         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

{-
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.

Note [Eager reflexivity check]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have

  newtype X = MkX (Int -> X)

and

  [W] X ~R X

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.

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.

Here's another place where this reflexivity check is key:
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 [Newtypes can blow the stack]
       ; checkReductionDepth (ctEvLoc ev) ty1
       ; addUsedDataCons 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 False new_ev ReprEq ty1' ty1' ty2 ps_ty2 }

---------
-- ^ Decompose a type application.
-- All input types must be flat. See Note [Canonicalising type applications]
can_eq_app :: CtEvidence       -- :: s1 t1 ~r s2 t2
           -> EqRel            -- r
           -> Xi -> Xi         -- s1 t1
           -> Xi -> Xi         -- s2 t2
           -> TcS (StopOrContinue Ct)

-- AppTys only decompose for nominal equality, so this case just leads
-- to an irreducible constraint; see typecheck/should_compile/T10494
-- See Note [Decomposing equality], note {4}
can_eq_app ev ReprEq _ _ _ _
  = do { traceTcS "failing to decompose representational AppTy equality" (ppr ev)
       ; continueWith (CIrredEvCan { cc_ev = ev }) }
          -- no need to call canEqFailure, because that flattens, and the
          -- types involved here are already flat

can_eq_app ev NomEq s1 t1 s2 t2
  | CtDerived { ctev_loc = loc } <- ev
  = do { emitNewDerivedEq loc (mkTcEqPred t1 t2)
       ; 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 }
  | CtGiven { ctev_evar = evar, ctev_loc = loc } <- ev
  = do { let co   = mkTcCoVarCo evar
             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"

------------------------
canTyConApp :: CtEvidence -> EqRel
            -> TyCon -> [TcType]
            -> TyCon -> [TcType]
            -> TcS (StopOrContinue Ct)
-- See Note [Decomposing TyConApps]
canTyConApp ev eq_rel tc1 tys1 tc2 tys2
  | tc1 == tc2
  , length tys1 == length tys2
  = do { inerts <- getTcSInerts
       ; if can_decompose inerts
         then do { traceTcS "canTyConApp"
                       (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 }

  -- Fail straight away for better error messages
  -- See Note [Use canEqFailure in canDecomposableTyConApp]
  | eq_rel == ReprEq && not (isGenerativeTyCon tc1 Representational &&
                             isGenerativeTyCon tc2 Representational)
  = canEqFailure ev eq_rel ty1 ty2
  | otherwise
  = canEqHardFailure ev eq_rel ty1 ty2
  where
    ty1 = mkTyConApp tc1 tys1
    ty2 = mkTyConApp tc2 tys2

    loc  = ctEvLoc ev
    pred = ctEvPred ev

     -- See Note [Decomposing equality]
    can_decompose inerts
      =  isInjectiveTyCon tc1 (eqRelRole eq_rel)
      || (ctEvFlavour ev /= Given && isEmptyBag (matchableGivens loc pred inerts))

{-
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 one 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 (TF 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.

Here is another case:

  [G] Age ~R 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!

For example, see typecheck/should_compile/T10493, repeated here:

  import Data.Ord (Down)  -- no constructor

  foo :: Coercible (Down Int) Int => Down Int -> Int
  foo = coerce

That should compile, but only because we use canEqFailure and not
canEqHardFailure.

Note [Decomposing equality]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we have a constraint (of any flavour and role) that looks like
T tys1 ~ T tys2, what can we conclude about tys1 and tys2? The answer,
of course, is "it depends". This Note spells it all out.

In this Note, "decomposition" refers to taking the constraint
  [fl] (T tys1 ~X T tys2)
(for some flavour fl and some role X) and replacing it with
  [fls'] (tys1 ~Xs' tys2)
where that notation indicates a list of new constraints, where the
new constraints may have different flavours and different roles.

The key property to consider is injectivity. When decomposing a Given the
decomposition is sound if and only if T is injective in all of its type
arguments. When decomposing a Wanted, the decomposition is sound (assuming the
correct roles in the produced equality constraints), but it may be a guess --
that is, an unforced decision by the constraint solver. Decomposing Wanteds
over injective TyCons does not entail guessing. But sometimes we want to
decompose a Wanted even when the TyCon involved is not injective! (See below.)

So, in broad strokes, we want this rule:

(*) Decompose a constraint (T tys1 ~X T tys2) if and only if T is injective
at role X.

Pursuing the details requires exploring three axes:
* Flavour: Given vs. Derived vs. Wanted
* Role: Nominal vs. Representational
* TyCon species: datatype vs. newtype vs. data family vs. type family vs. type variable

(So a type variable isn't a TyCon, but it's convenient to put the AppTy case
in the same table.)

Right away, we can say that Derived behaves just as Wanted for the purposes
of decomposition. The difference between Derived and Wanted is the handling of
evidence. Since decomposition in these cases isn't a matter of soundness but of
guessing, we want the same behavior regardless of evidence.

Here is a table (discussion following) detailing where decomposition of
   (T s1 ... sn) ~r (T t1 .. tn)
is allowed.  The first four lines (Data types ... type family) refer
to TyConApps with various TyCons T; the last line is for AppTy, where
there is presumably a type variable at the head, so it's actually
   (s s1 ... sn) ~r (t t1 .. tn)

NOMINAL               GIVEN                       WANTED

Datatype               YES                         YES
Newtype                YES                         YES
Data family            YES                         YES
Type family            YES, in injective args{1}   YES, in injective args{1}
Type variable          YES                         YES

REPRESENTATIONAL      GIVEN                       WANTED

Datatype               YES                         YES
Newtype                NO{2}                      MAYBE{2}
Data family            NO{3}                      MAYBE{3}
Type family             NO                          NO
Type variable          NO{4}                       NO{4}

{1}: Type families can be injective in some, but not all, of their arguments,
so we want to do partial decomposition. This is quite different than the way
other decomposition is done, where the decomposed equalities replace the original
one. We thus proceed much like we do with superclasses: emitting new Givens
when "decomposing" a partially-injective type family Given and new Deriveds
when "decomposing" a partially-injective type family Wanted. (As of the time of
writing, 13 June 2015, the implementation of injective type families has not
been merged, but it should be soon. Please delete this parenthetical if the
implementation is indeed merged.)

{2}: See Note [Decomposing newtypes at representational role]

{3}: Because of the possibility of newtype instances, we must treat
data families like newtypes. See also Note [Decomposing newtypes at
representational role]. See #10534 and test case
typecheck/should_fail/T10534.

{4}: Because type variables can stand in for newtypes, we conservatively do not
decompose AppTys over representational equality.

In the implementation of can_eq_nc and friends, we don't directly pattern
match using lines like in the tables above, as those tables don't cover
all cases (what about PrimTyCon? tuples?). Instead we just ask about injectivity,
boiling the tables above down to rule (*). The exceptions to rule (*) are for
injective type families, which are handled separately from other decompositions,
and the MAYBE entries above.

Note [Decomposing newtypes at representational role]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This note discusses the 'newtype' line in the REPRESENTATIONAL table
in Note [Decomposing equality]. (At nominal role, newtypes are fully
decomposable.)

Here is a representative example of why representational equality over
newtypes is tricky:

  newtype Nt a = Mk Bool         -- NB: a is not used in the RHS,
  type role Nt representational  -- but the user gives it an R role anyway

If we have [W] Nt alpha ~R Nt beta, we *don't* want to decompose to
[W] alpha ~R beta, because it's possible that alpha and beta aren't
representationally equal. Here's another example.

  newtype Nt a = MkNt (Id a)
  type family Id a where Id a = a

  [W] Nt Int ~R Nt Age

Because of its use of a type family, Nt's parameter will get inferred to have
a nominal role. Thus, decomposing the wanted will yield [W] Int ~N Age, which
is unsatisfiable. Unwrapping, though, leads to a solution.

Conclusion:
 * Unwrap newtypes before attempting to decompose them.
   This is done in can_eq_nc'.

It all comes from the fact that newtypes aren't necessarily injective
w.r.t. representational equality.

Furthermore, as explained in Note [NthCo and newtypes] in Coercion, we can't use
NthCo on representational coercions over newtypes. NthCo comes into play
only when decomposing givens.

Conclusion:
 * Do not decompose [G] N s ~R N t

Is it sensible to decompose *Wanted* constraints over newtypes?  Yes!
It's the only way we could ever prove (IO Int ~R IO Age), recalling
that IO is a newtype.

However we must be careful.  Consider

  type role Nt representational

  [G] Nt a ~R Nt b       (1)
  [W] NT alpha ~R Nt b   (2)
  [W] alpha ~ a          (3)

If we focus on (3) first, we'll substitute in (2), and now it's
identical to the given (1), so we succeed.  But if we focus on (2)
first, and decompose it, we'll get (alpha ~R b), which is not soluble.
This is exactly like the question of overlapping Givens for class
constraints: see Note [Instance and Given overlap] in TcInteract.

Conclusion:
  * Decompose [W] N s ~R N t  iff there no given constraint that could
    later solve it.
-}

canDecomposableTyConAppOK :: CtEvidence -> EqRel
                          -> TyCon -> [TcType] -> [TcType]
                          -> TcS ()
-- Precondition: tys1 and tys2 are the same length, hence "OK"
canDecomposableTyConAppOK ev eq_rel tc tys1 tys2
  = case ev of
     CtDerived { ctev_loc = loc }
        -> unifyDeriveds loc tc_roles tys1 tys2

     CtWanted { ctev_evar = evar, ctev_loc = loc }
        -> do { cos <- zipWith3M (unifyWanted loc) tc_roles tys1 tys2
              ; setWantedEvBind evar (EvCoercion (mkTcTyConAppCo role tc cos)) }

     CtGiven { ctev_evar = evar, ctev_loc = loc }
        -> do { let ev_co = mkTcCoVarCo evar
              ; 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 ]
              ; emitWorkNC given_evs }
  where
    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 [Use canEqFailure in canDecomposableTyConApp]
canEqFailure :: CtEvidence -> EqRel
             -> TcType -> TcType -> TcS (StopOrContinue Ct)
canEqFailure ev NomEq ty1 ty2
  = canEqHardFailure ev NomEq ty1 ty2
canEqFailure ev ReprEq ty1 ty2
  = do { (xi1, co1) <- flatten FM_FlattenAll ev ty1
       ; (xi2, co2) <- flatten FM_FlattenAll ev ty2
            -- We must flatten the types before putting them in the
            -- inert set, so that we are sure to kick them out when
            -- new equalities become available
       ; traceTcS "canEqFailure with ReprEq" $
         vcat [ ppr ev, ppr ty1, ppr ty2, ppr xi1, ppr xi2 ]
       ; rewriteEqEvidence ev ReprEq NotSwapped xi1 xi2 co1 co2
         `andWhenContinue` \ new_ev ->
         continueWith (CIrredEvCan { cc_ev = new_ev }) }

-- | Call when canonicalizing an equality fails with utterly no hope.
canEqHardFailure :: CtEvidence -> EqRel
                 -> TcType -> TcType -> TcS (StopOrContinue Ct)
-- See Note [Make sure that insolubles are fully rewritten]
canEqHardFailure ev eq_rel ty1 ty2
  = do { (s1, co1) <- flatten FM_SubstOnly ev ty1
       ; (s2, co2) <- flatten FM_SubstOnly ev ty2
       ; rewriteEqEvidence ev eq_rel NotSwapped s1 s2 co1 co2
         `andWhenContinue` \ new_ev ->
    do { emitInsoluble (mkNonCanonical new_ev)
       ; stopWith new_ev "Definitely not equal" }}

{-
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 just 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.

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

However, over-eager decomposition gives bad error messages
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
we get an error        "Can't match Array ~ Maybe",
but we'd prefer to get "Can't match Array b ~ Maybe c".

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.

Note [Make sure that insolubles are fully rewritten]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When an equality fails, we still want to rewrite the equality
all the way down, so that it accurately reflects
 (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 TcSMonad.
And if we don't do this there is a bad danger that
TcSimplify.applyTyVarDefaulting will find a variable
that has in fact been substituted.

Note [Do not decompose Given polytype equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider [G] (forall a. t1 ~ forall a. t2).  Can we decompose this?
No -- what would the evidence look like?  So instead we simply discard
this given evidence.


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.

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

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.

Note [Occurs check error]
~~~~~~~~~~~~~~~~~~~~~~~~~
If we have an occurs check error, are we necessarily hosed? Say our
tyvar is tv1 and the type it appears in is xi2. Because xi2 is function
free, then if we're computing w.r.t. nominal equality, then, yes, we're
hosed. Nothing good can come from (a ~ [a]). If we're computing w.r.t.
representational equality, this is a little subtler. Once again, (a ~R [a])
is a bad thing, but (a ~R N a) for a newtype N might be just fine. This
means also that (a ~ b a) might be fine, because `b` might become a newtype.

So, we must check: does tv1 appear in xi2 under any type constructor that
is generative w.r.t. representational equality? That's what isTyVarUnderDatatype
does. (The other name I considered, isTyVarUnderTyConGenerativeWrtReprEq was
a bit verbose. And the shorter name gets the point across.)

See also #10715, which induced this addition.

-}

canCFunEqCan :: CtEvidence
             -> TyCon -> [TcType]   -- LHS
             -> TcTyVar             -- RHS
             -> TcS (StopOrContinue Ct)
-- ^ Canonicalise a CFunEqCan.  We know that
--     the arg types are already flat,
-- and the RHS is a fsk, which we must *not* substitute.
-- So just substitute in the LHS
canCFunEqCan ev fn tys fsk
  = do { (tys', cos) <- flattenManyNom ev tys
                        -- cos :: tys' ~ tys
       ; let lhs_co  = mkTcTyConAppCo Nominal fn cos
                        -- :: F tys' ~ F tys
             new_lhs = mkTyConApp fn tys'
             fsk_ty  = mkTyVarTy fsk
       ; 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')
       ; continueWith (CFunEqCan { cc_ev = ev', cc_fun = fn
                                 , cc_tyargs = tys', cc_fsk = fsk }) } }

---------------------
canEqTyVar :: CtEvidence -> EqRel -> SwapFlag
           -> TcTyVar             -- already flat
           -> TcType              -- already flat
           -> TcS (StopOrContinue Ct)
-- A TyVar on LHS, but so far un-zonked
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
         -- 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
       ; canEqTyVar2 dflags ev eq_rel swapped tv1 ps_ty2 }

canEqTyVar2 :: DynFlags
            -> CtEvidence   -- lhs ~ rhs (or, if swapped, orhs ~ olhs)
            -> EqRel
            -> SwapFlag
            -> TcTyVar      -- lhs, flat
            -> TcType       -- rhs, flat
            -> TcS (StopOrContinue Ct)
-- LHS is an inert type variable,
-- and RHS is fully rewritten, but with type synonyms
-- preserved as much as possible

canEqTyVar2 dflags ev eq_rel swapped tv1 xi2
  | Just tv2 <- getTyVar_maybe xi2
  = canEqTyVarTyVar ev eq_rel swapped tv1 tv2

  | OC_OK xi2' <- occurCheckExpand dflags tv1 xi2  -- No occurs check
     -- 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
  = do { let k1 = tyVarKind tv1
             k2 = typeKind xi2'
       ; rewriteEqEvidence ev eq_rel swapped xi1 xi2' co1 (mkTcReflCo role xi2')
         `andWhenContinue` \ new_ev ->
         if k2 `isSubKind` k1
         then   -- Establish CTyEqCan kind invariant
                -- Reorientation has done its best, but the kinds might
                -- simply be incompatible
               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 }

  | otherwise  -- Occurs check error
  = rewriteEqEvidence ev eq_rel swapped xi1 xi2 co1 co2
    `andWhenContinue` \ new_ev ->
    if eq_rel == NomEq || isTyVarUnderDatatype tv1 xi2
      -- See Note [Occurs check error]

    then do { emitInsoluble (mkNonCanonical new_ev)
              -- 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
            ; 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.
    else do { traceTcS "Occurs-check in representational equality"
                              (ppr xi1 $$ ppr xi2)
            ; continueWith (CIrredEvCan { cc_ev = new_ev }) }
  where
    role = eqRelRole eq_rel
    xi1  = mkTyVarTy tv1
    co1  = mkTcReflCo role xi1
    co2  = mkTcReflCo role xi2

canEqTyVarTyVar :: CtEvidence           -- tv1 ~ rhs (or rhs ~ tv1, if swapped)
                -> EqRel
                -> SwapFlag
                -> TcTyVar -> TcTyVar   -- tv1, tv2
                -> TcS (StopOrContinue Ct)
-- Both LHS and RHS rewrote to a type variable
-- See Note [Canonical orientation for tyvar/tyvar equality constraints]
canEqTyVarTyVar ev eq_rel swapped tv1 tv2
  | tv1 == tv2
  = do { setEvBindIfWanted ev (EvCoercion $ mkTcReflCo role xi1)
       ; stopWith ev "Equal tyvars" }

  | incompat_kind   = incompatibleKind ev xi1 k1 xi2 k2

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

  | 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
  where
    role = eqRelRole eq_rel
    xi1 = mkTyVarTy tv1
    co1 = mkTcReflCo role xi1
    xi2 = mkTyVarTy tv2
    co2 = mkTcReflCo role xi2
    k1  = tyVarKind tv1
    k2  = tyVarKind tv2
    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
        -- 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 })

{- We don't do this any more
   See Note [Orientation of equalities with fmvs] in TcFlatten
    -- tv1 is the flatten meta-var
    do_fmv swapped tv1 xi1 xi2 co1 co2
      | same_kind
      = canon_eq swapped tv1 xi1 xi2 co1 co2
      | 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,
                 ppr tv1 <+> dcolon <+> ppr (tyVarKind tv1) $$
                 ppr xi2 <+> dcolon <+> ppr (typeKind xi2) )
        ASSERT2( isWanted ev, ppr ev )  -- Only wanteds have flatten meta-vars
        do { tv_ty <- newFlexiTcSTy (tyVarKind tv1)
           ; new_ev <- newWantedEvVarNC (ctEvLoc ev)
                                        (mkTcEqPredRole (eqRelRole eq_rel)
                                                        tv_ty xi2)
           ; emitWorkNC [new_ev]
           ; canon_eq swapped tv1 xi1 tv_ty co1 (ctEvCoercion new_ev) }
-}

    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]
      | Just lvl1 <- metaTyVarTcLevel_maybe tv1
      = case metaTyVarTcLevel_maybe tv2 of
          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
      -- This is not because it'll be solved; but because
      -- 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)))

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

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

incompatibleKind new_ev s1 k1 s2 k2   -- See Note [Equalities with incompatible kinds]
  = ASSERT( isKind k1 && isKind k2 )
    do { traceTcS "canEqLeaf: incompatible kinds" (vcat [ppr k1, ppr k2])

         -- Create a derived kind-equality, and solve it
       ; emitNewDerivedEq kind_co_loc (mkTcEqPred k1 k2)

         -- Put the not-currently-soluble thing into the inert set
       ; continueWith (CIrredEvCan { cc_ev = new_ev }) }
  where
    loc = ctEvLoc new_ev
    kind_co_loc = setCtLocOrigin loc (KindEqOrigin s1 s2 (ctLocOrigin loc))

{-
Note [Canonical orientation for tyvar/tyvar equality constraints]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we have a ~ b where both 'a' and 'b' are TcTyVars, which way
round should be oriented in the CTyEqCan?  The rules, implemented by
canEqTyVarTyVar, are these

 * If either is a flatten-meta-variables, it goes on the left.

 * If one is a strict sub-kind of the other e.g.
       (alpha::?) ~ (beta::*)
   orient them so RHS is a subkind of LHS.  That way we will replace
   'a' with 'b', correctly narrowing the kind.
   This establishes the subkind invariant of CTyEqCan.

 * Put a meta-tyvar on the left if possible
       alpha[3] ~ r

 * If both are meta-tyvars, put the more touchable one (deepest level
   number) on the left, so there is the best chance of unifying it
        alpha[3] ~ beta[2]

 * If both are meta-tyvars and both at the same level, put a SigTv
   on the right if possible
        alpha[2] ~ beta[2](sig-tv)
   That way, when we unify alpha := beta, we don't lose the SigTv flag.

 * Put a meta-tv with a System Name on the left if possible so it
   gets eliminated (improves error messages)

 * If one is a flatten-skolem, put it on the left so that it is
   substituted out  Note [Elminate flat-skols]
        fsk ~ a

Note [Avoid unnecessary swaps]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we swap without actually improving matters, we can get an infnite loop.
Consider
    work item:  a ~ b
   inert item:  b ~ c
We canonicalise the work-time to (a ~ c).  If we then swap it before
aeding to the inert set, we'll add (c ~ a), and therefore kick out the
inert guy, so we get
   new work item:  b ~ c
   inert item:     c ~ a
And now the cycle just repeats

Note [Eliminate flat-skols]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have  [G] Num (F [a])
then we flatten to
     [G] Num fsk
     [G] F [a] ~ fsk
where fsk is a flatten-skolem (FlatSkol). Suppose we have
      type instance F [a] = a
then we'll reduce the second constraint to
     [G] a ~ fsk
and then replace all uses of 'a' with fsk.  That's bad because
in error messages intead of saying 'a' we'll say (F [a]).  In all
places, including those where the programmer wrote 'a' in the first
place.  Very confusing!  See Trac #7862.

Solution: re-orient a~fsk to fsk~a, so that we preferentially eliminate
the fsk.

Note [Equalities with incompatible kinds]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
canEqLeaf is about to make a CTyEqCan or CFunEqCan; but both have the
invariant that LHS and RHS satisfy the kind invariants for CTyEqCan,
CFunEqCan.  What if we try to unify two things with incompatible
kinds?

eg    a ~ b  where a::*, b::*->*
or    a ~ b  where a::*, b::k, k is a kind variable

The CTyEqCan compatKind invariant is important.  If we make a CTyEqCan
for a~b, then we might well *substitute* 'b' for 'a', and that might make
a well-kinded type ill-kinded; and that is bad (eg typeKind can crash, see
Trac #7696).

So instead for these ill-kinded equalities we generate a CIrredCan,
and put it in the inert set, which keeps it out of the way until a
subsequent substitution (on kind variables, say) re-activates it.

NB: it is important that the types s1,s2 are flattened and zonked
    so that their kinds k1, k2 are inert wrt the substitution.  That
    means that they can only become the same if we change the inert
    set, which in turn will kick out the irreducible equality
    E.g. it is WRONG to make an irred (a:k1)~(b:k2)
         if we already have a substitution k1:=k2

NB: it's important that the new CIrredCan goes in the inert set rather
than back into the work list. We used to do the latter, but that led
to an infinite loop when we encountered it again, and put it back in
the work list again.

See also Note [Kind orientation for CTyEqCan] and
         Note [Kind orientation for CFunEqCan] in TcRnTypes

Note [Type synonyms and canonicalization]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We treat type synonym applications as xi types, that is, they do not
count as type function applications.  However, we do need to be a bit
careful with type synonyms: like type functions they may not be
generative or injective.  However, unlike type functions, they are
parametric, so there is no problem in expanding them whenever we see
them, since we do not need to know anything about their arguments in
order to expand them; this is what justifies not having to treat them
as specially as type function applications.  The thing that causes
some subtleties is that we prefer to leave type synonym applications
*unexpanded* whenever possible, in order to generate better error
messages.

If we encounter an equality constraint with type synonym applications
on both sides, or a type synonym application on one side and some sort
of type application on the other, we simply must expand out the type
synonyms in order to continue decomposing the equality constraint into
primitive equality constraints.  For example, suppose we have

  type F a = [Int]

and we encounter the equality

  F a ~ [b]

In order to continue we must expand F a into [Int], giving us the
equality

  [Int] ~ [b]

which we can then decompose into the more primitive equality
constraint

  Int ~ b.

However, if we encounter an equality constraint with a type synonym
application on one side and a variable on the other side, we should
NOT (necessarily) expand the type synonym, since for the purpose of
good error messages we want to leave type synonyms unexpanded as much
as possible.  Hence the ps_ty1, ps_ty2 argument passed to canEqTyVar.

-}

{-
************************************************************************
*                                                                      *
                  Evidence transformation
*                                                                      *
************************************************************************
-}

data StopOrContinue a
  = ContinueWith a    -- The constraint was not solved, although it may have
                      --   been rewritten

  | Stop CtEvidence   -- The (rewritten) constraint was solved
         SDoc         -- Tells how it was solved
                      -- Any new sub-goals have been put on the work list

instance Functor StopOrContinue where
  fmap f (ContinueWith x) = ContinueWith (f x)
  fmap _ (Stop ev s)      = Stop ev s

instance Outputable a => Outputable (StopOrContinue a) where
  ppr (Stop ev s)      = ptext (sLit "Stop") <> parens s <+> ppr ev
  ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w

continueWith :: a -> TcS (StopOrContinue a)
continueWith = return . ContinueWith

stopWith :: CtEvidence -> String -> TcS (StopOrContinue a)
stopWith ev s = return (Stop ev (text s))

andWhenContinue :: TcS (StopOrContinue a)
                -> (a -> TcS (StopOrContinue b))
                -> TcS (StopOrContinue b)
andWhenContinue tcs1 tcs2
  = do { r <- tcs1
       ; case r of
           Stop ev s       -> return (Stop ev s)
           ContinueWith ct -> tcs2 ct }
infixr 0 `andWhenContinue`    -- allow chaining with ($)

rewriteEvidence :: CtEvidence   -- old evidence
                -> TcPredType   -- new predicate
                -> TcCoercion   -- Of type :: new predicate ~ <type of old evidence>
                -> TcS (StopOrContinue CtEvidence)
-- Returns Just new_ev iff either (i)  'co' is reflexivity
--                             or (ii) 'co' is not reflexivity, and 'new_pred' not cached
-- In either case, there is nothing new to do with new_ev
{-
     rewriteEvidence old_ev new_pred co
Main purpose: create new evidence for new_pred;
              unless new_pred is cached already
* Returns a new_ev : new_pred, with same wanted/given/derived flag as old_ev
* If old_ev was wanted, create a binding for old_ev, in terms of new_ev
* If old_ev was given, AND not cached, create a binding for new_ev, in terms of old_ev
* Returns Nothing if new_ev is already cached

        Old evidence    New predicate is               Return new evidence
        flavour                                        of same flavor
        -------------------------------------------------------------------
        Wanted          Already solved or in inert     Nothing
        or Derived      Not                            Just new_evidence

        Given           Already in inert               Nothing
                        Not                            Just new_evidence

Note [Rewriting with Refl]
~~~~~~~~~~~~~~~~~~~~~~~~~~
If the coercion is just reflexivity then you may re-use the same
variable.  But be careful!  Although the coercion is Refl, new_pred
may reflect the result of unification alpha := ty, so new_pred might
not _look_ the same as old_pred, and it's vital to proceed from now on
using new_pred.

The flattener preserves type synonyms, so they should appear in new_pred
as well as in old_pred; that is important for good error messages.
 -}


rewriteEvidence old_ev@(CtDerived {}) new_pred _co
  = -- If derived, don't even look at the coercion.
    -- This is very important, DO NOT re-order the equations for
    -- rewriteEvidence to put the isTcReflCo test first!
    -- Why?  Because for *Derived* constraints, c, the coercion, which
    -- was produced by flattening, may contain suspended calls to
    -- (ctEvTerm c), which fails for Derived constraints.
    -- (Getting this wrong caused Trac #7384.)
    continueWith (old_ev { ctev_pred = new_pred })

rewriteEvidence old_ev new_pred co
  | isTcReflCo co -- See Note [Rewriting with Refl]
  = continueWith (old_ev { ctev_pred = new_pred })

rewriteEvidence ev@(CtGiven { ctev_evar = old_evar , ctev_loc = loc }) new_pred co
  = do { new_ev <- newGivenEvVar loc (new_pred, new_tm)
       ; continueWith new_ev }
  where
    -- mkEvCast optimises ReflCo
    new_tm = mkEvCast (EvId old_evar) (tcDowngradeRole Representational
                                                       (ctEvRole ev)
                                                       (mkTcSymCo co))

rewriteEvidence ev@(CtWanted { ctev_evar = evar, ctev_loc = loc }) new_pred co
  = do { (new_ev, freshness) <- newWantedEvVar loc new_pred
       ; MASSERT( tcCoercionRole co == ctEvRole ev )
       ; setWantedEvBind evar (mkEvCast (ctEvTerm new_ev)
                                 (tcDowngradeRole Representational (ctEvRole ev) co))
       ; case freshness of
            Fresh  -> continueWith new_ev
            Cached -> stopWith ev "Cached wanted" }


rewriteEqEvidence :: CtEvidence         -- Old evidence :: olhs ~ orhs (not swapped)
                                        --              or orhs ~ olhs (swapped)
                  -> EqRel
                  -> SwapFlag
                  -> TcType -> TcType   -- New predicate  nlhs ~ nrhs
                                        -- Should be zonked, because we use typeKind on nlhs/nrhs
                  -> TcCoercion         -- lhs_co, of type :: nlhs ~ olhs
                  -> TcCoercion         -- rhs_co, of type :: nrhs ~ orhs
                  -> TcS (StopOrContinue CtEvidence)  -- Of type nlhs ~ nrhs
-- For (rewriteEqEvidence (Given g olhs orhs) False nlhs nrhs lhs_co rhs_co)
-- we generate
-- If not swapped
--      g1 : nlhs ~ nrhs = lhs_co ; g ; sym rhs_co
-- If 'swapped'
--      g1 : nlhs ~ nrhs = lhs_co ; Sym g ; sym rhs_co
--
-- For (Wanted w) we do the dual thing.
-- New  w1 : nlhs ~ nrhs
-- If not swapped
--      w : olhs ~ orhs = sym lhs_co ; w1 ; rhs_co
-- If swapped
--      w : orhs ~ olhs = sym rhs_co ; sym w1 ; lhs_co
--
-- It's all a form of rewwriteEvidence, specialised for equalities
rewriteEqEvidence old_ev eq_rel swapped nlhs nrhs lhs_co rhs_co
  | CtDerived {} <- old_ev  -- Don't force the evidence for a Derived
  = continueWith (old_ev { ctev_pred = new_pred })

  | NotSwapped <- swapped
  , isTcReflCo lhs_co      -- See Note [Rewriting with Refl]
  , isTcReflCo rhs_co
  = continueWith (old_ev { ctev_pred = new_pred })

  | CtGiven { ctev_evar = old_evar } <- old_ev
  = do { let new_tm = EvCoercion (lhs_co
                                  `mkTcTransCo` maybeSym swapped (mkTcCoVarCo old_evar)
                                  `mkTcTransCo` mkTcSymCo rhs_co)
       ; new_ev <- newGivenEvVar loc' (new_pred, new_tm)
       ; continueWith new_ev }

  | CtWanted { ctev_evar = evar } <- old_ev
  = do { new_evar <- newWantedEvVarNC loc' new_pred
       ; let co = maybeSym swapped $
                  mkTcSymCo lhs_co
                  `mkTcTransCo` ctEvCoercion new_evar
                  `mkTcTransCo` rhs_co
       ; setWantedEvBind evar (EvCoercion co)
       ; traceTcS "rewriteEqEvidence" (vcat [ppr old_ev, ppr nlhs, ppr nrhs, ppr co])
       ; continueWith new_evar }

  | otherwise
  = panic "rewriteEvidence"
  where
    new_pred = mkTcEqPredRole (eqRelRole eq_rel) nlhs nrhs

      -- equality is like a type class. Bumping the depth is necessary because
      -- of recursive newtypes, where "reducing" a newtype can actually make
      -- it bigger. See Note [Newtypes can blow the stack].
    loc'     = bumpCtLocDepth (ctEvLoc old_ev)

{- Note [unifyWanted and unifyDerived]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When decomposing equalities we often create new wanted constraints for
(s ~ t).  But what if s=t?  Then it'd be faster to return Refl right away.
Similar remarks apply for Derived.

Rather than making an equality test (which traverses the structure of the
type, perhaps fruitlessly, unifyWanted traverses the common structure, and
bales out when it finds a difference by creating a new Wanted constraint.
But where it succeeds in finding common structure, it just builds a coercion
to reflect it.
-}

unifyWanted :: CtLoc -> Role -> TcType -> TcType -> TcS TcCoercion
-- Return coercion witnessing the equality of the two types,
-- emitting new work equalities where necessary to achieve that
-- Very good short-cut when the two types are equal, or nearly so
-- See Note [unifyWanted and unifyDerived]
-- The returned coercion's role matches the input parameter
unifyWanted _   Phantom ty1      ty2      = return (mkTcPhantomCo ty1 ty2)
unifyWanted loc role    orig_ty1 orig_ty2
  = go orig_ty1 orig_ty2
  where
    go ty1 ty2 | Just ty1' <- tcView ty1 = go ty1' ty2
    go ty1 ty2 | Just ty2' <- tcView ty2 = go ty1 ty2'

    go (FunTy s1 t1) (FunTy s2 t2)
      = do { co_s <- unifyWanted loc role s1 s2
           ; co_t <- unifyWanted loc role t1 t2
           ; return (mkTcTyConAppCo role funTyCon [co_s,co_t]) }
    go (TyConApp tc1 tys1) (TyConApp tc2 tys2)
      | tc1 == tc2, tys1 `equalLength` tys2
      , isInjectiveTyCon tc1 role -- don't look under newtypes at Rep equality
      = do { cos <- zipWith3M (unifyWanted loc) (tyConRolesX role tc1) tys1 tys2
           ; return (mkTcTyConAppCo role tc1 cos) }
    go (TyVarTy tv) ty2
      = do { mb_ty <- isFilledMetaTyVar_maybe tv
           ; case mb_ty of
                Just ty1' -> go ty1' ty2
                Nothing   -> bale_out }
    go ty1 (TyVarTy tv)
      = do { mb_ty <- isFilledMetaTyVar_maybe tv
           ; case mb_ty of
                Just ty2' -> go ty1 ty2'
                Nothing   -> bale_out }
    go _ _ = bale_out

    bale_out = do { ev <- newWantedEvVarNC loc (mkTcEqPredRole role
                                                  orig_ty1 orig_ty2)
                  ; emitWorkNC [ev]
                  ; return (ctEvCoercion ev) }

unifyDeriveds :: CtLoc -> [Role] -> [TcType] -> [TcType] -> TcS ()
-- See Note [unifyWanted and unifyDerived]
unifyDeriveds loc roles tys1 tys2 = zipWith3M_ (unify_derived loc) roles tys1 tys2

unifyDerived :: CtLoc -> Role -> Pair TcType -> TcS ()
-- See Note [unifyWanted and unifyDerived]
unifyDerived loc role (Pair ty1 ty2) = unify_derived loc role ty1 ty2

unify_derived :: CtLoc -> Role -> TcType -> TcType -> TcS ()
-- Create new Derived and put it in the work list
-- Should do nothing if the two types are equal
-- See Note [unifyWanted and unifyDerived]
unify_derived _   Phantom _        _        = return ()
unify_derived loc role    orig_ty1 orig_ty2
  = go orig_ty1 orig_ty2
  where
    go ty1 ty2 | Just ty1' <- tcView ty1 = go ty1' ty2
    go ty1 ty2 | Just ty2' <- tcView ty2 = go ty1 ty2'

    go (FunTy s1 t1) (FunTy s2 t2)
      = do { unify_derived loc role s1 s2
           ; unify_derived loc role t1 t2 }
    go (TyConApp tc1 tys1) (TyConApp tc2 tys2)
      | tc1 == tc2, tys1 `equalLength` tys2
      , isInjectiveTyCon tc1 role
      = unifyDeriveds loc (tyConRolesX role tc1) tys1 tys2
    go (TyVarTy tv) ty2
      = do { mb_ty <- isFilledMetaTyVar_maybe tv
           ; case mb_ty of
                Just ty1' -> go ty1' ty2
                Nothing   -> bale_out }
    go ty1 (TyVarTy tv)
      = do { mb_ty <- isFilledMetaTyVar_maybe tv
           ; case mb_ty of
                Just ty2' -> go ty1 ty2'
                Nothing   -> bale_out }
    go _ _ = bale_out

    bale_out = emitNewDerivedEq loc (mkTcEqPredRole role orig_ty1 orig_ty2)

maybeSym :: SwapFlag -> TcCoercion -> TcCoercion
maybeSym IsSwapped  co = mkTcSymCo co
maybeSym NotSwapped co = co
