TcInteract.lhs 83 KB
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\begin{code}
module TcInteract ( 
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     solveInteract, AtomicInert, tyVarsOfInert,
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     InertSet, emptyInert, updInertSet, extractUnsolved, solveOne, foldISEqCts
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  ) where  

#include "HsVersions.h"

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import BasicTypes 
import TcCanonical
import VarSet
import Type

import Id 
import Var

import TcType
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import HsBinds
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import InstEnv
import Class
import TyCon
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import Name

import FunDeps

import Control.Monad ( when ) 

import Coercion
import Outputable

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import TcRnTypes
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import TcErrors
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import TcSMonad
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import Bag
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import qualified Data.Map as Map
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import Control.Monad( unless )
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import FastString ( sLit ) 
import DynFlags
\end{code}

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Note [InertSet invariants]
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~~~~~~~~~~~~~~~~~~~~~~~~~~~
An InertSet is a bag of canonical constraints, with the following invariants:

  1 No two constraints react with each other. 
    
    A tricky case is when there exists a given (solved) dictionary 
    constraint and a wanted identical constraint in the inert set, but do 
    not react because reaction would create loopy dictionary evidence for 
    the wanted. See note [Recursive dictionaries]

  2 Given equalities form an idempotent substitution [none of the
    given LHS's occur in any of the given RHS's or reactant parts]

  3 Wanted equalities also form an idempotent substitution
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  4 The entire set of equalities is acyclic.

  5 Wanted dictionaries are inert with the top-level axiom set 

  6 Equalities of the form tv1 ~ tv2 always have a touchable variable
    on the left (if possible).
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  7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
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    will be marked as solved right before being pushed into the inert set. 
    See note [Touchables and givens].
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  8 No Given constraint mentions a touchable unification variable,
    except if the
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Note that 6 and 7 are /not/ enforced by canonicalization but rather by 
insertion in the inert list, ie by TcInteract. 

During the process of solving, the inert set will contain some
previously given constraints, some wanted constraints, and some given
constraints which have arisen from solving wanted constraints. For
now we do not distinguish between given and solved constraints.

Note that we must switch wanted inert items to given when going under an
implication constraint (when in top-level inference mode).

\begin{code}

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data CCanMap a = CCanMap { cts_givder  :: Map.Map a CanonicalCts
                                          -- Invariant: all Given or Derived
                         , cts_wanted  :: Map.Map a CanonicalCts } 
                                          -- Invariant: all Wanted
cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts 
cCanMapToBag cmap = Map.fold unionBags rest_cts  (cts_givder cmap)
  where rest_cts = Map.fold unionBags emptyCCan (cts_wanted cmap) 

emptyCCanMap :: CCanMap a 
emptyCCanMap = CCanMap { cts_givder = Map.empty, cts_wanted = Map.empty } 

updCCanMap:: Ord a => (a,CanonicalCt) -> CCanMap a -> CCanMap a 
updCCanMap (a,ct) cmap 
  = case cc_flavor ct of 
      Wanted {} 
          -> cmap { cts_wanted = Map.insertWith unionBags a this_ct (cts_wanted cmap) } 
      _ 
          -> cmap { cts_givder = Map.insertWith unionBags a this_ct (cts_givder cmap) }
  where this_ct = singleCCan ct 

getRelevantCts :: Ord a => a -> CCanMap a -> (CanonicalCts, CCanMap a) 
-- Gets the relevant constraints and returns the rest of the CCanMap
getRelevantCts a cmap 
    = let relevant = unionBags (Map.findWithDefault emptyCCan a (cts_wanted cmap)) 
                               (Map.findWithDefault emptyCCan a (cts_givder cmap)) 
          residual_map = cmap { cts_wanted = Map.delete a (cts_wanted cmap) 
                              , cts_givder = Map.delete a (cts_givder cmap) } 
      in (relevant, residual_map) 

extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a) 
-- Gets the wanted constraints and returns a residual CCanMap
extractUnsolvedCMap cmap = 
  let unsolved = Map.fold unionBags emptyCCan (cts_wanted cmap) 
  in (unsolved, cmap { cts_wanted = Map.empty})

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-- See Note [InertSet invariants]
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data InertSet 
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  = IS { inert_eqs          :: CanonicalCts               -- Equalities only (CTyEqCan)

       , inert_dicts        :: CCanMap Class              -- Dictionaries only 
       , inert_ips          :: CCanMap (IPName Name)      -- Implicit parameters 
       , inert_funeqs       :: CCanMap TyCon              -- Type family equalities only 
               -- This representation allows us to quickly get to the relevant 
               -- inert constraints when interacting a work item with the inert set.


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       , inert_fds  :: FDImprovements        -- List of pairwise improvements that have kicked in already
                                             -- and reside either in the worklist or in the inerts 
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       }
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tyVarsOfInert :: InertSet -> TcTyVarSet 
tyVarsOfInert (IS { inert_eqs    = eqs
                  , inert_dicts  = dictmap
                  , inert_ips    = ipmap
                  , inert_funeqs = funeqmap }) = tyVarsOfCanonicals cts 
  where cts = eqs `andCCan` cCanMapToBag dictmap 
                  `andCCan` cCanMapToBag ipmap `andCCan` cCanMapToBag funeqmap

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type FDImprovement  = (PredType,PredType) 
type FDImprovements = [(PredType,PredType)] 

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instance Outputable InertSet where
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  ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
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                , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is))) 
                , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is))) 
                , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
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                ]
                       
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emptyInert :: InertSet
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emptyInert = IS { inert_eqs    = Bag.emptyBag
                , inert_dicts  = emptyCCanMap
                , inert_ips    = emptyCCanMap
                , inert_funeqs = emptyCCanMap 
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                , inert_fds = [] }
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updInertSet :: InertSet -> AtomicInert -> InertSet 
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updInertSet is item 
  | isCTyEqCan item                     -- Other equality 
  = let eqs' = inert_eqs is `Bag.snocBag` item 
    in is { inert_eqs = eqs' } 
  | Just cls <- isCDictCan_Maybe item   -- Dictionary 
  = is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) } 
  | Just x  <- isCIPCan_Maybe item      -- IP 
  = is { inert_ips   = updCCanMap (x,item) (inert_ips is) }  
  | Just tc <- isCFunEqCan_Maybe item   -- Function equality 
  = is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
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  | otherwise 
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  = pprPanic "Unknown form of constraint!" (ppr item)
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updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet 
updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is } 
updInertSetFDImprs is Nothing    = is 
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foldISEqCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a 
-- Fold over the equalities of the inerts
foldISEqCtsM k z IS { inert_eqs = eqs } 
  = Bag.foldlBagM k z eqs 

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foldISEqCts :: (a -> AtomicInert -> a) -> a -> InertSet -> a
foldISEqCts k z IS { inert_eqs = eqs }
  = Bag.foldlBag k z eqs

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extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
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-- Postcondition: the canonical cts returnd are the very same as the 
-- WantedEvVars in their canonical form. 
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extractUnsolved is@(IS {inert_eqs = eqs}) 
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  = let is_solved  = is { inert_eqs    = solved_eqs
                        , inert_dicts  = solved_dicts
                        , inert_ips    = solved_ips
                        , inert_funeqs = solved_funeqs } 
    in (is_solved, unsolved)
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  where (unsolved_eqs, solved_eqs)       = Bag.partitionBag isWantedCt eqs 
        (unsolved_ips, solved_ips)       = extractUnsolvedCMap (inert_ips is) 
        (unsolved_dicts, solved_dicts)   = extractUnsolvedCMap (inert_dicts is) 
        (unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is) 
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        unsolved = unsolved_eqs `unionBags` 
                   unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs
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haveBeenImproved :: FDImprovements -> PredType -> PredType -> Bool 
haveBeenImproved [] _ _ = False 
haveBeenImproved ((pty1,pty2):fdimprs) pty1' pty2' 
 | tcEqPred pty1 pty1' && tcEqPred pty2 pty2' 
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 = True
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 | tcEqPred pty1 pty2' && tcEqPred pty2 pty1'
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 = True
 | otherwise
 = haveBeenImproved fdimprs pty1' pty2'
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getFDImprovements :: InertSet -> FDImprovements
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-- Return a list of the improvements that have kicked in so far 
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getFDImprovements = inert_fds
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\end{code}

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{-- DV: This note will go away! 

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Note [Touchables and givens]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Touchable variables will never show up in givens which are inputs to
the solver.  However, touchables may show up in givens generated by the flattener.  
For example,

  axioms:
    G Int ~ Char
    F Char ~ Int

  wanted:
    F (G alpha) ~w Int
  
canonicalises to

  G alpha ~g b
  F b ~w Int

which can be put in the inert set.  Suppose we also have a wanted

  alpha ~w Int

We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
Int.  Instead, after reacting alpha ~w Int with the whole inert set,
we observe that we can solve it by unifying alpha with Int, so we mark
it as solved and put it back in the *work list*. [We also immediately unify
alpha := Int, without telling anyone, see trySpontaneousSolve function, to 
avoid doing this in the end.]

Later, because it is solved (given, in effect), we can use it to rewrite 
G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually, 
we will dispatch the remaining wanted constraints using the top-level axioms.

Finally, note that after reacting a wanted equality with the entire inert set
we may end up with something like

  b ~w alpha

which we should flip around to generate the solved constraint alpha ~s b.

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-} 



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%*********************************************************************
%*                                                                   * 
*                      Main Interaction Solver                       *
*                                                                    *
**********************************************************************

Note [Basic plan] 
~~~~~~~~~~~~~~~~~
1. Canonicalise (unary)
2. Pairwise interaction (binary)
    * Take one from work list 
    * Try all pair-wise interactions with each constraint in inert
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   As an optimisation, we prioritize the equalities both in the 
   worklist and in the inerts. 

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3. Try to solve spontaneously for equalities involving touchables 
4. Top-level interaction (binary wrt top-level)
   Superclass decomposition belongs in (4), see note [Superclasses]

\begin{code}
type AtomicInert = CanonicalCt     -- constraint pulled from InertSet
type WorkItem    = CanonicalCt     -- constraint pulled from WorkList

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-- A mixture of Given, Wanted, and Derived constraints. 
-- We split between equalities and the rest to process equalities first. 
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type WorkList = CanonicalCts
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unionWorkLists :: WorkList -> WorkList -> WorkList 
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unionWorkLists = andCCan
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isEmptyWorkList :: WorkList -> Bool 
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isEmptyWorkList = isEmptyCCan 
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emptyWorkList :: WorkList
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emptyWorkList = emptyCCan
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workListFromCCan :: CanonicalCt -> WorkList 
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workListFromCCan = singleCCan
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------------------------
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data StopOrContinue 
  = Stop			-- Work item is consumed
  | ContinueWith WorkItem	-- Not consumed

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

-- Results after interacting a WorkItem as far as possible with an InertSet
data StageResult
  = SR { sr_inerts     :: InertSet
           -- The new InertSet to use (REPLACES the old InertSet)
       , sr_new_work   :: WorkList
           -- Any new work items generated (should be ADDED to the old WorkList)
           -- Invariant: 
           --    sr_stop = Just workitem => workitem is *not* in sr_inerts and
           --                               workitem is inert wrt to sr_inerts
       , sr_stop       :: StopOrContinue
       }

instance Outputable StageResult where
  ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
    = ptext (sLit "SR") <+> 
      braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
             	  , ptext (sLit "new work =") <+> ppr work <> comma
             	  , ptext (sLit "stop =") <+> ppr stop])

type SimplifierStage = WorkItem -> InertSet -> TcS StageResult 

-- Combine a sequence of simplifier 'stages' to create a pipeline 
runSolverPipeline :: [(String, SimplifierStage)]
                  -> InertSet -> WorkItem 
                  -> TcS (InertSet, WorkList)
-- Precondition: non-empty list of stages 
runSolverPipeline pipeline inerts workItem
  = do { traceTcS "Start solver pipeline" $ 
            vcat [ ptext (sLit "work item =") <+> ppr workItem
                 , ptext (sLit "inerts    =") <+> ppr inerts]

       ; let itr_in = SR { sr_inerts = inerts
                        , sr_new_work = emptyWorkList
                        , sr_stop = ContinueWith workItem }
       ; itr_out <- run_pipeline pipeline itr_in
       ; let new_inert 
              = case sr_stop itr_out of 
       	          Stop              -> sr_inerts itr_out
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                  ContinueWith item -> sr_inerts itr_out `updInertSet` item
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       ; return (new_inert, sr_new_work itr_out) }
  where 
    run_pipeline :: [(String, SimplifierStage)]
                 -> StageResult -> TcS StageResult
    run_pipeline [] itr                         = return itr
    run_pipeline _  itr@(SR { sr_stop = Stop }) = return itr

    run_pipeline ((name,stage):stages) 
                 (SR { sr_new_work = accum_work
                     , sr_inerts   = inerts
                     , sr_stop     = ContinueWith work_item })
      = do { itr <- stage work_item inerts 
           ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
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           ; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
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           ; run_pipeline stages itr' }
\end{code}

Example 1:
  Inert:   {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
  Reagent: a ~ [b] (given)

React with (c~d)     ==> IR (ContinueWith (a~[b]))  True    []
React with (F a ~ t) ==> IR (ContinueWith (a~[b]))  False   [F [b] ~ t]
React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True    []

Example 2:
  Inert:  {c ~w d, F a ~g t, b ~w Int, a ~w ty}
  Reagent: a ~w [b]

React with (c ~w d)   ==> IR (ContinueWith (a~[b]))  True    []
React with (F a ~g t) ==> IR (ContinueWith (a~[b]))  True    []    (can't rewrite given with wanted!)
etc.

Example 3:
  Inert:  {a ~ Int, F Int ~ b} (given)
  Reagent: F a ~ b (wanted)

React with (a ~ Int)   ==> IR (ContinueWith (F Int ~ b)) True []
React with (F Int ~ b) ==> IR Stop True []    -- after substituting we re-canonicalize and get nothing

\begin{code}
-- Main interaction solver: we fully solve the worklist 'in one go', 
-- returning an extended inert set.
--
-- See Note [Touchables and givens].
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solveInteract :: InertSet -> Bag (CtFlavor,EvVar) -> TcS InertSet
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solveInteract inert ws 
  = do { dyn_flags <- getDynFlags
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       ; sctx <- getTcSContext 

       ; traceTcS "solveInteract, before clever canonicalization:" $ 
         ppr (mapBag (\(ct,ev) -> (ct,evVarPred ev)) ws)

       ; can_ws    <- foldlBagM (tryPreSolveAndCanon sctx inert) emptyCCan ws

       ; traceTcS "solveInteract, after clever canonicalization:" $ 
         ppr can_ws

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       ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert can_ws }

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tryPreSolveAndCanon :: SimplContext -> InertSet -> CanonicalCts -> (CtFlavor, EvVar) -> TcS CanonicalCts
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-- Checks if this constraint can be immediately solved from a constraint in the 
-- inert set or in the previously encountered CanonicalCts and only then  
-- canonicalise it. See Note [Avoiding the superclass explosion]
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tryPreSolveAndCanon sctx is cts_acc (fl,ev_var)
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  | ClassP clas tys <- evVarPred ev_var 
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  , not $ simplEqsOnly sctx -- And we *can* discharge constraints from other constraints
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  = do { let (relevant_inert_dicts,_) = getRelevantCts clas (inert_dicts is) 
       ; b <- dischargeFromCans (cts_acc `unionBags` relevant_inert_dicts)
                                (fl,ev_var,clas,tys)
       ; extra_cts <- if b then return emptyCCan else mkCanonical fl ev_var 
       ; return (cts_acc `unionBags` extra_cts) }
  | otherwise 
  = do { extra_cts <- mkCanonical fl ev_var
       ; return (cts_acc `unionBags` extra_cts) }

dischargeFromCans :: CanonicalCts -> (CtFlavor,EvVar,Class,[Type]) -> TcS Bool
dischargeFromCans cans (fl,ev,clas,tys) 
  = Bag.foldlBagM discharge_ct False cans 
  where discharge_ct :: Bool -> CanonicalCt -> TcS Bool 
        discharge_ct True _ct = return True
        discharge_ct False (CDictCan { cc_id = ev1, cc_flavor = fl1
                                     , cc_class = clas1, cc_tyargs = tys1 })
          | clas1 == clas
          , (and $ zipWith tcEqType tys tys1)
          , fl1 `canSolve` fl 
          = setEvBind ev (EvId ev1) >> return True
        discharge_ct False _ct = return False
\end{code}

Note [Avoiding the superclass explosion] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Consider the example: 
  f = [(0,1,0,1,0)] 
We have 5 wanted (Num alpha) constraints. If we simply try to canonicalize and add them
in our worklist, we will also get all of their superclasses as Derived, hence we will 
have an inert set that contains 5*n constraints, where n is the number of superclasses 
of of Num. That is bad for the additional reason that we keep *all* the Derived, even 
for identical class constraints (for reasons related to recursive dictionaries). 

Instead, what we do with tryPreSolveAndCanon, is when we encounter a new constraint, 
such as the second (Num alpha) above we very quickly see if it can be immediately 
discharged by a class constraint in our inert set or the previous canonicals. If so, 
we add nothing to the returned canonical constraints.

For our particular example this will reduce the size of the inert set that we use from 
5*n to just n. And hence the number of all possible interactions that we have to look 
through is significantly smaller!

\begin{code}
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solveOne :: InertSet -> WorkItem -> TcS InertSet 
solveOne inerts workItem 
  = do { dyn_flags <- getDynFlags
       ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
       }

-----------------
solveInteractWithDepth :: (Int, Int, [WorkItem])
                       -> InertSet -> WorkList -> TcS InertSet
solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws 
  | isEmptyWorkList ws
  = return inert

  | n > max_depth 
  = solverDepthErrorTcS n stack

  | otherwise 
  = do { traceTcS "solveInteractWithDepth" $ 
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              vcat [ text "Current depth =" <+> ppr n
                   , text "Max depth =" <+> ppr max_depth ]

	      -- Solve equalities first
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       ; let (eqs, non_eqs) = Bag.partitionBag isCTyEqCan ws
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       ; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
       ; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
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------------------
-- Fully interact the given work item with an inert set, and return a
-- new inert set which has assimilated the new information.
solveOneWithDepth :: (Int, Int, [WorkItem])
                  -> InertSet -> WorkItem -> TcS InertSet
solveOneWithDepth (max_depth, n, stack) inert work
  = do { traceTcS0 (indent ++ "Solving {") (ppr work)
       ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
         
       ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)

	 -- Recursively solve the new work generated 
         -- from workItem, with a greater depth
       ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack)
                                new_inert new_work 

       ; traceTcS0 (indent ++ "Done }") (ppr work) 
       ; return res_inert }
  where
    indent = replicate (2*n) ' '

thePipeline :: [(String,SimplifierStage)]
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thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
              , ("interact with inerts",    interactWithInertsStage)
              , ("spontaneous solve",       spontaneousSolveStage)
              , ("top-level reactions",     topReactionsStage) ]
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\end{code}

*********************************************************************************
*                                                                               * 
                       The spontaneous-solve Stage
*                                                                               *
*********************************************************************************

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Note [Efficient Orientation] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are two cases where we have to be careful about 
orienting equalities to get better efficiency. 

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Case 1: In Rewriting Equalities (function rewriteEqLHS) 
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    When rewriting two equalities with the same LHS:
          (a)  (tv ~ xi1) 
          (b)  (tv ~ xi2) 
    We have a choice of producing work (xi1 ~ xi2) (up-to the
    canonicalization invariants) However, to prevent the inert items
    from getting kicked out of the inerts first, we prefer to
    canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
    ~ xi1) if (a) comes from the inert set.
    
    This choice is implemented using the WhichComesFromInert flag. 
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Case 2: Functional Dependencies 
    Again, we should prefer, if possible, the inert variables on the RHS

Case 3: IP improvement work
    We must always rewrite so that the inert type is on the right. 
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\begin{code}
spontaneousSolveStage :: SimplifierStage 
spontaneousSolveStage workItem inerts 
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  = do { mSolve <- trySpontaneousSolve workItem

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       ; case mSolve of 
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           SPCantSolve -> -- No spontaneous solution for him, keep going
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               return $ SR { sr_new_work   = emptyWorkList
                           , sr_inerts     = inerts
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                           , sr_stop       = ContinueWith workItem }

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           SPSolved workItem'
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               | not (isGivenCt workItem) 
	       	 -- Original was wanted or derived but we have now made him 
                 -- given so we have to interact him with the inerts due to
                 -- its status change. This in turn may produce more work.
		 -- We do this *right now* (rather than just putting workItem'
		 -- back into the work-list) because we've solved 
               -> do { (new_inert, new_work) <- runSolverPipeline 
                             [ ("recursive interact with inert eqs", interactWithInertEqsStage)
                             , ("recursive interact with inerts", interactWithInertsStage)
                             ] inerts workItem'
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                     ; return $ SR { sr_new_work = new_work 
                                   , sr_inerts   = new_inert -- will include workItem' 
                                   , sr_stop     = Stop }
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                     }
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               | otherwise 
                   -> -- Original was given; he must then be inert all right, and
                      -- workList' are all givens from flattening
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                      return $ SR { sr_new_work = emptyWorkList
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                                  , sr_inerts   = inerts `updInertSet` workItem' 
                                  , sr_stop     = Stop }
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           SPError -> -- Return with no new work
               return $ SR { sr_new_work = emptyWorkList
                           , sr_inerts   = inerts
                           , sr_stop     = Stop }
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       }
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data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
-- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
-- SPSolved workItem' gives us a new *given* to go on 
-- SPError means that it's completely impossible to solve this equality, eg due to a kind error


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-- @trySpontaneousSolve wi@ solves equalities where one side is a
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-- touchable unification variable.
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--     	    See Note [Touchables and givens] 
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trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
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  | isGiven gw
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  = return SPCantSolve
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  | Just tv2 <- tcGetTyVar_maybe xi
  = do { tch1 <- isTouchableMetaTyVar tv1
       ; tch2 <- isTouchableMetaTyVar tv2
       ; case (tch1, tch2) of
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           (True,  True)  -> trySpontaneousEqTwoWay cv gw tv1 tv2
           (True,  False) -> trySpontaneousEqOneWay cv gw tv1 xi
           (False, True)  -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
	   _ -> return SPCantSolve }
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  | otherwise
  = do { tch1 <- isTouchableMetaTyVar tv1
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       ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
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                 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:" (ppr workItem) 
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                         ; return SPCantSolve }
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       }
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  -- No need for 
  --      trySpontaneousSolve (CFunEqCan ...) = ...
  -- See Note [No touchables as FunEq RHS] in TcSMonad
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trySpontaneousSolve _ = return SPCantSolve
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----------------
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trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
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-- tv is a MetaTyVar, not untouchable
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trySpontaneousEqOneWay cv gw tv xi	
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  | not (isSigTyVar tv) || isTyVarTy xi 
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  = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts 
                               -- so we have its more specific kind in our hands
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       ; if kxi `isSubKind` tyVarKind tv then
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             solveWithIdentity cv gw tv xi
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         else if tyVarKind tv `isSubKind` kxi then 
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             return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
                                -- This case covers the  a_touchable :: * ~ b_untouchable :: ?? 
                                -- which has to be deferred or floated out for someone else to solve 
                                -- it in a scope where 'b' is no longer untouchable.
         else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
                 ; return SPError }
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       }
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  | otherwise -- Still can't solve, sig tyvar and non-variable rhs
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  = return SPCantSolve
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----------------
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trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
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-- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
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trySpontaneousEqTwoWay cv gw tv1 tv2
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  | k1 `isSubKind` k2
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  , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
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  | k2 `isSubKind` k1 
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  = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
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  | otherwise -- None is a subkind of the other, but they are both touchable! 
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  = do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
       ; return SPError }
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  where
    k1 = tyVarKind tv1
    k2 = tyVarKind tv2
    nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
\end{code}

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Note [Kind errors] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the wanted problem: 
      alpha ~ (# Int, Int #) 
where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint, 
but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay' 
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simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and 
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get quantified over in inference mode. That's bad because we do know at this point that the 
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constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
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The same applies in canonicalization code in case of kind errors in the givens. 
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However, when we canonicalize givens we only check for compatibility (@compatKind@). 
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If there were a kind error in the givens, this means some form of inconsistency or dead code.
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You may think that when we spontaneously solve wanteds we may have to look through the 
bindings to determine the right kind of the RHS type. E.g one may be worried that xi is 
@alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
so this situation can't happen. 
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Note [Spontaneous solving and kind compatibility] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note that our canonical constraints insist that only *given* equalities (tv ~ xi) 
or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds. 

  - We have to require this because: 
        Given equalities can be freely used to rewrite inside 
        other types or constraints.
  - We do not have to do the same for wanteds because:
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        First, wanted equations (tv ~ xi) where tv is a touchable
        unification variable may have kinds that do not agree (the
        kind of xi must be a sub kind of the kind of tv).  Second, any
        potential kind mismatch will result in the constraint not
        being soluble, which will be reported anyway. This is the
        reason that @trySpontaneousOneWay@ and @trySpontaneousTwoWay@
        will perform a kind compatibility check, and only then will
        they proceed to @solveWithIdentity@.
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Caveat: 
  - Givens from higher-rank, such as: 
          type family T b :: * -> * -> * 
          type instance T Bool = (->) 

          f :: forall a. ((T a ~ (->)) => ...) -> a -> ... 
          flop = f (...) True 
     Whereas we would be able to apply the type instance, we would not be able to 
     use the given (T Bool ~ (->)) in the body of 'flop' 

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Note [Avoid double unifications] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The spontaneous solver has to return a given which mentions the unified unification
variable *on the left* of the equality. Here is what happens if not: 
  Original wanted:  (a ~ alpha),  (alpha ~ Int) 
We spontaneously solve the first wanted, without changing the order! 
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      given : a ~ alpha      [having unified alpha := a] 
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Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
At the end we spontaneously solve that guy, *reunifying*  [alpha := Int] 

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We avoid this problem by orienting the resulting given so that the unification
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variable is on the left.  [Note that alternatively we could attempt to
enforce this at canonicalization]
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See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
double unifications is the main reason we disallow touchable
unification variables as RHS of type family equations: F xis ~ alpha.
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\begin{code}
----------------
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solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
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-- Solve with the identity coercion 
-- Precondition: kind(xi) is a sub-kind of kind(tv)
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-- Precondition: CtFlavor is Wanted or Derived
-- See [New Wanted Superclass Work] to see why solveWithIdentity 
--     must work for Derived as well as Wanted
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-- Returns: workItem where 
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--        workItem = the new Given constraint
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solveWithIdentity cv wd tv xi 
  = do { traceTcS "Sneaky unification:" $ 
                       vcat [text "Coercion variable:  " <+> ppr wd, 
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                             text "Coercion:           " <+> pprEq (mkTyVarTy tv) xi,
                             text "Left  Kind is     : " <+> ppr (typeKind (mkTyVarTy tv)),
                             text "Right Kind is     : " <+> ppr (typeKind xi)
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                  ]
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       ; setWantedTyBind tv xi        -- Set tv := xi_unflat
       ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi xi

       ; case wd of Wanted {}  -> setWantedCoBind cv xi 
                    Derived {} -> setDerivedCoBind cv xi
                    _ -> pprPanic "Can't spontaneously solve given!" empty

       ; return $ SPSolved (CTyEqCan { cc_id = cv_given
                                     , cc_flavor = mkGivenFlavor wd UnkSkol
                                     , cc_tyvar  = tv, cc_rhs = xi })
       }
                  
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\end{code}


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*********************************************************************************
*                                                                               * 
                       The interact-with-inert Stage
*                                                                               *
*********************************************************************************

\begin{code}
-- Interaction result of  WorkItem <~> AtomicInert
data InteractResult
   = IR { ir_stop         :: StopOrContinue
            -- Stop
            --   => Reagent (work item) consumed.
            -- ContinueWith new_reagent
            --   => Reagent transformed but keep gathering interactions. 
            --      The transformed item remains inert with respect 
            --      to any previously encountered inerts.

        , ir_inert_action :: InertAction
            -- Whether the inert item should remain in the InertSet.

        , ir_new_work     :: WorkList
            -- new work items to add to the WorkList
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        , ir_improvement  :: Maybe FDImprovement -- In case improvement kicked in
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        }

-- What to do with the inert reactant.
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data InertAction = KeepInert 
                 | DropInert 
                 | KeepTransformedInert CanonicalCt -- Keep a slightly transformed inert
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mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
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mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing 
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mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
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mkIRStop keep newWork = return $ IR Stop keep newWork Nothing

mkIRStop_RecordImprovement :: Monad m => InertAction -> WorkList -> FDImprovement -> m InteractResult 
mkIRStop_RecordImprovement keep newWork fdimpr = return $ IR Stop keep newWork (Just fdimpr) 

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dischargeWorkItem :: Monad m => m InteractResult
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dischargeWorkItem = mkIRStop KeepInert emptyWorkList
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noInteraction :: Monad m => WorkItem -> m InteractResult
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noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
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data WhichComesFromInert = LeftComesFromInert | RightComesFromInert 
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     -- See Note [Efficient Orientation] 
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---------------------------------------------------
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-- Interact a single WorkItem with the equalities of an inert set as far as possible, i.e. until we 
-- get a Stop result from an individual reaction (i.e. when the WorkItem is consumed), or until we've 
-- interact the WorkItem with the entire equalities of the InertSet

interactWithInertEqsStage :: SimplifierStage 
interactWithInertEqsStage workItem inert
  = foldISEqCtsM interactNext initITR inert 
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  where initITR = SR { sr_inerts   = IS { inert_eqs    = emptyCCan -- Will fold over equalities
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                                        , inert_dicts  = inert_dicts inert
                                        , inert_ips    = inert_ips inert 
                                        , inert_funeqs = inert_funeqs inert
                                        , inert_fds    = inert_fds inert
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                                        }
                     , sr_new_work = emptyWorkList
                     , sr_stop     = ContinueWith workItem }

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---------------------------------------------------
-- Interact a single WorkItem with *non-equality* constraints in the inert set. 
-- Precondition: equality interactions must have already happened, hence we have 
-- to pick up some information from the incoming inert, before folding over the 
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-- "Other" constraints it contains!

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interactWithInertsStage :: SimplifierStage
interactWithInertsStage workItem inert
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  = let (relevant, inert_residual) = getISRelevant workItem inert 
        initITR = SR { sr_inerts   = inert_residual
                     , sr_new_work = emptyWorkList
                     , sr_stop     = ContinueWith workItem } 
    in Bag.foldlBagM interactNext initITR relevant 
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  where 
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    getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet) 
    getISRelevant (CDictCan { cc_class = cls } ) is 
      = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is) 
        in (relevant, is { inert_dicts = residual_map }) 
    getISRelevant (CFunEqCan { cc_fun = tc } ) is 
      = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is) 
        in (relevant, is { inert_funeqs = residual_map })
    getISRelevant (CIPCan { cc_ip_nm = nm }) is 
      = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
        in (relevant, is { inert_ips = residual_map }) 
    -- An equality, finally, may kick everything except equalities out 
    -- because we have already interacted the equalities in interactWithInertEqsStage
    getISRelevant _eq_ct is  -- Equality, everything is relevant for this one 
                             -- TODO: if we were caching variables, we'd know that only 
                             --       some are relevant. Experiment with this for now. 
      = let cts = cCanMapToBag (inert_ips is) `unionBags` 
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                    cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
        in (cts, is { inert_dicts  = emptyCCanMap
                    , inert_ips    = emptyCCanMap
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                    , inert_funeqs = emptyCCanMap })
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interactNext :: StageResult -> AtomicInert -> TcS StageResult 
interactNext it inert  
  | ContinueWith workItem <- sr_stop it
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  = do { let inerts      = sr_inerts it 
             fdimprs_old = getFDImprovements inerts 

       ; ir <- interactWithInert fdimprs_old inert workItem 

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       -- New inerts depend on whether we KeepInert or not and must
       -- be updated with FD improvement information from the interaction result (ir)
       ; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir)
             upd_inert  = case ir_inert_action ir of
                            KeepInert                   -> inerts `updInertSet` inert
                            DropInert                   -> inerts
                            KeepTransformedInert inert' -> inerts `updInertSet` inert'
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       ; return $ SR { sr_inerts   = inerts_new
                     , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
                     , sr_stop     = ir_stop ir } }
  | otherwise 
  = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
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-- Do a single interaction of two constraints.
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interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
interactWithInert fdimprs inert workitem 
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  =  do { ctxt <- getTcSContext
        ; let is_allowed  = allowedInteraction (simplEqsOnly ctxt) inert workitem 
              inert_ev    = cc_id inert 
              work_ev     = cc_id workitem 

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        -- Never interact a wanted and a derived where the derived's evidence
        -- mentions the wanted evidence in an unguarded way.
        -- See Note [Superclasses and recursive dictionaries]
        -- and Note [New Wanted Superclass Work]
        -- We don't have to do this for givens, as we fully know the evidence for them.
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        ; rec_ev_ok <- 
            case (cc_flavor inert, cc_flavor workitem) of 
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              (Wanted {}, Derived {}) -> isGoodRecEv work_ev  inert_ev
              (Derived {}, Wanted {}) -> isGoodRecEv inert_ev work_ev
              _                       -> return True
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        ; if is_allowed && rec_ev_ok then 
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              doInteractWithInert fdimprs inert workitem 
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          else 
              noInteraction workitem 
        }

allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool 
-- Allowed interactions 
allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
allowedInteraction eqs_only (CIPCan {})   (CIPCan {})   = not eqs_only
allowedInteraction _ _ _ = True 

--------------------------------------------
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doInteractWithInert :: FDImprovements -> CanonicalCt -> CanonicalCt -> TcS InteractResult
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-- Identical class constraints.

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doInteractWithInert fdimprs
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           (CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 }) 
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  workItem@(CDictCan { cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
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  | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
  = solveOneFromTheOther (d1,fl1) workItem 

  | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
  = 	 -- See Note [When improvement happens]
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    do { let pty1 = ClassP cls1 tys1
             pty2 = ClassP cls2 tys2
             work_item_pred_loc = (pty2, pprFlavorArising fl2)
             inert_pred_loc     = (pty1, pprFlavorArising fl1)
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	     loc                = combineCtLoc fl1 fl2
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             eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
                             -- See Note [Efficient Orientation]
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       ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs 
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       ; fd_work <- canWanteds wevvars 
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              	 -- See Note [Generating extra equalities]
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       ; traceTcS "Checking if improvements existed." (ppr fdimprs)
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       ; if isEmptyWorkList fd_work || haveBeenImproved fdimprs pty1 pty2 then
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             -- Must keep going
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             mkIRContinue workItem KeepInert fd_work 
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         else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
                 ; mkIRStop_RecordImprovement KeepInert 
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                      (fd_work `unionWorkLists` workListFromCCan workItem) (pty1,pty2)
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                 }
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         -- See Note [FunDep Reactions]
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       }

-- Class constraint and given equality: use the equality to rewrite
-- the class constraint. 
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doInteractWithInert _fdimprs
                    (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi }) 
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                    (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis }) 
  | ifl `canRewrite` wfl 
  , tv `elemVarSet` tyVarsOfTypes xis
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  = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
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            -- Continue with rewritten Dictionary because we can only be in the 
            -- interactWithEqsStage, so the dictionary is inert. 
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       ; mkIRContinue rewritten_dict KeepInert emptyWorkList }
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doInteractWithInert _fdimprs 
                    (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis }) 
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           workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
  | wfl `canRewrite` ifl
  , tv `elemVarSet` tyVarsOfTypes xis
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  = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
       ; mkIRContinue workItem DropInert (workListFromCCan rewritten_dict) }
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-- Class constraint and given equality: use the equality to rewrite
-- the class constraint.
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doInteractWithInert _fdimprs 
                    (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi }) 
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                    (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty }) 
  | ifl `canRewrite` wfl
  , tv `elemVarSet` tyVarsOfType ty 
  = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty) 
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       ; mkIRContinue rewritten_ip KeepInert emptyWorkList } 
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doInteractWithInert _fdimprs 
                    (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty }) 
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           workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
  | wfl `canRewrite` ifl
  , tv `elemVarSet` tyVarsOfType ty
  = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty) 
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       ; mkIRContinue workItem DropInert (workListFromCCan rewritten_ip) }
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-- Two implicit parameter constraints.  If the names are the same,
-- but their types are not, we generate a wanted type equality 
-- that equates the type (this is "improvement").  
-- However, we don't actually need the coercion evidence,
-- so we just generate a fresh coercion variable that isn't used anywhere.
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doInteractWithInert _fdimprs 
                    (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 }) 
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           workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
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  | nm1 == nm2 && isGiven wfl && isGiven ifl
  = 	-- See Note [Overriding implicit parameters]
        -- Dump the inert item, override totally with the new one
	-- Do not require type equality
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    mkIRContinue workItem DropInert emptyWorkList
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  | nm1 == nm2 && ty1 `tcEqType` ty2 
  = solveOneFromTheOther (id1,ifl) workItem 

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  | nm1 == nm2
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  =  	-- See Note [When improvement happens]
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    do { co_var <- newWantedCoVar ty2 ty1 -- See Note [Efficient Orientation]
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       ; let flav = Wanted (combineCtLoc ifl wfl) 
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       ; cans <- mkCanonical flav co_var 
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       ; mkIRContinue workItem KeepInert cans }
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-- Never rewrite a given with a wanted equality, and a type function
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-- equality can never rewrite an equality. We rewrite LHS *and* RHS 
-- of function equalities so that our inert set exposes everything that 
-- we know about equalities.
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-- Inert: equality, work item: function equality
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doInteractWithInert _fdimprs
                    (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 }) 
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                    (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
                               , cc_tyargs = args, cc_rhs = xi2 })
  | ifl `canRewrite` wfl 
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  , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
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  = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2) 
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       ; mkIRStop KeepInert (workListFromCCan rewritten_funeq) } 
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         -- Must Stop here, because we may no longer be inert after the rewritting.
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-- Inert: function equality, work item: equality
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doInteractWithInert _fdimprs
                    (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
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                              , cc_tyargs = args, cc_rhs = xi1 }) 
           workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
  | wfl `canRewrite` ifl
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  , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
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  = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1) 
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       ; mkIRContinue workItem DropInert (workListFromCCan rewritten_funeq) } 
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         -- One may think that we could (KeepTransformedInert rewritten_funeq) 
         -- but that is wrong, because it may end up not being inert with respect 
         -- to future inerts. Example: 
         -- Original inert = {    F xis ~  [a], b ~ Maybe Int } 
         -- Work item comes along = a ~ [b] 
         -- If we keep { F xis ~ [b] } in the inert set we will end up with: 
         --      { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] } 
         -- At the end, which is *not* inert. So we should unfortunately DropInert here.
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doInteractWithInert _fdimprs
                    (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
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                               , cc_tyargs = args1, cc_rhs = xi1 }) 
           workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
                               , cc_tyargs = args2, cc_rhs = xi2 })
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  | fl1 `canSolve` fl2 && lhss_match
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  = do { cans <- rewriteEqLHS LeftComesFromInert  (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2) 
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       ; mkIRStop KeepInert cans } 
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  | fl2 `canSolve` fl1 && lhss_match
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  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1) 
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       ; mkIRContinue workItem DropInert cans }
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  where
    lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2) 

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doInteractWithInert _fdimprs 
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           (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 }) 
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           workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
-- Check for matching LHS 
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  | fl1 `canSolve` fl2 && tv1 == tv2 
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  = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2) 
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       ; mkIRStop KeepInert cans } 
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  | fl2 `canSolve` fl1 && tv1 == tv2 
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  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1) 
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       ; mkIRContinue workItem DropInert cans }
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-- Check for rewriting RHS 
  | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2 
  = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2) 
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       ; mkIRStop KeepInert rewritten_eq }
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  | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
  = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1) 
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       ; mkIRContinue workItem DropInert rewritten_eq } 
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-- Fall-through case for all other situations
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doInteractWithInert _fdimprs _ workItem = noInteraction workItem
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-------------------------
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-- Equational Rewriting 
rewriteDict  :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
rewriteDict (cv,tv,xi) (dv,gw,cl,xis) 
  = do { let cos  = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
             args = substTysWith [tv] [xi] xis
             con  = classTyCon cl 
             dict_co = mkTyConCoercion con cos 
       ; dv' <- newDictVar cl args 
       ; case gw of 
           Wanted {}         -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
           _given_or_derived -> setDictBind dv' (EvCast dv dict_co) 
       ; return (CDictCan { cc_id = dv'
                          , cc_flavor = gw 
                          , cc_class = cl 
                          , cc_tyargs = args }) } 

rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt 
rewriteIP (cv,tv,xi) (ipid,gw,nm,ty) 
  = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty     -- ty[tv] ~ t[xi] 
             ty'   = substTyWith [tv] [xi] ty
       ; ipid' <- newIPVar nm ty' 
       ; case gw of 
           Wanted {}         -> setIPBind ipid  (EvCast ipid' (mkSymCoercion ip_co))
           _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co) 
       ; return (CIPCan { cc_id = ipid'
                        , cc_flavor = gw
                        , cc_ip_nm = nm
                        , cc_ip_ty = ty' }) }
   
rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
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rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2)                   -- cv2 :: F args ~ xi2
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  = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args 
             args'   = substTysWith [tv] [xi1] args 
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             fun_co  = mkTyConCoercion tc arg_cos                 -- fun_co :: F args ~ F args'

             xi2'    = substTyWith [tv] [xi1] xi2
             xi2_co  = substTyWith [tv] [mkCoVarCoercion cv1] xi2 -- xi2_co :: xi2 ~ xi2' 
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       ; cv2' <- case gw of 
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                   Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2'
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                                   ; setWantedCoBind cv2 $ 
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                                     fun_co `mkTransCoercion` 
                                            mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion xi2_co
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                                   ; return cv2' } 
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                   _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2' $
                                  mkSymCoercion fun_co `mkTransCoercion` 
                                                mkCoVarCoercion cv2 `mkTransCoercion` xi2_co
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       ; return (CFunEqCan { cc_id = cv2'
                           , cc_flavor = gw
                           , cc_tyargs = args'
                           , cc_fun = tc 
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                           , cc_rhs = xi2' }) }
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rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
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-- Use the first equality to rewrite the second, flavors already checked. 
-- E.g.          c1 : tv1 ~ xi1   c2 : tv2 ~ xi2
-- rewrites c2 to give
--               c2' : tv2 ~ xi2[xi1/tv1]
-- We must do an occurs check to sure the new constraint is canonical
-- So we might return an empty bag
rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2) 
  | Just tv2' <- tcGetTyVar_maybe xi2'
  , tv2 == tv2'	 -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
  = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2')) 
       ; return emptyCCan } 
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  | otherwise
  = do { cv2' <-
           case gw of
             Wanted {}
                 -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2'
                       ; setWantedCoBind cv2 $
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                         mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion co2'
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                       ; return cv2' }
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             _giv_or_der 
                 -> newGivOrDerCoVar (mkTyVarTy tv2) xi2' $ 
                    mkCoVarCoercion cv2 `mkTransCoercion` co2'

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       ; canEq gw cv2' (mkTyVarTy tv2) xi2' 
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       }
  where 
    xi2' = substTyWith [tv1] [xi1] xi2 
    co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2  -- xi2 ~ xi2[xi1/tv1]

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rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
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-- Used to ineract two equalities of the following form: 
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-- First Equality:   co1: (XXX ~ xi1)  
-- Second Equality:  cv2: (XXX ~ xi2) 
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-- Where the cv1 `canSolve` cv2 equality 
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-- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1), 
--    See Note [Efficient Orientation] for that 
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rewriteEqLHS which (co1,xi1) (cv2,gw,xi2) 
  = do { cv2' <- case (isWanted gw, which) of 
                   (True,LeftComesFromInert) ->
                       do { cv2' <- newWantedCoVar xi2 xi1 
                          ; setWantedCoBind cv2 $ 
                            co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
                          ; return cv2' } 
                   (True,RightComesFromInert) -> 
                       do { cv2' <- newWantedCoVar xi1 xi2 
                          ; setWantedCoBind cv2 $ 
                            co1 `mkTransCoercion` mkCoVarCoercion cv2'
                          ; return cv2' } 
                   (False,LeftComesFromInert) ->
                       newGivOrDerCoVar xi2 xi1 $ 
                       mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1 
                   (False,RightComesFromInert) -> 
                        newGivOrDerCoVar xi1 xi2 $ 
                        mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
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       ; mkCanonical gw cv2'
       }
                                           
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solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult 
-- First argument inert, second argument workitem. They both represent 
-- wanted/given/derived evidence for the *same* predicate so we try here to 
-- discharge one directly from the other. 
--
-- Precondition: value evidence only (implicit parameters, classes) 
--               not coercion
solveOneFromTheOther (iid,ifl) workItem 
      -- Both derived needs a special case. You might think that we do not need
      -- two evidence terms for the same claim. But, since the evidence is partial, 
      -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
      -- See also Example 3 in Note [Superclasses and recursive dictionaries] 
  | isDerived ifl && isDerived wfl 
  = noInteraction workItem 

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  | ifl `canSolve` wfl
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  = do { unless (isGiven wfl) $ setEvBind wid (EvId iid) 
           -- Overwrite the binding, if one exists
	   -- For Givens, which are lambda-bound, nothing to overwrite,
       ; dischargeWorkItem }

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  | otherwise  -- wfl `canSolve` ifl 
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  = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)