    {-# LANGUAGE CPP #-}

    module TcInteract (
         solveSimpleGivens,    -- Solves [EvVar],GivenLoc
         solveSimpleWanteds    -- Solves Cts
      ) where

    #include "HsVersions.h"

    import BasicTypes ()
    import HsTypes ( hsIPNameFS )
    import FastString
    import TcCanonical
    import TcFlatten
    import VarSet
    import Type
    import Kind (isKind, isConstraintKind )
    import Unify
    import InstEnv( lookupInstEnv, instanceDFunId )
    import CoAxiom(sfInteractTop, sfInteractInert)

    import Var
    import TcType
    import PrelNames ( knownNatClassName, knownSymbolClassName, ipClassNameKey
                     , typeableClassName, callStackTyConKey )
    import Id( idType )
    import Class
    import TyCon
    import FunDeps
    import FamInst
    import Inst( tyVarsOfCt )

    import TcEvidence
    import Outputable

    import TcRnTypes
    import TcErrors
    import TcSMonad
    import Bag

    import Data.List( partition, foldl', deleteFirstsBy )

    import VarEnv

    import Control.Monad
    import Pair (Pair(..))
    import Unique( hasKey )
    import DynFlags
    import Util

    {-
    **********************************************************************
    *                                                                    *
    *                      Main Interaction Solver                       *
    *                                                                    *
    **********************************************************************

    Note [Basic Simplifier Plan]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    1. Pick an element from the WorkList if there exists one with depth
       less than our context-stack depth.

    2. Run it down the 'stage' pipeline. Stages are:
          - canonicalization
          - inert reactions
          - spontaneous reactions
          - top-level intreactions
       Each stage returns a StopOrContinue and may have sideffected
       the inerts or worklist.

       The threading of the stages is as follows:
          - If (Stop) is returned by a stage then we start again from Step 1.
          - If (ContinueWith ct) is returned by a stage, we feed 'ct' on to
            the next stage in the pipeline.
    4. If the element has survived (i.e. ContinueWith x) the last stage
       then we add him in the inerts and jump back to Step 1.

    If in Step 1 no such element exists, we have exceeded our context-stack
    depth and will simply fail.

    Note [Unflatten after solving the simple wanteds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We unflatten after solving the wc_simples of an implication, and before attempting
    to float. This means that

     * The fsk/fmv flatten-skolems only survive during solveSimples.  We don't
       need to worry about then across successive passes over the constraint tree.
       (E.g. we don't need the old ic_fsk field of an implication.

     * When floating an equality outwards, we don't need to worry about floating its
       associated flattening constraints.

     * Another tricky case becomes easy: Trac #4935
           type instance F True a b = a
           type instance F False a b = b

           [w] F c a b ~ gamma
           (c ~ True) => a ~ gamma
           (c ~ False) => b ~ gamma

       Obviously this is soluble with gamma := F c a b, and unflattening
       will do exactly that after solving the simple constraints and before
       attempting the implications.  Before, when we were not unflattening,
       we had to push Wanted funeqs in as new givens.  Yuk!

       Another example that becomes easy: indexed_types/should_fail/T7786
          [W] BuriedUnder sub k Empty ~ fsk
          [W] Intersect fsk inv ~ s
          [w] xxx[1] ~ s
          [W] forall[2] . (xxx[1] ~ Empty)
                       => Intersect (BuriedUnder sub k Empty) inv ~ Empty

    Note [Running plugins on unflattened wanteds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    There is an annoying mismatch between solveSimpleGivens and
    solveSimpleWanteds, because the latter needs to fiddle with the inert
    set, unflatten and and zonk the wanteds.  It passes the zonked wanteds
    to runTcPluginsWanteds, which produces a replacement set of wanteds,
    some additional insolubles and a flag indicating whether to go round
    the loop again.  If so, prepareInertsForImplications is used to remove
    the previous wanteds (which will still be in the inert set).  Note
    that prepareInertsForImplications will discard the insolubles, so we
    must keep track of them separately.
    -}

    solveSimpleGivens :: CtLoc -> [EvVar] -> TcS ()
    solveSimpleGivens loc givens
      | null givens  -- Shortcut for common case
      = return ()
      | otherwise
      = go (map mk_given_ct givens)
      where
        mk_given_ct ev_id = mkNonCanonical (CtGiven { ctev_evtm = EvId ev_id
                                                    , ctev_pred = evVarPred ev_id
                                                    , ctev_loc  = loc })
        go givens = do { solveSimples (listToBag givens)
                       ; new_givens <- runTcPluginsGiven
                       ; when (notNull new_givens) (go new_givens)
                       }

    solveSimpleWanteds :: Cts -> TcS WantedConstraints
    solveSimpleWanteds = go emptyBag
      where
        go insols0 wanteds
          = do { solveSimples wanteds
               ; (implics, tv_eqs, fun_eqs, insols, others) <- getUnsolvedInerts
               ; unflattened_eqs <- unflatten tv_eqs fun_eqs
                  -- See Note [Unflatten after solving the simple wanteds]

               ; zonked <- zonkSimples (others `andCts` unflattened_eqs)
                 -- Postcondition is that the wl_simples are zonked

               ; (wanteds', insols', rerun) <- runTcPluginsWanted zonked
                  -- See Note [Running plugins on unflattened wanteds]
               ; let all_insols = insols0 `unionBags` insols `unionBags` insols'
               ; if rerun then do { updInertTcS prepareInertsForImplications
                                  ; go all_insols wanteds' }
                          else return (WC { wc_simple = wanteds'
                                          , wc_insol  = all_insols
                                          , wc_impl   = implics }) }

    -- The main solver loop implements Note [Basic Simplifier Plan]
    ---------------------------------------------------------------
    solveSimples :: Cts -> TcS ()
    -- Returns the final InertSet in TcS
    -- Has no effect on work-list or residual-iplications
    -- The constraints are initially examined in left-to-right order

    solveSimples cts
      = {-# SCC "solveSimples" #-}
        do { dyn_flags <- getDynFlags
           ; updWorkListTcS (\wl -> foldrBag extendWorkListCt wl cts)
           ; solve_loop (maxSubGoalDepth dyn_flags) }
      where
        solve_loop max_depth
          = {-# SCC "solve_loop" #-}
            do { sel <- selectNextWorkItem max_depth
               ; case sel of
                  NoWorkRemaining     -- Done, successfuly (modulo frozen)
                    -> return ()
                  MaxDepthExceeded cnt ct -- Failure, depth exceeded
                    -> wrapErrTcS $ solverDepthErrorTcS cnt (ctEvidence ct)
                  NextWorkItem ct     -- More work, loop around!
                    -> do { runSolverPipeline thePipeline ct; solve_loop max_depth } }

    -- | Extract the (inert) givens and invoke the plugins on them.
    -- Remove solved givens from the inert set and emit insolubles, but
    -- return new work produced so that 'solveSimpleGivens' can feed it back
    -- into the main solver.
    runTcPluginsGiven :: TcS [Ct]
    runTcPluginsGiven = do
      (givens,_,_) <- fmap splitInertCans getInertCans
      if null givens
        then return []
        else do
          p <- runTcPlugins (givens,[],[])
          let (solved_givens, _, _) = pluginSolvedCts p
          updInertCans (removeInertCts solved_givens)
          mapM_ emitInsoluble (pluginBadCts p)
          return (pluginNewCts p)

    -- | Given a bag of (flattened, zonked) wanteds, invoke the plugins on
    -- them and produce an updated bag of wanteds (possibly with some new
    -- work) and a bag of insolubles.  The boolean indicates whether
    -- 'solveSimpleWanteds' should feed the updated wanteds back into the
    -- main solver.
    runTcPluginsWanted :: Cts -> TcS (Cts, Cts, Bool)
    runTcPluginsWanted zonked_wanteds
      | isEmptyBag zonked_wanteds = return (zonked_wanteds, emptyBag, False)
      | otherwise                 = do
        (given,derived,_) <- fmap splitInertCans getInertCans
        p <- runTcPlugins (given, derived, bagToList zonked_wanteds)
        let (solved_givens, solved_deriveds, solved_wanteds) = pluginSolvedCts p
            (_, _, wanteds) = pluginInputCts p
        updInertCans (removeInertCts $ solved_givens ++ solved_deriveds)
        mapM_ setEv solved_wanteds
        return ( listToBag $ pluginNewCts p ++ wanteds
               , listToBag $ pluginBadCts p
               , notNull (pluginNewCts p) )
      where
        setEv :: (EvTerm,Ct) -> TcS ()
        setEv (ev,ct) = case ctEvidence ct of
          CtWanted {ctev_evar = evar} -> setEvBind evar ev
          _ -> panic "runTcPluginsWanted.setEv: attempt to solve non-wanted!"

    -- | A triple of (given, derived, wanted) constraints to pass to plugins
    type SplitCts  = ([Ct], [Ct], [Ct])

    -- | A solved triple of constraints, with evidence for wanteds
    type SolvedCts = ([Ct], [Ct], [(EvTerm,Ct)])

    -- | Represents collections of constraints generated by typechecker
    -- plugins
    data TcPluginProgress = TcPluginProgress
        { pluginInputCts  :: SplitCts
          -- ^ Original inputs to the plugins with solved/bad constraints
          -- removed, but otherwise unmodified
        , pluginSolvedCts :: SolvedCts
          -- ^ Constraints solved by plugins
        , pluginBadCts    :: [Ct]
          -- ^ Constraints reported as insoluble by plugins
        , pluginNewCts    :: [Ct]
          -- ^ New constraints emitted by plugins
        }

    -- | Starting from a triple of (given, derived, wanted) constraints,
    -- invoke each of the typechecker plugins in turn and return
    --
    --  * the remaining unmodified constraints,
    --  * constraints that have been solved,
    --  * constraints that are insoluble, and
    --  * new work.
    --
    -- Note that new work generated by one plugin will not be seen by
    -- other plugins on this pass (but the main constraint solver will be
    -- re-invoked and they will see it later).  There is no check that new
    -- work differs from the original constraints supplied to the plugin:
    -- the plugin itself should perform this check if necessary.
    runTcPlugins :: SplitCts -> TcS TcPluginProgress
    runTcPlugins all_cts = do
        gblEnv <- getGblEnv
        foldM do_plugin initialProgress (tcg_tc_plugins gblEnv)
      where
        do_plugin :: TcPluginProgress -> TcPluginSolver -> TcS TcPluginProgress
        do_plugin p solver = do
            result <- runTcPluginTcS (uncurry3 solver (pluginInputCts p))
            return $ progress p result

        progress :: TcPluginProgress -> TcPluginResult -> TcPluginProgress
        progress p (TcPluginContradiction bad_cts) =
           p { pluginInputCts = discard bad_cts (pluginInputCts p)
             , pluginBadCts   = bad_cts ++ pluginBadCts p
             }
        progress p (TcPluginOk solved_cts new_cts) =
          p { pluginInputCts  = discard (map snd solved_cts) (pluginInputCts p)
            , pluginSolvedCts = add solved_cts (pluginSolvedCts p)
            , pluginNewCts    = new_cts ++ pluginNewCts p
            }

        initialProgress = TcPluginProgress all_cts ([], [], []) [] []

        discard :: [Ct] -> SplitCts -> SplitCts
        discard cts (xs, ys, zs) =
            (xs `without` cts, ys `without` cts, zs `without` cts)

        without :: [Ct] -> [Ct] -> [Ct]
        without = deleteFirstsBy eqCt

        eqCt :: Ct -> Ct -> Bool
        eqCt c c' = case (ctEvidence c, ctEvidence c') of
          (CtGiven   pred _ _, CtGiven   pred' _ _) -> pred `eqType` pred'
          (CtWanted  pred _ _, CtWanted  pred' _ _) -> pred `eqType` pred'
          (CtDerived pred _  , CtDerived pred' _  ) -> pred `eqType` pred'
          (_                 , _                  ) -> False

        add :: [(EvTerm,Ct)] -> SolvedCts -> SolvedCts
        add xs scs = foldl' addOne scs xs

        addOne :: SolvedCts -> (EvTerm,Ct) -> SolvedCts
        addOne (givens, deriveds, wanteds) (ev,ct) = case ctEvidence ct of
          CtGiven  {} -> (ct:givens, deriveds, wanteds)
          CtDerived{} -> (givens, ct:deriveds, wanteds)
          CtWanted {} -> (givens, deriveds, (ev,ct):wanteds)

    type WorkItem = Ct
    type SimplifierStage = WorkItem -> TcS (StopOrContinue Ct)

    data SelectWorkItem
           = NoWorkRemaining      -- No more work left (effectively we're done!)
           | MaxDepthExceeded SubGoalCounter Ct
                                  -- More work left to do but this constraint has exceeded
                                  -- the maximum depth for one of the subgoal counters and we
                                  -- must stop
           | NextWorkItem Ct      -- More work left, here's the next item to look at

    selectNextWorkItem :: SubGoalDepth -- Max depth allowed
                       -> TcS SelectWorkItem
    selectNextWorkItem max_depth
      = updWorkListTcS_return pick_next
      where
        pick_next :: WorkList -> (SelectWorkItem, WorkList)
        pick_next wl
          = case selectWorkItem wl of
              (Nothing,_)
                  -> (NoWorkRemaining,wl)           -- No more work
              (Just ct, new_wl)
                  | Just cnt <- subGoalDepthExceeded max_depth (ctLocDepth (ctLoc ct)) -- Depth exceeded
                  -> (MaxDepthExceeded cnt ct,new_wl)
              (Just ct, new_wl)
                  -> (NextWorkItem ct, new_wl)      -- New workitem and worklist

    runSolverPipeline :: [(String,SimplifierStage)] -- The pipeline
                      -> WorkItem                   -- The work item
                      -> TcS ()
    -- Run this item down the pipeline, leaving behind new work and inerts
    runSolverPipeline pipeline workItem
      = do { initial_is <- getTcSInerts
           ; traceTcS "Start solver pipeline {" $
                      vcat [ ptext (sLit "work item = ") <+> ppr workItem
                           , ptext (sLit "inerts    = ") <+> ppr initial_is]

           ; bumpStepCountTcS    -- One step for each constraint processed
           ; final_res  <- run_pipeline pipeline (ContinueWith workItem)

           ; final_is <- getTcSInerts
           ; case final_res of
               Stop ev s       -> do { traceFireTcS ev s
                                     ; traceTcS "End solver pipeline (discharged) }"
                                           (ptext (sLit "inerts =") <+> ppr final_is)
                                     ; return () }
               ContinueWith ct -> do { traceFireTcS (ctEvidence ct) (ptext (sLit "Kept as inert"))
                                     ; traceTcS "End solver pipeline (not discharged) }" $
                                           vcat [ ptext (sLit "final_item =") <+> ppr ct
                                                , pprTvBndrs (varSetElems $ tyVarsOfCt ct)
                                                , ptext (sLit "inerts     =") <+> ppr final_is]
                                     ; insertInertItemTcS ct }
           }
      where run_pipeline :: [(String,SimplifierStage)] -> StopOrContinue Ct
                         -> TcS (StopOrContinue Ct)
            run_pipeline [] res        = return res
            run_pipeline _ (Stop ev s) = return (Stop ev s)
            run_pipeline ((stg_name,stg):stgs) (ContinueWith ct)
              = do { traceTcS ("runStage " ++ stg_name ++ " {")
                              (text "workitem   = " <+> ppr ct)
                   ; res <- stg ct
                   ; traceTcS ("end stage " ++ stg_name ++ " }") empty
                   ; run_pipeline stgs res }

    {-
    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
    -}

    thePipeline :: [(String,SimplifierStage)]
    thePipeline = [ ("canonicalization",        TcCanonical.canonicalize)
                  , ("interact with inerts",    interactWithInertsStage)
                  , ("top-level reactions",     topReactionsStage) ]

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

    Note [The Solver Invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We always add Givens first.  So you might think that the solver has
    the invariant

       If the work-item is Given,
       then the inert item must Given

    But this isn't quite true.  Suppose we have,
        c1: [W] beta ~ [alpha], c2 : [W] blah, c3 :[W] alpha ~ Int
    After processing the first two, we get
         c1: [G] beta ~ [alpha], c2 : [W] blah
    Now, c3 does not interact with the the given c1, so when we spontaneously
    solve c3, we must re-react it with the inert set.  So we can attempt a
    reaction between inert c2 [W] and work-item c3 [G].

    It *is* true that [Solver Invariant]
       If the work-item is Given,
       AND there is a reaction
       then the inert item must Given
    or, equivalently,
       If the work-item is Given,
       and the inert item is Wanted/Derived
       then there is no reaction
    -}

    -- Interaction result of  WorkItem <~> Ct

    type StopNowFlag = Bool    -- True <=> stop after this interaction

    interactWithInertsStage :: WorkItem -> TcS (StopOrContinue Ct)
    -- Precondition: if the workitem is a CTyEqCan then it will not be able to
    -- react with anything at this stage.

    interactWithInertsStage wi
      = do { inerts <- getTcSInerts
           ; let ics = inert_cans inerts
           ; case wi of
                 CTyEqCan    {} -> interactTyVarEq ics wi
                 CFunEqCan   {} -> interactFunEq   ics wi
                 CIrredEvCan {} -> interactIrred   ics wi
                 CDictCan    {} -> interactDict    ics wi
                 _ -> pprPanic "interactWithInerts" (ppr wi) }
                    -- CHoleCan are put straight into inert_frozen, so never get here
                    -- CNonCanonical have been canonicalised

    data InteractResult = IRKeep | IRReplace | IRDelete
    instance Outputable InteractResult where
      ppr IRKeep    = ptext (sLit "keep")
      ppr IRReplace = ptext (sLit "replace")
      ppr IRDelete  = ptext (sLit "delete")

    solveOneFromTheOther :: CtEvidence  -- Inert
                         -> CtEvidence  -- WorkItem
                         -> TcS (InteractResult, StopNowFlag)
    -- Preconditions:
    -- 1) inert and work item represent evidence for the /same/ predicate
    -- 2) ip/class/irred evidence (no coercions) only
    solveOneFromTheOther ev_i ev_w
      | isDerived ev_w
      = return (IRKeep, True)

      | isDerived ev_i -- The inert item is Derived, we can just throw it away,
                       -- The ev_w is inert wrt earlier inert-set items,
                       -- so it's safe to continue on from this point
      = return (IRDelete, False)

      | CtWanted { ctev_evar = ev_id } <- ev_w
      = do { setEvBind ev_id (ctEvTerm ev_i)
           ; return (IRKeep, True) }

      | CtWanted { ctev_evar = ev_id } <- ev_i
      = do { setEvBind ev_id (ctEvTerm ev_w)
           ; return (IRReplace, True) }

      | otherwise      -- If both are Given, we already have evidence; no need to duplicate
                       -- But the work item *overrides* the inert item (hence IRReplace)
                       -- See Note [Shadowing of Implicit Parameters]
      = return (IRReplace, True)

    {-
    *********************************************************************************
    *                                                                               *
                       interactIrred
    *                                                                               *
    *********************************************************************************
    -}

    -- Two pieces of irreducible evidence: if their types are *exactly identical*
    -- we can rewrite them. We can never improve using this:
    -- if we want ty1 :: Constraint and have ty2 :: Constraint it clearly does not
    -- mean that (ty1 ~ ty2)
    interactIrred :: InertCans -> Ct -> TcS (StopOrContinue Ct)

    interactIrred inerts workItem@(CIrredEvCan { cc_ev = ev_w })
      | let pred = ctEvPred ev_w
            (matching_irreds, others) = partitionBag (\ct -> ctPred ct `tcEqType` pred)
                                                     (inert_irreds inerts)
      , (ct_i : rest) <- bagToList matching_irreds
      , let ctev_i = ctEvidence ct_i
      = ASSERT( null rest )
        do { (inert_effect, stop_now) <- solveOneFromTheOther ctev_i ev_w
           ; case inert_effect of
                IRKeep    -> return ()
                IRDelete  -> updInertIrreds (\_ -> others)
                IRReplace -> updInertIrreds (\_ -> others `snocCts` workItem)
                             -- These const upd's assume that solveOneFromTheOther
                             -- has no side effects on InertCans
           ; if stop_now then
                return (Stop ev_w (ptext (sLit "Irred equal") <+> parens (ppr inert_effect)))
           ; else
                continueWith workItem }

      | otherwise
      = continueWith workItem

    interactIrred _ wi = pprPanic "interactIrred" (ppr wi)

    {-
    *********************************************************************************
    *                                                                               *
                       interactDict
    *                                                                               *
    *********************************************************************************
    -}

    interactDict :: InertCans -> Ct -> TcS (StopOrContinue Ct)
    interactDict inerts workItem@(CDictCan { cc_ev = ev_w, cc_class = cls, cc_tyargs = tys })
      -- don't ever try to solve CallStack IPs directly from other dicts,
      -- we always build new dicts instead.
      -- See Note [Overview of implicit CallStacks]
      | [_ip, ty] <- tys
      , isWanted ev_w
      , Just mkEvCs <- isCallStackIP (ctEvLoc ev_w) cls ty
      = do let ev_cs =
                 case lookupInertDict inerts (ctEvLoc ev_w) cls tys of
                   Just ev | isGiven ev -> mkEvCs (ctEvTerm ev)
                   _ -> mkEvCs (EvCallStack EvCsEmpty)

           -- now we have ev_cs :: CallStack, but the evidence term should
           -- be a dictionary, so we have to coerce ev_cs to a
           -- dictionary for `IP ip CallStack`
           let ip_ty = mkClassPred cls tys
           let ev_tm = mkEvCast (EvCallStack ev_cs) (TcCoercion $ wrapIP ip_ty)
           addSolvedDict ev_w cls tys
           setEvBind (ctEvId ev_w) ev_tm
           stopWith ev_w "Wanted CallStack IP"

      | Just ctev_i <- lookupInertDict inerts (ctEvLoc ev_w) cls tys
      = do { (inert_effect, stop_now) <- solveOneFromTheOther ctev_i ev_w
           ; case inert_effect of
               IRKeep    -> return ()
               IRDelete  -> updInertDicts $ \ ds -> delDict ds cls tys
               IRReplace -> updInertDicts $ \ ds -> addDict ds cls tys workItem
           ; if stop_now then
                return (Stop ev_w (ptext (sLit "Dict equal") <+> parens (ppr inert_effect)))
             else
                continueWith workItem }

      | cls `hasKey` ipClassNameKey
      , isGiven ev_w
      = interactGivenIP inerts workItem

      | otherwise
      = do { mapBagM_ (addFunDepWork workItem) (findDictsByClass (inert_dicts inerts) cls)
                   -- Standard thing: create derived fds and keep on going. Importantly we don't
                   -- throw workitem back in the worklist because this can cause loops (see #5236)
           ; continueWith workItem  }

    interactDict _ wi = pprPanic "interactDict" (ppr wi)

    interactGivenIP :: InertCans -> Ct -> TcS (StopOrContinue Ct)
    -- Work item is Given (?x:ty)
    -- See Note [Shadowing of Implicit Parameters]
    interactGivenIP inerts workItem@(CDictCan { cc_ev = ev, cc_class = cls
                                              , cc_tyargs = tys@(ip_str:_) })
      = do { updInertCans $ \cans -> cans { inert_dicts = addDict filtered_dicts cls tys workItem }
           ; stopWith ev "Given IP" }
      where
        dicts           = inert_dicts inerts
        ip_dicts        = findDictsByClass dicts cls
        other_ip_dicts  = filterBag (not . is_this_ip) ip_dicts
        filtered_dicts  = addDictsByClass dicts cls other_ip_dicts

        -- Pick out any Given constraints for the same implicit parameter
        is_this_ip (CDictCan { cc_ev = ev, cc_tyargs = ip_str':_ })
           = isGiven ev && ip_str `tcEqType` ip_str'
        is_this_ip _ = False

    interactGivenIP _ wi = pprPanic "interactGivenIP" (ppr wi)

    addFunDepWork :: Ct -> Ct -> TcS ()
    addFunDepWork work_ct inert_ct
      = do {  let fd_eqns :: [Equation CtLoc]
                  fd_eqns = [ eqn { fd_loc = derived_loc }
                            | eqn <- improveFromAnother inert_pred work_pred ]
           ; rewriteWithFunDeps fd_eqns
                    -- We don't really rewrite tys2, see below _rewritten_tys2, so that's ok
                    -- NB: We do create FDs for given to report insoluble equations that arise
                    -- from pairs of Givens, and also because of floating when we approximate
                    -- implications. The relevant test is: typecheck/should_fail/FDsFromGivens.hs
                    -- Also see Note [When improvement happens]
        }
      where
        work_pred  = ctPred work_ct
        inert_pred = ctPred inert_ct
        work_loc   = ctLoc work_ct
        inert_loc  = ctLoc inert_ct
        derived_loc = work_loc { ctl_origin = FunDepOrigin1 work_pred  work_loc
                                                            inert_pred inert_loc }

    {-
    Note [Shadowing of Implicit Parameters]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider the following example:

    f :: (?x :: Char) => Char
    f = let ?x = 'a' in ?x

    The "let ?x = ..." generates an implication constraint of the form:

    ?x :: Char => ?x :: Char

    Furthermore, the signature for `f` also generates an implication
    constraint, so we end up with the following nested implication:

    ?x :: Char => (?x :: Char => ?x :: Char)

    Note that the wanted (?x :: Char) constraint may be solved in
    two incompatible ways:  either by using the parameter from the
    signature, or by using the local definition.  Our intention is
    that the local definition should "shadow" the parameter of the
    signature, and we implement this as follows: when we add a new
    *given* implicit parameter to the inert set, it replaces any existing
    givens for the same implicit parameter.

    This works for the normal cases but it has an odd side effect
    in some pathological programs like this:

    -- This is accepted, the second parameter shadows
    f1 :: (?x :: Int, ?x :: Char) => Char
    f1 = ?x

    -- This is rejected, the second parameter shadows
    f2 :: (?x :: Int, ?x :: Char) => Int
    f2 = ?x

    Both of these are actually wrong:  when we try to use either one,
    we'll get two incompatible wnated constraints (?x :: Int, ?x :: Char),
    which would lead to an error.

    I can think of two ways to fix this:

      1. Simply disallow multiple constratits for the same implicit
        parameter---this is never useful, and it can be detected completely
        syntactically.

      2. Move the shadowing machinery to the location where we nest
         implications, and add some code here that will produce an
         error if we get multiple givens for the same implicit parameter.

    *********************************************************************************
    *                                                                               *
                       interactFunEq
    *                                                                               *
    *********************************************************************************
    -}

    interactFunEq :: InertCans -> Ct -> TcS (StopOrContinue Ct)
    -- Try interacting the work item with the inert set
    interactFunEq inerts workItem@(CFunEqCan { cc_ev = ev, cc_fun = tc
                                             , cc_tyargs = args, cc_fsk = fsk })
      | Just (CFunEqCan { cc_ev = ev_i, cc_fsk = fsk_i }) <- matching_inerts
      = if ev_i `canRewriteOrSame` ev
        then  -- Rewrite work-item using inert
          do { traceTcS "reactFunEq (discharge work item):" $
               vcat [ text "workItem =" <+> ppr workItem
                    , text "inertItem=" <+> ppr ev_i ]
             ; reactFunEq ev_i fsk_i ev fsk
             ; stopWith ev "Inert rewrites work item" }
        else  -- Rewrite intert using work-item
          do { traceTcS "reactFunEq (rewrite inert item):" $
               vcat [ text "workItem =" <+> ppr workItem
                    , text "inertItem=" <+> ppr ev_i ]
             ; updInertFunEqs $ \ feqs -> insertFunEq feqs tc args workItem
                   -- Do the updInertFunEqs before the reactFunEq, so that
                   -- we don't kick out the inertItem as well as consuming it!
             ; reactFunEq ev fsk ev_i fsk_i
             ; stopWith ev "Work item rewrites inert" }

      | Just ops <- isBuiltInSynFamTyCon_maybe tc
      = do { let matching_funeqs = findFunEqsByTyCon funeqs tc
           ; let interact = sfInteractInert ops args (lookupFlattenTyVar eqs fsk)
                 do_one (CFunEqCan { cc_tyargs = iargs, cc_fsk = ifsk, cc_ev = iev })
                    = mapM_ (unifyDerived (ctEvLoc iev) Nominal)
                            (interact iargs (lookupFlattenTyVar eqs ifsk))
                 do_one ct = pprPanic "interactFunEq" (ppr ct)
           ; mapM_ do_one matching_funeqs
           ; traceTcS "builtInCandidates 1: " $ vcat [ ptext (sLit "Candidates:") <+> ppr matching_funeqs
                                                     , ptext (sLit "TvEqs:") <+> ppr eqs ]
           ; return (ContinueWith workItem) }

      | otherwise
      = return (ContinueWith workItem)
      where
        eqs    = inert_eqs inerts
        funeqs = inert_funeqs inerts
        matching_inerts = findFunEqs funeqs tc args

    interactFunEq _ wi = pprPanic "interactFunEq" (ppr wi)

    lookupFlattenTyVar :: TyVarEnv EqualCtList -> TcTyVar -> TcType
    -- ^ Look up a flatten-tyvar in the inert nominal TyVarEqs;
    -- this is used only when dealing with a CFunEqCan
    lookupFlattenTyVar inert_eqs ftv
      = case lookupVarEnv inert_eqs ftv of
          Just (CTyEqCan { cc_rhs = rhs, cc_eq_rel = NomEq } : _) -> rhs
          _                                                       -> mkTyVarTy ftv

    reactFunEq :: CtEvidence -> TcTyVar    -- From this  :: F tys ~ fsk1
               -> CtEvidence -> TcTyVar    -- Solve this :: F tys ~ fsk2
               -> TcS ()
    reactFunEq from_this fsk1 (CtGiven { ctev_evtm = tm, ctev_loc = loc }) fsk2
      = do { let fsk_eq_co = mkTcSymCo (evTermCoercion tm)
                             `mkTcTransCo` ctEvCoercion from_this
                             -- :: fsk2 ~ fsk1
                 fsk_eq_pred = mkTcEqPred (mkTyVarTy fsk2) (mkTyVarTy fsk1)
           ; new_ev <- newGivenEvVar loc (fsk_eq_pred, EvCoercion fsk_eq_co)
           ; emitWorkNC [new_ev] }

    reactFunEq from_this fuv1 (CtWanted { ctev_evar = evar }) fuv2
      = dischargeFmv evar fuv2 (ctEvCoercion from_this) (mkTyVarTy fuv1)

    reactFunEq _ _ solve_this@(CtDerived {}) _
      = pprPanic "reactFunEq" (ppr solve_this)

    {-
    Note [Cache-caused loops]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    It is very dangerous to cache a rewritten wanted family equation as 'solved' in our
    solved cache (which is the default behaviour or xCtEvidence), because the interaction
    may not be contributing towards a solution. Here is an example:

    Initial inert set:
      [W] g1 : F a ~ beta1
    Work item:
      [W] g2 : F a ~ beta2
    The work item will react with the inert yielding the _same_ inert set plus:
        i)   Will set g2 := g1 `cast` g3
        ii)  Will add to our solved cache that [S] g2 : F a ~ beta2
        iii) Will emit [W] g3 : beta1 ~ beta2
    Now, the g3 work item will be spontaneously solved to [G] g3 : beta1 ~ beta2
    and then it will react the item in the inert ([W] g1 : F a ~ beta1). So it
    will set
          g1 := g ; sym g3
    and what is g? Well it would ideally be a new goal of type (F a ~ beta2) but
    remember that we have this in our solved cache, and it is ... g2! In short we
    created the evidence loop:

            g2 := g1 ; g3
            g3 := refl
            g1 := g2 ; sym g3

    To avoid this situation we do not cache as solved any workitems (or inert)
    which did not really made a 'step' towards proving some goal. Solved's are
    just an optimization so we don't lose anything in terms of completeness of
    solving.

    Note [Efficient Orientation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we are interacting two FunEqCans with the same LHS:
              (inert)  ci :: (F ty ~ xi_i)
              (work)   cw :: (F ty ~ xi_w)
    We prefer to keep the inert (else we pass the work item on down
    the pipeline, which is a bit silly).  If we keep the inert, we
    will (a) discharge 'cw'
         (b) produce a new equality work-item (xi_w ~ xi_i)
    Notice the orientation (xi_w ~ xi_i) NOT (xi_i ~ xi_w):
        new_work :: xi_w ~ xi_i
        cw := ci ; sym new_work
    Why?  Consider the simplest case when xi1 is a type variable.  If
    we generate xi1~xi2, porcessing that constraint will kick out 'ci'.
    If we generate xi2~xi1, there is less chance of that happening.
    Of course it can and should still happen if xi1=a, xi1=Int, say.
    But we want to avoid it happening needlessly.

    Similarly, if we *can't* keep the inert item (because inert is Wanted,
    and work is Given, say), we prefer to orient the new equality (xi_i ~
    xi_w).

    Note [Carefully solve the right CFunEqCan]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
       ---- OLD COMMENT, NOW NOT NEEDED
       ---- because we now allow multiple
       ---- wanted FunEqs with the same head
    Consider the constraints
      c1 :: F Int ~ a      -- Arising from an application line 5
      c2 :: F Int ~ Bool   -- Arising from an application line 10
    Suppose that 'a' is a unification variable, arising only from
    flattening.  So there is no error on line 5; it's just a flattening
    variable.  But there is (or might be) an error on line 10.

    Two ways to combine them, leaving either (Plan A)
      c1 :: F Int ~ a      -- Arising from an application line 5
      c3 :: a ~ Bool       -- Arising from an application line 10
    or (Plan B)
      c2 :: F Int ~ Bool   -- Arising from an application line 10
      c4 :: a ~ Bool       -- Arising from an application line 5

    Plan A will unify c3, leaving c1 :: F Int ~ Bool as an error
    on the *totally innocent* line 5.  An example is test SimpleFail16
    where the expected/actual message comes out backwards if we use
    the wrong plan.

    The second is the right thing to do.  Hence the isMetaTyVarTy
    test when solving pairwise CFunEqCan.

    *********************************************************************************
    *                                                                               *
                       interactTyVarEq
    *                                                                               *
    *********************************************************************************
    -}

    interactTyVarEq :: InertCans -> Ct -> TcS (StopOrContinue Ct)
    -- CTyEqCans are always consumed, so always returns Stop
    interactTyVarEq inerts workItem@(CTyEqCan { cc_tyvar = tv
                                              , cc_rhs = rhs
                                              , cc_ev = ev
                                              , cc_eq_rel = eq_rel })
      | (ev_i : _) <- [ ev_i | CTyEqCan { cc_ev = ev_i, cc_rhs = rhs_i }
                                 <- findTyEqs inerts tv
                             , ev_i `canRewriteOrSame` ev
                             , rhs_i `tcEqType` rhs ]
      =  -- Inert:     a ~ b
         -- Work item: a ~ b
        do { when (isWanted ev) $
             setEvBind (ctev_evar ev) (ctEvTerm ev_i)
           ; stopWith ev "Solved from inert" }

      | Just tv_rhs <- getTyVar_maybe rhs
      , (ev_i : _) <- [ ev_i | CTyEqCan { cc_ev = ev_i, cc_rhs = rhs_i }
                                 <- findTyEqs inerts tv_rhs
                             , ev_i `canRewriteOrSame` ev
                             , rhs_i `tcEqType` mkTyVarTy tv ]
      =  -- Inert:     a ~ b
         -- Work item: b ~ a
        do { when (isWanted ev) $
             setEvBind (ctev_evar ev)
                       (EvCoercion (mkTcSymCo (ctEvCoercion ev_i)))
           ; stopWith ev "Solved from inert (r)" }

      | otherwise
      = do { tclvl <- getTcLevel
           ; if canSolveByUnification tclvl ev eq_rel tv rhs
             then do { solveByUnification ev tv rhs
                     ; n_kicked <- kickOutRewritable Given NomEq tv
                                   -- Given because the tv := xi is given
                                   -- NomEq because only nom. equalities are solved
                                   -- by unification
                     ; return (Stop ev (ptext (sLit "Spontaneously solved") <+> ppr_kicked n_kicked)) }

             else do { traceTcS "Can't solve tyvar equality"
                           (vcat [ text "LHS:" <+> ppr tv <+> dcolon <+> ppr (tyVarKind tv)
                                 , ppWhen (isMetaTyVar tv) $
                                   nest 4 (text "TcLevel of" <+> ppr tv
                                           <+> text "is" <+> ppr (metaTyVarTcLevel tv))
                                 , text "RHS:" <+> ppr rhs <+> dcolon <+> ppr (typeKind rhs)
                                 , text "TcLevel =" <+> ppr tclvl ])
                     ; n_kicked <- kickOutRewritable (ctEvFlavour ev)
                                                     (ctEvEqRel ev)
                                                     tv
                     ; updInertCans (\ ics -> addInertCan ics workItem)
                     ; return (Stop ev (ptext (sLit "Kept as inert") <+> ppr_kicked n_kicked)) } }

    interactTyVarEq _ wi = pprPanic "interactTyVarEq" (ppr wi)

    -- @trySpontaneousSolve wi@ solves equalities where one side is a
    -- touchable unification variable.
    -- Returns True <=> spontaneous solve happened
    canSolveByUnification :: TcLevel -> CtEvidence -> EqRel
                          -> TcTyVar -> Xi -> Bool
    canSolveByUnification tclvl gw eq_rel tv xi
      | ReprEq <- eq_rel   -- we never solve representational equalities this way.
      = False

      | isGiven gw   -- See Note [Touchables and givens]
      = False

      | isTouchableMetaTyVar tclvl tv
      = case metaTyVarInfo tv of
          SigTv -> is_tyvar xi
          _     -> True

      | otherwise    -- Untouchable
      = False
      where
        is_tyvar xi
          = case tcGetTyVar_maybe xi of
              Nothing -> False
              Just tv -> case tcTyVarDetails tv of
                           MetaTv { mtv_info = info }
                                       -> case info of
                                            SigTv -> True
                                            _     -> False
                           SkolemTv {} -> True
                           FlatSkol {} -> False
                           RuntimeUnk  -> True

    solveByUnification :: CtEvidence -> TcTyVar -> Xi -> TcS ()
    -- Solve with the identity coercion
    -- Precondition: kind(xi) is a sub-kind of kind(tv)
    -- Precondition: CtEvidence is Wanted or Derived
    -- Precondition: CtEvidence is nominal
    -- See [New Wanted Superclass Work] to see why solveByUnification
    --     must work for Derived as well as Wanted
    -- Returns: workItem where
    --        workItem = the new Given constraint
    --
    -- NB: No need for an occurs check here, because solveByUnification always
    --     arises from a CTyEqCan, a *canonical* constraint.  Its invariants
    --     say that in (a ~ xi), the type variable a does not appear in xi.
    --     See TcRnTypes.Ct invariants.
    --
    -- Post: tv is unified (by side effect) with xi;
    --       we often write tv := xi
    solveByUnification wd tv xi
      = do { let tv_ty = mkTyVarTy tv
           ; traceTcS "Sneaky unification:" $
                           vcat [text "Unifies:" <+> ppr tv <+> ptext (sLit ":=") <+> ppr xi,
                                 text "Coercion:" <+> pprEq tv_ty xi,
                                 text "Left Kind is:" <+> ppr (typeKind tv_ty),
                                 text "Right Kind is:" <+> ppr (typeKind xi) ]

           ; let xi' = defaultKind xi
                   -- We only instantiate kind unification variables
                   -- with simple kinds like *, not OpenKind or ArgKind
                   -- cf TcUnify.uUnboundKVar

           ; setWantedTyBind tv xi'
           ; when (isWanted wd) $
             setEvBind (ctEvId wd) (EvCoercion (mkTcNomReflCo xi')) }

    ppr_kicked :: Int -> SDoc
    ppr_kicked 0 = empty
    ppr_kicked n = parens (int n <+> ptext (sLit "kicked out"))

    kickOutRewritable :: CtFlavour    -- Flavour of the equality that is
                                      -- being added to the inert set
                      -> EqRel        -- of the new equality
                      -> TcTyVar      -- The new equality is tv ~ ty
                      -> TcS Int
    kickOutRewritable new_flavour new_eq_rel new_tv
      | not ((new_flavour, new_eq_rel) `eqCanRewriteFR` (new_flavour, new_eq_rel))
      = return 0  -- If new_flavour can't rewrite itself, it can't rewrite
                  -- anything else, so no need to kick out anything
                  -- This is a common case: wanteds can't rewrite wanteds

      | otherwise
      = do { ics <- getInertCans
           ; let (kicked_out, ics') = kick_out new_flavour new_eq_rel new_tv ics
           ; setInertCans ics'
           ; updWorkListTcS (appendWorkList kicked_out)

           ; unless (isEmptyWorkList kicked_out) $
             csTraceTcS $
             hang (ptext (sLit "Kick out, tv =") <+> ppr new_tv)
                2 (vcat [ text "n-kicked =" <+> int (workListSize kicked_out)
                        , text "n-kept fun-eqs =" <+> int (sizeFunEqMap (inert_funeqs ics'))
                        , ppr kicked_out ])
           ; return (workListSize kicked_out) }

    kick_out :: CtFlavour -> EqRel -> TcTyVar -> InertCans -> (WorkList, InertCans)
    kick_out new_flavour new_eq_rel new_tv (IC { inert_eqs      = tv_eqs
                                               , inert_dicts    = dictmap
                                               , inert_funeqs   = funeqmap
                                               , inert_irreds   = irreds
                                               , inert_insols   = insols })
      = (kicked_out, inert_cans_in)
      where
                    -- NB: Notice that don't rewrite
                    -- inert_solved_dicts, and inert_solved_funeqs
                    -- optimistically. But when we lookup we have to
                    -- take the substitution into account
        inert_cans_in = IC { inert_eqs      = tv_eqs_in
                           , inert_dicts    = dicts_in
                           , inert_funeqs   = feqs_in
                           , inert_irreds   = irs_in
                           , inert_insols   = insols_in }

        kicked_out = WL { wl_eqs    = tv_eqs_out
                        , wl_funeqs = feqs_out
                        , wl_rest   = bagToList (dicts_out `andCts` irs_out
                                                 `andCts` insols_out)
                        , wl_implics = emptyBag }

        (tv_eqs_out, tv_eqs_in) = foldVarEnv kick_out_eqs ([], emptyVarEnv) tv_eqs
        (feqs_out,   feqs_in)   = partitionFunEqs  kick_out_ct funeqmap
        (dicts_out,  dicts_in)  = partitionDicts   kick_out_ct dictmap
        (irs_out,    irs_in)    = partitionBag     kick_out_irred irreds
        (insols_out, insols_in) = partitionBag     kick_out_ct    insols
          -- Kick out even insolubles; see Note [Kick out insolubles]

        can_rewrite :: CtEvidence -> Bool
        can_rewrite = ((new_flavour, new_eq_rel) `eqCanRewriteFR`) . ctEvFlavourRole

        kick_out_ct :: Ct -> Bool
        kick_out_ct ct = kick_out_ctev (ctEvidence ct)

        kick_out_ctev :: CtEvidence -> Bool
        kick_out_ctev ev =  can_rewrite ev
                         && new_tv `elemVarSet` tyVarsOfType (ctEvPred ev)
             -- See Note [Kicking out inert constraints]

        kick_out_irred :: Ct -> Bool
        kick_out_irred ct =  can_rewrite (cc_ev ct)
                          && new_tv `elemVarSet` closeOverKinds (tyVarsOfCt ct)
              -- See Note [Kicking out Irreds]

        kick_out_eqs :: EqualCtList -> ([Ct], TyVarEnv EqualCtList)
                     -> ([Ct], TyVarEnv EqualCtList)
        kick_out_eqs eqs (acc_out, acc_in)
          = (eqs_out ++ acc_out, case eqs_in of
                                   []      -> acc_in
                                   (eq1:_) -> extendVarEnv acc_in (cc_tyvar eq1) eqs_in)
          where
            (eqs_in, eqs_out) = partition keep_eq eqs

        -- implements criteria K1-K3 in Note [The inert equalities] in TcFlatten
        keep_eq (CTyEqCan { cc_tyvar = tv, cc_rhs = rhs_ty, cc_ev = ev
                          , cc_eq_rel = eq_rel })
          | tv == new_tv
          = not (can_rewrite ev)  -- (K1)

          | otherwise
          = check_k2 && check_k3
          where
            check_k2 = not (ev `eqCanRewrite` ev)
                    || not (can_rewrite ev)
                    || not (new_tv `elemVarSet` tyVarsOfType rhs_ty)

            check_k3
              | can_rewrite ev
              = case eq_rel of
                  NomEq  -> not (rhs_ty `eqType` mkTyVarTy new_tv)
                  ReprEq -> not (isTyVarExposed new_tv rhs_ty)

              | otherwise
              = True

        keep_eq ct = pprPanic "keep_eq" (ppr ct)

    {-
    Note [Kicking out inert constraints]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Given a new (a -> ty) inert, we want to kick out an existing inert
    constraint if
      a) the new constraint can rewrite the inert one
      b) 'a' is free in the inert constraint (so that it *will*)
         rewrite it if we kick it out.

    For (b) we use tyVarsOfCt, which returns the type variables /and
    the kind variables/ that are directly visible in the type. Hence we
    will have exposed all the rewriting we care about to make the most
    precise kinds visible for matching classes etc. No need to kick out
    constraints that mention type variables whose kinds contain this
    variable!  (Except see Note [Kicking out Irreds].)

    Note [Kicking out Irreds]
    ~~~~~~~~~~~~~~~~~~~~~~~~~
    There is an awkward special case for Irreds.  When we have a
    kind-mis-matched equality constraint (a:k1) ~ (ty:k2), we turn it into
    an Irred (see Note [Equalities with incompatible kinds] in
    TcCanonical). So in this case the free kind variables of k1 and k2
    are not visible.  More precisely, the type looks like
       (~) k1 (a:k1) (ty:k2)
    because (~) has kind forall k. k -> k -> Constraint.  So the constraint
    itself is ill-kinded.  We can "see" k1 but not k2.  That's why we use
    closeOverKinds to make sure we see k2.

    This is not pretty. Maybe (~) should have kind
       (~) :: forall k1 k1. k1 -> k2 -> Constraint

    Note [Kick out insolubles]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have an insoluble alpha ~ [alpha], which is insoluble
    because an occurs check.  And then we unify alpha := [Int].
    Then we really want to rewrite the insouluble to [Int] ~ [[Int]].
    Now it can be decomposed.  Otherwise we end up with a "Can't match
    [Int] ~ [[Int]]" which is true, but a bit confusing because the
    outer type constructors match.

    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!
          given : a ~ alpha      [having unified alpha := a]
    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]

    We avoid this problem by orienting the resulting given so that the unification
    variable is on the left.  [Note that alternatively we could attempt to
    enforce this at canonicalization]

    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.

    Note [Superclasses and recursive dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        Overlaps with Note [SUPERCLASS-LOOP 1]
                      Note [SUPERCLASS-LOOP 2]
                      Note [Recursive instances and superclases]
        ToDo: check overlap and delete redundant stuff

    Right before adding a given into the inert set, we must
    produce some more work, that will bring the superclasses
    of the given into scope. The superclass constraints go into
    our worklist.

    When we simplify a wanted constraint, if we first see a matching
    instance, we may produce new wanted work. To (1) avoid doing this work
    twice in the future and (2) to handle recursive dictionaries we may ``cache''
    this item as given into our inert set WITHOUT adding its superclass constraints,
    otherwise we'd be in danger of creating a loop [In fact this was the exact reason
    for doing the isGoodRecEv check in an older version of the type checker].

    But now we have added partially solved constraints to the worklist which may
    interact with other wanteds. Consider the example:

    Example 1:

        class Eq b => Foo a b        --- 0-th selector
        instance Eq a => Foo [a] a   --- fooDFun

    and wanted (Foo [t] t). We are first going to see that the instance matches
    and create an inert set that includes the solved (Foo [t] t) but not its superclasses:
           d1 :_g Foo [t] t                 d1 := EvDFunApp fooDFun d3
    Our work list is going to contain a new *wanted* goal
           d3 :_w Eq t

    Ok, so how do we get recursive dictionaries, at all:

    Example 2:

        data D r = ZeroD | SuccD (r (D r));

        instance (Eq (r (D r))) => Eq (D r) where
            ZeroD     == ZeroD     = True
            (SuccD a) == (SuccD b) = a == b
            _         == _         = False;

        equalDC :: D [] -> D [] -> Bool;
        equalDC = (==);

    We need to prove (Eq (D [])). Here's how we go:

            d1 :_w Eq (D [])

    by instance decl, holds if
            d2 :_w Eq [D []]
            where   d1 = dfEqD d2

    *BUT* we have an inert set which gives us (no superclasses):
            d1 :_g Eq (D [])
    By the instance declaration of Eq we can show the 'd2' goal if
            d3 :_w Eq (D [])
            where   d2 = dfEqList d3
                    d1 = dfEqD d2
    Now, however this wanted can interact with our inert d1 to set:
            d3 := d1
    and solve the goal. Why was this interaction OK? Because, if we chase the
    evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
    are really setting
            d3 := dfEqD2 (dfEqList d3)
    which is FINE because the use of d3 is protected by the instance function
    applications.

    So, our strategy is to try to put solved wanted dictionaries into the
    inert set along with their superclasses (when this is meaningful,
    i.e. when new wanted goals are generated) but solve a wanted dictionary
    from a given only in the case where the evidence variable of the
    wanted is mentioned in the evidence of the given (recursively through
    the evidence binds) in a protected way: more instance function applications
    than superclass selectors.

    Here are some more examples from GHC's previous type checker

    Example 3:
    This code arises in the context of "Scrap Your Boilerplate with Class"

        class Sat a
        class Data ctx a
        instance  Sat (ctx Char)             => Data ctx Char       -- dfunData1
        instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]        -- dfunData2

        class Data Maybe a => Foo a

        instance Foo t => Sat (Maybe t)                             -- dfunSat

        instance Data Maybe a => Foo a                              -- dfunFoo1
        instance Foo a        => Foo [a]                            -- dfunFoo2
        instance                 Foo [Char]                         -- dfunFoo3

    Consider generating the superclasses of the instance declaration
             instance Foo a => Foo [a]

    So our problem is this
        [G] d0 : Foo t
        [W] d1 : Data Maybe [t]   -- Desired superclass

    We may add the given in the inert set, along with its superclasses
    [assuming we don't fail because there is a matching instance, see
     topReactionsStage, given case ]
      Inert:
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      WorkList
        [W] d1 : Data Maybe [t]

    Solve d1 using instance dfunData2; d1 := dfunData2 d2 d3
      Inert:
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      Solved:
            d1 : Data Maybe [t]
      WorkList
        [W] d2 : Sat (Maybe [t])
        [W] d3 : Data Maybe t

    Now, we may simplify d2 using dfunSat; d2 := dfunSat d4
      Inert:
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      Solved:
            d1 : Data Maybe [t]
            d2 : Sat (Maybe [t])
      WorkList:
        [W] d3 : Data Maybe t
        [W] d4 : Foo [t]

    Now, we can just solve d3 from d01; d3 := d01
      Inert
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      Solved:
            d1 : Data Maybe [t]
            d2 : Sat (Maybe [t])
      WorkList
        [W] d4 : Foo [t]

    Now, solve d4 using dfunFoo2;  d4 := dfunFoo2 d5
      Inert
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      Solved:
            d1 : Data Maybe [t]
            d2 : Sat (Maybe [t])
            d4 : Foo [t]
      WorkList:
        [W] d5 : Foo t

    Now, d5 can be solved! d5 := d0

    Result
       d1 := dfunData2 d2 d3
       d2 := dfunSat d4
       d3 := d01
       d4 := dfunFoo2 d5
       d5 := d0

          d0 :_g Foo t
          d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3
          d2 :_g Sat (Maybe [t])          d2 := dfunSat d4
          d4 :_g Foo [t]                  d4 := dfunFoo2 d5
          d5 :_g Foo t                    d5 := dfunFoo1 d7
      WorkList:
          d7 :_w Data Maybe t
          d6 :_g Data Maybe [t]
          d8 :_g Data Maybe t            d8 := EvDictSuperClass d5 0
          d01 :_g Data Maybe t

    Now, two problems:
       [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
           we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
           that must not be used (look at case interactInert where both inert and workitem
           are givens). So we have several options:
           - Drop the workitem always (this will drop d8)
                  This feels very unsafe -- what if the work item was the "good" one
                  that should be used later to solve another wanted?
           - Don't drop anyone: the inert set may contain multiple givens!
                  [This is currently implemented]

    The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
      [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
          d7. Now the [isRecDictEv] function in the ineration solver
          [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
          precisely because chasing the evidence of d8 leads us to an unguarded use of d7.

          So, no interaction happens there. Then we meet d01 and there is no recursion
          problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!

    Note [SUPERCLASS-LOOP 1]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    We have to be very, very careful when generating superclasses, lest we
    accidentally build a loop. Here's an example:

      class S a

      class S a => C a where { opc :: a -> a }
      class S b => D b where { opd :: b -> b }

      instance C Int where
         opc = opd

      instance D Int where
         opd = opc

    From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
    Simplifying, we may well get:
            $dfCInt = :C ds1 (opd dd)
            dd  = $dfDInt
            ds1 = $p1 dd
    Notice that we spot that we can extract ds1 from dd.

    Alas!  Alack! We can do the same for (instance D Int):

            $dfDInt = :D ds2 (opc dc)
            dc  = $dfCInt
            ds2 = $p1 dc

    And now we've defined the superclass in terms of itself.
    Two more nasty cases are in
            tcrun021
            tcrun033

    Solution:
      - Satisfy the superclass context *all by itself*
        (tcSimplifySuperClasses)
      - And do so completely; i.e. no left-over constraints
        to mix with the constraints arising from method declarations

    Note [SUPERCLASS-LOOP 2]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    We need to be careful when adding "the constaint we are trying to prove".
    Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where

            class Ord a => C a where
            instance Ord [a] => C [a] where ...

    Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
    superclasses of C [a] to avails.  But we must not overwrite the binding
    for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
    build a loop!

    Here's another variant, immortalised in tcrun020
            class Monad m => C1 m
            class C1 m => C2 m x
            instance C2 Maybe Bool
    For the instance decl we need to build (C1 Maybe), and it's no good if
    we run around and add (C2 Maybe Bool) and its superclasses to the avails
    before we search for C1 Maybe.

    Here's another example
            class Eq b => Foo a b
            instance Eq a => Foo [a] a
    If we are reducing
            (Foo [t] t)

    we'll first deduce that it holds (via the instance decl).  We must not
    then overwrite the Eq t constraint with a superclass selection!

    At first I had a gross hack, whereby I simply did not add superclass constraints
    in addWanted, though I did for addGiven and addIrred.  This was sub-optimal,
    because it lost legitimate superclass sharing, and it still didn't do the job:
    I found a very obscure program (now tcrun021) in which improvement meant the
    simplifier got two bites a the cherry... so something seemed to be an Stop
    first time, but reducible next time.

    Now we implement the Right Solution, which is to check for loops directly
    when adding superclasses.  It's a bit like the occurs check in unification.

    Note [Recursive instances and superclases]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this code, which arises in the context of "Scrap Your
    Boilerplate with Class".

        class Sat a
        class Data ctx a
        instance  Sat (ctx Char)             => Data ctx Char
        instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]

        class Data Maybe a => Foo a

        instance Foo t => Sat (Maybe t)

        instance Data Maybe a => Foo a
        instance Foo a        => Foo [a]
        instance                 Foo [Char]

    In the instance for Foo [a], when generating evidence for the superclasses
    (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
    Using the instance for Data, we therefore need
            (Sat (Maybe [a], Data Maybe a)
    But we are given (Foo a), and hence its superclass (Data Maybe a).
    So that leaves (Sat (Maybe [a])).  Using the instance for Sat means
    we need (Foo [a]).  And that is the very dictionary we are bulding
    an instance for!  So we must put that in the "givens".  So in this
    case we have
            Given:  Foo a, Foo [a]
            Wanted: Data Maybe [a]

    BUT we must *not not not* put the *superclasses* of (Foo [a]) in
    the givens, which is what 'addGiven' would normally do. Why? Because
    (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
    by selecting a superclass from Foo [a], which simply makes a loop.

    On the other hand we *must* put the superclasses of (Foo a) in
    the givens, as you can see from the derivation described above.

    Conclusion: in the very special case of tcSimplifySuperClasses
    we have one 'given' (namely the "this" dictionary) whose superclasses
    must not be added to 'givens' by addGiven.

    There is a complication though.  Suppose there are equalities
          instance (Eq a, a~b) => Num (a,b)
    Then we normalise the 'givens' wrt the equalities, so the original
    given "this" dictionary is cast to one of a different type.  So it's a
    bit trickier than before to identify the "special" dictionary whose
    superclasses must not be added. See test
       indexed-types/should_run/EqInInstance

    We need a persistent property of the dictionary to record this
    special-ness.  Current I'm using the InstLocOrigin (a bit of a hack,
    but cool), which is maintained by dictionary normalisation.
    Specifically, the InstLocOrigin is
                 NoScOrigin
    then the no-superclass thing kicks in.  WATCH OUT if you fiddle
    with InstLocOrigin!

    ************************************************************************
    *                                                                      *
    *          Functional dependencies, instantiation of equations
    *                                                                      *
    ************************************************************************

    When we spot an equality arising from a functional dependency,
    we now use that equality (a "wanted") to rewrite the work-item
    constraint right away.  This avoids two dangers

     Danger 1: If we send the original constraint on down the pipeline
               it may react with an instance declaration, and in delicate
               situations (when a Given overlaps with an instance) that
               may produce new insoluble goals: see Trac #4952

     Danger 2: If we don't rewrite the constraint, it may re-react
               with the same thing later, and produce the same equality
               again --> termination worries.

    To achieve this required some refactoring of FunDeps.lhs (nicer
    now!).
    -}

    rewriteWithFunDeps :: [Equation CtLoc] -> TcS ()
    -- NB: The returned constraints are all Derived
    -- Post: returns no trivial equalities (identities) and all EvVars returned are fresh
    rewriteWithFunDeps eqn_pred_locs
     = mapM_ instFunDepEqn eqn_pred_locs

    instFunDepEqn :: Equation CtLoc -> TcS ()
    -- Post: Returns the position index as well as the corresponding FunDep equality
    instFunDepEqn (FDEqn { fd_qtvs = tvs, fd_eqs = eqs, fd_loc = loc })
      = do { (subst, _) <- instFlexiTcS tvs  -- Takes account of kind substitution
           ; mapM_ (do_one subst) eqs }
      where
        do_one subst (FDEq { fd_ty_left = ty1, fd_ty_right = ty2 })
           = unifyDerived loc Nominal $
             Pair (Type.substTy subst ty1) (Type.substTy subst ty2)

    {-
    *********************************************************************************
    *                                                                               *
                           The top-reaction Stage
    *                                                                               *
    *********************************************************************************
    -}

    topReactionsStage :: WorkItem -> TcS (StopOrContinue Ct)
    topReactionsStage wi
     = do { inerts <- getTcSInerts
          ; tir <- doTopReact inerts wi
          ; case tir of
              ContinueWith wi -> return (ContinueWith wi)
              Stop ev s       -> return (Stop ev (ptext (sLit "Top react:") <+> s)) }

    doTopReact :: InertSet -> WorkItem -> TcS (StopOrContinue Ct)
    -- The work item does not react with the inert set, so try interaction with top-level
    -- instances. Note:
    --
    --   (a) The place to add superclasses in not here in doTopReact stage.
    --       Instead superclasses are added in the worklist as part of the
    --       canonicalization process. See Note [Adding superclasses].
    --
    --   (b) See Note [Given constraint that matches an instance declaration]
    --       for some design decisions for given dictionaries.

    doTopReact inerts work_item
      = do { traceTcS "doTopReact" (ppr work_item)
           ; case work_item of
               CDictCan {}  -> doTopReactDict inerts work_item
               CFunEqCan {} -> doTopReactFunEq work_item
               _  -> -- Any other work item does not react with any top-level equations
                     return (ContinueWith work_item)  }

    --------------------
    doTopReactDict :: InertSet -> Ct -> TcS (StopOrContinue Ct)
    -- Try to use type-class instance declarations to simplify the constraint
    doTopReactDict inerts work_item@(CDictCan { cc_ev = fl, cc_class = cls
                                              , cc_tyargs = xis })
      | not (isWanted fl)   -- Never use instances for Given or Derived constraints
      = try_fundeps_and_return

      | Just ev <- lookupSolvedDict inerts loc cls xis   -- Cached
      = do { setEvBind dict_id (ctEvTerm ev);
           ; stopWith fl "Dict/Top (cached)" }

      | otherwise  -- Not cached
       = do { lkup_inst_res <- matchClassInst inerts cls xis loc
             ; case lkup_inst_res of
                   GenInst wtvs ev_term -> do { addSolvedDict fl cls xis
                                              ; solve_from_instance wtvs ev_term }
                   NoInstance -> try_fundeps_and_return }
       where
         dict_id = ASSERT( isWanted fl ) ctEvId fl
         pred = mkClassPred cls xis
         loc = ctEvLoc fl

         solve_from_instance :: [CtEvidence] -> EvTerm -> TcS (StopOrContinue Ct)
          -- Precondition: evidence term matches the predicate workItem
         solve_from_instance evs ev_term
            | null evs
            = do { traceTcS "doTopReact/found nullary instance for" $
                   ppr dict_id
                 ; setEvBind dict_id ev_term
                 ; stopWith fl "Dict/Top (solved, no new work)" }
            | otherwise
            = do { traceTcS "doTopReact/found non-nullary instance for" $
                   ppr dict_id
                 ; setEvBind dict_id ev_term
                 ; let mk_new_wanted ev
                           = mkNonCanonical (ev {ctev_loc = bumpCtLocDepth CountConstraints loc })
                 ; updWorkListTcS (extendWorkListCts (map mk_new_wanted evs))
                 ; stopWith fl "Dict/Top (solved, more work)" }

         -- We didn't solve it; so try functional dependencies with
         -- the instance environment, and return
         -- NB: even if there *are* some functional dependencies against the
         -- instance environment, there might be a unique match, and if
         -- so we make sure we get on and solve it first. See Note [Weird fundeps]
         try_fundeps_and_return
           = do { instEnvs <- getInstEnvs
                ; let fd_eqns :: [Equation CtLoc]
                      fd_eqns = [ fd { fd_loc = loc { ctl_origin = FunDepOrigin2 pred (ctl_origin loc)
                                                                                 inst_pred inst_loc } }
                                | fd@(FDEqn { fd_loc = inst_loc, fd_pred1 = inst_pred })
                                <- improveFromInstEnv instEnvs pred ]
                ; rewriteWithFunDeps fd_eqns
                ; continueWith work_item }

    doTopReactDict _ w = pprPanic "doTopReactDict" (ppr w)

    --------------------
    doTopReactFunEq :: Ct -> TcS (StopOrContinue Ct)
    doTopReactFunEq work_item@(CFunEqCan { cc_ev = old_ev, cc_fun = fam_tc
                                         , cc_tyargs = args , cc_fsk = fsk })
      = ASSERT(isTypeFamilyTyCon fam_tc) -- No associated data families
                                         -- have reached this far
        ASSERT( not (isDerived old_ev) )   -- CFunEqCan is never Derived
        -- Look up in top-level instances, or built-in axiom
        do { match_res <- matchFam fam_tc args   -- See Note [MATCHING-SYNONYMS]
           ; case match_res of {
               Nothing -> do { try_improvement; continueWith work_item } ;
               Just (ax_co, rhs_ty)

        -- Found a top-level instance

        | Just (tc, tc_args) <- tcSplitTyConApp_maybe rhs_ty
        , isTypeFamilyTyCon tc
        , tc_args `lengthIs` tyConArity tc    -- Short-cut
        -> shortCutReduction old_ev fsk ax_co tc tc_args
             -- Try shortcut; see Note [Short cut for top-level reaction]

        | isGiven old_ev  -- Not shortcut
        -> do { let final_co = mkTcSymCo (ctEvCoercion old_ev) `mkTcTransCo` ax_co
                    -- final_co :: fsk ~ rhs_ty
              ; new_ev <- newGivenEvVar deeper_loc (mkTcEqPred (mkTyVarTy fsk) rhs_ty,
                                                    EvCoercion final_co)
              ; emitWorkNC [new_ev]   -- Non-cannonical; that will mean we flatten rhs_ty
              ; stopWith old_ev "Fun/Top (given)" }

        | not (fsk `elemVarSet` tyVarsOfType rhs_ty)
        -> do { dischargeFmv (ctEvId old_ev) fsk ax_co rhs_ty
              ; traceTcS "doTopReactFunEq" $
                vcat [ text "old_ev:" <+> ppr old_ev
                     , nest 2 (text ":=") <+> ppr ax_co ]
              ; stopWith old_ev "Fun/Top (wanted)" }

        | otherwise -- We must not assign ufsk := ...ufsk...!
        -> do { alpha_ty <- newFlexiTcSTy (tyVarKind fsk)
              ; new_ev <- newWantedEvVarNC loc (mkTcEqPred alpha_ty rhs_ty)
              ; emitWorkNC [new_ev]
                  -- By emitting this as non-canonical, we deal with all
                  -- flattening, occurs-check, and ufsk := ufsk issues
              ; let final_co = ax_co `mkTcTransCo` mkTcSymCo (ctEvCoercion new_ev)
                  --    ax_co :: fam_tc args ~ rhs_ty
                  --       ev :: alpha ~ rhs_ty
                  --     ufsk := alpha
                  -- final_co :: fam_tc args ~ alpha
              ; dischargeFmv (ctEvId old_ev) fsk final_co alpha_ty
              ; traceTcS "doTopReactFunEq (occurs)" $
                vcat [ text "old_ev:" <+> ppr old_ev
                     , nest 2 (text ":=") <+> ppr final_co
                     , text "new_ev:" <+> ppr new_ev ]
              ; stopWith old_ev "Fun/Top (wanted)" } } }
      where
        loc = ctEvLoc old_ev
        deeper_loc = bumpCtLocDepth CountTyFunApps loc

        try_improvement
          | Just ops <- isBuiltInSynFamTyCon_maybe fam_tc
          = do { inert_eqs <- getInertEqs
               ; let eqns = sfInteractTop ops args (lookupFlattenTyVar inert_eqs fsk)
               ; mapM_ (unifyDerived loc Nominal) eqns }
          | otherwise
          = return ()

    doTopReactFunEq w = pprPanic "doTopReactFunEq" (ppr w)

    shortCutReduction :: CtEvidence -> TcTyVar -> TcCoercion
                      -> TyCon -> [TcType] -> TcS (StopOrContinue Ct)
    shortCutReduction old_ev fsk ax_co fam_tc tc_args
      | isGiven old_ev
      = ASSERT( ctEvEqRel old_ev == NomEq )
        runFlatten $
        do { let fmode = mkFlattenEnv FM_FlattenAll old_ev
           ; (xis, cos) <- flatten_many fmode (repeat Nominal) tc_args
                   -- ax_co :: F args ~ G tc_args
                   -- cos   :: xis ~ tc_args
                   -- old_ev :: F args ~ fsk
                   -- G cos ; sym ax_co ; old_ev :: G xis ~ fsk

           ; new_ev <- newGivenEvVar deeper_loc
                             ( mkTcEqPred (mkTyConApp fam_tc xis) (mkTyVarTy fsk)
                             , EvCoercion (mkTcTyConAppCo Nominal fam_tc cos
                                            `mkTcTransCo` mkTcSymCo ax_co
                                            `mkTcTransCo` ctEvCoercion old_ev) )

           ; let new_ct = CFunEqCan { cc_ev = new_ev, cc_fun = fam_tc, cc_tyargs = xis, cc_fsk = fsk }
           ; emitFlatWork new_ct
           ; stopWith old_ev "Fun/Top (given, shortcut)" }

      | otherwise
      = ASSERT( not (isDerived old_ev) )   -- Caller ensures this
        ASSERT( ctEvEqRel old_ev == NomEq )
        runFlatten $
        do { let fmode = mkFlattenEnv FM_FlattenAll old_ev
           ; (xis, cos) <- flatten_many fmode (repeat Nominal) tc_args
                   -- ax_co :: F args ~ G tc_args
                   -- cos   :: xis ~ tc_args
                   -- G cos ; sym ax_co ; old_ev :: G xis ~ fsk
                   -- new_ev :: G xis ~ fsk
                   -- old_ev :: F args ~ fsk := ax_co ; sym (G cos) ; new_ev

           ; new_ev <- newWantedEvVarNC loc (mkTcEqPred (mkTyConApp fam_tc xis) (mkTyVarTy fsk))
           ; setEvBind (ctEvId old_ev)
                       (EvCoercion (ax_co `mkTcTransCo` mkTcSymCo (mkTcTyConAppCo Nominal fam_tc cos)
                                          `mkTcTransCo` ctEvCoercion new_ev))

           ; let new_ct = CFunEqCan { cc_ev = new_ev, cc_fun = fam_tc, cc_tyargs = xis, cc_fsk = fsk }
           ; emitFlatWork new_ct
           ; stopWith old_ev "Fun/Top (wanted, shortcut)" }
      where
        loc = ctEvLoc old_ev
        deeper_loc = bumpCtLocDepth CountTyFunApps loc

    dischargeFmv :: EvVar -> TcTyVar -> TcCoercion -> TcType -> TcS ()
    -- (dischargeFmv x fmv co ty)
    --     [W] x :: F tys ~ fuv
    --        co :: F tys ~ ty
    -- Precondition: fuv is not filled, and fuv `notElem` ty
    --
    -- Then set fuv := ty,
    --      set x := co
    --      kick out any inert things that are now rewritable
    dischargeFmv evar fmv co xi
      = ASSERT2( not (fmv `elemVarSet` tyVarsOfType xi), ppr evar $$ ppr fmv $$ ppr xi )
        do { setWantedTyBind fmv xi
           ; setEvBind evar (EvCoercion co)
           ; n_kicked <- kickOutRewritable Given NomEq fmv
           ; traceTcS "dischargeFuv" (ppr fmv <+> equals <+> ppr xi $$ ppr_kicked n_kicked) }

    {-
    Note [Cached solved FunEqs]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When trying to solve, say (FunExpensive big-type ~ ty), it's important
    to see if we have reduced (FunExpensive big-type) before, lest we
    simply repeat it.  Hence the lookup in inert_solved_funeqs.  Moreover
    we must use `canRewriteOrSame` because both uses might (say) be Wanteds,
    and we *still* want to save the re-computation.

    Note [MATCHING-SYNONYMS]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    When trying to match a dictionary (D tau) to a top-level instance, or a
    type family equation (F taus_1 ~ tau_2) to a top-level family instance,
    we do *not* need to expand type synonyms because the matcher will do that for us.

    Note [RHS-FAMILY-SYNONYMS]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    The RHS of a family instance is represented as yet another constructor which is
    like a type synonym for the real RHS the programmer declared. Eg:
        type instance F (a,a) = [a]
    Becomes:
        :R32 a = [a]      -- internal type synonym introduced
        F (a,a) ~ :R32 a  -- instance

    When we react a family instance with a type family equation in the work list
    we keep the synonym-using RHS without expansion.

    Note [FunDep and implicit parameter reactions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Currently, our story of interacting two dictionaries (or a dictionary
    and top-level instances) for functional dependencies, and implicit
    paramters, is that we simply produce new Derived equalities.  So for example

            class D a b | a -> b where ...
        Inert:
            d1 :g D Int Bool
        WorkItem:
            d2 :w D Int alpha

        We generate the extra work item
            cv :d alpha ~ Bool
        where 'cv' is currently unused.  However, this new item can perhaps be
        spontaneously solved to become given and react with d2,
        discharging it in favour of a new constraint d2' thus:
            d2' :w D Int Bool
            d2 := d2' |> D Int cv
        Now d2' can be discharged from d1

    We could be more aggressive and try to *immediately* solve the dictionary
    using those extra equalities, but that requires those equalities to carry
    evidence and derived do not carry evidence.

    If that were the case with the same inert set and work item we might dischard
    d2 directly:

            cv :w alpha ~ Bool
            d2 := d1 |> D Int cv

    But in general it's a bit painful to figure out the necessary coercion,
    so we just take the first approach. Here is a better example. Consider:
        class C a b c | a -> b
    And:
         [Given]  d1 : C T Int Char
         [Wanted] d2 : C T beta Int
    In this case, it's *not even possible* to solve the wanted immediately.
    So we should simply output the functional dependency and add this guy
    [but NOT its superclasses] back in the worklist. Even worse:
         [Given] d1 : C T Int beta
         [Wanted] d2: C T beta Int
    Then it is solvable, but its very hard to detect this on the spot.

    It's exactly the same with implicit parameters, except that the
    "aggressive" approach would be much easier to implement.

    Note [When improvement happens]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We fire an improvement rule when

      * Two constraints match (modulo the fundep)
          e.g. C t1 t2, C t1 t3    where C a b | a->b
        The two match because the first arg is identical

    Note that we *do* fire the improvement if one is Given and one is Derived (e.g. a
    superclass of a Wanted goal) or if both are Given.

    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
      Given:  C a b  ... and hance by superclasses, (G a, L a b)
      Wanted: G (Maybe a)
    Use the instance decl to get
      Wanted: C a b'
    The (C a b') is inert, so we generate its Derived superclasses (L a b'),
    and now we need improvement between that derived superclass an the Given (L a b)

    Test typecheck/should_fail/FDsFromGivens also shows why it's a good idea to
    emit Derived FDs for givens as well.

    Note [Weird fundeps]
    ~~~~~~~~~~~~~~~~~~~~
    Consider   class Het a b | a -> b where
                  het :: m (f c) -> a -> m b

               class GHet (a :: * -> *) (b :: * -> *) | a -> b
               instance            GHet (K a) (K [a])
               instance Het a b => GHet (K a) (K b)

    The two instances don't actually conflict on their fundeps,
    although it's pretty strange.  So they are both accepted. Now
    try   [W] GHet (K Int) (K Bool)
    This triggers fudeps from both instance decls; but it also
    matches a *unique* instance decl, and we should go ahead and
    pick that one right now.  Otherwise, if we don't, it ends up
    unsolved in the inert set and is reported as an error.

    Trac #7875 is a case in point.

    Note [Overriding implicit parameters]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider
       f :: (?x::a) -> Bool -> a

       g v = let ?x::Int = 3
             in (f v, let ?x::Bool = True in f v)

    This should probably be well typed, with
       g :: Bool -> (Int, Bool)

    So the inner binding for ?x::Bool *overrides* the outer one.
    Hence a work-item Given overrides an inert-item Given.

    Note [Given constraint that matches an instance declaration]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    What should we do when we discover that one (or more) top-level
    instances match a given (or solved) class constraint? We have
    two possibilities:

      1. Reject the program. The reason is that there may not be a unique
         best strategy for the solver. Example, from the OutsideIn(X) paper:
           instance P x => Q [x]
           instance (x ~ y) => R [x] y

           wob :: forall a b. (Q [b], R b a) => a -> Int

           g :: forall a. Q [a] => [a] -> Int
           g x = wob x

           will generate the impliation constraint:
                Q [a] => (Q [beta], R beta [a])
           If we react (Q [beta]) with its top-level axiom, we end up with a
           (P beta), which we have no way of discharging. On the other hand,
           if we react R beta [a] with the top-level we get  (beta ~ a), which
           is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
           now solvable by the given Q [a].

         However, this option is restrictive, for instance [Example 3] from
         Note [Recursive instances and superclases] will fail to work.

      2. Ignore the problem, hoping that the situations where there exist indeed
         such multiple strategies are rare: Indeed the cause of the previous
         problem is that (R [x] y) yields the new work (x ~ y) which can be
         *spontaneously* solved, not using the givens.

    We are choosing option 2 below but we might consider having a flag as well.

    Note [New Wanted Superclass Work]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Even in the case of wanted constraints, we may add some superclasses
    as new given work. The reason is:

            To allow FD-like improvement for type families. Assume that
            we have a class
                 class C a b | a -> b
            and we have to solve the implication constraint:
                 C a b => C a beta
            Then, FD improvement can help us to produce a new wanted (beta ~ b)

            We want to have the same effect with the type family encoding of
            functional dependencies. Namely, consider:
                 class (F a ~ b) => C a b
            Now suppose that we have:
                   given: C a b
                   wanted: C a beta
            By interacting the given we will get given (F a ~ b) which is not
            enough by itself to make us discharge (C a beta). However, we
            may create a new derived equality from the super-class of the
            wanted constraint (C a beta), namely derived (F a ~ beta).
            Now we may interact this with given (F a ~ b) to get:
                      derived :  beta ~ b
            But 'beta' is a touchable unification variable, and hence OK to
            unify it with 'b', replacing the derived evidence with the identity.

            This requires trySpontaneousSolve to solve *derived*
            equalities that have a touchable in their RHS, *in addition*
            to solving wanted equalities.

    We also need to somehow use the superclasses to quantify over a minimal,
    constraint see note [Minimize by Superclasses] in TcSimplify.

    Finally, here is another example where this is useful.

    Example 1:
    ----------
       class (F a ~ b) => C a b
    And we are given the wanteds:
          w1 : C a b
          w2 : C a c
          w3 : b ~ c
    We surely do *not* want to quantify over (b ~ c), since if someone provides
    dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
    of (b ~ c), hence no extra evidence is necessary. Here is what will happen:

         Step 1: We will get new *given* superclass work,
                 provisionally to our solving of w1 and w2

                   g1: F a ~ b, g2 : F a ~ c,
                   w1 : C a b, w2 : C a c, w3 : b ~ c

                 The evidence for g1 and g2 is a superclass evidence term:

                   g1 := sc w1, g2 := sc w2

         Step 2: The givens will solve the wanted w3, so that
                   w3 := sym (sc w1) ; sc w2

         Step 3: Now, one may naively assume that then w2 can be solve from w1
                 after rewriting with the (now solved equality) (b ~ c).

                 But this rewriting is ruled out by the isGoodRectDict!

    Conclusion, we will (correctly) end up with the unsolved goals
        (C a b, C a c)

    NB: The desugarer needs be more clever to deal with equalities
        that participate in recursive dictionary bindings.
    -}

    data LookupInstResult
      = NoInstance
      | GenInst [CtEvidence] EvTerm

    instance Outputable LookupInstResult where
      ppr NoInstance = text "NoInstance"
      ppr (GenInst ev t) = text "GenInst" <+> ppr ev <+> ppr t

    matchClassInst :: InertSet -> Class -> [Type] -> CtLoc -> TcS LookupInstResult

    matchClassInst _ clas [ ty ] _
      | className clas == knownNatClassName
      , Just n <- isNumLitTy ty = makeDict (EvNum n)

      | className clas == knownSymbolClassName
      , Just s <- isStrLitTy ty = makeDict (EvStr s)

      where
      {- This adds a coercion that will convert the literal into a dictionary
         of the appropriate type.  See Note [KnownNat & KnownSymbol and EvLit]
         in TcEvidence.  The coercion happens in 2 steps:

         Integer -> SNat n     -- representation of literal to singleton
         SNat n  -> KnownNat n -- singleton to dictionary

         The process is mirrored for Symbols:
         String    -> SSymbol n
         SSymbol n -> KnownSymbol n
      -}
      makeDict evLit
        | Just (_, co_dict) <- tcInstNewTyCon_maybe (classTyCon clas) [ty]
              -- co_dict :: KnownNat n ~ SNat n
        , [ meth ]   <- classMethods clas
        , Just tcRep <- tyConAppTyCon_maybe -- SNat
                          $ funResultTy         -- SNat n
                          $ dropForAlls         -- KnownNat n => SNat n
                          $ idType meth         -- forall n. KnownNat n => SNat n
        , Just (_, co_rep) <- tcInstNewTyCon_maybe tcRep [ty]
              -- SNat n ~ Integer
        = return (GenInst [] $ mkEvCast (EvLit evLit) (mkTcSymCo (mkTcTransCo co_dict co_rep)))

        | otherwise
        = panicTcS (text "Unexpected evidence for" <+> ppr (className clas)
                         $$ vcat (map (ppr . idType) (classMethods clas)))

    matchClassInst _ clas [k,t] loc
      | className clas == typeableClassName = matchTypeableClass clas k t loc

    matchClassInst inerts clas tys loc
       = do { dflags <- getDynFlags
            ; traceTcS "matchClassInst" $ vcat [ text "pred =" <+> ppr pred
                                               , text "inerts=" <+> ppr inerts ]
            ; instEnvs <- getInstEnvs
            ; case lookupInstEnv instEnvs clas tys of
                ([], _, _)               -- Nothing matches
                    -> do { traceTcS "matchClass not matching" $
                            vcat [ text "dict" <+> ppr pred ]
                          ; return NoInstance }

                ([(ispec, inst_tys)], [], _) -- A single match
                    | not (xopt Opt_IncoherentInstances dflags)
                    , not (isEmptyBag unifiable_givens)
                    -> -- See Note [Instance and Given overlap]
                       do { traceTcS "Delaying instance application" $
                              vcat [ text "Work item=" <+> pprType (mkClassPred clas tys)
                                   , text "Relevant given dictionaries=" <+> ppr unifiable_givens ]
                          ; return NoInstance  }

                    | otherwise
                    -> do   { let dfun_id = instanceDFunId ispec
                            ; traceTcS "matchClass success" $
                              vcat [text "dict" <+> ppr pred,
                                    text "witness" <+> ppr dfun_id
                                                   <+> ppr (idType dfun_id) ]
                                      -- Record that this dfun is needed
                            ; match_one dfun_id inst_tys }

                (matches, _, _)    -- More than one matches
                                   -- Defer any reactions of a multitude
                                   -- until we learn more about the reagent
                    -> do   { traceTcS "matchClass multiple matches, deferring choice" $
                              vcat [text "dict" <+> ppr pred,
                                    text "matches" <+> ppr matches]
                            ; return NoInstance } }
       where
         pred = mkClassPred clas tys

         match_one :: DFunId -> [Maybe TcType] -> TcS LookupInstResult
                      -- See Note [DFunInstType: instantiating types] in InstEnv
         match_one dfun_id mb_inst_tys
           = do { checkWellStagedDFun pred dfun_id loc
                ; (tys, dfun_phi) <- instDFunType dfun_id mb_inst_tys
                ; let (theta, _) = tcSplitPhiTy dfun_phi
                ; if null theta then
                      return (GenInst [] (EvDFunApp dfun_id tys []))
                  else do
                { evc_vars <- instDFunConstraints loc theta
                ; let new_ev_vars = freshGoals evc_vars
                          -- new_ev_vars are only the real new variables that can be emitted
                      dfun_app = EvDFunApp dfun_id tys (map (ctEvTerm . fst) evc_vars)
                ; return $ GenInst new_ev_vars dfun_app } }

         unifiable_givens :: Cts
         unifiable_givens = filterBag matchable $
                            findDictsByClass (inert_dicts $ inert_cans inerts) clas

         matchable (CDictCan { cc_class = clas_g, cc_tyargs = sys, cc_ev = fl })
           | isGiven fl
           , Just {} <- tcUnifyTys bind_meta_tv tys sys
           = ASSERT( clas_g == clas ) True
           | otherwise = False -- No overlap with a solved, already been taken care of
                               -- by the overlap check with the instance environment.

         matchable ct = pprPanic "Expecting dictionary!" (ppr ct)

         bind_meta_tv :: TcTyVar -> BindFlag
         -- Any meta tyvar may be unified later, so we treat it as
         -- bindable when unifying with givens. That ensures that we
         -- conservatively assume that a meta tyvar might get unified with
         -- something that matches the 'given', until demonstrated
         -- otherwise.
         bind_meta_tv tv | isMetaTyVar tv = BindMe
                         | otherwise      = Skolem

    {- Note [Instance and Given overlap]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Example, from the OutsideIn(X) paper:
           instance P x => Q [x]
           instance (x ~ y) => R y [x]

           wob :: forall a b. (Q [b], R b a) => a -> Int

           g :: forall a. Q [a] => [a] -> Int
           g x = wob x

    This will generate the impliation constraint:
                Q [a] => (Q [beta], R beta [a])
    If we react (Q [beta]) with its top-level axiom, we end up with a
    (P beta), which we have no way of discharging. On the other hand,
    if we react R beta [a] with the top-level we get  (beta ~ a), which
    is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
    now solvable by the given Q [a].

    The solution is that:
      In matchClassInst (and thus in topReact), we return a matching
      instance only when there is no Given in the inerts which is
      unifiable to this particular dictionary.

      We treat any meta-tyvar as "unifiable" for this purpose,
      *including* untouchable ones

    The end effect is that, much as we do for overlapping instances, we
    delay choosing a class instance if there is a possibility of another
    instance OR a given to match our constraint later on. This fixes
    Trac #4981 and #5002.

    Other notes:

    * This is arguably not easy to appear in practice due to our
      aggressive prioritization of equality solving over other
      constraints, but it is possible. I've added a test case in
      typecheck/should-compile/GivenOverlapping.hs

    * Another "live" example is Trac #10195

    * We ignore the overlap problem if -XIncoherentInstances is in force:
      see Trac #6002 for a worked-out example where this makes a
      difference.

    * Moreover notice that our goals here are different than the goals of
      the top-level overlapping checks. There we are interested in
      validating the following principle:

          If we inline a function f at a site where the same global
          instance environment is available as the instance environment at
          the definition site of f then we should get the same behaviour.

      But for the Given Overlap check our goal is just related to completeness of
      constraint solving.
    -}

    -- | Assumes that we've checked that this is the 'Typeable' class,
    -- and it was applied to the correc arugment.
    matchTypeableClass :: Class -> Kind -> Type -> CtLoc -> TcS LookupInstResult
    matchTypeableClass clas _k t loc

      -- See Note [No Typeable for qualified types]
      | isForAllTy t                               = return NoInstance
      -- Is the type of the form `C => t`?
      | Just (t1,_) <- splitFunTy_maybe t,
        isConstraintKind (typeKind t1)             = return NoInstance

      | Just (tc, ks) <- splitTyConApp_maybe t
      , all isKind ks                              = doTyCon tc ks
      | Just (f,kt)       <- splitAppTy_maybe t    = doTyApp f kt
      | Just _            <- isNumLitTy t          = mkSimpEv (EvTypeableTyLit t)
      | Just _            <- isStrLitTy t          = mkSimpEv (EvTypeableTyLit t)
      | otherwise                                  = return NoInstance

      where
      -- Representation for type constructor applied to some kinds
      doTyCon tc ks =
        case mapM kindRep ks of
          Nothing    -> return NoInstance
          Just kReps -> mkSimpEv (EvTypeableTyCon tc kReps)

      {- Representation for an application of a type to a type-or-kind.
      This may happen when the type expression starts with a type variable.
      Example (ignoring kind parameter):
        Typeable (f Int Char)                      -->
        (Typeable (f Int), Typeable Char)          -->
        (Typeable f, Typeable Int, Typeable Char)  --> (after some simp. steps)
        Typeable f
      -}
      doTyApp f tk
        | isKind tk = return NoInstance -- We can't solve until we know the ctr.
        | otherwise =
          do ct1 <- subGoal f
             ct2 <- subGoal tk
             let realSubs = [ c | (c,Fresh) <- [ct1,ct2] ]
             return $ GenInst realSubs
                    $ EvTypeable $ EvTypeableTyApp (getEv ct1,f) (getEv ct2,tk)

      -- Representation for concrete kinds.  We just use the kind itself,
      -- but first check to make sure that it is "simple" (i.e., made entirely
      -- out of kind constructors).
      kindRep ki = do (_,ks) <- splitTyConApp_maybe ki
                      mapM_ kindRep ks
                      return ki

      getEv (ct,_fresh) = ctEvTerm ct

      -- Emit a `Typeable` constraint for the given type.
      subGoal ty = do let goal = mkClassPred clas [ typeKind ty, ty ]
                      newWantedEvVar loc goal

      mkSimpEv ev = return (GenInst [] (EvTypeable ev))

    {- Note [No Typeable for polytype or for constraints]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We do not support impredicative typeable, such as
       Typeable (forall a. a->a)
       Typeable (Eq a => a -> a)
       Typeable (() => Int)
       Typeable (((),()) => Int)

    See Trac #9858.  For forall's the case is clear: we simply don't have
    a TypeRep for them.  For qualified but not polymorphic types, like
    (Eq a => a -> a), things are murkier.  But:

     * We don't need a TypeRep for these things.  TypeReps are for
       monotypes only.

      * Perhaps we could treat `=>` as another type constructor for `Typeable`
        purposes, and thus support things like `Eq Int => Int`, however,
        at the current state of affairs this would be an odd exception as
        no other class works with impredicative types.
        For now we leave it off, until we have a better story for impredicativity.
    -}

    -- | Is the constraint for an implicit CallStack parameter?
    isCallStackIP :: CtLoc -> Class -> Type -> Maybe (EvTerm -> EvCallStack)
    isCallStackIP loc cls ty
      | Just (tc, []) <- splitTyConApp_maybe ty
      , cls `hasKey` ipClassNameKey && tc `hasKey` callStackTyConKey
      = occOrigin (ctLocOrigin loc)
      where
      -- We only want to grab constraints that arose due to the use of an IP or a
      -- function call. See Note [Overview of implicit CallStacks]
      occOrigin (OccurrenceOf n)
        = Just (EvCsPushCall n locSpan)
      occOrigin (IPOccOrigin n)
        = Just (EvCsTop ('?' `consFS` hsIPNameFS n) locSpan)
      occOrigin _
        = Nothing
      locSpan
        = ctLocSpan loc
    isCallStackIP _ _ _
      = Nothing