typecheck/TcInteract.hs

    {-# LANGUAGE CPP #-}

    module TcInteract (
         solveSimpleGivens,   -- Solves [Ct]
         solveSimpleWanteds,  -- Solves Cts

         solveCallStack,      -- for use in TcSimplify
      ) where

    #include "HsVersions.h"

    import BasicTypes ( infinity, IntWithInf, intGtLimit )
    import HsTypes ( HsIPName(..) )
    import TcCanonical
    import TcFlatten
    import TcUnify( canSolveByUnification )
    import VarSet
    import Type
    import InstEnv( DFunInstType, lookupInstEnv, instanceDFunId )
    import CoAxiom( sfInteractTop, sfInteractInert )

    import Var
    import TcType
    import Name
    import PrelNames ( knownNatClassName, knownSymbolClassName,
                       typeableClassName, coercibleTyConKey,
                       heqTyConKey, ipClassKey )
    import TysWiredIn ( typeNatKind, typeSymbolKind, heqDataCon,
                        coercibleDataCon )
    import TysPrim    ( eqPrimTyCon, eqReprPrimTyCon )
    import Id( idType )
    import CoAxiom ( Eqn, CoAxiom(..), CoAxBranch(..), fromBranches )
    import Class
    import TyCon
    import DataCon( dataConWrapId )
    import FunDeps
    import FamInst
    import FamInstEnv
    import Unify ( tcUnifyTyWithTFs )

    import TcEvidence
    import Outputable

    import TcRnTypes
    import TcSMonad
    import Bag
    import MonadUtils ( concatMapM )

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

    import Control.Monad
    import Maybes( isJust )
    import Pair (Pair(..))
    import Unique( hasKey )
    import DynFlags
    import Util
    import qualified GHC.LanguageExtensions as LangExt

    {-
    **********************************************************************
    *                                                                    *
    *                      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 them 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 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 :: [Ct] -> TcS Cts
    solveSimpleGivens givens
      | null givens  -- Shortcut for common case
      = return emptyCts
      | otherwise
      = do { go givens
           ; takeGivenInsolubles }
      where
        go givens = do { solveSimples (listToBag givens)
                       ; new_givens <- runTcPluginsGiven
                       ; when (notNull new_givens) $
                         go new_givens }

    solveSimpleWanteds :: Cts -> TcS WantedConstraints
    -- NB: 'simples' may contain /derived/ equalities, floated
    --     out from a nested implication. So don't discard deriveds!
    solveSimpleWanteds simples
      = do { traceTcS "solveSimples {" (ppr simples)
           ; dflags <- getDynFlags
           ; (n,wc) <- go 1 (solverIterations dflags) (emptyWC { wc_simple = simples })
           ; traceTcS "solveSimples end }" $
                 vcat [ text "iterations =" <+> ppr n
                      , text "residual =" <+> ppr wc ]
           ; return wc }
      where
        go :: Int -> IntWithInf -> WantedConstraints -> TcS (Int, WantedConstraints)
        go n limit wc
          | n `intGtLimit` limit
          = failTcS (hang (text "solveSimpleWanteds: too many iterations"
                           <+> parens (text "limit =" <+> ppr limit))
                        2 (vcat [ text "Set limit with -fsolver-iterations=n; n=0 for no limit"
                                , text "Simples =" <+> ppr simples
                                , text "WC ="      <+> ppr wc ]))

         | isEmptyBag (wc_simple wc)
         = return (n,wc)

         | otherwise
         = do { -- Solve
                (unif_count, wc1) <- solve_simple_wanteds wc

                -- Run plugins
              ; (rerun_plugin, wc2) <- runTcPluginsWanted wc1
                 -- See Note [Running plugins on unflattened wanteds]

              ; if unif_count == 0 && not rerun_plugin
                then return (n, wc2)             -- Done
                else do { traceTcS "solveSimple going round again:" (ppr rerun_plugin)
                        ; go (n+1) limit wc2 } }      -- Loop

    solve_simple_wanteds :: WantedConstraints -> TcS (Int, WantedConstraints)
    -- Try solving these constraints
    -- Affects the unification state (of course) but not the inert set
    solve_simple_wanteds (WC { wc_simple = simples1, wc_insol = insols1, wc_impl = implics1 })
      = nestTcS $
        do { solveSimples simples1
           ; (implics2, tv_eqs, fun_eqs, insols2, others) <- getUnsolvedInerts
           ; (unif_count, unflattened_eqs) <- reportUnifications $
                                              unflatten tv_eqs fun_eqs
                -- See Note [Unflatten after solving the simple wanteds]
           ; return ( unif_count
                    , WC { wc_simple = others `andCts` unflattened_eqs
                         , wc_insol  = insols1 `andCts` insols2
                         , wc_impl   = implics1 `unionBags` implics2 }) }

    {- Note [The solveSimpleWanteds loop]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Solving a bunch of simple constraints is done in a loop,
    (the 'go' loop of 'solveSimpleWanteds'):
      1. Try to solve them; unflattening may lead to improvement that
         was not exploitable during solving
      2. Try the plugin
      3. If step 1 did improvement during unflattening; or if the plugin
         wants to run again, go back to step 1

    Non-obviously, improvement can also take place during
    the unflattening that takes place in step (1). See TcFlatten,
    See Note [Unflattening can force the solver to iterate]
    -}

    -- 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-implications
    -- The constraints are initially examined in left-to-right order

    solveSimples cts
      = {-# SCC "solveSimples" #-}
        do { updWorkListTcS (\wl -> foldrBag extendWorkListCt wl cts)
           ; solve_loop }
      where
        solve_loop
          = {-# SCC "solve_loop" #-}
            do { sel <- selectNextWorkItem
               ; case sel of
                  Nothing -> return ()
                  Just ct -> do { runSolverPipeline thePipeline ct
                                ; solve_loop } }

    -- | 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 { plugins <- getTcPlugins
           ; if null plugins then return [] else
        do { givens <- getInertGivens
           ; if null givens then return [] else
        do { p <- runTcPlugins plugins (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 :: WantedConstraints -> TcS (Bool, WantedConstraints)
    runTcPluginsWanted wc@(WC { wc_simple = simples1, wc_insol = insols1, wc_impl = implics1 })
      | isEmptyBag simples1
      = return (False, wc)
      | otherwise
      = do { plugins <- getTcPlugins
           ; if null plugins then return (False, wc) else

        do { given <- getInertGivens
           ; simples1 <- zonkSimples simples1    -- Plugin requires zonked inputs
           ; let (wanted, derived) = partition isWantedCt (bagToList simples1)
           ; p <- runTcPlugins plugins (given, derived, wanted)
           ; let (_, _,                solved_wanted)   = pluginSolvedCts p
                 (_, unsolved_derived, unsolved_wanted) = pluginInputCts p
                 new_wanted                             = pluginNewCts p

    -- SLPJ: I'm deeply suspicious of this
    --       ; updInertCans (removeInertCts $ solved_givens ++ solved_deriveds)

           ; mapM_ setEv solved_wanted
           ; return ( notNull (pluginNewCts p)
                    , WC { wc_simple = listToBag new_wanted `andCts` listToBag unsolved_wanted
                                                            `andCts` listToBag unsolved_derived
                         , wc_insol  = listToBag (pluginBadCts p) `andCts` insols1
                         , wc_impl   = implics1 } ) } }
      where
        setEv :: (EvTerm,Ct) -> TcS ()
        setEv (ev,ct) = case ctEvidence ct of
          CtWanted { ctev_dest = dest } -> setWantedEvTerm dest 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
        }

    getTcPlugins :: TcS [TcPluginSolver]
    getTcPlugins = do { tcg_env <- getGblEnv; return (tcg_tc_plugins tcg_env) }

    -- | 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 :: [TcPluginSolver] -> SplitCts -> TcS TcPluginProgress
    runTcPlugins plugins all_cts
      = foldM do_plugin initialProgress plugins
      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)

    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 [ text "work item = " <+> ppr workItem
                           , text "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) }"
                                           (text "inerts =" <+> ppr final_is)
                                     ; return () }
               ContinueWith ct -> do { traceFireTcS (ctEvidence ct) (text "Kept as inert")
                                     ; traceTcS "End solver pipeline (kept as inert) }" $
                                           vcat [ text "final_item =" <+> ppr ct
                                                , pprTvBndrs $ tyCoVarsOfCtList ct
                                                , text "inerts     =" <+> ppr final_is]
                                     ; addInertCan 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      -- Keep the existing inert constraint in the inert set
       | IRReplace   -- Replace the existing inert constraint with the work item
       | IRDelete    -- Delete the existing inert constraint from the inert set

    instance Outputable InteractResult where
      ppr IRKeep    = text "keep"
      ppr IRReplace = text "replace"
      ppr IRDelete  = text "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 constraints only; not used for equalities
    solveOneFromTheOther ev_i ev_w
      | isDerived ev_w         -- Work item is Derived; just discard it
      = return (IRKeep, True)

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

      | CtWanted { ctev_loc = loc_w } <- ev_w
      , prohibitedSuperClassSolve (ctEvLoc ev_i) loc_w
      = return (IRDelete, False)

      | CtWanted { ctev_dest = dest } <- ev_w
           -- Inert is Given or Wanted
      = do { setWantedEvTerm dest (ctEvTerm ev_i)
           ; return (IRKeep, True) }

      | CtWanted { ctev_loc = loc_i } <- ev_i   -- Work item is Given
      , prohibitedSuperClassSolve (ctEvLoc ev_w) loc_i
      = return (IRKeep, False)  -- Just discard the un-usable Given
                                -- This never actually happens because
                                -- Givens get processed first

      | CtWanted { ctev_dest = dest } <- ev_i
      = do { setWantedEvTerm dest (ctEvTerm ev_w)
           ; return (IRReplace, True) }

      -- So they are both Given
      -- See Note [Replacement vs keeping]
      | lvl_i == lvl_w
      = do { binds <- getTcEvBindsMap
           ; return (same_level_strategy binds, True) }

      | otherwise   -- Both are Given, levels differ
      = return (different_level_strategy, True)
      where
         pred  = ctEvPred ev_i
         loc_i = ctEvLoc ev_i
         loc_w = ctEvLoc ev_w
         lvl_i = ctLocLevel loc_i
         lvl_w = ctLocLevel loc_w

         different_level_strategy
           | isIPPred pred, lvl_w > lvl_i = IRReplace
           | lvl_w < lvl_i                = IRReplace
           | otherwise                    = IRKeep

         same_level_strategy binds        -- Both Given
           | GivenOrigin (InstSC s_i) <- ctLocOrigin loc_i
           = case ctLocOrigin loc_w of
                GivenOrigin (InstSC s_w) | s_w < s_i -> IRReplace
                                         | otherwise -> IRKeep
                _                                    -> IRReplace

           | GivenOrigin (InstSC {}) <- ctLocOrigin loc_w
           = IRKeep

           | has_binding binds ev_w
           , not (has_binding binds ev_i)
           = IRReplace

           | otherwise = IRKeep

         has_binding binds ev = isJust (lookupEvBind binds (ctEvId ev))

    {-
    Note [Replacement vs keeping]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we have two Given constraints both of type (C tys), say, which should
    we keep?  More subtle than you might think!

      * Constraints come from different levels (different_level_strategy)

          - For implicit parameters we want to keep the innermost (deepest)
            one, so that it overrides the outer one.
            See Note [Shadowing of Implicit Parameters]

          - For everything else, we want to keep the outermost one.  Reason: that
            makes it more likely that the inner one will turn out to be unused,
            and can be reported as redundant.  See Note [Tracking redundant constraints]
            in TcSimplify.

            It transpires that using the outermost one is reponsible for an
            8% performance improvement in nofib cryptarithm2, compared to
            just rolling the dice.  I didn't investigate why.

      * Constaints coming from the same level (i.e. same implication)

           - Always get rid of InstSC ones if possible, since they are less
             useful for solving.  If both are InstSC, choose the one with
             the smallest TypeSize
             See Note [Solving superclass constraints] in TcInstDcls

           - Keep the one that has a non-trivial evidence binding.
                Example:  f :: (Eq a, Ord a) => blah
                then we may find [G] d3 :: Eq a
                                 [G] d2 :: Eq a
                  with bindings  d3 = sc_sel (d1::Ord a)
                We want to discard d2 in favour of the superclass selection from
                the Ord dictionary.
             Why? See Note [Tracking redundant constraints] in TcSimplify again.

      * Finally, when there is still a choice, use IRKeep rather than
        IRReplace, to avoid unnecessary munging of the inert set.

    Doing the depth-check for implicit parameters, rather than making the work item
    always overrride, is important.  Consider

        data T a where { T1 :: (?x::Int) => T Int; T2 :: T a }

        f :: (?x::a) => T a -> Int
        f T1 = ?x
        f T2 = 3

    We have a [G] (?x::a) in the inert set, and at the pattern match on T1 we add
    two new givens in the work-list:  [G] (?x::Int)
                                      [G] (a ~ Int)
    Now consider these steps
      - process a~Int, kicking out (?x::a)
      - process (?x::Int), the inner given, adding to inert set
      - process (?x::a), the outer given, overriding the inner given
    Wrong!  The depth-check ensures that the inner implicit parameter wins.
    (Actually I think that the order in which the work-list is processed means
    that this chain of events won't happen, but that's very fragile.)

    *********************************************************************************
    *                                                                               *
                       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 `tcEqTypeNoKindCheck` 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 (text "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 })
      | isWanted ev_w
      , Just ip_name      <- isCallStackPred (ctPred workItem)
      , OccurrenceOf func <- ctLocOrigin (ctEvLoc ev_w)
      -- If we're given a CallStack constraint that arose from a function
      -- call, we need to push the current call-site onto the stack instead
      -- of solving it directly from a given.
      -- See Note [Overview of implicit CallStacks]
      = do { let loc = ctEvLoc ev_w

             -- First we emit a new constraint that will capture the
             -- given CallStack.
           ; let new_loc      = setCtLocOrigin loc (IPOccOrigin (HsIPName ip_name))
                                -- We change the origin to IPOccOrigin so
                                -- this rule does not fire again.
                                -- See Note [Overview of implicit CallStacks]

           ; mb_new <- newWantedEvVar new_loc (ctEvPred ev_w)
           ; emitWorkNC (freshGoals [mb_new])

             -- Then we solve the wanted by pushing the call-site onto the
             -- newly emitted CallStack.
           ; let ev_cs = EvCsPushCall func (ctLocSpan loc) (getEvTerm mb_new)
           ; solveCallStack ev_w ev_cs
           ; stopWith ev_w "Wanted CallStack IP" }

      | Just ctev_i <- lookupInertDict inerts 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 (text "Dict equal" <+> parens (ppr inert_effect)))
             else
                continueWith workItem }

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

      | otherwise
      = do { addFunDepWork inerts ev_w cls
           ; continueWith workItem  }

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

    addFunDepWork :: InertCans -> CtEvidence -> Class -> TcS ()
    -- Add derived constraints from type-class functional dependencies.
    addFunDepWork inerts work_ev cls
      = mapBagM_ add_fds (findDictsByClass (inert_dicts inerts) cls)
                   -- No need to check flavour; fundeps work between
                   -- any pair of constraints, regardless of flavour
                   -- Importantly we don't throw workitem back in the
                   -- worklist because this can cause loops (see #5236)
      where
        work_pred = ctEvPred work_ev
        work_loc  = ctEvLoc work_ev
        add_fds inert_ct
          = emitFunDepDeriveds $
            improveFromAnother derived_loc inert_pred work_pred
                   -- 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
          where
            inert_pred = ctPred inert_ct
            inert_loc  = ctLoc inert_ct
            derived_loc = work_loc { ctl_origin = FunDepOrigin1 work_pred  work_loc
                                                                inert_pred inert_loc }

    {-
    **********************************************************************
    *                                                                    *
                       Implicit parameters
    *                                                                    *
    **********************************************************************
    -}

    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)

    {- 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.

    Similarly, 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.

    All 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 constraints 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 `funEqCanDischarge` 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 inert using work-item
          ASSERT2( ev `funEqCanDischarge` ev_i, ppr ev $$ ppr ev_i )
          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" }

      | otherwise   -- Try improvement
      = do { improveLocalFunEqs loc inerts tc args fsk
           ; continueWith workItem }
      where
        loc             = ctEvLoc ev
        funeqs          = inert_funeqs inerts
        matching_inerts = findFunEq funeqs tc args

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

    improveLocalFunEqs :: CtLoc -> InertCans -> TyCon -> [TcType] -> TcTyVar
                       -> TcS ()
    -- Generate derived improvement equalities, by comparing
    -- the current work item with inert CFunEqs
    -- E.g.   x + y ~ z,   x + y' ~ z   =>   [D] y ~ y'
    improveLocalFunEqs loc inerts fam_tc args fsk
      | not (null improvement_eqns)
      = do { traceTcS "interactFunEq improvements: " $
             vcat [ text "Eqns:" <+> ppr improvement_eqns
                  , text "Candidates:" <+> ppr funeqs_for_tc
                  , text "Model:" <+> ppr model ]
           ; mapM_ (unifyDerived loc Nominal) improvement_eqns }
      | otherwise
      = return ()
      where
        model         = inert_model inerts
        funeqs        = inert_funeqs inerts
        funeqs_for_tc = findFunEqsByTyCon funeqs fam_tc
        rhs           = lookupFlattenTyVar model fsk

        --------------------
        improvement_eqns
          | Just ops <- isBuiltInSynFamTyCon_maybe fam_tc
          =    -- Try built-in families, notably for arithmethic
             concatMap (do_one_built_in ops) funeqs_for_tc

          | Injective injective_args <- familyTyConInjectivityInfo fam_tc
          =    -- Try improvement from type families with injectivity annotations
             concatMap (do_one_injective injective_args) funeqs_for_tc

          | otherwise
          = []

        --------------------
        do_one_built_in ops (CFunEqCan { cc_tyargs = iargs, cc_fsk = ifsk })
          = sfInteractInert ops args rhs iargs (lookupFlattenTyVar model ifsk)
        do_one_built_in _ _ = pprPanic "interactFunEq 1" (ppr fam_tc)

        --------------------
        -- See Note [Type inference for type families with injectivity]
        do_one_injective injective_args
                        (CFunEqCan { cc_tyargs = iargs, cc_fsk = ifsk })
          | rhs `tcEqType` lookupFlattenTyVar model ifsk
          = [Pair arg iarg | (arg, iarg, True)
                               <- zip3 args iargs injective_args ]
          | otherwise
          = []
        do_one_injective _ _ = pprPanic "interactFunEq 2" (ppr fam_tc)

    -------------
    lookupFlattenTyVar :: InertModel -> TcTyVar -> TcType
    -- See Note [lookupFlattenTyVar]
    lookupFlattenTyVar model ftv
      = case lookupDVarEnv model ftv of
          Just (CTyEqCan { cc_rhs = rhs, cc_eq_rel = NomEq }) -> rhs
          _                                                   -> mkTyVarTy ftv

    reactFunEq :: CtEvidence -> TcTyVar    -- From this  :: F args1 ~ fsk1
               -> CtEvidence -> TcTyVar    -- Solve this :: F args2 ~ fsk2
               -> TcS ()
    reactFunEq from_this fsk1 solve_this fsk2
      | CtGiven { ctev_evar = evar, ctev_loc = loc } <- solve_this
      = do { let fsk_eq_co = mkTcSymCo (mkTcCoVarCo evar) `mkTcTransCo`
                             ctEvCoercion from_this
                             -- :: fsk2 ~ fsk1
                 fsk_eq_pred = mkTcEqPredLikeEv solve_this
                                 (mkTyVarTy fsk2) (mkTyVarTy fsk1)

           ; new_ev <- newGivenEvVar loc (fsk_eq_pred, EvCoercion fsk_eq_co)
           ; emitWorkNC [new_ev] }

      | otherwise
      = do { traceTcS "reactFunEq" (ppr from_this $$ ppr fsk1 $$
                                    ppr solve_this $$ ppr fsk2)
           ; dischargeFmv solve_this fsk2 (ctEvCoercion from_this) (mkTyVarTy fsk1)
           ; traceTcS "reactFunEq done" (ppr from_this $$ ppr fsk1 $$
                                         ppr solve_this $$ ppr fsk2) }

    {- Note [lookupFlattenTyVar]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Supppose we have an injective function F and
      inert_funeqs:   F t1 ~ fsk1
                      F t2 ~ fsk2
      model           fsk1 ~ fsk2

    We never rewrite the RHS (cc_fsk) of a CFunEqCan.  But we /do/ want to
    get the [D] t1 ~ t2 from the injectiveness of F.  So we look up the
    cc_fsk of CFunEqCans in the model when trying to find derived
    equalities arising from injectivity.

    Note [Type inference for type families with injectivity]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have a type family with an injectivity annotation:
        type family F a b = r | r -> b

    Then if we have two CFunEqCan constraints for F with the same RHS
       F s1 t1 ~ rhs
       F s2 t2 ~ rhs
    then we can use the injectivity to get a new Derived constraint on
    the injective argument
      [D] t1 ~ t2

    That in turn can help GHC solve constraints that would otherwise require
    guessing.  For example, consider the ambiguity check for
       f :: F Int b -> Int
    We get the constraint
       [W] F Int b ~ F Int beta
    where beta is a unification variable.  Injectivity lets us pick beta ~ b.

    Injectivity information is also used at the call sites. For example:
       g = f True
    gives rise to
       [W] F Int b ~ Bool
    from which we can derive b.  This requires looking at the defining equations of
    a type family, ie. finding equation with a matching RHS (Bool in this example)
    and infering values of type variables (b in this example) from the LHS patterns
    of the matching equation.  For closed type families we have to perform
    additional apartness check for the selected equation to check that the selected
    is guaranteed to fire for given LHS arguments.

    These new constraints are simply *Derived* constraints; they have no evidence.
    We could go further and offer evidence from decomposing injective type-function
    applications, but that would require new evidence forms, and an extension to
    FC, so we don't do that right now (Dec 14).

    See also Note [Injective type families] in TyCon

    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 `eqCanDischarge` ev
                             , rhs_i `tcEqType` rhs ]
      =  -- Inert:     a ~ ty
         -- Work item: a ~ ty
        do { setEvBindIfWanted ev $
              EvCoercion (tcDowngradeRole (eqRelRole eq_rel)
                                          (ctEvRole ev_i)
                                          (ctEvCoercion 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 `eqCanDischarge` ev
                             , rhs_i `tcEqType` mkTyVarTy tv ]
      =  -- Inert:     a ~ b
         -- Work item: b ~ a
        do { setEvBindIfWanted ev $
               EvCoercion (mkTcSymCo $
                           tcDowngradeRole (eqRelRole eq_rel)
                                           (ctEvRole ev_i)
                                           (ctEvCoercion ev_i))

           ; stopWith ev "Solved from inert (r)" }

      | ReprEq <- eq_rel   -- We never solve representational
      = unsolved_inert     -- equalities by unification

      | isGiven ev         -- See Note [Touchables and givens]
      = unsolved_inert

      | otherwise
      = do { tclvl <- getTcLevel
           ; if canSolveByUnification tclvl tv rhs
             then do { solveByUnification ev tv rhs
                     ; n_kicked <- kickOutAfterUnification tv
                     ; return (Stop ev (text "Solved by unification" <+> ppr_kicked n_kicked)) }

             else unsolved_inert }

      where
        unsolved_inert
          = 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) ])
               ; addInertEq workItem
               ; return (Stop ev (text "Kept as inert")) }

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

    solveByUnification :: CtEvidence -> TcTyVar -> Xi -> TcS ()
    -- Solve with the identity coercion
    -- Precondition: kind(xi) equals kind(tv)
    -- Precondition: CtEvidence is Wanted or Derived
    -- Precondition: CtEvidence is nominal
    -- 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 <+> text ":=" <+> ppr xi,
                                 text "Coercion:" <+> pprEq tv_ty xi,
                                 text "Left Kind is:" <+> ppr (typeKind tv_ty),
                                 text "Right Kind is:" <+> ppr (typeKind xi) ]

           ; unifyTyVar tv xi
           ; setEvBindIfWanted wd (EvCoercion (mkTcNomReflCo xi)) }

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

    {- 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.

    ************************************************************************
    *                                                                      *
    *          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.hs (nicer
    now!).
    -}

    emitFunDepDeriveds :: [FunDepEqn CtLoc] -> TcS ()
    emitFunDepDeriveds fd_eqns
      = mapM_ do_one_FDEqn fd_eqns
      where
        do_one_FDEqn (FDEqn { fd_qtvs = tvs, fd_eqs = eqs, fd_loc = loc })
         | null tvs  -- Common shortcut
         = mapM_ (unifyDerived loc Nominal) eqs
         | otherwise
         = do { (subst, _) <- instFlexiTcS tvs  -- Takes account of kind substitution
              ; mapM_ (do_one_eq loc subst) eqs }

        do_one_eq loc subst (Pair ty1 ty2)
           = unifyDerived loc Nominal $
             Pair (Type.substTyUnchecked subst ty1) (Type.substTyUnchecked subst ty2)

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

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

    doTopReact :: 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].

    doTopReact work_item
      = do { traceTcS "doTopReact" (ppr work_item)
           ; case work_item of
               CDictCan {}  -> do { inerts <- getTcSInerts
                                  ; doTopReactDict inerts work_item }
               CFunEqCan {} -> doTopReactFunEq work_item
               _  -> -- Any other work item does not react with any top-level equations
                     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 })
      | isGiven fl   -- Never use instances for Given constraints
      = do { try_fundep_improvement
           ; continueWith work_item }

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

      | isDerived fl  -- Use type-class instances for Deriveds, in the hope
                      -- of generating some improvements
                      -- C.f. Example 3 of Note [The improvement story]
                      -- It's easy because no evidence is involved
       = do { dflags <- getDynFlags
            ; lkup_inst_res <- matchClassInst dflags inerts cls xis dict_loc
            ; case lkup_inst_res of
                   GenInst { lir_new_theta = preds
                           , lir_safe_over = s } ->
                     do { emitNewDeriveds dict_loc preds
                        ; unless s $ insertSafeOverlapFailureTcS work_item
                        ; stopWith fl "Dict/Top (solved)" }

                   NoInstance ->
                     do { -- If there is no instance, try improvement
                          try_fundep_improvement
                        ; continueWith work_item } }

      | otherwise  -- Wanted, but not cached
       = do { dflags <- getDynFlags
            ; lkup_inst_res <- matchClassInst dflags inerts cls xis dict_loc
            ; case lkup_inst_res of
                   GenInst { lir_new_theta = theta
                           , lir_mk_ev     = mk_ev
                           , lir_safe_over = s } ->
                     do { addSolvedDict fl cls xis
                        ; unless s $ insertSafeOverlapFailureTcS work_item
                        ; solve_from_instance theta mk_ev }
                   NoInstance ->
                     do { try_fundep_improvement
                        ; continueWith work_item } }
       where
         dict_pred   = mkClassPred cls xis
         dict_loc    = ctEvLoc fl
         dict_origin = ctLocOrigin dict_loc
         deeper_loc  = zap_origin (bumpCtLocDepth dict_loc)

         zap_origin loc  -- After applying an instance we can set ScOrigin to
                         -- infinity, so that prohibitedSuperClassSolve never fires
           | ScOrigin {} <- dict_origin
           = setCtLocOrigin loc (ScOrigin infinity)
           | otherwise
           = loc

         solve_from_instance :: [TcPredType]
                             -> ([EvTerm] -> EvTerm) -> TcS (StopOrContinue Ct)
          -- Precondition: evidence term matches the predicate workItem
         solve_from_instance theta mk_ev
            | null theta
            = do { traceTcS "doTopReact/found nullary instance for" $ ppr fl
                 ; setWantedEvBind (ctEvId fl) (mk_ev [])
                 ; stopWith fl "Dict/Top (solved, no new work)" }
            | otherwise
            = do { checkReductionDepth deeper_loc dict_pred
                 ; traceTcS "doTopReact/found non-nullary instance for" $ ppr fl
                 ; evc_vars <- mapM (newWanted deeper_loc) theta
                 ; setWantedEvBind (ctEvId fl) (mk_ev (map getEvTerm evc_vars))
                 ; emitWorkNC (freshGoals evc_vars)
                 ; stopWith fl "Dict/Top (solved, more work)" }

         -- We didn't solve it; so try functional dependencies with
         -- the instance environment, and return
         -- See also Note [Weird fundeps]
         try_fundep_improvement
            = do { traceTcS "try_fundeps" (ppr work_item)
                 ; instEnvs <- getInstEnvs
                 ; emitFunDepDeriveds $
                   improveFromInstEnv instEnvs mk_ct_loc dict_pred }

         mk_ct_loc :: PredType   -- From instance decl
                   -> SrcSpan    -- also from instance deol
                   -> CtLoc
         mk_ct_loc inst_pred inst_loc
           = dict_loc { ctl_origin = FunDepOrigin2 dict_pred dict_origin
                                                   inst_pred inst_loc }

    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 })
      = do { match_res <- matchFam fam_tc args
                               -- Look up in top-level instances, or built-in axiom
                               -- See Note [MATCHING-SYNONYMS]
           ; case match_res of
               Nothing -> do { improveTopFunEqs (ctEvLoc old_ev) fam_tc args fsk
                             ; continueWith work_item }
               Just (ax_co, rhs_ty)
                 -> reduce_top_fun_eq old_ev fsk ax_co rhs_ty }

    doTopReactFunEq w = pprPanic "doTopReactFunEq" (ppr w)

    reduce_top_fun_eq :: CtEvidence -> TcTyVar -> TcCoercion -> TcType
                      -> TcS (StopOrContinue Ct)
    -- Found an applicable top-level axiom: use it to reduce
    reduce_top_fun_eq old_ev fsk ax_co rhs_ty
      | 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 (mkPrimEqPred (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)" }

      -- So old_ev is Wanted or Derived
      | not (fsk `elemVarSet` tyCoVarsOfType rhs_ty)
      = do { dischargeFmv 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 <- case old_ev of
               CtWanted {}  -> do { (ev, _) <- newWantedEq loc Nominal alpha_ty rhs_ty
                                  ; updWorkListTcS $
                                      extendWorkListEq (mkNonCanonical ev)
                                  ; return ev }
               CtDerived {} -> do { ev <- newDerivedNC loc pred
                                  ; updWorkListTcS (extendWorkListDerived loc ev)
                                  ; return ev }
                 where pred = mkPrimEqPred alpha_ty rhs_ty
               _ -> pprPanic "reduce_top_fun_eq" (ppr old_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 old_ev fsk final_co alpha_ty
           ; traceTcS "doTopReactFunEq (occurs)" $
             vcat [ text "old_ev:" <+> ppr old_ev
                  , nest 2 (text ":=") <+>
                       if isDerived old_ev then text "(derived)"
                       else ppr final_co
                  , text "new_ev:" <+> ppr new_ev ]
           ; stopWith old_ev "Fun/Top (wanted)" }
      where
        loc = ctEvLoc old_ev
        deeper_loc = bumpCtLocDepth loc

    improveTopFunEqs :: CtLoc -> TyCon -> [TcType] -> TcTyVar -> TcS ()
    improveTopFunEqs loc fam_tc args fsk
      = do { model <- getInertModel
           ; fam_envs <- getFamInstEnvs
           ; eqns <- improve_top_fun_eqs fam_envs fam_tc args
                                        (lookupFlattenTyVar model fsk)
           ; mapM_ (unifyDerived loc Nominal) eqns }

    improve_top_fun_eqs :: FamInstEnvs
                        -> TyCon -> [TcType] -> TcType
                        -> TcS [Eqn]
    improve_top_fun_eqs fam_envs fam_tc args rhs_ty
      | Just ops <- isBuiltInSynFamTyCon_maybe fam_tc
      = return (sfInteractTop ops args rhs_ty)

      -- see Note [Type inference for type families with injectivity]
      | isOpenTypeFamilyTyCon fam_tc
      , Injective injective_args <- familyTyConInjectivityInfo fam_tc
      = -- it is possible to have several compatible equations in an open type
        -- family but we only want to derive equalities from one such equation.
        concatMapM (injImproveEqns injective_args) (take 1 $
          buildImprovementData (lookupFamInstEnvByTyCon fam_envs fam_tc)
                               fi_tys fi_rhs (const Nothing))

      | Just ax <- isClosedSynFamilyTyConWithAxiom_maybe fam_tc
      , Injective injective_args <- familyTyConInjectivityInfo fam_tc
      = concatMapM (injImproveEqns injective_args) $
          buildImprovementData (fromBranches (co_ax_branches ax))
                               cab_lhs cab_rhs Just

      | otherwise
      = return []
         where
          buildImprovementData
              :: [a]                     -- axioms for a TF (FamInst or CoAxBranch)
              -> (a -> [Type])           -- get LHS of an axiom
              -> (a -> Type)             -- get RHS of an axiom
              -> (a -> Maybe CoAxBranch) -- Just => apartness check required
              -> [( [Type], TCvSubst, [TyVar], Maybe CoAxBranch )]
                 -- Result:
                 -- ( [arguments of a matching axiom]
                 -- , RHS-unifying substitution
                 -- , axiom variables without substitution
                 -- , Maybe matching axiom [Nothing - open TF, Just - closed TF ] )
          buildImprovementData axioms axiomLHS axiomRHS wrap =
              [ (ax_args, subst, unsubstTvs, wrap axiom)
              | axiom <- axioms
              , let ax_args = axiomLHS axiom
              , let ax_rhs  = axiomRHS axiom
              , Just subst <- [tcUnifyTyWithTFs False ax_rhs rhs_ty]
              , let tvs           = tyCoVarsOfTypesList ax_args
                    notInSubst tv = not (tv `elemVarEnv` getTvSubstEnv subst)
                    unsubstTvs    = filter (notInSubst <&&> isTyVar) tvs ]

          injImproveEqns :: [Bool]
                         -> ([Type], TCvSubst, [TyCoVar], Maybe CoAxBranch)
                         -> TcS [Eqn]
          injImproveEqns inj_args (ax_args, theta, unsubstTvs, cabr) = do
            (theta', _) <- instFlexiTcS unsubstTvs
            -- The use of deterministically ordered list for `unsubstTvs`
            -- is not strictly necessary here, we only use the substitution
            -- part of the result of instFlexiTcS. If we used the second
            -- part of the tuple, which is the range of the substitution then
            -- the order could be important.
            let subst = theta `unionTCvSubst` theta'
            return [ Pair (substTyUnchecked subst ax_arg) arg
                       -- NB: the ax_arg part is on the left
                       -- see Note [Improvement orientation]
                   | case cabr of
                      Just cabr' -> apartnessCheck (substTys subst ax_args) cabr'
                      _          -> True
                   , (ax_arg, arg, True) <- zip3 ax_args args inj_args ]

    shortCutReduction :: CtEvidence -> TcTyVar -> TcCoercion
                      -> TyCon -> [TcType] -> TcS (StopOrContinue Ct)
    -- See Note [Top-level reductions for type functions]
    shortCutReduction old_ev fsk ax_co fam_tc tc_args
      = ASSERT( ctEvEqRel old_ev == NomEq)
        do { (xis, cos) <- flattenManyNom old_ev 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 <- case ctEvFlavour old_ev of
               Given -> newGivenEvVar deeper_loc
                             ( mkPrimEqPred (mkTyConApp fam_tc xis) (mkTyVarTy fsk)
                             , EvCoercion (mkTcTyConAppCo Nominal fam_tc cos
                                            `mkTcTransCo` mkTcSymCo ax_co
                                            `mkTcTransCo` ctEvCoercion old_ev) )

               Derived -> newDerivedNC deeper_loc $
                          mkPrimEqPred (mkTyConApp fam_tc xis)
                                       (mkTyVarTy fsk)

               Wanted ->
                 do { (new_ev, new_co) <- newWantedEq deeper_loc Nominal
                                            (mkTyConApp fam_tc xis) (mkTyVarTy fsk)
                    ; setWantedEq (ctev_dest old_ev) $
                         ax_co `mkTcTransCo` mkTcSymCo (mkTcTyConAppCo Nominal
                                                          fam_tc cos)
                               `mkTcTransCo` new_co
                    ; return new_ev }

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

    dischargeFmv :: CtEvidence -> TcTyVar -> TcCoercion -> TcType -> TcS ()
    -- (dischargeFmv x fmv co ty)
    --     [W] ev :: F tys ~ fmv
    --         co :: F tys ~ xi
    -- Precondition: fmv is not filled, and fuv `notElem` xi
    --
    -- Then set fmv := xi,
    --      set ev := co
    --      kick out any inert things that are now rewritable
    --
    -- Does not evaluate 'co' if 'ev' is Derived
    dischargeFmv ev fmv co xi
      = ASSERT2( not (fmv `elemVarSet` tyCoVarsOfType xi), ppr ev $$ ppr fmv $$ ppr xi )
        do { setEvBindIfWanted ev (EvCoercion co)
           ; unflattenFmv fmv xi
           ; n_kicked <- kickOutAfterUnification fmv
           ; traceTcS "dischargeFmv" (ppr fmv <+> equals <+> ppr xi $$ ppr_kicked n_kicked) }

    {- Note [Top-level reductions for type functions]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    c.f. Note [The flattening story] in TcFlatten

    Suppose we have a CFunEqCan  F tys ~ fmv/fsk, and a matching axiom.
    Here is what we do, in four cases:

    * Wanteds: general firing rule
        (work item) [W]        x : F tys ~ fmv
        instantiate axiom: ax_co : F tys ~ rhs

       Then:
          Discharge   fmv := alpha
          Discharge   x := ax_co ; sym x2
          New wanted  [W] x2 : alpha ~ rhs  (Non-canonical)
       This is *the* way that fmv's get unified; even though they are
       "untouchable".

       NB: it can be the case that fmv appears in the (instantiated) rhs.
       In that case the new Non-canonical wanted will be loopy, but that's
       ok.  But it's good reason NOT to claim that it is canonical!

    * Wanteds: short cut firing rule
      Applies when the RHS of the axiom is another type-function application
          (work item)        [W] x : F tys ~ fmv
          instantiate axiom: ax_co : F tys ~ G rhs_tys

      It would be a waste to create yet another fmv for (G rhs_tys).
      Instead (shortCutReduction):
          - Flatten rhs_tys (cos : rhs_tys ~ rhs_xis)
          - Add G rhs_xis ~ fmv to flat cache  (note: the same old fmv)
          - New canonical wanted   [W] x2 : G rhs_xis ~ fmv  (CFunEqCan)
          - Discharge x := ax_co ; G cos ; x2

    * Givens: general firing rule
          (work item)        [G] g : F tys ~ fsk
          instantiate axiom: ax_co : F tys ~ rhs

       Now add non-canonical given (since rhs is not flat)
          [G] (sym g ; ax_co) : fsk ~ rhs  (Non-canonical)

    * Givens: short cut firing rule
      Applies when the RHS of the axiom is another type-function application
          (work item)        [G] g : F tys ~ fsk
          instantiate axiom: ax_co : F tys ~ G rhs_tys

      It would be a waste to create yet another fsk for (G rhs_tys).
      Instead (shortCutReduction):
         - Flatten rhs_tys: flat_cos : tys ~ flat_tys
         - Add new Canonical given
              [G] (sym (G flat_cos) ; co ; g) : G flat_tys ~ fsk   (CFunEqCan)

    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 `funEqCanDischarge` 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 [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 fundeps from both instance decls;
          [D] K Bool ~ K [a]
          [D] K Bool ~ K beta
    And there's a risk of complaining about Bool ~ [a].  But in fact
    the Wanted matches the second instance, so we never get as far
    as the fundeps.

    Trac #7875 is a case in point.

    Note [Improvement orientation]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    A very delicate point is the orientation of derived equalities
    arising from injectivity improvement (Trac #12522).  Suppse we have
      type family F x = t | t -> x
      type instance F (a, Int) = (Int, G a)
    where G is injective; and wanted constraints

      [W] TF (alpha, beta) ~ fuv
      [W] fuv ~ (Int, <some type>)

    The injectivity will give rise to derived constraionts

      [D] gamma1 ~ alpha
      [D] Int ~ beta

    The fresh unification variable gamma1 comes from the fact that we
    can only do "partial improvement" here; see Section 5.2 of
    "Injective type families for Haskell" (HS'15).

    Now, it's very important to orient the equations this way round,
    so that the fresh unification variable will be eliminated in
    favour of alpha.  If we instead had
       [D] alpha ~ gamma1
    then we would unify alpha := gamma1; and kick out the wanted
    constraint.  But when we grough it back in, it'd look like
       [W] TF (gamma1, beta) ~ fuv
    and exactly the same thing would happen again!  Infnite loop.

    This all sesms fragile, and it might seem more robust to avoid
    introducing gamma1 in the first place, in the case where the
    actual argument (alpha, beta) partly matches the improvement
    template.  But that's a bit tricky, esp when we remember that the
    kinds much match too; so it's easier to let the normal machinery
    handle it.  Instead we are careful to orient the new derived
    equality with the template on the left.  Delicate, but it works.
    -}

    {- *******************************************************************
    *                                                                    *
                           Class lookup
    *                                                                    *
    **********************************************************************-}

    -- | Indicates if Instance met the Safe Haskell overlapping instances safety
    -- check.
    --
    -- See Note [Safe Haskell Overlapping Instances] in TcSimplify
    -- See Note [Safe Haskell Overlapping Instances Implementation] in TcSimplify
    type SafeOverlapping = Bool

    data LookupInstResult
      = NoInstance
      | GenInst { lir_new_theta :: [TcPredType]
                , lir_mk_ev     :: [EvTerm] -> EvTerm
                , lir_safe_over :: SafeOverlapping }

    instance Outputable LookupInstResult where
      ppr NoInstance = text "NoInstance"
      ppr (GenInst { lir_new_theta = ev
                   , lir_safe_over = s })
        = text "GenInst" <+> vcat [ppr ev, ss]
        where ss = text $ if s then "[safe]" else "[unsafe]"

    matchClassInst :: DynFlags -> InertSet -> Class -> [Type] -> CtLoc -> TcS LookupInstResult
    matchClassInst dflags inerts clas tys loc
    -- First check whether there is an in-scope Given that could
    -- match this constraint.  In that case, do not use top-level
    -- instances.  See Note [Instance and Given overlap]
      | not (xopt LangExt.IncoherentInstances dflags)
      , not (naturallyCoherentClass clas)
      , let matchable_givens = matchableGivens loc pred inerts
      , not (isEmptyBag matchable_givens)
      = do { traceTcS "Delaying instance application" $
               vcat [ text "Work item=" <+> pprClassPred clas tys
                    , text "Potential matching givens:" <+> ppr matchable_givens ]
           ; return NoInstance }
      where
         pred = mkClassPred clas tys

    matchClassInst dflags _ clas tys loc
     = do { traceTcS "matchClassInst" $ vcat [ text "pred =" <+> ppr (mkClassPred clas tys) ]
          ; res <- match_class_inst dflags clas tys loc
          ; traceTcS "matchClassInst result" $ ppr res
          ; return res }

    match_class_inst :: DynFlags -> Class -> [Type] -> CtLoc -> TcS LookupInstResult
    match_class_inst dflags clas tys loc
      | cls_name == knownNatClassName     = matchKnownNat        clas tys
      | cls_name == knownSymbolClassName  = matchKnownSymbol     clas tys
      | isCTupleClass clas                = matchCTuple          clas tys
      | cls_name == typeableClassName     = matchTypeable        clas tys
      | clas `hasKey` heqTyConKey         = matchLiftedEquality       tys
      | clas `hasKey` coercibleTyConKey   = matchLiftedCoercible      tys
      | otherwise                         = matchInstEnv dflags clas tys loc
      where
        cls_name = className clas

    {- 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

    From 'g' we get the impliation constraint:
                forall a. 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 partial 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.  But not skolems like 'a' in
      the implication constraint above.

    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:

    * The check is done *first*, so that it also covers classes
      with built-in instance solving, such as
         - constraint tuples
         - natural numbers
         - Typeable

    * The given-overlap problem 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; another is #10177.

    * 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.

    * The solution is only a partial one.  Consider the above example with
           g :: forall a. Q [a] => [a] -> Int
           g x = let v = wob x
                 in v
      and suppose we have -XNoMonoLocalBinds, so that we attempt to find the most
      general type for 'v'.  When generalising v's type we'll simplify its
      Q [alpha] constraint, but we don't have Q [a] in the 'givens', so we
      will use the instance declaration after all. Trac #11948 was a case in point

    All of this is disgustingly delicate, so to discourage people from writing
    simplifiable class givens, we warn about signatures that contain them;#
    see TcValidity Note [Simplifiable given constraints].
    -}

    {- *******************************************************************
    *                                                                    *
                    Class lookup in the instance environment
    *                                                                    *
    **********************************************************************-}

    matchInstEnv :: DynFlags -> Class -> [Type] -> CtLoc -> TcS LookupInstResult
    matchInstEnv dflags clas tys loc
       = do { instEnvs <- getInstEnvs
            ; let safeOverlapCheck = safeHaskell dflags `elem` [Sf_Safe, Sf_Trustworthy]
                  (matches, unify, unsafeOverlaps) = lookupInstEnv True instEnvs clas tys
                  safeHaskFail = safeOverlapCheck && not (null unsafeOverlaps)
            ; case (matches, unify, safeHaskFail) of

                -- Nothing matches
                ([], _, _)
                    -> do { traceTcS "matchClass not matching" $
                            vcat [ text "dict" <+> ppr pred ]
                          ; return NoInstance }

                -- A single match (& no safe haskell failure)
                ([(ispec, inst_tys)], [], False)
                    -> 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 (null unsafeOverlaps) dfun_id inst_tys }

                -- More than one matches (or Safe Haskell fail!). Defer any
                -- reactions of a multitude until we learn more about the reagent
                (matches, _, _)
                    -> 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 :: SafeOverlapping -> DFunId -> [DFunInstType] -> TcS LookupInstResult
                      -- See Note [DFunInstType: instantiating types] in InstEnv
         match_one so dfun_id mb_inst_tys
           = do { checkWellStagedDFun pred dfun_id loc
                ; (tys, theta) <- instDFunType dfun_id mb_inst_tys
                ; return $ GenInst { lir_new_theta = theta
                                   , lir_mk_ev     = EvDFunApp dfun_id tys
                                   , lir_safe_over = so } }

    {- ********************************************************************
    *                                                                     *
                       Class lookup for CTuples
    *                                                                     *
    ***********************************************************************-}

    matchCTuple :: Class -> [Type] -> TcS LookupInstResult
    matchCTuple clas tys   -- (isCTupleClass clas) holds
      = return (GenInst { lir_new_theta = tys
                        , lir_mk_ev     = tuple_ev
                        , lir_safe_over = True })
                -- The dfun *is* the data constructor!
      where
         data_con = tyConSingleDataCon (classTyCon clas)
         tuple_ev = EvDFunApp (dataConWrapId data_con) tys

    {- ********************************************************************
    *                                                                     *
                       Class lookup for Literals
    *                                                                     *
    ***********************************************************************-}

    matchKnownNat :: Class -> [Type] -> TcS LookupInstResult
    matchKnownNat clas [ty]     -- clas = KnownNat
      | Just n <- isNumLitTy ty = makeLitDict clas ty (EvNum n)
    matchKnownNat _ _           = return NoInstance

    matchKnownSymbol :: Class -> [Type] -> TcS LookupInstResult
    matchKnownSymbol clas [ty]  -- clas = KnownSymbol
      | Just n <- isStrLitTy ty = makeLitDict clas ty (EvStr n)
    matchKnownSymbol _ _       = return NoInstance

    makeLitDict :: Class -> Type -> EvLit -> TcS LookupInstResult
    -- makeLitDict 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 -}
    makeLitDict clas ty 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
        , let ev_tm = mkEvCast (EvLit evLit) (mkTcSymCo (mkTcTransCo co_dict co_rep))
        = return $ GenInst { lir_new_theta = []
                           , lir_mk_ev     = \_ -> ev_tm
                           , lir_safe_over = True }

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

    {- ********************************************************************
    *                                                                     *
                       Class lookup for Typeable
    *                                                                     *
    ***********************************************************************-}

    -- | Assumes that we've checked that this is the 'Typeable' class,
    -- and it was applied to the correct argument.
    matchTypeable :: Class -> [Type] -> TcS LookupInstResult
    matchTypeable clas [k,t]  -- clas = Typeable
      -- For the first two cases, See Note [No Typeable for polytypes or qualified types]
      | isForAllTy k                      = return NoInstance   -- Polytype
      | isJust (tcSplitPredFunTy_maybe t) = return NoInstance   -- Qualified type

      -- Now cases that do work
      | k `eqType` typeNatKind                 = doTyLit knownNatClassName    t
      | k `eqType` typeSymbolKind              = doTyLit knownSymbolClassName t
      | Just (tc, ks) <- splitTyConApp_maybe t -- See Note [Typeable (T a b c)]
      , onlyNamedBndrsApplied tc ks            = doTyConApp clas t ks
      | Just (f,kt)   <- splitAppTy_maybe t    = doTyApp    clas t f kt

    matchTypeable _ _ = return NoInstance

    doTyConApp :: Class -> Type -> [Kind] -> TcS LookupInstResult
    -- Representation for type constructor applied to some kinds
    doTyConApp clas ty args
      = return $ GenInst (map (mk_typeable_pred clas) args)
                         (\tms -> EvTypeable ty $ EvTypeableTyCon tms)
                         True

    -- Representation for concrete kinds.  We just use the kind itself,
    -- but first we must make sure that we've instantiated all kind-
    -- polymorphism, but no more.
    onlyNamedBndrsApplied :: TyCon -> [KindOrType] -> Bool
    onlyNamedBndrsApplied tc ks
     = all isNamedBinder used_bndrs &&
       not (any isNamedBinder leftover_bndrs)
     where
       bndrs                        = tyConBinders tc
       (used_bndrs, leftover_bndrs) = splitAtList ks bndrs

    doTyApp :: Class -> Type -> Type -> KindOrType -> TcS LookupInstResult
    -- 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 clas ty f tk
      | isForAllTy (typeKind f)
      = return NoInstance -- We can't solve until we know the ctr.
      | otherwise
      = return $ GenInst [mk_typeable_pred clas f, mk_typeable_pred clas tk]
                         (\[t1,t2] -> EvTypeable ty $ EvTypeableTyApp t1 t2)
                         True

    -- Emit a `Typeable` constraint for the given type.
    mk_typeable_pred :: Class -> Type -> PredType
    mk_typeable_pred clas ty = mkClassPred clas [ typeKind ty, ty ]

      -- Typeable is implied by KnownNat/KnownSymbol. In the case of a type literal
      -- we generate a sub-goal for the appropriate class. See #10348 for what
      -- happens when we fail to do this.
    doTyLit :: Name -> Type -> TcS LookupInstResult
    doTyLit kc t = do { kc_clas <- tcLookupClass kc
                      ; let kc_pred    = mkClassPred kc_clas [ t ]
                            mk_ev [ev] = EvTypeable t $ EvTypeableTyLit ev
                            mk_ev _    = panic "doTyLit"
                      ; return (GenInst [kc_pred] mk_ev True) }

    {- Note [Typeable (T a b c)]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    For type applications we always decompose using binary application,
    vai doTyApp, until we get to a *kind* instantiation.  Exmaple
       Proxy :: forall k. k -> *

    To solve Typeable (Proxy (* -> *) Maybe) we
      - First decompose with doTyApp,
        to get (Typeable (Proxy (* -> *))) and Typeable Maybe
      - Then sovle (Typeable (Proxy (* -> *))) with doTyConApp

    If we attempt to short-cut by solving it all at once, via
    doTyCOnAPp

    Note [No Typeable for polytypes or qualified types]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    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.
    -}

    solveCallStack :: CtEvidence -> EvCallStack -> TcS ()
    solveCallStack ev ev_cs = do
      -- We're given 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`. See Note [Overview of implicit CallStacks]
      let ev_tm = mkEvCast (EvCallStack ev_cs) (wrapIP (ctEvPred ev))
      setWantedEvBind (ctEvId ev) ev_tm

    {- ********************************************************************
    *                                                                     *
                       Class lookup for lifted equality
    *                                                                     *
    ***********************************************************************-}

    -- See also Note [The equality types story] in TysPrim
    matchLiftedEquality :: [Type] -> TcS LookupInstResult
    matchLiftedEquality args
      = return (GenInst { lir_new_theta = [ mkTyConApp eqPrimTyCon args ]
                        , lir_mk_ev     = EvDFunApp (dataConWrapId heqDataCon) args
                        , lir_safe_over = True })

    -- See also Note [The equality types story] in TysPrim
    matchLiftedCoercible :: [Type] -> TcS LookupInstResult
    matchLiftedCoercible args@[k, t1, t2]
      = return (GenInst { lir_new_theta = [ mkTyConApp eqReprPrimTyCon args' ]
                        , lir_mk_ev     = EvDFunApp (dataConWrapId coercibleDataCon)
                                                    args
                        , lir_safe_over = True })
      where
        args' = [k, k, t1, t2]
    matchLiftedCoercible args = pprPanic "matchLiftedCoercible" (ppr args)