\begin{code}

    module TcInteract (
         solveInteract, solveInteractGiven, solveInteractWanted,
         AtomicInert, tyVarsOfInert,
         InertSet, emptyInert, updInertSet, extractUnsolved, solveOne,
      ) where

    #include "HsVersions.h"

    import BasicTypes
    import TcCanonical
    import VarSet
    import Type

    import Id
    import Var

    import TcType
    import HsBinds

    import Inst( tyVarsOfEvVar )
    import Class
    import TyCon
    import Name

    import FunDeps

    import Coercion
    import Outputable

    import TcRnTypes
    import TcErrors
    import TcSMonad
    import Bag
    import qualified Data.Map as Map

    import Control.Monad( when )

    import FastString ( sLit )
    import DynFlags

\end{code} Note [InertSet invariants] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ An InertSet is a bag of canonical constraints, with the following invariants: 1 No two constraints react with each other. A tricky case is when there exists a given (solved) dictionary constraint and a wanted identical constraint in the inert set, but do not react because reaction would create loopy dictionary evidence for the wanted. See note [Recursive dictionaries] 2 Given equalities form an idempotent substitution [none of the given LHS's occur in any of the given RHS's or reactant parts] 3 Wanted equalities also form an idempotent substitution 4 The entire set of equalities is acyclic. 5 Wanted dictionaries are inert with the top-level axiom set 6 Equalities of the form tv1 ~ tv2 always have a touchable variable on the left (if possible). 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints will be marked as solved right before being pushed into the inert set. See note [Touchables and givens]. 8 No Given constraint mentions a touchable unification variable, except if the Note that 6 and 7 are /not/ enforced by canonicalization but rather by insertion in the inert list, ie by TcInteract. During the process of solving, the inert set will contain some previously given constraints, some wanted constraints, and some given constraints which have arisen from solving wanted constraints. For now we do not distinguish between given and solved constraints. Note that we must switch wanted inert items to given when going under an implication constraint (when in top-level inference mode). \begin{code}

    data CCanMap a = CCanMap { cts_given   :: Map.Map a CanonicalCts
                                              -- Invariant: all Given
                             , cts_derived :: Map.Map a CanonicalCts
                                              -- Invariant: all Derived
                             , cts_wanted  :: Map.Map a CanonicalCts }
                                              -- Invariant: all Wanted

    cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts
    cCanMapToBag cmap = Map.fold unionBags rest_wder (cts_given cmap)
      where rest_wder = Map.fold unionBags rest_der  (cts_wanted cmap)
            rest_der  = Map.fold unionBags emptyCCan (cts_derived cmap)

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

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

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

    extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a)
    -- Gets the wanted or derived constraints and returns a residual
    -- CCanMap with only givens.
    extractUnsolvedCMap cmap =
      let wntd = Map.fold unionBags emptyCCan (cts_wanted cmap)
          derd = Map.fold unionBags emptyCCan (cts_derived cmap)
      in (wntd `unionBags` derd,
               cmap { cts_wanted = Map.empty, cts_derived = Map.empty })

    -- See Note [InertSet invariants]
    data InertSet
      = IS { inert_eqs          :: CanonicalCts               -- Equalities only (CTyEqCan)
           , inert_dicts        :: CCanMap Class              -- Dictionaries only
           , inert_ips          :: CCanMap (IPName Name)      -- Implicit parameters
           , inert_frozen       :: CanonicalCts
           , inert_funeqs       :: CCanMap TyCon              -- Type family equalities only
                   -- This representation allows us to quickly get to the relevant
                   -- inert constraints when interacting a work item with the inert set.
           }

    tyVarsOfInert :: InertSet -> TcTyVarSet
    tyVarsOfInert (IS { inert_eqs    = eqs
                      , inert_dicts  = dictmap
                      , inert_ips    = ipmap
                      , inert_frozen = frozen
                      , inert_funeqs = funeqmap }) = tyVarsOfCanonicals cts
      where
        cts = eqs `andCCan` frozen `andCCan` cCanMapToBag dictmap
                  `andCCan` cCanMapToBag ipmap `andCCan` cCanMapToBag funeqmap

    instance Outputable InertSet where
      ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
                    , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is)))
                    , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is)))
                    , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
                    , vcat (map ppr (Bag.bagToList $ inert_frozen is))
                    ]

    emptyInert :: InertSet
    emptyInert = IS { inert_eqs    = Bag.emptyBag
                    , inert_frozen = Bag.emptyBag
                    , inert_dicts  = emptyCCanMap
                    , inert_ips    = emptyCCanMap
                    , inert_funeqs = emptyCCanMap }

    updInertSet :: InertSet -> AtomicInert -> InertSet
    updInertSet is item
      | isCTyEqCan item                     -- Other equality
      = let eqs' = inert_eqs is `Bag.snocBag` item
        in is { inert_eqs = eqs' }
      | Just cls <- isCDictCan_Maybe item   -- Dictionary
      = is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) }
      | Just x  <- isCIPCan_Maybe item      -- IP
      = is { inert_ips   = updCCanMap (x,item) (inert_ips is) }
      | Just tc <- isCFunEqCan_Maybe item   -- Function equality
      = is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
      | otherwise
      = is { inert_frozen = inert_frozen is `Bag.snocBag` item }

    extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
    -- Postcondition: the returned canonical cts are either Derived, or Wanted.
    extractUnsolved is@(IS {inert_eqs = eqs})
      = let is_solved  = is { inert_eqs    = solved_eqs
                            , inert_dicts  = solved_dicts
                            , inert_ips    = solved_ips
                            , inert_frozen = emptyCCan
                            , inert_funeqs = solved_funeqs }
        in (is_solved, unsolved)

      where (unsolved_eqs, solved_eqs)       = Bag.partitionBag (not.isGivenCt) eqs
            (unsolved_ips, solved_ips)       = extractUnsolvedCMap (inert_ips is)
            (unsolved_dicts, solved_dicts)   = extractUnsolvedCMap (inert_dicts is)
            (unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is)

            unsolved = unsolved_eqs `unionBags` inert_frozen is `unionBags`
                       unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs

\end{code} %********************************************************************* %* * * Main Interaction Solver * * * ********************************************************************** Note [Basic plan] ~~~~~~~~~~~~~~~~~ 1. Canonicalise (unary) 2. Pairwise interaction (binary) * Take one from work list * Try all pair-wise interactions with each constraint in inert As an optimisation, we prioritize the equalities both in the worklist and in the inerts. 3. Try to solve spontaneously for equalities involving touchables 4. Top-level interaction (binary wrt top-level) Superclass decomposition belongs in (4), see note [Superclasses] \begin{code}

    type AtomicInert = CanonicalCt     -- constraint pulled from InertSet
    type WorkItem    = CanonicalCt     -- constraint pulled from WorkList

    -- A mixture of Given, Wanted, and Derived constraints.
    -- We split between equalities and the rest to process equalities first.
    type WorkList = CanonicalCts

    unionWorkLists :: WorkList -> WorkList -> WorkList
    unionWorkLists = andCCan

    isEmptyWorkList :: WorkList -> Bool
    isEmptyWorkList = isEmptyCCan

    emptyWorkList :: WorkList
    emptyWorkList = emptyCCan

    workListFromCCan :: CanonicalCt -> WorkList
    workListFromCCan = singleCCan

    ------------------------
    data StopOrContinue
      = Stop			-- Work item is consumed
      | ContinueWith WorkItem	-- Not consumed

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

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

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

    type SubGoalDepth = Int	  -- Starts at zero; used to limit infinite
         		    	  -- recursion of sub-goals
    type SimplifierStage = SubGoalDepth -> WorkItem -> InertSet -> TcS StageResult

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

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

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

\end{code} Example 1: Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given) Reagent: a ~ [b] (given) React with (c~d) ==> IR (ContinueWith (a~[b])) True [] React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t] React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True [] Example 2: Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty} Reagent: a ~w [b] React with (c ~w d) ==> IR (ContinueWith (a~[b])) True [] React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!) etc. Example 3: Inert: {a ~ Int, F Int ~ b} (given) Reagent: F a ~ b (wanted) React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True [] React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing \begin{code}

    -- Main interaction solver: we fully solve the worklist 'in one go',
    -- returning an extended inert set.
    --
    -- See Note [Touchables and givens].
    solveInteractGiven :: InertSet -> GivenLoc -> [EvVar] -> TcS InertSet
    solveInteractGiven inert gloc evs
      = do { (_, inert_ret) <- solveInteract inert $ listToBag $
                               map mk_given evs
           ; return inert_ret }
      where
        flav = Given gloc
        mk_given ev = mkEvVarX ev flav

    solveInteractWanted :: InertSet -> [WantedEvVar] -> TcS InertSet
    solveInteractWanted inert wvs
      = do { (_,inert_ret) <- solveInteract inert $ listToBag $
                              map wantedToFlavored wvs
           ; return inert_ret }

    solveInteract :: InertSet -> Bag FlavoredEvVar -> TcS (Bool, InertSet)
    -- Post: (True,  inert_set) means we managed to discharge all constraints
    --                          without actually doing any interactions!
    --       (False, inert_set) means some interactions occurred
    solveInteract inert ws
      = do { dyn_flags <- getDynFlags
           ; sctx <- getTcSContext

           ; traceTcS "solveInteract, before clever canonicalization:" $
             vcat [ text "ws = " <+>  ppr (mapBag (\(EvVarX ev ct)
                                                       -> (ct,evVarPred ev)) ws)
                  , text "inert = " <+> ppr inert ]

           ; (flag, inert_ret) <- foldlBagM (tryPreSolveAndInteract sctx dyn_flags) (True,inert) ws

           ; traceTcS "solveInteract, after clever canonicalization (and interaction):" $
             vcat [ text "No interaction happened = " <+> ppr flag
                  , text "inert_ret = " <+> ppr inert_ret ]

           ; return (flag, inert_ret) }

    tryPreSolveAndInteract :: SimplContext
                           -> DynFlags
                           -> (Bool, InertSet)
                           -> FlavoredEvVar
                           -> TcS (Bool, InertSet)
    -- Returns: True if it was able to discharge this constraint AND all previous ones
    tryPreSolveAndInteract sctx dyn_flags (all_previous_discharged, inert)
                           flavev@(EvVarX ev_var fl)
      = do { let inert_cts = get_inert_cts (evVarPred ev_var)

           ; this_one_discharged <- dischargeFromCCans inert_cts flavev

           ; if this_one_discharged
             then return (all_previous_discharged, inert)

             else do
           { extra_cts <- mkCanonical fl ev_var
           ; inert_ret <- solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[])
                                                 inert extra_cts
           ; return (False, inert_ret) } }

      where
        get_inert_cts (ClassP clas _)
          | simplEqsOnly sctx = emptyCCan
          | otherwise         = fst (getRelevantCts clas (inert_dicts inert))
        get_inert_cts (IParam {})
          = emptyCCan -- We must not do the same thing for IParams, because (contrary
                      -- to dictionaries), work items /must/ override inert items.
                     -- See Note [Overriding implicit parameters] in TcInteract.
        get_inert_cts (EqPred {})
          = inert_eqs inert `unionBags` cCanMapToBag (inert_funeqs inert)

    dischargeFromCCans :: CanonicalCts -> FlavoredEvVar -> TcS Bool
    -- See if this (pre-canonicalised) work-item is identical to a
    -- one already in the inert set. Reasons:
    --    a) Avoid creating superclass constraints for millions of incoming (Num a) constraints
    --    b) Termination for improve_eqs in TcSimplify.simpl_loop
    dischargeFromCCans cans (EvVarX ev fl)
      = Bag.foldrBag discharge_ct (return False) cans
      where
        the_pred = evVarPred ev

        discharge_ct :: CanonicalCt -> TcS Bool -> TcS Bool
        discharge_ct ct _rest
          | evVarPred (cc_id ct) `tcEqPred` the_pred
          , cc_flavor ct `canSolve` fl
          = do { when (isWanted fl) $ set_ev_bind ev (cc_id ct)
               	 -- Deriveds need no evidence
        	         -- For Givens, we already have evidence, and we don't need it twice
               ; return True }
          where
             set_ev_bind x y
                | EqPred {} <- evVarPred y = setEvBind x (EvCoercion (mkCoVarCoercion y))
                | otherwise                = setEvBind x (EvId y)

        discharge_ct _ct rest = rest

\end{code} Note [Avoiding the superclass explosion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This note now is not as significant as it used to be because we no longer add the superclasses of Wanted as Derived, except only if they have equality superclasses or superclasses with functional dependencies. The fear was that hundreds of identical wanteds would give rise each to the same superclass or equality Derived's which would lead to a blo-up in the number of interactions. Instead, what we do with tryPreSolveAndCanon, is when we encounter a new constraint, we very quickly see if it can be immediately discharged by a class constraint in our inert set or the previous canonicals. If so, we add nothing to the returned canonical constraints. \begin{code}

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

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

      | n > max_depth
      = solverDepthErrorTcS n stack

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

    	      -- Solve equalities first
           ; let (eqs, non_eqs) = Bag.partitionBag isCTyEqCan ws
           ; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
           ; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }

    ------------------
    -- Fully interact the given work item with an inert set, and return a
    -- new inert set which has assimilated the new information.
    solveOneWithDepth :: (Int, Int, [WorkItem])
                      -> InertSet -> WorkItem -> TcS InertSet
    solveOneWithDepth (max_depth, depth, stack) inert work
      = do { traceFireTcS depth (text "Solving {" <+> ppr work)
           ; (new_inert, new_work) <- runSolverPipeline depth thePipeline inert work

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

           ; traceFireTcS depth (text "Done }" <+> ppr work)

           ; return res_inert }

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

\end{code} ********************************************************************************* * * The spontaneous-solve Stage * * ********************************************************************************* Note [Efficient Orientation] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ There are two cases where we have to be careful about orienting equalities to get better efficiency. Case 1: In Rewriting Equalities (function rewriteEqLHS) When rewriting two equalities with the same LHS: (a) (tv ~ xi1) (b) (tv ~ xi2) We have a choice of producing work (xi1 ~ xi2) (up-to the canonicalization invariants) However, to prevent the inert items from getting kicked out of the inerts first, we prefer to canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2 ~ xi1) if (a) comes from the inert set. This choice is implemented using the WhichComesFromInert flag. Case 2: Functional Dependencies Again, we should prefer, if possible, the inert variables on the RHS Case 3: IP improvement work We must always rewrite so that the inert type is on the right. \begin{code}

    spontaneousSolveStage :: SimplifierStage
    spontaneousSolveStage depth workItem inerts
      = do { mSolve <- trySpontaneousSolve workItem

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

               SPSolved workItem'
                   | not (isGivenCt workItem)
    	       	 -- Original was wanted or derived but we have now made him
                     -- given so we have to interact him with the inerts due to
                     -- its status change. This in turn may produce more work.
    		 -- We do this *right now* (rather than just putting workItem'
    		 -- back into the work-list) because we've solved
                   -> do { bumpStepCountTcS
    	       	     ; traceFireTcS depth (ptext (sLit "Spontaneous (w/d)") <+> ppr workItem)
                         ; (new_inert, new_work) <- runSolverPipeline depth
                                 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
                                 , ("recursive interact with inerts", interactWithInertsStage)
                                 ] inerts workItem'
                         ; return $ SR { sr_new_work = new_work
                                       , sr_inerts   = new_inert -- will include workItem'
                                       , sr_stop     = Stop }
                         }
                   | otherwise
                       -> -- Original was given; he must then be inert all right, and
                          -- workList' are all givens from flattening
                          do { bumpStepCountTcS
    	       	         ; traceFireTcS depth (ptext (sLit "Spontaneous (g)") <+> ppr workItem)
                             ; return $ SR { sr_new_work = emptyWorkList
                                           , sr_inerts   = inerts `updInertSet` workItem'
                                           , sr_stop     = Stop } }
               SPError -> -- Return with no new work
                   return $ SR { sr_new_work = emptyWorkList
                               , sr_inerts   = inerts
                               , sr_stop     = Stop }
           }

    data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
    -- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
    -- SPSolved workItem' gives us a new *given* to go on
    -- SPError means that it's completely impossible to solve this equality, eg due to a kind error

    -- @trySpontaneousSolve wi@ solves equalities where one side is a
    -- touchable unification variable.
    --     	    See Note [Touchables and givens]
    trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
    trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
      | isGiven gw
      = return SPCantSolve
      | Just tv2 <- tcGetTyVar_maybe xi
      = do { tch1 <- isTouchableMetaTyVar tv1
           ; tch2 <- isTouchableMetaTyVar tv2
           ; case (tch1, tch2) of
               (True,  True)  -> trySpontaneousEqTwoWay cv gw tv1 tv2
               (True,  False) -> trySpontaneousEqOneWay cv gw tv1 xi
               (False, True)  -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
    	   _ -> return SPCantSolve }
      | otherwise
      = do { tch1 <- isTouchableMetaTyVar tv1
           ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
                     else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:"
                                        (ppr workItem)
                             ; return SPCantSolve }
           }

      -- No need for
      --      trySpontaneousSolve (CFunEqCan ...) = ...
      -- See Note [No touchables as FunEq RHS] in TcSMonad
    trySpontaneousSolve _ = return SPCantSolve

    ----------------
    trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
    -- tv is a MetaTyVar, not untouchable
    trySpontaneousEqOneWay cv gw tv xi
      | not (isSigTyVar tv) || isTyVarTy xi
      = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts
                                   -- so we have its more specific kind in our hands
           ; if kxi `isSubKind` tyVarKind tv then
                 solveWithIdentity cv gw tv xi
             else return SPCantSolve
    {-
             else if tyVarKind tv `isSubKind` kxi then
                 return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
                                    -- This case covers the  a_touchable :: * ~ b_untouchable :: ??
                                    -- which has to be deferred or floated out for someone else to solve
                                    -- it in a scope where 'b' is no longer untouchable.
             else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
                     ; return SPError }
    -}
           }
      | otherwise -- Still can't solve, sig tyvar and non-variable rhs
      = return SPCantSolve

    ----------------
    trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
    -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
    trySpontaneousEqTwoWay cv gw tv1 tv2
      | k1 `isSubKind` k2
      , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
      | k2 `isSubKind` k1
      = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
      | otherwise -- None is a subkind of the other, but they are both touchable!
      = return SPCantSolve
        -- do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
        --   ; return SPError }
      where
        k1 = tyVarKind tv1
        k2 = tyVarKind tv2
        nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)

\end{code} Note [Kind errors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider the wanted problem: alpha ~ (# Int, Int #) where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint, but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay' simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and get quantified over in inference mode. That's bad because we do know at this point that the constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on. The same applies in canonicalization code in case of kind errors in the givens. However, when we canonicalize givens we only check for compatibility (@compatKind@). If there were a kind error in the givens, this means some form of inconsistency or dead code. You may think that when we spontaneously solve wanteds we may have to look through the bindings to determine the right kind of the RHS type. E.g one may be worried that xi is @alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *). But we orient our constraints so that spontaneously solved ones can rewrite all other constraint so this situation can't happen. Note [Spontaneous solving and kind compatibility] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Note that our canonical constraints insist that *all* equalities (tv ~ xi) or (F xis ~ rhs) require the LHS and the RHS to have *compatible* the same kinds. ("compatible" means one is a subKind of the other.) - It can't be *equal* kinds, because b) wanted constraints don't necessarily have identical kinds eg alpha::? ~ Int b) a solved wanted constraint becomes a given - SPJ thinks that *given* constraints (tv ~ tau) always have that tau has a sub-kind of tv; and when solving wanted constraints in trySpontaneousEqTwoWay we re-orient to achieve this. - Note that the kind invariant is maintained by rewriting. Eg wanted1 rewrites wanted2; if both were compatible kinds before, wanted2 will be afterwards. Similarly givens. Caveat: - Givens from higher-rank, such as: type family T b :: * -> * -> * type instance T Bool = (->) f :: forall a. ((T a ~ (->)) => ...) -> a -> ... flop = f (...) True Whereas we would be able to apply the type instance, we would not be able to use the given (T Bool ~ (->)) in the body of 'flop' 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. \begin{code}

    ----------------

    solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
    -- Solve with the identity coercion
    -- Precondition: kind(xi) is a sub-kind of kind(tv)
    -- Precondition: CtFlavor is Wanted or Derived
    -- See [New Wanted Superclass Work] to see why solveWithIdentity
    --     must work for Derived as well as Wanted
    -- Returns: workItem where
    --        workItem = the new Given constraint
    solveWithIdentity cv wd tv xi
      = do { traceTcS "Sneaky unification:" $
                           vcat [text "Coercion variable:  " <+> ppr wd,
                                 text "Coercion:           " <+> pprEq (mkTyVarTy tv) xi,
                                 text "Left  Kind is     : " <+> ppr (typeKind (mkTyVarTy tv)),
                                 text "Right Kind is     : " <+> ppr (typeKind xi)
                      ]

           ; setWantedTyBind tv xi
           ; cv_given <- newGivenCoVar (mkTyVarTy tv) xi xi

           ; when (isWanted wd) (setCoBind cv xi)
               -- We don't want to do this for Derived, that's why we use 'when (isWanted wd)'

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

\end{code} ********************************************************************************* * * 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 \begin{code}

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

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

            , ir_new_work     :: WorkList
                -- new work items to add to the WorkList

            , ir_fire :: Maybe String    -- Tells whether a rule fired, and if so what
            }

    -- What to do with the inert reactant.
    data InertAction = KeepInert | DropInert

    mkIRContinue :: String -> WorkItem -> InertAction -> WorkList -> TcS InteractResult
    mkIRContinue rule wi keep newWork
      = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = keep
                    , ir_new_work = newWork, ir_fire = Just rule }

    mkIRStopK :: String -> WorkList -> TcS InteractResult
    mkIRStopK rule newWork
      = return $ IR { ir_stop = Stop, ir_inert_action = KeepInert
                    , ir_new_work = newWork, ir_fire = Just rule }

    mkIRStopD :: String -> WorkList -> TcS InteractResult
    mkIRStopD rule newWork
      = return $ IR { ir_stop = Stop, ir_inert_action = DropInert
                    , ir_new_work = newWork, ir_fire = Just rule }

    noInteraction :: Monad m => WorkItem -> m InteractResult
    noInteraction wi
      = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = KeepInert
                    , ir_new_work = emptyWorkList, ir_fire = Nothing }

    data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
         -- See Note [Efficient Orientation]

    ---------------------------------------------------
    -- Interact a single WorkItem with the equalities of an inert set as
    -- far as possible, i.e. until we get a Stop result from an individual
    -- reaction (i.e. when the WorkItem is consumed), or until we've
    -- interact the WorkItem with the entire equalities of the InertSet

    interactWithInertEqsStage :: SimplifierStage
    interactWithInertEqsStage depth workItem inert
      = Bag.foldlBagM (interactNext depth) initITR (inert_eqs inert)
      where
        initITR = SR { sr_inerts   = inert { inert_eqs = emptyCCan }
                     , sr_new_work = emptyWorkList
                     , sr_stop     = ContinueWith workItem }

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

    interactWithInertsStage :: SimplifierStage
    interactWithInertsStage depth workItem inert
      = let (relevant, inert_residual) = getISRelevant workItem inert
            initITR = SR { sr_inerts   = inert_residual
                         , sr_new_work = emptyWorkList
                         , sr_stop     = ContinueWith workItem }
        in Bag.foldlBagM (interactNext depth) initITR relevant
      where
        getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
        getISRelevant (CFrozenErr {}) is = (emptyCCan, is)
                      -- Nothing s relevant; we have alread interacted
                      -- it with the equalities in the inert set

        getISRelevant (CDictCan { cc_class = cls } ) is
          = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
            in (relevant, is { inert_dicts = residual_map })
        getISRelevant (CFunEqCan { cc_fun = tc } ) is
          = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
            in (relevant, is { inert_funeqs = residual_map })
        getISRelevant (CIPCan { cc_ip_nm = nm }) is
          = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
            in (relevant, is { inert_ips = residual_map })
        -- An equality, finally, may kick everything except equalities out
        -- because we have already interacted the equalities in interactWithInertEqsStage
        getISRelevant _eq_ct is  -- Equality, everything is relevant for this one
                                 -- TODO: if we were caching variables, we'd know that only
                                 --       some are relevant. Experiment with this for now.
          = let cts = cCanMapToBag (inert_ips is) `unionBags`
                        cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
            in (cts, is { inert_dicts  = emptyCCanMap
                        , inert_ips    = emptyCCanMap
                        , inert_funeqs = emptyCCanMap })

    interactNext :: SubGoalDepth -> StageResult -> AtomicInert -> TcS StageResult
    interactNext depth it inert
      | ContinueWith work_item <- sr_stop it
      = do { let inerts = sr_inerts it

           ; IR { ir_new_work = new_work, ir_inert_action = inert_action
                , ir_fire = fire_info, ir_stop = stop }
                <- interactWithInert inert work_item

           ; let mk_msg rule
          	       = text rule <+> keep_doc
          	         <+> vcat [ ptext (sLit "Inert =") <+> ppr inert
          	                  , ptext (sLit "Work =")  <+> ppr work_item
          	                  , ppUnless (isEmptyBag new_work) $
                                ptext (sLit "New =") <+> ppr new_work ]
                 keep_doc = case inert_action of
                     	  KeepInert -> ptext (sLit "[keep]")
                     	  DropInert -> ptext (sLit "[drop]")
           ; case fire_info of
               Just rule -> do { bumpStepCountTcS
                               ; traceFireTcS depth (mk_msg rule) }
               Nothing  -> return ()

           -- New inerts depend on whether we KeepInert or not
           ; let inerts_new = case inert_action of
                                KeepInert -> inerts `updInertSet` inert
                                DropInert -> inerts

           ; return $ SR { sr_inerts   = inerts_new
                         , sr_new_work = sr_new_work it `unionWorkLists` new_work
                         , sr_stop     = stop } }
      | otherwise
      = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }

    -- Do a single interaction of two constraints.
    interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult
    interactWithInert inert workItem
      = do { ctxt <- getTcSContext
           ; let is_allowed  = allowedInteraction (simplEqsOnly ctxt) inert workItem

           ; if is_allowed then
                  doInteractWithInert inert workItem
              else
                  noInteraction workItem
           }

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

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

    doInteractWithInert
      inertItem@(CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
       workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
      | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
      = solveOneFromTheOther "Cls/Cls" (EvId d1,fl1) workItem

      | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
      = 	 -- See Note [When improvement happens]
        do { let pty1 = ClassP cls1 tys1
                 pty2 = ClassP cls2 tys2
                 inert_pred_loc     = (pty1, pprFlavorArising fl1)
                 work_item_pred_loc = (pty2, pprFlavorArising fl2)
                 fd_eqns = improveFromAnother
                                      inert_pred_loc     -- the template
                                      work_item_pred_loc -- the one we aim to rewrite
                                      -- See Note [Efficient Orientation]

           ; m <- rewriteWithFunDeps fd_eqns tys2 fl2
           ; case m of
               Nothing -> noInteraction workItem
               Just (rewritten_tys2, cos2, fd_work)
                 | tcEqTypes tys1 rewritten_tys2
                 -> -- Solve him on the spot in this case
    	     	case fl2 of
    	          Given   {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
                      Derived {} -> mkIRStopK "Cls/Cls fundep (solved)" fd_work
    		  Wanted  {}
    		    | isDerived fl1
                       -> do { setDictBind d2 (EvCast d1 dict_co)
    			 ; let inert_w = inertItem { cc_flavor = fl2 }
    			   -- A bit naughty: we take the inert Derived,
    			   -- turn it into a Wanted, use it to solve the work-item
    			   -- and put it back into the work-list
    			   -- Maybe rather than starting again, we could *replace* the
    			   -- inert item, but its safe and simple to restart
                             ; mkIRStopD "Cls/Cls fundep (solved)" (inert_w `consBag` fd_work) }

    		    | otherwise
                        -> do { setDictBind d2 (EvCast d1 dict_co)
                              ; mkIRStopK "Cls/Cls fundep (solved)" fd_work }

                 | otherwise
                 -> -- We could not quite solve him, but we still rewrite him
    	        -- Example: class C a b c | a -> b
    		--          Given: C Int Bool x, Wanted: C Int beta y
    		--          Then rewrite the wanted to C Int Bool y
    		--          but note that is still not identical to the given
    		-- The important thing is that the rewritten constraint is
    		-- inert wrt the given.
    		-- However it is not necessarily inert wrt previous inert-set items.
                    --      class C a b c d |  a -> b, b c -> d
    		--      Inert: c1: C b Q R S, c2: C P Q a b
    		--      Work: C P alpha R beta
    		--      Does not react with c1; reacts with c2, with alpha:=Q
    		--      NOW it reacts with c1!
    		-- So we must stop, and put the rewritten constraint back in the work list
                    do { d2' <- newDictVar cls1 rewritten_tys2
                       ; case fl2 of
                           Given {}   -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
                           Wanted {}  -> setDictBind d2 (EvCast d2' dict_co)
                           Derived {} -> return ()
                       ; let workItem' = workItem { cc_id = d2', cc_tyargs = rewritten_tys2 }
                       ; mkIRStopK "Cls/Cls fundep (partial)" (workItem' `consBag` fd_work) }

                 where
                   dict_co = mkTyConCoercion (classTyCon cls1) cos2
      }

    -- Class constraint and given equality: use the equality to rewrite
    -- the class constraint.
    doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
                        (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
      | ifl `canRewrite` wfl
      , tv `elemVarSet` tyVarsOfTypes xis
      = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
                -- Continue with rewritten Dictionary because we can only be in the
                -- interactWithEqsStage, so the dictionary is inert.
           ; mkIRContinue "Eq/Cls" rewritten_dict KeepInert emptyWorkList }

    doInteractWithInert (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
               workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
      | wfl `canRewrite` ifl
      , tv `elemVarSet` tyVarsOfTypes xis
      = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
           ; mkIRContinue "Cls/Eq" workItem DropInert (workListFromCCan rewritten_dict) }

    -- Class constraint and given equality: use the equality to rewrite
    -- the class constraint.
    doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
                        (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
      | ifl `canRewrite` wfl
      , tv `elemVarSet` tyVarsOfType ty
      = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
           ; mkIRContinue "Eq/IP" rewritten_ip KeepInert emptyWorkList }

    doInteractWithInert (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
               workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
      | wfl `canRewrite` ifl
      , tv `elemVarSet` tyVarsOfType ty
      = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
           ; mkIRContinue "IP/Eq" workItem DropInert (workListFromCCan rewritten_ip) }

    -- Two implicit parameter constraints.  If the names are the same,
    -- but their types are not, we generate a wanted type equality
    -- that equates the type (this is "improvement").
    -- However, we don't actually need the coercion evidence,
    -- so we just generate a fresh coercion variable that isn't used anywhere.
    doInteractWithInert (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
               workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
      | nm1 == nm2 && isGiven wfl && isGiven ifl
      = 	-- See Note [Overriding implicit parameters]
            -- Dump the inert item, override totally with the new one
    	-- Do not require type equality
    	-- For example, given let ?x::Int = 3 in let ?x::Bool = True in ...
    	--              we must *override* the outer one with the inner one
        mkIRContinue "IP/IP override" workItem DropInert emptyWorkList

      | nm1 == nm2 && ty1 `tcEqType` ty2
      = solveOneFromTheOther "IP/IP" (EvId id1,ifl) workItem

      | nm1 == nm2
      =  	-- See Note [When improvement happens]
        do { co_var <- newCoVar ty2 ty1 -- See Note [Efficient Orientation]
           ; let flav = Wanted (combineCtLoc ifl wfl)
           ; cans <- mkCanonical flav co_var
           ; mkIRContinue "IP/IP fundep" workItem KeepInert cans }

    -- Never rewrite a given with a wanted equality, and a type function
    -- equality can never rewrite an equality. We rewrite LHS *and* RHS
    -- of function equalities so that our inert set exposes everything that
    -- we know about equalities.

    -- Inert: equality, work item: function equality
    doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
                        (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
                                   , cc_tyargs = args, cc_rhs = xi2 })
      | ifl `canRewrite` wfl
      , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
      = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
           ; mkIRStopK "Eq/FunEq" (workListFromCCan rewritten_funeq) }
             -- Must Stop here, because we may no longer be inert after the rewritting.

    -- Inert: function equality, work item: equality
    doInteractWithInert (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
                                  , cc_tyargs = args, cc_rhs = xi1 })
               workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
      | wfl `canRewrite` ifl
      , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
      = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
           ; mkIRContinue "FunEq/Eq" workItem DropInert (workListFromCCan rewritten_funeq) }
             -- One may think that we could (KeepTransformedInert rewritten_funeq)
             -- but that is wrong, because it may end up not being inert with respect
             -- to future inerts. Example:
             -- Original inert = {    F xis ~  [a], b ~ Maybe Int }
             -- Work item comes along = a ~ [b]
             -- If we keep { F xis ~ [b] } in the inert set we will end up with:
             --      { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] }
             -- At the end, which is *not* inert. So we should unfortunately DropInert here.

    doInteractWithInert (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
                                   , cc_tyargs = args1, cc_rhs = xi1 })
               workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
                                   , cc_tyargs = args2, cc_rhs = xi2 })
      | fl1 `canSolve` fl2 && lhss_match
      = do { cans <- rewriteEqLHS LeftComesFromInert  (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
           ; mkIRStopK "FunEq/FunEq" cans }
      | fl2 `canSolve` fl1 && lhss_match
      = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
           ; mkIRContinue "FunEq/FunEq" workItem DropInert cans }
      where
        lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)

    doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
               workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
    -- Check for matching LHS
      | fl1 `canSolve` fl2 && tv1 == tv2
      = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
           ; mkIRStopK "Eq/Eq lhs" cans }

      | fl2 `canSolve` fl1 && tv1 == tv2
      = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
           ; mkIRContinue "Eq/Eq lhs" workItem DropInert cans }

    -- Check for rewriting RHS
      | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
      = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
           ; mkIRStopK "Eq/Eq rhs" rewritten_eq }

      | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
      = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
           ; mkIRContinue "Eq/Eq rhs" workItem DropInert rewritten_eq }

    doInteractWithInert (CTyEqCan   { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
                        (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
      | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
      = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
           ; mkIRStopK "Frozen/Eq" rewritten_frozen }

    doInteractWithInert (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
               workItem@(CTyEqCan   { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
      | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
      = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
           ; mkIRContinue "Frozen/Eq" workItem DropInert rewritten_frozen }

    -- Fall-through case for all other situations
    doInteractWithInert _ workItem = noInteraction workItem

    -------------------------
    -- Equational Rewriting
    rewriteDict  :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
    rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
      = do { let cos  = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
                 args = substTysWith [tv] [xi] xis
                 con  = classTyCon cl
                 dict_co = mkTyConCoercion con cos
           ; dv' <- newDictVar cl args
           ; case gw of
               Wanted {}         -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
               Given {}          -> setDictBind dv' (EvCast dv dict_co)
               Derived {}        -> return () -- Derived dicts we don't set any evidence

           ; return (CDictCan { cc_id = dv'
                              , cc_flavor = gw
                              , cc_class = cl
                              , cc_tyargs = args }) }

    rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
    rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
      = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty     -- ty[tv] ~ t[xi]
                 ty'   = substTyWith [tv] [xi] ty
           ; ipid' <- newIPVar nm ty'
           ; case gw of
               Wanted {}         -> setIPBind ipid  (EvCast ipid' (mkSymCoercion ip_co))
               Given {}          -> setIPBind ipid' (EvCast ipid ip_co)
               Derived {}        -> return () -- Derived ips: we don't set any evidence

           ; return (CIPCan { cc_id = ipid'
                            , cc_flavor = gw
                            , cc_ip_nm = nm
                            , cc_ip_ty = ty' }) }

    rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
    rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2)                   -- cv2 :: F args ~ xi2
      = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
                 args'   = substTysWith [tv] [xi1] args
                 fun_co  = mkTyConCoercion tc arg_cos                 -- fun_co :: F args ~ F args'

                 xi2'    = substTyWith [tv] [xi1] xi2
                 xi2_co  = substTyWith [tv] [mkCoVarCoercion cv1] xi2 -- xi2_co :: xi2 ~ xi2'

           ; cv2' <- newCoVar (mkTyConApp tc args') xi2'
           ; case gw of
               Wanted {} -> setCoBind cv2  (fun_co               `mkTransCoercion`
                                            mkCoVarCoercion cv2' `mkTransCoercion`
                                            mkSymCoercion xi2_co)
               Given {}  -> setCoBind cv2' (mkSymCoercion fun_co `mkTransCoercion`
                                            mkCoVarCoercion cv2  `mkTransCoercion`
                                            xi2_co)
               Derived {} -> return ()

           ; return (CFunEqCan { cc_id = cv2'
                               , cc_flavor = gw
                               , cc_tyargs = args'
                               , cc_fun = tc
                               , cc_rhs = xi2' }) }

    rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
    -- Use the first equality to rewrite the second, flavors already checked.
    -- E.g.          c1 : tv1 ~ xi1   c2 : tv2 ~ xi2
    -- rewrites c2 to give
    --               c2' : tv2 ~ xi2[xi1/tv1]
    -- We must do an occurs check to sure the new constraint is canonical
    -- So we might return an empty bag
    rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
      | Just tv2' <- tcGetTyVar_maybe xi2'
      , tv2 == tv2'	 -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
      = do { when (isWanted gw) (setCoBind cv2 (mkSymCoercion co2'))
           ; return emptyCCan }
      | otherwise
      = do { cv2' <- newCoVar (mkTyVarTy tv2) xi2'
           ; case gw of
                 Wanted {} -> setCoBind cv2 $ mkCoVarCoercion cv2' `mkTransCoercion`
                                              mkSymCoercion co2'
                 Given {}  -> setCoBind cv2' $ mkCoVarCoercion cv2 `mkTransCoercion`
                                               co2'
                 Derived {} -> return ()
           ; canEq gw cv2' (mkTyVarTy tv2) xi2' }
      where
        xi2' = substTyWith [tv1] [xi1] xi2
        co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2  -- xi2 ~ xi2[xi1/tv1]

    rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
    -- Used to ineract two equalities of the following form:
    -- First Equality:   co1: (XXX ~ xi1)
    -- Second Equality:  cv2: (XXX ~ xi2)
    -- Where the cv1 `canRewrite` cv2 equality
    -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
    --    See Note [Efficient Orientation] for that
    rewriteEqLHS LeftComesFromInert (co1,xi1) (cv2,gw,xi2)
      = do { cv2' <- newCoVar xi2 xi1
           ; case gw of
               Wanted {} -> setCoBind cv2 $
                            co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
               Given {}  -> setCoBind cv2' $
                            mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
               Derived {} -> return ()
           ; mkCanonical gw cv2' }

    rewriteEqLHS RightComesFromInert (co1,xi1) (cv2,gw,xi2)
      = do { cv2' <- newCoVar xi1 xi2
           ; case gw of
               Wanted {} -> setCoBind cv2 $
                            co1 `mkTransCoercion` mkCoVarCoercion cv2'
               Given {}  -> setCoBind cv2' $
                            mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
               Derived {} -> return ()
           ; mkCanonical gw cv2' }

    rewriteFrozen :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor) -> TcS WorkList
    rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
      = do { cv2' <- newCoVar ty2a' ty2b'  -- ty2a[xi1/tv1] ~ ty2b[xi1/tv1]
           ; case fl2 of
                 Wanted {} -> setCoBind cv2 $ co2a'                `mkTransCoercion`
                           	         	  mkCoVarCoercion cv2' `mkTransCoercion`
                           	         	  mkSymCoercion co2b'

                 Given {} -> setCoBind cv2' $ mkSymCoercion co2a'  `mkTransCoercion`
                          	 		  mkCoVarCoercion cv2  `mkTransCoercion`
                          	 		  co2b'

                 Derived {} -> return ()

          ; return (singleCCan $ CFrozenErr { cc_id = cv2', cc_flavor = fl2 }) }
      where
        (ty2a, ty2b) = coVarKind cv2          -- cv2 : ty2a ~ ty2b
        ty2a' = substTyWith [tv1] [xi1] ty2a
        ty2b' = substTyWith [tv1] [xi1] ty2b

        co2a' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2a  -- ty2a ~ ty2a[xi1/tv1]
        co2b' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2b  -- ty2b ~ ty2b[xi1/tv1]

    solveOneFromTheOther :: String -> (EvTerm, CtFlavor) -> CanonicalCt -> TcS InteractResult
    -- First argument inert, second argument work-item. They both represent
    -- wanted/given/derived evidence for the *same* predicate so
    -- we can discharge one directly from the other.
    --
    -- Precondition: value evidence only (implicit parameters, classes)
    --               not coercion
    solveOneFromTheOther info (ev_term,ifl) workItem
      | isDerived wfl
      = mkIRStopK ("Solved[DW] " ++ info) emptyWorkList

      | isDerived ifl -- The inert item is Derived, we can just throw it away,
        	      	  -- The workItem is inert wrt earlier inert-set items,
    		  -- so it's safe to continue on from this point
      = mkIRContinue ("Solved[DI] " ++ info) workItem DropInert emptyWorkList

      | otherwise
      = ASSERT( ifl `canSolve` wfl )
          -- Because of Note [The Solver Invariant], plus Derived dealt with
        do { when (isWanted wfl) $ setEvBind wid ev_term
               -- Overwrite the binding, if one exists
    	   -- If both are Given, we already have evidence; no need to duplicate
           ; mkIRStopK ("Solved " ++ info) emptyWorkList }
      where
         wfl = cc_flavor workItem
         wid = cc_id workItem

\end{code} Note [Superclasses and recursive dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Overlaps with Note [SUPERCLASS-LOOP 1] Note [SUPERCLASS-LOOP 2] Note [Recursive instances and superclases] ToDo: check overlap and delete redundant stuff Right before adding a given into the inert set, we must produce some more work, that will bring the superclasses of the given into scope. The superclass constraints go into our worklist. When we simplify a wanted constraint, if we first see a matching instance, we may produce new wanted work. To (1) avoid doing this work twice in the future and (2) to handle recursive dictionaries we may ``cache'' this item as given into our inert set WITHOUT adding its superclass constraints, otherwise we'd be in danger of creating a loop [In fact this was the exact reason for doing the isGoodRecEv check in an older version of the type checker]. But now we have added partially solved constraints to the worklist which may interact with other wanteds. Consider the example: Example 1: class Eq b => Foo a b --- 0-th selector instance Eq a => Foo [a] a --- fooDFun and wanted (Foo [t] t). We are first going to see that the instance matches and create an inert set that includes the solved (Foo [t] t) but not its superclasses: d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3 Our work list is going to contain a new *wanted* goal d3 :_w Eq t Ok, so how do we get recursive dictionaries, at all: Example 2: data D r = ZeroD | SuccD (r (D r)); instance (Eq (r (D r))) => Eq (D r) where ZeroD == ZeroD = True (SuccD a) == (SuccD b) = a == b _ == _ = False; equalDC :: D [] -> D [] -> Bool; equalDC = (==); We need to prove (Eq (D [])). Here's how we go: d1 :_w Eq (D []) by instance decl, holds if d2 :_w Eq [D []] where d1 = dfEqD d2 *BUT* we have an inert set which gives us (no superclasses): d1 :_g Eq (D []) By the instance declaration of Eq we can show the 'd2' goal if d3 :_w Eq (D []) where d2 = dfEqList d3 d1 = dfEqD d2 Now, however this wanted can interact with our inert d1 to set: d3 := d1 and solve the goal. Why was this interaction OK? Because, if we chase the evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we are really setting d3 := dfEqD2 (dfEqList d3) which is FINE because the use of d3 is protected by the instance function applications. So, our strategy is to try to put solved wanted dictionaries into the inert set along with their superclasses (when this is meaningful, i.e. when new wanted goals are generated) but solve a wanted dictionary from a given only in the case where the evidence variable of the wanted is mentioned in the evidence of the given (recursively through the evidence binds) in a protected way: more instance function applications than superclass selectors. Here are some more examples from GHC's previous type checker Example 3: This code arises in the context of "Scrap Your Boilerplate with Class" class Sat a class Data ctx a instance Sat (ctx Char) => Data ctx Char -- dfunData1 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2 class Data Maybe a => Foo a instance Foo t => Sat (Maybe t) -- dfunSat instance Data Maybe a => Foo a -- dfunFoo1 instance Foo a => Foo [a] -- dfunFoo2 instance Foo [Char] -- dfunFoo3 Consider generating the superclasses of the instance declaration instance Foo a => Foo [a] So our problem is this d0 :_g Foo t d1 :_w Data Maybe [t] We may add the given in the inert set, along with its superclasses [assuming we don't fail because there is a matching instance, see tryTopReact, given case ] Inert: d0 :_g Foo t WorkList d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0 d1 :_w Data Maybe [t] Then d2 can readily enter the inert, and we also do solving of the wanted Inert: d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 WorkList d2 :_w Sat (Maybe [t]) d3 :_w Data Maybe t d01 :_g Data Maybe t Now, we may simplify d2 more: Inert: d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d1 :_g Data Maybe [t] d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 WorkList: d3 :_w Data Maybe t d4 :_w Foo [t] d01 :_g Data Maybe t Now, we can just solve d3. Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 WorkList d4 :_w Foo [t] d01 :_g Data Maybe t And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist: Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 d4 :_g Foo [t] d4 := dfunFoo2 d5 WorkList: d5 :_w Foo t d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0 d01 :_g Data Maybe t Now, d5 can be solved! (and its superclass enter scope) Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 d4 :_g Foo [t] d4 := dfunFoo2 d5 d5 :_g Foo t d5 := dfunFoo1 d7 WorkList: d7 :_w Data Maybe t d6 :_g Data Maybe [t] d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0 d01 :_g Data Maybe t Now, two problems: [1] Suppose we pick d8 and we react him with d01. Which of the two givens should we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence that must not be used (look at case interactInert where both inert and workitem are givens). So we have several options: - Drop the workitem always (this will drop d8) This feels very unsafe -- what if the work item was the "good" one that should be used later to solve another wanted? - Don't drop anyone: the inert set may contain multiple givens! [This is currently implemented] The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2: [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted d7. Now the [isRecDictEv] function in the ineration solver [case inert-given workitem-wanted] will prevent us from interacting d7 := d8 precisely because chasing the evidence of d8 leads us to an unguarded use of d7. So, no interaction happens there. Then we meet d01 and there is no recursion problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01! Note [SUPERCLASS-LOOP 1] ~~~~~~~~~~~~~~~~~~~~~~~~ We have to be very, very careful when generating superclasses, lest we accidentally build a loop. Here's an example: class S a class S a => C a where { opc :: a -> a } class S b => D b where { opd :: b -> b } instance C Int where opc = opd instance D Int where opd = opc From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int} Simplifying, we may well get: $dfCInt = :C ds1 (opd dd) dd = $dfDInt ds1 = $p1 dd Notice that we spot that we can extract ds1 from dd. Alas! Alack! We can do the same for (instance D Int): $dfDInt = :D ds2 (opc dc) dc = $dfCInt ds2 = $p1 dc And now we've defined the superclass in terms of itself. Two more nasty cases are in tcrun021 tcrun033 Solution: - Satisfy the superclass context *all by itself* (tcSimplifySuperClasses) - And do so completely; i.e. no left-over constraints to mix with the constraints arising from method declarations Note [SUPERCLASS-LOOP 2] ~~~~~~~~~~~~~~~~~~~~~~~~ We need to be careful when adding "the constaint we are trying to prove". Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where class Ord a => C a where instance Ord [a] => C [a] where ... Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the superclasses of C [a] to avails. But we must not overwrite the binding for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just build a loop! Here's another variant, immortalised in tcrun020 class Monad m => C1 m class C1 m => C2 m x instance C2 Maybe Bool For the instance decl we need to build (C1 Maybe), and it's no good if we run around and add (C2 Maybe Bool) and its superclasses to the avails before we search for C1 Maybe. Here's another example class Eq b => Foo a b instance Eq a => Foo [a] a If we are reducing (Foo [t] t) we'll first deduce that it holds (via the instance decl). We must not then overwrite the Eq t constraint with a superclass selection! At first I had a gross hack, whereby I simply did not add superclass constraints in addWanted, though I did for addGiven and addIrred. This was sub-optimal, becuase it lost legitimate superclass sharing, and it still didn't do the job: I found a very obscure program (now tcrun021) in which improvement meant the simplifier got two bites a the cherry... so something seemed to be an Stop first time, but reducible next time. Now we implement the Right Solution, which is to check for loops directly when adding superclasses. It's a bit like the occurs check in unification. Note [Recursive instances and superclases] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider this code, which arises in the context of "Scrap Your Boilerplate with Class". class Sat a class Data ctx a instance Sat (ctx Char) => Data ctx Char instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] class Data Maybe a => Foo a instance Foo t => Sat (Maybe t) instance Data Maybe a => Foo a instance Foo a => Foo [a] instance Foo [Char] In the instance for Foo [a], when generating evidence for the superclasses (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]). Using the instance for Data, we therefore need (Sat (Maybe [a], Data Maybe a) But we are given (Foo a), and hence its superclass (Data Maybe a). So that leaves (Sat (Maybe [a])). Using the instance for Sat means we need (Foo [a]). And that is the very dictionary we are bulding an instance for! So we must put that in the "givens". So in this case we have Given: Foo a, Foo [a] Wanted: Data Maybe [a] BUT we must *not not not* put the *superclasses* of (Foo [a]) in the givens, which is what 'addGiven' would normally do. Why? Because (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted by selecting a superclass from Foo [a], which simply makes a loop. On the other hand we *must* put the superclasses of (Foo a) in the givens, as you can see from the derivation described above. Conclusion: in the very special case of tcSimplifySuperClasses we have one 'given' (namely the "this" dictionary) whose superclasses must not be added to 'givens' by addGiven. There is a complication though. Suppose there are equalities instance (Eq a, a~b) => Num (a,b) Then we normalise the 'givens' wrt the equalities, so the original given "this" dictionary is cast to one of a different type. So it's a bit trickier than before to identify the "special" dictionary whose superclasses must not be added. See test indexed-types/should_run/EqInInstance We need a persistent property of the dictionary to record this special-ness. Current I'm using the InstLocOrigin (a bit of a hack, but cool), which is maintained by dictionary normalisation. Specifically, the InstLocOrigin is NoScOrigin then the no-superclass thing kicks in. WATCH OUT if you fiddle with InstLocOrigin! 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. ********************************************************************************* * * The top-reaction Stage * * ********************************************************************************* \begin{code}

    -- If a work item has any form of interaction with top-level we get this
    data TopInteractResult
      = NoTopInt         -- No top-level interaction
                         -- Equivalent to (SomeTopInt emptyWorkList (ContinueWith work_item))
      | SomeTopInt
          { tir_new_work  :: WorkList	-- Sub-goals or new work (could be given,
                                            --                        for superclasses)
          , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
          }                       		-- NB: in ``given'' (solved) form if the
                                  		-- original was wanted or given and instance match
                                  		-- was found, but may also be in wanted form if we
                                            -- only reacted with functional dependencies
    					-- arising from top-level instances.

    topReactionsStage :: SimplifierStage
    topReactionsStage depth workItem inerts
      = do { tir <- tryTopReact workItem
           ; case tir of
               NoTopInt ->
                   return $ SR { sr_inerts   = inerts
                               , sr_new_work = emptyWorkList
                               , sr_stop     = ContinueWith workItem }
               SomeTopInt tir_new_work tir_new_inert ->
                   do { bumpStepCountTcS
                      ; traceFireTcS depth (ptext (sLit "Top react")
                           <+> vcat [ ptext (sLit "Work =") <+> ppr workItem
                                    , ptext (sLit "New =") <+> ppr tir_new_work ])
                      ; return $ SR { sr_inerts   = inerts
                               	, sr_new_work = tir_new_work
                               	, sr_stop     = tir_new_inert
                               	} }
           }

    tryTopReact :: WorkItem -> TcS TopInteractResult
    tryTopReact workitem
      = do {  -- A flag controls the amount of interaction allowed
              -- See Note [Simplifying RULE lhs constraints]
             ctxt <- getTcSContext
           ; if allowedTopReaction (simplEqsOnly ctxt) workitem
             then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
                     ; doTopReact workitem }
             else return NoTopInt
           }

    allowedTopReaction :: Bool -> WorkItem -> Bool
    allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
    allowedTopReaction _        _             = True

    doTopReact :: WorkItem -> TcS TopInteractResult
    -- The work item does not react with the inert set, so try interaction with top-level instances
    -- NB: The place to add superclasses in *not* in doTopReact stage. Instead superclasses are
    --     added in the worklist as part of the canonicalisation process.
    -- See Note [Adding superclasses] in TcCanonical.

    -- Given dictionary
    -- See Note [Given constraint that matches an instance declaration]
    doTopReact (CDictCan { cc_flavor = Given {} })
      = return NoTopInt -- NB: Superclasses already added since it's canonical

    -- Derived dictionary: just look for functional dependencies
    doTopReact workItem@(CDictCan { cc_flavor = fl@(Derived loc)
                                  , cc_class = cls, cc_tyargs = xis })
      = do { instEnvs <- getInstEnvs
           ; let fd_eqns = improveFromInstEnv instEnvs
                                                    (ClassP cls xis, pprArisingAt loc)
           ; m <- rewriteWithFunDeps fd_eqns xis fl
           ; case m of
               Nothing -> return NoTopInt
               Just (xis',_,fd_work) ->
                   let workItem' = workItem { cc_tyargs = xis' }
                       -- Deriveds are not supposed to have identity (cc_id is unused!)
                   in return $ SomeTopInt { tir_new_work  = fd_work
                                          , tir_new_inert = ContinueWith workItem' } }

    -- Wanted dictionary
    doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl@(Wanted loc)
                                  , cc_class = cls, cc_tyargs = xis })
      = do { -- See Note [MATCHING-SYNONYMS]
           ; lkp_inst_res <- matchClassInst cls xis loc
           ; case lkp_inst_res of
               NoInstance ->
                 do { traceTcS "doTopReact/ no class instance for" (ppr dv)

                    ; instEnvs <- getInstEnvs
                    ; let fd_eqns = improveFromInstEnv instEnvs
                                                             (ClassP cls xis, pprArisingAt loc)
                    ; m <- rewriteWithFunDeps fd_eqns xis fl
                    ; case m of
                        Nothing -> return NoTopInt
                        Just (xis',cos,fd_work) ->
                            do { let dict_co = mkTyConCoercion (classTyCon cls) cos
                               ; dv'<- newDictVar cls xis'
                               ; setDictBind dv (EvCast dv' dict_co)
                               ; let workItem' = CDictCan { cc_id = dv', cc_flavor = fl,
                                                            cc_class = cls, cc_tyargs = xis' }
                               ; return $
                                 SomeTopInt { tir_new_work  = singleCCan workItem' `andCCan` fd_work
                                            , tir_new_inert = Stop } } }

               GenInst wtvs ev_term -- Solved
    	   	   -- No need to do fundeps stuff here; the instance
    		   -- matches already so we won't get any more info
    		   -- from functional dependencies
                 | null wtvs
                 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
                       ; setDictBind dv ev_term
                        -- Solved in one step and no new wanted work produced.
                        -- i.e we directly matched a top-level instance
                        -- No point in caching this in 'inert'; hence Stop
                       ; return $ SomeTopInt { tir_new_work  = emptyWorkList
                                             , tir_new_inert = Stop } }

                 | otherwise
                 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
                       ; setDictBind dv ev_term
                            -- Solved and new wanted work produced, you may cache the
                            -- (tentatively solved) dictionary as Given! (used to be: Derived)
                       ; let solved   = workItem { cc_flavor = given_fl }
                             given_fl = Given (setCtLocOrigin loc UnkSkol)
                       ; inst_work <- canWanteds wtvs
                       ; return $ SomeTopInt { tir_new_work  = inst_work
                                             , tir_new_inert = ContinueWith solved } }
           }

    -- Type functions
    doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
                          , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
      = ASSERT (isSynFamilyTyCon tc)   -- No associated data families have reached that far
        do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
           ; case match_res of
               MatchInstNo
                 -> return NoTopInt
               MatchInstSingle (rep_tc, rep_tys)
                 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
                             Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
    			    -- Eagerly expand away the type synonym on the
    			    -- RHS of a type function, so that it never
    			    -- appears in an error message
                                -- See Note [Type synonym families] in TyCon
                             coe = mkTyConApp coe_tc rep_tys
                       ; cv' <- case fl of
                                  Wanted {} -> do { cv' <- newCoVar rhs_ty xi
                                                  ; setCoBind cv $
                                                        coe `mkTransCoercion`
                                                          mkCoVarCoercion cv'
                                                  ; return cv' }
                                  Given {}   -> newGivenCoVar xi rhs_ty $
                                                mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
                                  Derived {} -> newDerivedId (EqPred xi rhs_ty)
                       ; can_cts <- mkCanonical fl cv'
                       ; return $ SomeTopInt can_cts Stop }
               _
                 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
           }

    -- Any other work item does not react with any top-level equations
    doTopReact _workItem = return NoTopInt

\end{code} 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 wanted 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 :w alpha ~ Bool where 'cv' is currently unused. However, this new item reacts 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. With the same inert set and work item we might dischard d2 directly: cv :w alpha ~ Bool d2 := d1 |> D Int cv But in general it's a bit painful to figure out the necessary coercion, so we just take the first approach. Here is a better example. Consider: class C a b c | a -> b And: [Given] d1 : C T Int Char [Wanted] d2 : C T beta Int In this case, it's *not even possible* to solve the wanted immediately. So we should simply output the functional dependency and add this guy [but NOT its superclasses] back in the worklist. Even worse: [Given] d1 : C T Int beta [Wanted] d2: C T beta Int Then it is solvable, but its very hard to detect this on the spot. It's exactly the same with implicit parameters, except that the "aggressive" approach would be much easier to implement. Note [When improvement happens] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We fire an improvement rule when * Two constraints match (modulo the fundep) e.g. C t1 t2, C t1 t3 where C a b | a->b The two match because the first arg is identical * At least one is not Given. If they are both given, we don't fire the reaction because we have no way of constructing evidence for a new equality nor does it seem right to create a new wanted goal (because the goal will most likely contain untouchables, which can't be solved anyway)! Note that we *do* fire the improvement if one is Given and one is Derived. The latter can be a superclass of a wanted goal. Example (tcfail138) class L a b | a -> b class (G a, L a b) => C a b instance C a b' => G (Maybe a) instance C a b => C (Maybe a) a instance L (Maybe a) a When solving the superclasses of the (C (Maybe a) a) instance, we get Given: C a b ... and hance by superclasses, (G a, L a b) Wanted: G (Maybe a) Use the instance decl to get Wanted: C a b' The (C a b') is inert, so we generate its Derived superclasses (L a b'), and now we need improvement between that derived superclass an the Given (L a b) Note [Overriding implicit parameters] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider f :: (?x::a) -> Bool -> a g v = let ?x::Int = 3 in (f v, let ?x::Bool = True in f v) This should probably be well typed, with g :: Bool -> (Int, Bool) So the inner binding for ?x::Bool *overrides* the outer one. Hence a work-item Given overrides an inert-item Given. Note [Given constraint that matches an instance declaration] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ What should we do when we discover that one (or more) top-level instances match a given (or solved) class constraint? We have two possibilities: 1. Reject the program. The reason is that there may not be a unique best strategy for the solver. Example, from the OutsideIn(X) paper: instance P x => Q [x] instance (x ~ y) => R [x] y wob :: forall a b. (Q [b], R b a) => a -> Int g :: forall a. Q [a] => [a] -> Int g x = wob x will generate the impliation constraint: Q [a] => (Q [beta], R beta [a]) If we react (Q [beta]) with its top-level axiom, we end up with a (P beta), which we have no way of discharging. On the other hand, if we react R beta [a] with the top-level we get (beta ~ a), which is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is now solvable by the given Q [a]. However, this option is restrictive, for instance [Example 3] from Note [Recursive dictionaries] will fail to work. 2. Ignore the problem, hoping that the situations where there exist indeed such multiple strategies are rare: Indeed the cause of the previous problem is that (R [x] y) yields the new work (x ~ y) which can be *spontaneously* solved, not using the givens. We are choosing option 2 below but we might consider having a flag as well. Note [New Wanted Superclass Work] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Even in the case of wanted constraints, we may add some superclasses as new given work. The reason is: To allow FD-like improvement for type families. Assume that we have a class class C a b | a -> b and we have to solve the implication constraint: C a b => C a beta Then, FD improvement can help us to produce a new wanted (beta ~ b) We want to have the same effect with the type family encoding of functional dependencies. Namely, consider: class (F a ~ b) => C a b Now suppose that we have: given: C a b wanted: C a beta By interacting the given we will get given (F a ~ b) which is not enough by itself to make us discharge (C a beta). However, we may create a new derived equality from the super-class of the wanted constraint (C a beta), namely derived (F a ~ beta). Now we may interact this with given (F a ~ b) to get: derived : beta ~ b But 'beta' is a touchable unification variable, and hence OK to unify it with 'b', replacing the derived evidence with the identity. This requires trySpontaneousSolve to solve *derived* equalities that have a touchable in their RHS, *in addition* to solving wanted equalities. We also need to somehow use the superclasses to quantify over a minimal, constraint see note [Minimize by Superclasses] in TcSimplify. Finally, here is another example where this is useful. Example 1: ---------- class (F a ~ b) => C a b And we are given the wanteds: w1 : C a b w2 : C a c w3 : b ~ c We surely do *not* want to quantify over (b ~ c), since if someone provides dictionaries for (C a b) and (C a c), these dictionaries can provide a proof of (b ~ c), hence no extra evidence is necessary. Here is what will happen: Step 1: We will get new *given* superclass work, provisionally to our solving of w1 and w2 g1: F a ~ b, g2 : F a ~ c, w1 : C a b, w2 : C a c, w3 : b ~ c The evidence for g1 and g2 is a superclass evidence term: g1 := sc w1, g2 := sc w2 Step 2: The givens will solve the wanted w3, so that w3 := sym (sc w1) ; sc w2 Step 3: Now, one may naively assume that then w2 can be solve from w1 after rewriting with the (now solved equality) (b ~ c). But this rewriting is ruled out by the isGoodRectDict! Conclusion, we will (correctly) end up with the unsolved goals (C a b, C a c) NB: The desugarer needs be more clever to deal with equalities that participate in recursive dictionary bindings. \begin{code}

    data LookupInstResult
      = NoInstance
      | GenInst [WantedEvVar] EvTerm

    matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
    matchClassInst clas tys loc
       = do { let pred = mkClassPred clas tys
            ; mb_result <- matchClass clas tys
            ; case mb_result of
                MatchInstNo   -> return NoInstance
                MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
                                                   -- we learn more about the reagent
                MatchInstSingle (dfun_id, mb_inst_tys) ->
                  do { checkWellStagedDFun pred dfun_id loc

     	-- It's possible that not all the tyvars are in
    	-- the substitution, tenv. For example:
    	--	instance C X a => D X where ...
    	-- (presumably there's a functional dependency in class C)
    	-- Hence mb_inst_tys :: Either TyVar TcType

                     ; tys <- instDFunTypes mb_inst_tys
                     ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
                     ; if null theta then
                           return (GenInst [] (EvDFunApp dfun_id tys []))
                       else do
                         { ev_vars <- instDFunConstraints theta
                         ; let wevs = [EvVarX w loc | w <- ev_vars]
                         ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }
                     }
            }

\end{code}