typecheck/TcSMonad.hs

    {-# LANGUAGE CPP, TypeFamilies #-}

    -- Type definitions for the constraint solver
    module TcSMonad (

        -- The work list
        WorkList(..), isEmptyWorkList, emptyWorkList,
        extendWorkListNonEq, extendWorkListCt, extendWorkListDerived,
        extendWorkListCts, extendWorkListEq, extendWorkListFunEq,
        appendWorkList,
        selectNextWorkItem,
        workListSize, workListWantedCount,
        updWorkListTcS,

        -- The TcS monad
        TcS, runTcS, runTcSDeriveds, runTcSWithEvBinds,
        failTcS, warnTcS, addErrTcS,
        runTcSEqualities,
        nestTcS, nestImplicTcS,

        runTcPluginTcS, addUsedDataCons, deferTcSForAllEq,

        -- Tracing etc
        panicTcS, traceTcS,
        traceFireTcS, bumpStepCountTcS, csTraceTcS,
        wrapErrTcS, wrapWarnTcS,

        -- Evidence creation and transformation
        MaybeNew(..), freshGoals, isFresh, getEvTerm,

        newTcEvBinds,
        newWantedEq,
        newWanted, newWantedEvVar, newWantedEvVarNC, newDerivedNC,
        newBoundEvVarId,
        unifyTyVar, unflattenFmv, reportUnifications,
        setEvBind, setWantedEq, setEqIfWanted,
        setWantedEvTerm, setWantedEvBind, setEvBindIfWanted,
        newEvVar, newGivenEvVar, newGivenEvVars,
        emitNewDerived, emitNewDeriveds, emitNewDerivedEq,
        checkReductionDepth,

        getInstEnvs, getFamInstEnvs,                -- Getting the environments
        getTopEnv, getGblEnv, getLclEnv,
        getTcEvBinds, getTcEvBindsFromVar, getTcLevel,
        getTcEvBindsMap,
        tcLookupClass,

        -- Inerts
        InertSet(..), InertCans(..),
        updInertTcS, updInertCans, updInertDicts, updInertIrreds,
        getNoGivenEqs, setInertCans,
        getInertEqs, getInertCans, getInertModel, getInertGivens,
        emptyInert, getTcSInerts, setTcSInerts, takeGivenInsolubles,
        matchableGivens, prohibitedSuperClassSolve,
        getUnsolvedInerts,
        removeInertCts, getPendingScDicts,
        addInertCan, addInertEq, insertFunEq,
        emitInsoluble, emitWorkNC,

        -- The Model
        InertModel, kickOutAfterUnification,

        -- Inert Safe Haskell safe-overlap failures
        addInertSafehask, insertSafeOverlapFailureTcS, updInertSafehask,
        getSafeOverlapFailures,

        -- Inert CDictCans
        lookupInertDict, findDictsByClass, addDict, addDictsByClass,
        delDict, partitionDicts, foldDicts, filterDicts,

        -- Inert CTyEqCans
        EqualCtList, findTyEqs, foldTyEqs, isInInertEqs,

        -- Inert solved dictionaries
        addSolvedDict, lookupSolvedDict,

        -- Irreds
        foldIrreds,

        -- The flattening cache
        lookupFlatCache, extendFlatCache, newFlattenSkolem,            -- Flatten skolems

        -- Inert CFunEqCans
        updInertFunEqs, findFunEq, sizeFunEqMap, filterFunEqs,
        findFunEqsByTyCon, partitionFunEqs, foldFunEqs,

        instDFunType,                              -- Instantiation

        -- MetaTyVars
        newFlexiTcSTy, instFlexiTcS,
        cloneMetaTyVar, demoteUnfilledFmv,

        TcLevel, isTouchableMetaTyVarTcS,
        isFilledMetaTyVar_maybe, isFilledMetaTyVar,
        zonkTyCoVarsAndFV, zonkTcType, zonkTcTypes, zonkTcTyVar, zonkCo,
        zonkSimples, zonkWC,

        -- References
        newTcRef, readTcRef, updTcRef,

        -- Misc
        getDefaultInfo, getDynFlags, getGlobalRdrEnvTcS,
        matchFam, matchFamTcM,
        checkWellStagedDFun,
        pprEq                                    -- Smaller utils, re-exported from TcM
                                                 -- TODO (DV): these are only really used in the
                                                 -- instance matcher in TcSimplify. I am wondering
                                                 -- if the whole instance matcher simply belongs
                                                 -- here
    ) where

    #include "HsVersions.h"

    import HscTypes

    import qualified Inst as TcM
    import InstEnv
    import FamInst
    import FamInstEnv

    import qualified TcRnMonad as TcM
    import qualified TcMType as TcM
    import qualified TcEnv as TcM
           ( checkWellStaged, topIdLvl, tcGetDefaultTys, tcLookupClass )
    import Kind
    import TcType
    import DynFlags
    import Type
    import Coercion
    import Unify

    import TcEvidence
    import Class
    import TyCon
    import TcErrors   ( solverDepthErrorTcS )

    import Name
    import RdrName ( GlobalRdrEnv)
    import qualified RnEnv as TcM
    import Var
    import VarEnv
    import VarSet
    import Outputable
    import Bag
    import UniqSupply
    import Util
    import TcRnTypes

    import Unique
    import UniqFM
    import Maybes

    import TrieMap
    import Control.Monad
    #if __GLASGOW_HASKELL__ > 710
    import qualified Control.Monad.Fail as MonadFail
    #endif
    import MonadUtils
    import Data.IORef
    import Data.List ( foldl', partition )

    #ifdef DEBUG
    import Digraph
    #endif

    {-
    ************************************************************************
    *                                                                      *
    *                            Worklists                                *
    *  Canonical and non-canonical constraints that the simplifier has to  *
    *  work on. Including their simplification depths.                     *
    *                                                                      *
    *                                                                      *
    ************************************************************************

    Note [WorkList priorities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    A WorkList contains canonical and non-canonical items (of all flavors).
    Notice that each Ct now has a simplification depth. We may
    consider using this depth for prioritization as well in the future.

    As a simple form of priority queue, our worklist separates out
    equalities (wl_eqs) from the rest of the canonical constraints,
    so that it's easier to deal with them first, but the separation
    is not strictly necessary. Notice that non-canonical constraints
    are also parts of the worklist.

    Note [Process derived items last]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We can often solve all goals without processing *any* derived constraints.
    The derived constraints are just there to help us if we get stuck.  So
    we keep them in a separate list.

    -}

    -- See Note [WorkList priorities]
    data WorkList
      = WL { wl_eqs     :: [Ct]
           , wl_funeqs  :: [Ct]  -- LIFO stack of goals
           , wl_rest    :: [Ct]
           , wl_deriv   :: [CtEvidence]  -- Implicitly non-canonical
                                         -- See Note [Process derived items last]
           , wl_implics :: Bag Implication  -- See Note [Residual implications]
        }

    appendWorkList :: WorkList -> WorkList -> WorkList
    appendWorkList
        (WL { wl_eqs = eqs1, wl_funeqs = funeqs1, wl_rest = rest1
            , wl_deriv = ders1, wl_implics = implics1 })
        (WL { wl_eqs = eqs2, wl_funeqs = funeqs2, wl_rest = rest2
            , wl_deriv = ders2, wl_implics = implics2 })
       = WL { wl_eqs     = eqs1     ++ eqs2
            , wl_funeqs  = funeqs1  ++ funeqs2
            , wl_rest    = rest1    ++ rest2
            , wl_deriv   = ders1    ++ ders2
            , wl_implics = implics1 `unionBags`   implics2 }

    workListSize :: WorkList -> Int
    workListSize (WL { wl_eqs = eqs, wl_funeqs = funeqs, wl_deriv = ders, wl_rest = rest })
      = length eqs + length funeqs + length rest + length ders

    workListWantedCount :: WorkList -> Int
    workListWantedCount (WL { wl_eqs = eqs, wl_rest = rest })
      = count isWantedCt eqs + count isWantedCt rest

    extendWorkListEq :: Ct -> WorkList -> WorkList
    extendWorkListEq ct wl = wl { wl_eqs = ct : wl_eqs wl }

    extendWorkListEqs :: [Ct] -> WorkList -> WorkList
    extendWorkListEqs cts wl = wl { wl_eqs = cts ++ wl_eqs wl }

    extendWorkListFunEq :: Ct -> WorkList -> WorkList
    extendWorkListFunEq ct wl = wl { wl_funeqs = ct : wl_funeqs wl }

    extendWorkListNonEq :: Ct -> WorkList -> WorkList
    -- Extension by non equality
    extendWorkListNonEq ct wl = wl { wl_rest = ct : wl_rest wl }

    extendWorkListDerived :: CtLoc -> CtEvidence -> WorkList -> WorkList
    extendWorkListDerived loc ev wl
      | isDroppableDerivedLoc loc = wl { wl_deriv = ev : wl_deriv wl }
      | otherwise                 = extendWorkListEq (mkNonCanonical ev) wl

    extendWorkListDeriveds :: CtLoc -> [CtEvidence] -> WorkList -> WorkList
    extendWorkListDeriveds loc evs wl
      | isDroppableDerivedLoc loc = wl { wl_deriv = evs ++ wl_deriv wl }
      | otherwise                 = extendWorkListEqs (map mkNonCanonical evs) wl

    extendWorkListImplic :: Implication -> WorkList -> WorkList
    extendWorkListImplic implic wl = wl { wl_implics = implic `consBag` wl_implics wl }

    extendWorkListCt :: Ct -> WorkList -> WorkList
    -- Agnostic
    extendWorkListCt ct wl
     = case classifyPredType (ctPred ct) of
         EqPred NomEq ty1 _
           | Just (tc,_) <- tcSplitTyConApp_maybe ty1
           , isTypeFamilyTyCon tc
           -> extendWorkListFunEq ct wl
         EqPred {}
           -> extendWorkListEq ct wl

         _ -> extendWorkListNonEq ct wl

    extendWorkListCts :: [Ct] -> WorkList -> WorkList
    -- Agnostic
    extendWorkListCts cts wl = foldr extendWorkListCt wl cts

    isEmptyWorkList :: WorkList -> Bool
    isEmptyWorkList (WL { wl_eqs = eqs, wl_funeqs = funeqs
                        , wl_rest = rest, wl_deriv = ders, wl_implics = implics })
      = null eqs && null rest && null funeqs && isEmptyBag implics && null ders

    emptyWorkList :: WorkList
    emptyWorkList = WL { wl_eqs  = [], wl_rest = []
                       , wl_funeqs = [], wl_deriv = [], wl_implics = emptyBag }

    selectWorkItem :: WorkList -> Maybe (Ct, WorkList)
    selectWorkItem wl@(WL { wl_eqs = eqs, wl_funeqs = feqs
                          , wl_rest = rest })
      | ct:cts <- eqs  = Just (ct, wl { wl_eqs    = cts })
      | ct:fes <- feqs = Just (ct, wl { wl_funeqs = fes })
      | ct:cts <- rest = Just (ct, wl { wl_rest   = cts })
      | otherwise      = Nothing

    selectDerivedWorkItem  :: WorkList -> Maybe (Ct, WorkList)
    selectDerivedWorkItem wl@(WL { wl_deriv = ders })
      | ev:evs <- ders = Just (mkNonCanonical ev, wl { wl_deriv  = evs })
      | otherwise      = Nothing

    selectNextWorkItem :: TcS (Maybe Ct)
    selectNextWorkItem
      = do { wl_var <- getTcSWorkListRef
           ; wl <- wrapTcS (TcM.readTcRef wl_var)

           ; let try :: Maybe (Ct,WorkList) -> TcS (Maybe Ct) -> TcS (Maybe Ct)
                 try mb_work do_this_if_fail
                    | Just (ct, new_wl) <- mb_work
                    = do { checkReductionDepth (ctLoc ct) (ctPred ct)
                         ; wrapTcS (TcM.writeTcRef wl_var new_wl)
                         ; return (Just ct) }
                    | otherwise
                    = do_this_if_fail

           ; try (selectWorkItem wl) $

        do { ics <- getInertCans
           ; solve_deriveds <- keepSolvingDeriveds
           ; if inert_count ics == 0 && not solve_deriveds
             then return Nothing
             else try (selectDerivedWorkItem wl) (return Nothing) } }

    -- Pretty printing
    instance Outputable WorkList where
      ppr (WL { wl_eqs = eqs, wl_funeqs = feqs
              , wl_rest = rest, wl_implics = implics, wl_deriv = ders })
       = text "WL" <+> (braces $
         vcat [ ppUnless (null eqs) $
                text "Eqs =" <+> vcat (map ppr eqs)
              , ppUnless (null feqs) $
                text "Funeqs =" <+> vcat (map ppr feqs)
              , ppUnless (null rest) $
                text "Non-eqs =" <+> vcat (map ppr rest)
              , ppUnless (null ders) $
                text "Derived =" <+> vcat (map ppr ders)
              , ppUnless (isEmptyBag implics) $
                text "Implics =" <+> vcat (map ppr (bagToList implics))
              ])

    {- *********************************************************************
    *                                                                      *
                    InertSet: the inert set
    *                                                                      *
    *                                                                      *
    ********************************************************************* -}

    data InertSet
      = IS { inert_cans :: InertCans
                  -- Canonical Given, Wanted, Derived (no Solved)
                  -- Sometimes called "the inert set"

           , inert_flat_cache :: ExactFunEqMap (TcCoercion, TcType, CtFlavour)
                  -- See Note [Type family equations]
                  -- If    F tys :-> (co, ty, ev),
                  -- then  co :: F tys ~ ty
                  --
                  -- Just a hash-cons cache for use when flattening only
                  -- These include entirely un-processed goals, so don't use
                  -- them to solve a top-level goal, else you may end up solving
                  -- (w:F ty ~ a) by setting w:=w!  We just use the flat-cache
                  -- when allocating a new flatten-skolem.
                  -- Not necessarily inert wrt top-level equations (or inert_cans)

                  -- NB: An ExactFunEqMap -- this doesn't match via loose types!

           , inert_solved_dicts   :: DictMap CtEvidence
                  -- Of form ev :: C t1 .. tn
                  -- See Note [Solved dictionaries]
                  -- and Note [Do not add superclasses of solved dictionaries]
           }

    instance Outputable InertSet where
      ppr is = vcat [ ppr $ inert_cans is
                    , text "Solved dicts" <+> vcat (map ppr (bagToList (dictsToBag (inert_solved_dicts is)))) ]

    emptyInert :: InertSet
    emptyInert
      = IS { inert_cans = IC { inert_count    = 0
                             , inert_eqs      = emptyVarEnv
                             , inert_dicts    = emptyDicts
                             , inert_safehask = emptyDicts
                             , inert_funeqs   = emptyFunEqs
                             , inert_irreds   = emptyCts
                             , inert_insols   = emptyCts
                             , inert_model    = emptyVarEnv }
           , inert_flat_cache    = emptyExactFunEqs
           , inert_solved_dicts  = emptyDictMap }

    {- Note [Solved dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we apply a top-level instance declararation, we add the "solved"
    dictionary to the inert_solved_dicts.  In general, we use it to avoid
    creating a new EvVar when we have a new goal that we have solved in
    the past.

    But in particular, we can use it to create *recursive* dicationaries.
    The simplest, degnerate case is
        instance C [a] => C [a] where ...
    If we have
        [W] d1 :: C [x]
    then we can apply the instance to get
        d1 = $dfCList d
        [W] d2 :: C [x]
    Now 'd1' goes in inert_solved_dicts, and we can solve d2 directly from d1.
        d1 = $dfCList d
        d2 = d1

    See Note [Example of recursive dictionaries]
    Other notes about solved dictionaries

    * See also Note [Do not add superclasses of solved dictionaries]

    * The inert_solved_dicts field is not rewritten by equalities, so it may
      get out of date.

    Note [Do not add superclasses of solved dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Every member of inert_solved_dicts is the result of applying a dictionary
    function, NOT of applying superclass selection to anything.
    Consider

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

    Suppose we are trying to solve
      [G] d1 : Ord a
      [W] d2 : C [a]

    Then we'll use the instance decl to give

      [G] d1 : Ord a     Solved: d2 : C [a] = $dfCList d3
      [W] d3 : Ord [a]

    We must not add d4 : Ord [a] to the 'solved' set (by taking the
    superclass of d2), otherwise we'll use it to solve d3, without ever
    using d1, which would be a catastrophe.

    Solution: when extending the solved dictionaries, do not add superclasses.
    That's why each element of the inert_solved_dicts is the result of applying
    a dictionary function.

    Note [Example of recursive dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    --- Example 1

        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:

       [W] d1 : Eq (D [])
    By instance decl of Eq (D r):
       [W] d2 : Eq [D []]      where   d1 = dfEqD d2
    By instance decl of Eq [a]:
       [W] d3 : Eq (D [])      where   d2 = dfEqList d3
                                       d1 = dfEqD d2
    Now this wanted can interact with our "solved" d1 to get:
        d3 = d1

    -- Example 2:
    This code arises in the context of "Scrap Your Boilerplate with Class"

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

        class Data Maybe a => Foo a

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

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

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

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

    We may add the given in the inert set, along with its superclasses
      Inert:
        [G] d0 : Foo t
        [G] d01 : Data Maybe t   -- Superclass of d0
      WorkList
        [W] d1 : Data Maybe [t]

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

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

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

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

    Now, d5 can be solved! d5 := d0

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

    {- *********************************************************************
    *                                                                      *
                    InertCans: the canonical inerts
    *                                                                      *
    *                                                                      *
    ********************************************************************* -}

    data InertCans   -- See Note [Detailed InertCans Invariants] for more
      = IC { inert_model :: InertModel
                  -- See Note [inert_model: the inert model]

           , inert_eqs :: TyVarEnv EqualCtList
                  -- See Note [inert_eqs: the inert equalities]
                  -- All Given/Wanted CTyEqCans; index is the LHS tyvar

           , inert_funeqs :: FunEqMap Ct
                  -- All CFunEqCans; index is the whole family head type.
                  -- All Nominal (that's an invarint of all CFunEqCans)
                  -- LHS is fully rewritten (modulo eqCanRewrite constraints)
                  --     wrt inert_eqs/inert_model
                  -- We can get Derived ones from e.g.
                  --   (a) flattening derived equalities
                  --   (b) emitDerivedShadows

           , inert_dicts :: DictMap Ct
                  -- Dictionaries only
                  -- All fully rewritten (modulo flavour constraints)
                  --     wrt inert_eqs/inert_model

           , inert_safehask :: DictMap Ct
                  -- Failed dictionary resolution due to Safe Haskell overlapping
                  -- instances restriction. We keep this seperate from inert_dicts
                  -- as it doesn't cause compilation failure, just safe inference
                  -- failure.
                  --
                  -- ^ See Note [Safe Haskell Overlapping Instances Implementation]
                  -- in TcSimplify

           , inert_irreds :: Cts
                  -- Irreducible predicates

           , inert_insols :: Cts
                  -- Frozen errors (as non-canonicals)

           , inert_count :: Int
                  -- Number of Wanted goals in
                  --     inert_eqs, inert_dicts, inert_safehask, inert_irreds
                  -- Does not include insolubles
                  -- When non-zero, keep trying to solved
           }

    type InertModel  = TyVarEnv Ct
         -- If a -> ct, then ct is a
         --    nominal, Derived, canonical CTyEqCan for [D] (a ~N rhs)
         -- The index of the TyVarEnv is the 'a'
         -- All saturated info for Given, Wanted, Derived is here

    {- Note [Detailed InertCans Invariants]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The InertCans represents a collection of constraints with the following properties:

      * All canonical

      * No two dictionaries with the same head
      * No two CIrreds with the same type

      * Family equations inert wrt top-level family axioms

      * Dictionaries have no matching top-level instance

      * Given family or dictionary constraints don't mention touchable
        unification variables

      * Non-CTyEqCan constraints are fully rewritten with respect
        to the CTyEqCan equalities (modulo canRewrite of course;
        eg a wanted cannot rewrite a given)

      * CTyEqCan equalities: see Note [Applying the inert substitution]
                             in TcFlatten

    Note [Type family equations]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Type-family equations, of form (ev : F tys ~ ty), live in three places

      * The work-list, of course

      * The inert_flat_cache.  This is used when flattening, to get maximal
        sharing.  It contains lots of things that are still in the work-list.
        E.g Suppose we have (w1: F (G a) ~ Int), and (w2: H (G a) ~ Int) in the
            work list.  Then we flatten w1, dumping (w3: G a ~ f1) in the work
            list.  Now if we flatten w2 before we get to w3, we still want to
            share that (G a).

        Because it contains work-list things, DO NOT use the flat cache to solve
        a top-level goal.  Eg in the above example we don't want to solve w3
        using w3 itself!

      * The inert_funeqs are un-solved but fully processed and in the InertCans.

    Note [inert_model: the inert model]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * Part of the inert set is the “model”

       * The “Model” is an non-idempotent but no-occurs-check
         substitution, reflecting *all* *Nominal* equalities (a ~N ty)
         that are not immediately soluble by unification.

       * All the constraints in the model are Derived CTyEqCans
         That is if (a -> ty) is in the model, then
         we have an inert constraint [D] a ~N ty.

       * There are two sources of constraints in the model:

         - Derived constraints arising from functional dependencies, or
           decomposing injective arguments of type functions, and
           suchlike.

         - A Derived "shadow copy" for every Given or Wanted (a ~N ty) in
           inert_eqs.

       * The model is not subject to "kicking-out". Reason: we make a Derived
         shadow copy of any Given/Wanted (a ~ ty), and that Derived copy will
         be fully rewritten by the model before it is added

       * The principal reason for maintaining the model is to generate
         equalities that tell us how to unify a variable: that is, what
         Mark Jones calls "improvement". The same idea is sometimes also
         called "saturation"; find all the equalities that must hold in
         any solution.

       * Domain of the model = skolems + untouchables.
         A touchable unification variable wouuld have been unified first.

       * The inert_eqs are all Given/Wanted.  The Derived ones are in the
         inert_model only.

       * However inert_dicts, inert_funeqs, inert_irreds
         may well contain derived costraints.

    Note [inert_eqs: the inert equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    Definition [Can-rewrite relation]
    A "can-rewrite" relation between flavours, written f1 >= f2, is a
    binary relation with the following properties

      (R1) >= is transitive
      (R2) If f1 >= f, and f2 >= f,
           then either f1 >= f2 or f2 >= f1

    Lemma.  If f1 >= f then f1 >= f1
    Proof.  By property (R2), with f1=f2

    Definition [Generalised substitution]
    A "generalised substitution" S is a set of triples (a -f-> t), where
      a is a type variable
      t is a type
      f is a flavour
    such that
      (WF1) if (a -f1-> t1) in S
               (a -f2-> t2) in S
            then neither (f1 >= f2) nor (f2 >= f1) hold
      (WF2) if (a -f-> t) is in S, then t /= a

    Definition [Applying a generalised substitution]
    If S is a generalised substitution
       S(f,a) = t,  if (a -fs-> t) in S, and fs >= f
              = a,  otherwise
    Application extends naturally to types S(f,t), modulo roles.
    See Note [Flavours with roles].

    Theorem: S(f,a) is well defined as a function.
    Proof: Suppose (a -f1-> t1) and (a -f2-> t2) are both in S,
                   and  f1 >= f and f2 >= f
           Then by (R2) f1 >= f2 or f2 >= f1, which contradicts (WF1)

    Notation: repeated application.
      S^0(f,t)     = t
      S^(n+1)(f,t) = S(f, S^n(t))

    Definition: inert generalised substitution
    A generalised substitution S is "inert" iff

      (IG1) there is an n such that
            for every f,t, S^n(f,t) = S^(n+1)(f,t)

    By (IG1) we define S*(f,t) to be the result of exahaustively
    applying S(f,_) to t.

    ----------------------------------------------------------------
    Our main invariant:
       the inert CTyEqCans should be an inert generalised substitution
    ----------------------------------------------------------------

    Note that inertness is not the same as idempotence.  To apply S to a
    type, you may have to apply it recursive.  But inertness does
    guarantee that this recursive use will terminate.

    Note [Extending the inert equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Theorem [Stability under extension]
       This is the main theorem!
       Suppose we have a "work item"
           a -fw-> t
       and an inert generalised substitution S,
       such that
          (T1) S(fw,a) = a     -- LHS of work-item is a fixpoint of S(fw,_)
          (T2) S(fw,t) = t     -- RHS of work-item is a fixpoint of S(fw,_)
          (T3) a not in t      -- No occurs check in the work item

          (K1) for every (a -fs-> s) in S, then not (fw >= fs)
               Reason: the work item is fully rewritten by S, hence not (fs >= fw)
                       but if (fw >= fs) then the work item could rewrite
                       the inert item

          (K2) for every (b -fs-> s) in S, where b /= a, then
                  (K2a) not (fs >= fs)
               or (K2b) fs >= fw
               or (K2c) not (fw >= fs)
               or (K2d) a not in s

          (K3) See Note [K3: completeness of solving]
               If (b -fs-> s) is in S with (fw >= fs), then
            (K3a) If the role of fs is nominal: s /= a
            (K3b) If the role of fs is representational: EITHER
                    a not in s, OR
                    the path from the top of s to a includes at least one non-newtype

       then the extended substition T = S+(a -fw-> t)
       is an inert generalised substitution.

    Conditions (T1-T3) are established by the canonicaliser
    Conditions (K1-K3) are established by TcSMonad.kickOutRewriteable

    The idea is that
    * (T1-2) are guaranteed by exhaustively rewriting the work-item
      with S(fw,_).

    * T3 is guaranteed by a simple occurs-check on the work item.
      This is done during canonicalisation, in canEqTyVar;
      (invariant: a CTyEqCan never has an occurs check).

    * (K1-3) are the "kick-out" criteria.  (As stated, they are really the
      "keep" criteria.) If the current inert S contains a triple that does
      not satisfy (K1-3), then we remove it from S by "kicking it out",
      and re-processing it.

    * Note that kicking out is a Bad Thing, because it means we have to
      re-process a constraint.  The less we kick out, the better.
      TODO: Make sure that kicking out really *is* a Bad Thing. We've assumed
      this but haven't done the empirical study to check.

    * Assume we have  G>=G, G>=W and that's all.  Then, when performing
      a unification we add a new given  a -G-> ty.  But doing so does NOT require
      us to kick out an inert wanted that mentions a, because of (K2a).  This
      is a common case, hence good not to kick out.

    * Lemma (L2): if not (fw >= fw), then K1-K3 all hold.
      Proof: using Definition [Can-rewrite relation], fw can't rewrite anything
             and so K1-K3 hold.  Intuitively, since fw can't rewrite anything,
             adding it cannot cause any loops
      This is a common case, because Wanteds cannot rewrite Wanteds.

    * Lemma (L1): The conditions of the Main Theorem imply that there is no
                  (a -fs-> t) in S, s.t.  (fs >= fw).
      Proof. Suppose the contrary (fs >= fw).  Then because of (T1),
      S(fw,a)=a.  But since fs>=fw, S(fw,a) = s, hence s=a.  But now we
      have (a -fs-> a) in S, which contradicts (WF2).

    * The extended substitution satisfies (WF1) and (WF2)
      - (K1) plus (L1) guarantee that the extended substitution satisfies (WF1).
      - (T3) guarantees (WF2).

    * (K2) is about inertness.  Intuitively, any infinite chain T^0(f,t),
      T^1(f,t), T^2(f,T).... must pass through the new work item infnitely
      often, since the substution without the work item is inert; and must
      pass through at least one of the triples in S infnitely often.

      - (K2a): if not(fs>=fs) then there is no f that fs can rewrite (fs>=f),
        and hence this triple never plays a role in application S(f,a).
        It is always safe to extend S with such a triple.

        (NB: we could strengten K1) in this way too, but see K3.

      - (K2b): If this holds then, by (T2), b is not in t.  So applying the
        work item does not genenerate any new opportunities for applying S

      - (K2c): If this holds, we can't pass through this triple infinitely
        often, because if we did then fs>=f, fw>=f, hence by (R2)
          * either fw>=fs, contradicting K2c
          * or fs>=fw; so by the agument in K2b we can't have a loop

      - (K2d): if a not in s, we hae no further opportunity to apply the
        work item, similar to (K2b)

      NB: Dimitrios has a PDF that does this in more detail

    Key lemma to make it watertight.
      Under the conditions of the Main Theorem,
      forall f st fw >= f, a is not in S^k(f,t), for any k

    Also, consider roles more carefully. See Note [Flavours with roles]

    Note [K3: completeness of solving]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    (K3) is not necessary for the extended substitution
    to be inert.  In fact K1 could be made stronger by saying
       ... then (not (fw >= fs) or not (fs >= fs))
    But it's not enough for S to be inert; we also want completeness.
    That is, we want to be able to solve all soluble wanted equalities.
    Suppose we have

       work-item   b -G-> a
       inert-item  a -W-> b

    Assuming (G >= W) but not (W >= W), this fulfills all the conditions,
    so we could extend the inerts, thus:

       inert-items   b -G-> a
                     a -W-> b

    But if we kicked-out the inert item, we'd get

       work-item     a -W-> b
       inert-item    b -G-> a

    Then rewrite the work-item gives us (a -W-> a), which is soluble via Refl.
    So we add one more clause to the kick-out criteria

    Another way to understand (K3) is that we treat an inert item
            a -f-> b
    in the same way as
            b -f-> a
    So if we kick out one, we should kick out the other.  The orientation
    is somewhat accidental.

    When considering roles, we also need the second clause (K3b). Consider

      inert-item   a -W/R-> b c
      work-item    c -G/N-> a

    The work-item doesn't get rewritten by the inert, because (>=) doesn't hold.
    We've satisfied conditions (T1)-(T3) and (K1) and (K2). If all we had were
    condition (K3a), then we would keep the inert around and add the work item.
    But then, consider if we hit the following:

      work-item2   b -G/N-> Id

    where

      newtype Id x = Id x

    For similar reasons, if we only had (K3a), we wouldn't kick the
    representational inert out. And then, we'd miss solving the inert, which
    now reduced to reflexivity. The solution here is to kick out representational
    inerts whenever the tyvar of a work item is "exposed", where exposed means
    not under some proper data-type constructor, like [] or Maybe. See
    isTyVarExposed in TcType. This is encoded in (K3b).

    Note [Stability of flattening]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The inert_eqs and inert_model, *considered separately* are each stable;
    that is, substituting using them will terminate.  Considered *together*
    they are not.  E.g.

      Add: [G] a~[b] to inert set with model  [D] b~[a]

      We add [G] a~[b] to inert_eqs, and emit [D] a~[b]. At this point
      the combination of inert_eqs and inert_model is not stable.

      Then we canonicalise [D] a~[b] to [D] a~[[a]], and add that to
      insolubles as an occurs check.

    * When canonicalizing, the flattener respects flavours. In particular,
      when flattening a type variable 'a':
        * Derived:      look up 'a' in the inert_model
        * Given/Wanted: look up 'a' in the inert_eqs

    Note [Flavours with roles]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~
    The system described in Note [inert_eqs: the inert equalities]
    discusses an abstract
    set of flavours. In GHC, flavours have two components: the flavour proper,
    taken from {Wanted, Derived, Given} and the equality relation (often called
    role), taken from {NomEq, ReprEq}.
    When substituting w.r.t. the inert set,
    as described in Note [inert_eqs: the inert equalities],
    we must be careful to respect all components of a flavour.
    For example, if we have

      inert set: a -G/R-> Int
                 b -G/R-> Bool

      type role T nominal representational

    and we wish to compute S(W/R, T a b), the correct answer is T a Bool, NOT
    T Int Bool. The reason is that T's first parameter has a nominal role, and
    thus rewriting a to Int in T a b is wrong. Indeed, this non-congruence of
    substitution means that the proof in Note [The inert equalities] may need
    to be revisited, but we don't think that the end conclusion is wrong.

    Note [Examples of how the inert_model helps completeness]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    ----------- Example 2 (indexed-types/should_fail/T4093a)
      Ambiguity check for f: (Foo e ~ Maybe e) => Foo e

      We get [G] Foo e ~ Maybe e
             [W] Foo e ~ Foo ee      -- ee is a unification variable
             [W] Foo ee ~ Maybe ee

      Flatten: [G] Foo e ~ fsk
               [G] fsk ~ Maybe e   -- (A)

               [W] Foo ee ~ fmv
               [W] fmv ~ fsk       -- (B) From Foo e ~ Foo ee
               [W] fmv ~ Maybe ee

      --> rewrite (B) with (A)
               [W] Foo ee ~ fmv
               [W] fmv ~ Maybe e
               [W] fmv ~ Maybe ee

      But now awe appear to be stuck, since we don't rewrite Wanteds with
      Wanteds. But inert_model to the rescue.  In the model we first added
               fmv -> Maybe e
      Then when adding [W] fmv -> Maybe ee to the inert set, we noticed
      that the model can rewrite the constraint, and so emit [D] fmv ~ Maybe ee.
      That canonicalises to
               [D] Maybe e ~ Maybe ee
      and that soon yields ee := e, and all is well

    ----------- Example 3 (typecheck/should_compile/Improvement.hs)
        type instance F Int = Bool
        instance (b~Int) => C Bool b

        [W] w1 : C (F alpha) alpha, [W] w2 : F alpha ~ Bool

      If we rewrote wanteds with wanteds, we could rewrite w1 to
      C Bool alpha, use the instance to get alpha ~ Int, and solve
      the whole thing.

      And that is exactly what happens, in the *Derived* constraints.
      In effect we get

        [D] F alpha ~ fmv
        [D] C fmv alpha
        [D] fmv ~ Bool

      and now we can rewrite (C fmv alpha) with (fmv ~ Bool), ane
      we are off to the races.

    ----------- Example 4 (Trac #10009, a nasty example):

        f :: (UnF (F b) ~ b) => F b -> ()

        g :: forall a. (UnF (F a) ~ a) => a -> ()
        g _ = f (undefined :: F a)

      For g we get [G] UnF (F a) ~ a
                   [W] UnF (F beta) ~ beta
                   [W] F a ~ F beta
      Flatten:
          [G] g1: F a ~ fsk1         fsk1 := F a
          [G] g2: UnF fsk1 ~ fsk2    fsk2 := UnF fsk1
          [G] g3: fsk2 ~ a

          [W] w1: F beta ~ fmv1
          [W] w2: UnF fmv1 ~ fmv2
          [W] w3: beta ~ fmv2
          [W] w5: fmv1 ~ fsk1   -- From F a ~ F beta using flat-cache
                                -- and re-orient to put meta-var on left

      Unify beta := fmv2
          [W] w1: F fmv2 ~ fmv1
          [W] w2: UnF fmv1 ~ fmv2
          [W] w5: fmv1 ~ fsk1

      In the model, we have the shadow Deriveds of w1 and w2
      (I name them for convenience even though they are anonymous)
          [D] d1: F fmv2 ~ fmv1d
          [D] d2: fmv1d ~ fmv1
          [D] d3: UnF fmv1 ~ fmv2d
          [D] d4: fmv2d ~ fmv2

      Now we can rewrite d3 with w5, and match with g2, to get
          fmv2d := fsk2
          [D] d1: F fmv2 ~ fmv1d
          [D] d2: fmv1d ~ fmv1
          [D] d4: fmv2 ~ fsk2

      Use g2 to rewrite fsk2 to a.
          [D] d1: F fmv2 ~ fmv1d
          [D] d2: fmv1d ~ fmv1
          [D] d4: fmv2 ~ a

      Use d4 to rewrite d1, rewrite with g3,
      match with g1, to get
          fmv1d := fsk1
          [D] d2: fmv1 ~ fsk1
          [D] d4: fmv2 ~ a

      At this point we are stuck so we unflatten this set:
      See Note [Orientation of equalities with fmvs] in TcFlatten
          [W] w1: F fmv2 ~ fmv1
          [W] w2: UnF fmv1 ~ fmv2
          [W] w5: fmv1 ~ fsk1
          [D] d4: fmv2 ~ a

      Unflattening will discharge w1: fmv1 := F fmv2
      It can't discharge w2, so it is kept.  But we can
      unify fmv2 := fsk2, and that is "progress". Result
          [W] w2: UnF (F a) ~ a
          [W] w5: F a ~ fsk1

      And now both of these are easily proved in the next iteration.  Phew!
    -}

    instance Outputable InertCans where
      ppr (IC { inert_model = model, inert_eqs = eqs
              , inert_funeqs = funeqs, inert_dicts = dicts
              , inert_safehask = safehask, inert_irreds = irreds
              , inert_insols = insols, inert_count = count })
        = braces $ vcat
          [ ppUnless (isEmptyVarEnv eqs) $
            text "Equalities:"
              <+> pprCts (foldVarEnv (\eqs rest -> listToBag eqs `andCts` rest) emptyCts eqs)
          , ppUnless (isEmptyTcAppMap funeqs) $
            text "Type-function equalities =" <+> pprCts (funEqsToBag funeqs)
          , ppUnless (isEmptyTcAppMap dicts) $
            text "Dictionaries =" <+> pprCts (dictsToBag dicts)
          , ppUnless (isEmptyTcAppMap safehask) $
            text "Safe Haskell unsafe overlap =" <+> pprCts (dictsToBag safehask)
          , ppUnless (isEmptyCts irreds) $
            text "Irreds =" <+> pprCts irreds
          , ppUnless (isEmptyCts insols) $
            text "Insolubles =" <+> pprCts insols
          , ppUnless (isEmptyVarEnv model) $
            text "Model =" <+> pprCts (foldVarEnv consCts emptyCts model)
          , text "Unsolved goals =" <+> int count
          ]

    {- *********************************************************************
    *                                                                      *
                      Adding an inert
    *                                                                      *
    ************************************************************************

    Note [Adding an inert canonical constraint the InertCans]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * Adding any constraint c *other* than a CTyEqCan (TcSMonad.addInertCan):

        * If c can be rewritten by model, emit the shadow constraint [D] c
          as NonCanonical.   See Note [Emitting shadow constraints]

        * Reason for non-canonical: a CFunEqCan has a unique fmv on the RHS,
          so we must not duplicate it.

    * Adding a *nominal* CTyEqCan (a ~N ty) to the inert set (TcSMonad.addInertEq).

        (A) Always (G/W/D) kick out constraints that can be rewritten
            (respecting flavours) by the new constraint. This is done
            by kickOutRewritable.

        (B) Applies only to nominal equalities: a ~ ty.  Four cases:

            [Representational]   [G/W/D] a ~R ty:
              Just add it to inert_eqs

            [Derived Nominal]  [D] a ~N ty:
              1. Add (a~ty) to the model
                 NB: 'a' cannot be in fv(ty), because the constraint is canonical.

              2. (DShadow) Do emitDerivedShadows
                   For every inert G/W constraint c, st
                    (a) (a~ty) can rewrite c (see Note [Emitting shadow constraints]),
                        and
                    (b) the model cannot rewrite c
                   kick out a Derived *copy*, leaving the original unchanged.
                   Reason for (b) if the model can rewrite c, then we have already
                   generated a shadow copy

           [Given/Wanted Nominal]  [G/W] a ~N ty:
              1. Add it to inert_eqs
              2. Emit [D] a~ty
              Step (2) is needed to allow the current model to fully
              rewrite [D] a~ty before adding it using the [Derived Nominal]
              steps above.

              We must do this even for Givens, because
                 work-item [G] a ~ [b], model has [D] b ~ a.
              We need a shadow [D] a ~ [b] in the work-list
              When we process it, we'll rewrite to a ~ [a] and get an occurs check

    * Unifying a:=ty, is like adding [G] a~ty, but we can't make a [D]
      a~ty, as in step (1) of the [G/W] case above.  So instead, do
      kickOutAfterUnification:
        - Kick out from the model any equality (b~ty2) that mentions 'a'
          (i.e. a=b or a in ty2).  Example:
                [G] a ~ [b],    model [D] b ~ [a]

    Note [Emitting shadow constraints]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     * Given a new model element [D] a ~ ty, we want to emit shadow
       [D] constraints for any inert constraints 'c' that can be
       rewritten [D] a-> ty

     * And similarly given a new Given/Wanted 'c', we want to emit a
       shadow 'c' if the model can rewrite [D] c

    See modelCanRewrite.

    NB the use of rewritableTyVars. You might wonder whether, given the new
    constraint [D] fmv ~ ty and the inert [W] F alpha ~ fmv, do we want to
    emit a shadow constraint [D] F alpha ~ fmv?  No, we don't, because
    it'll literally be a duplicate (since we do not rewrite the RHS of a
    CFunEqCan) and hence immediately eliminated again.  Insetad we simply
    want to *kick-out* the [W] F alpha ~ fmv, so that it is reconsidered
    from a fudep point of view.  See Note [Kicking out CFunEqCan for
    fundeps]

    Note [Kicking out CFunEqCan for fundeps]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider:
       New:    [D] fmv1 ~ fmv2
       Inert:  [W] F alpha ~ fmv1
               [W] F beta  ~ fmv2

    The new (derived) equality certainly can't rewrite the inerts. But we
    *must* kick out the first one, to get:

       New:   [W] F alpha ~ fmv1
       Inert: [W] F beta ~ fmv2
       Model: [D] fmv1 ~ fmv2

    and now improvement will discover [D] alpha ~ beta. This is important;
    eg in Trac #9587.
    -}

    addInertEq :: Ct -> TcS ()
    -- This is a key function, because of the kick-out stuff
    -- Precondition: item /is/ canonical
    addInertEq ct@(CTyEqCan { cc_tyvar = tv })
      = do { traceTcS "addInertEq {" $
             text "Adding new inert equality:" <+> ppr ct
           ; ics <- getInertCans

           ; let (kicked_out, ics1) = kickOutRewritable (ctFlavourRole ct) tv ics
           ; ics2 <- add_inert_eq ics1 ct

           ; setInertCans ics2

           ; unless (isEmptyWorkList kicked_out) $
             do { updWorkListTcS (appendWorkList kicked_out)
                ; csTraceTcS $
                   hang (text "Kick out, tv =" <+> ppr tv)
                      2 (vcat [ text "n-kicked =" <+> int (workListSize kicked_out)
                              , ppr kicked_out ]) }

           ; traceTcS "addInertEq }" $ empty }
    addInertEq ct = pprPanic "addInertEq" (ppr ct)

    add_inert_eq :: InertCans -> Ct -> TcS InertCans
    add_inert_eq ics@(IC { inert_count = n
                         , inert_eqs = old_eqs
                         , inert_model = old_model })
                 ct@(CTyEqCan { cc_ev = ev, cc_eq_rel = eq_rel, cc_tyvar = tv
                              , cc_rhs = _rhs })
      | ReprEq <- eq_rel
      = return new_ics

      | isDerived ev
      = do { emitDerivedShadows ics tv
           ; return (ics { inert_model = extendVarEnv old_model tv ct }) }

      | otherwise   -- Given/Wanted Nominal equality [W] tv ~N ty
      = do { emitNewDerived loc pred
           ; return new_ics }
      where
        loc     = ctEvLoc ev
        pred    = ctEvPred ev
        new_ics = ics { inert_eqs   = addTyEq old_eqs tv ct
                      , inert_count = bumpUnsolvedCount ev n }

    add_inert_eq _ ct = pprPanic "addInertEq" (ppr ct)

    emitDerivedShadows :: InertCans -> TcTyVar -> TcS ()
    emitDerivedShadows IC { inert_eqs      = tv_eqs
                          , inert_dicts    = dicts
                          , inert_safehask = safehask
                          , inert_funeqs   = funeqs
                          , inert_irreds   = irreds
                          , inert_model    = model } new_tv
      | null shadows
      = return ()
      | otherwise
      = do { traceTcS "Emit derived shadows:" $
             vcat [ text "tyvar =" <+> ppr new_tv
                  , text "shadows =" <+> vcat (map ppr shadows) ]
           ; emitWork shadows }
      where
        shadows = foldDicts  get_ct dicts    $
                  foldDicts  get_ct safehask $
                  foldFunEqs get_ct funeqs   $
                  foldIrreds get_ct irreds   $
                  foldTyEqs  get_ct tv_eqs []
          -- Ignore insolubles

        get_ct ct cts | want_shadow ct = mkShadowCt ct : cts
                      | otherwise      = cts

        want_shadow ct
          =  not (isDerivedCt ct)              -- No need for a shadow of a Derived!
          && (new_tv `elemVarSet` rw_tvs)      -- New tv can rewrite ct, yielding a
                                               -- different ct
          && not (modelCanRewrite model rw_tvs)-- We have not already created a
                                               -- shadow
          where
            rw_tvs = rewritableTyCoVars ct

    mkShadowCt :: Ct -> Ct
    -- Produce a Derived shadow constraint from the input
    -- If it is a CFunEqCan, make it NonCanonical, to avoid
    --   duplicating the flatten-skolems
    -- Otherwise keep the canonical shape.  This just saves work, but
    -- is sometimes important; see Note [Keep CDictCan shadows as CDictCan]
    mkShadowCt ct
      | CFunEqCan {} <- ct = CNonCanonical { cc_ev = derived_ev }
      | otherwise          = ct { cc_ev = derived_ev }
      where
        ev = ctEvidence ct
        derived_ev = CtDerived { ctev_pred = ctEvPred ev
                               , ctev_loc  = ctEvLoc ev }

    {- Note [Keep CDictCan shadows as CDictCan]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Suppose we have
      class C a => D a b
    and [G] D a b, [G] C a in the inert set.  Now we insert
    [D] b ~ c.  We want to kick out a derived shadow for [D] D a b,
    so we can rewrite it with the new constraint, and perhaps get
    instance reduction or other consequences.

    BUT we do not want to kick out a *non-canonical* (D a b). If we
    did, we would do this:
      - rewrite it to [D] D a c, with pend_sc = True
      - use expandSuperClasses to add C a
      - go round again, which solves C a from the givens
    This loop goes on for ever and triggers the simpl_loop limit.

    Solution: kick out the CDictCan which will have pend_sc = False,
    becuase we've already added its superclasses.  So we won't re-add
    them.  If we forget the pend_sc flag, our cunning scheme for avoiding
    generating superclasses repeatedly will fail.

    See Trac #11379 for a case of this.
    -}

    modelCanRewrite :: InertModel -> TcTyCoVarSet -> Bool
    -- See Note [Emitting shadow constraints]
    -- True if there is any intersection between dom(model) and tvs
    modelCanRewrite model tvs = not (disjointUFM model tvs)
         -- The low-level use of disjointUFM might e surprising.
         -- InertModel = TyVarEnv Ct, and we want to see if its domain
         -- is disjoint from that of a TcTyCoVarSet.  So we drop down
         -- to the underlying UniqFM.  A bit yukky, but efficient.

    rewritableTyCoVars :: Ct -> TcTyVarSet
    -- The tyvars of a Ct that can be rewritten
    rewritableTyCoVars (CFunEqCan { cc_tyargs = tys }) = tyCoVarsOfTypes tys
    rewritableTyCoVars ct                              = tyCoVarsOfType (ctPred ct)

    --------------
    addInertCan :: Ct -> TcS ()  -- Constraints *other than* equalities
    addInertCan ct
      = do { traceTcS "insertInertCan {" $
             text "Trying to insert new inert item:" <+> ppr ct

           ; ics <- getInertCans
           ; setInertCans (add_item ics ct)

           -- Emit shadow derived if necessary
           -- See Note [Emitting shadow constraints]
           ; let rw_tvs = rewritableTyCoVars ct
           ; when (not (isDerivedCt ct) && modelCanRewrite (inert_model ics) rw_tvs)
                  (emitWork [mkShadowCt ct])

           ; traceTcS "addInertCan }" $ empty }

    add_item :: InertCans -> Ct -> InertCans
    add_item ics item@(CFunEqCan { cc_fun = tc, cc_tyargs = tys })
      = ics { inert_funeqs = insertFunEq (inert_funeqs ics) tc tys item }

    add_item ics item@(CIrredEvCan { cc_ev = ev })
      = ics { inert_irreds = inert_irreds ics `Bag.snocBag` item
            , inert_count = bumpUnsolvedCount ev (inert_count ics) }
           -- The 'False' is because the irreducible constraint might later instantiate
           -- to an equality.
           -- But since we try to simplify first, if there's a constraint function FC with
           --    type instance FC Int = Show
           -- we'll reduce a constraint (FC Int a) to Show a, and never add an inert irreducible

    add_item ics item@(CDictCan { cc_ev = ev, cc_class = cls, cc_tyargs = tys })
      = ics { inert_dicts = addDict (inert_dicts ics) cls tys item
            , inert_count = bumpUnsolvedCount ev (inert_count ics) }

    add_item _ item
      = pprPanic "upd_inert set: can't happen! Inserting " $
        ppr item   -- CTyEqCan is dealt with by addInertEq
                   -- Can't be CNonCanonical, CHoleCan,
                   -- because they only land in inert_insols

    bumpUnsolvedCount :: CtEvidence -> Int -> Int
    bumpUnsolvedCount ev n | isWanted ev = n+1
                           | otherwise   = n

    -----------------------------------------
    kickOutRewritable :: CtFlavourRole  -- Flavour/role of the equality that
                                        -- is being added to the inert set
                      -> TcTyVar        -- The new equality is tv ~ ty
                      -> InertCans
                      -> (WorkList, InertCans)
    -- See Note [kickOutRewritable]
    kickOutRewritable new_fr new_tv ics@(IC { inert_eqs      = tv_eqs
                                            , inert_dicts    = dictmap
                                            , inert_safehask = safehask
                                            , inert_funeqs   = funeqmap
                                            , inert_irreds   = irreds
                                            , inert_insols   = insols
                                            , inert_count    = n
                                            , inert_model    = model })
      | not (new_fr `eqCanRewriteFR` new_fr)
      = (emptyWorkList, ics)
            -- If new_fr can't rewrite itself, it can't rewrite
            -- anything else, so no need to kick out anything.
            -- (This is a common case: wanteds can't rewrite wanteds)
            -- Lemma (L2) in Note [Extending the inert equalities]

      | otherwise
      = (kicked_out, inert_cans_in)
      where
        inert_cans_in = IC { inert_eqs      = tv_eqs_in
                           , inert_dicts    = dicts_in
                           , inert_safehask = safehask   -- ??
                           , inert_funeqs   = feqs_in
                           , inert_irreds   = irs_in
                           , inert_insols   = insols_in
                           , inert_count    = n - workListWantedCount kicked_out
                           , inert_model    = model }
                         -- Leave the model unchanged

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

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

        fr_can_rewrite :: CtEvidence -> Bool
        fr_can_rewrite ev = new_fr `eqCanRewriteFR` (ctEvFlavourRole ev)

        kick_out_ct :: Ct -> Bool
        -- Kick it out if the new CTyEqCan can rewrite the inert
        -- one. See Note [kickOutRewritable]
        kick_out_ct ct
          = fr_can_rewrite ev
            && new_tv `elemVarSet` tyCoVarsOfType (ctEvPred ev)
          where
            ev = ctEvidence ct

        kick_out_fe :: Ct -> Bool
        kick_out_fe (CFunEqCan { cc_ev = ev, cc_tyargs = tys, cc_fsk = fsk })
          = new_tv == fsk  -- If RHS is new_tvs, kick out /regardless of flavour/
                           -- See Note [Kicking out CFunEqCan for fundeps]
            || (fr_can_rewrite ev
                && new_tv `elemVarSet` tyCoVarsOfTypes tys)
        kick_out_fe ct = pprPanic "kick_out_fe" (ppr ct)

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

        -- Implements criteria K1-K3 in Note [Extending the inert equalities]
        keep_eq (CTyEqCan { cc_tyvar = tv, cc_rhs = rhs_ty, cc_ev = ev
                          , cc_eq_rel = eq_rel })
          | tv == new_tv
          = not (fr_can_rewrite ev)  -- (K1)

          | otherwise
          = check_k2 && check_k3
          where
            fs = ctEvFlavourRole ev
            check_k2 = not (fs  `eqCanRewriteFR` fs)                   -- (K2a)
                    ||     (fs  `eqCanRewriteFR` new_fr)               -- (K2b)
                    || not (new_fr `eqCanRewriteFR` fs)                -- (K2c)
                    || not (new_tv `elemVarSet` tyCoVarsOfType rhs_ty) -- (K2d)

            check_k3
              | new_fr `eqCanRewriteFR` fs
              = case eq_rel of
                  NomEq  -> not (rhs_ty `eqType` mkTyVarTy new_tv)
                  ReprEq -> not (isTyVarExposed new_tv rhs_ty)

              | otherwise
              = True

        keep_eq ct = pprPanic "keep_eq" (ppr ct)

    kickOutAfterUnification :: TcTyVar -> TcS Int
    kickOutAfterUnification new_tv
      = do { ics <- getInertCans
           ; let (kicked_out1, ics1) = kickOutModel new_tv ics
                 (kicked_out2, ics2) = kickOutRewritable (Given,NomEq)
                                                         new_tv ics1
                         -- Given because the tv := xi is given; NomEq because
                         -- only nominal equalities are solved by unification
                 kicked_out = appendWorkList kicked_out1 kicked_out2
           ; setInertCans ics2
           ; updWorkListTcS (appendWorkList kicked_out)

           ; unless (isEmptyWorkList kicked_out) $
             csTraceTcS $
             hang (text "Kick out (unify), tv =" <+> ppr new_tv)
                2 (vcat [ text "n-kicked =" <+> int (workListSize kicked_out)
                        , text "kicked_out =" <+> ppr kicked_out
                        , text "Residual inerts =" <+> ppr ics2 ])
           ; return (workListSize kicked_out) }

    kickOutModel :: TcTyVar -> InertCans -> (WorkList, InertCans)
    kickOutModel new_tv ics@(IC { inert_model = model, inert_eqs = eqs })
      = (foldVarEnv add emptyWorkList der_out, ics { inert_model = new_model })
      where
        (der_out, new_model) = partitionVarEnv kick_out_der model

        kick_out_der :: Ct -> Bool
        kick_out_der (CTyEqCan { cc_tyvar = tv, cc_rhs = rhs })
          = new_tv == tv || new_tv `elemVarSet` tyCoVarsOfType rhs
        kick_out_der _ = False

        add :: Ct -> WorkList -> WorkList
        -- Don't kick out a Derived if there is a Given or Wanted with
        -- the same predicate.  The model is just a shadow copy, and the
        -- Given/Wanted will serve the purpose.
        add (CTyEqCan { cc_ev = ev, cc_tyvar = tv, cc_rhs = rhs }) wl
          | not (isInInertEqs eqs tv rhs) = extendWorkListDerived (ctEvLoc ev) ev wl
        add _ wl                          = wl

    {- Note [kickOutRewritable]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See also Note [inert_eqs: the inert equalities].

    When we add a new inert equality (a ~N ty) to the inert set,
    we must kick out any inert items that could be rewritten by the
    new equality, to maintain the inert-set invariants.

      - We want to kick out an existing inert constraint if
        a) the new constraint can rewrite the inert one
        b) 'a' is free in the inert constraint (so that it *will*)
           rewrite it if we kick it out.

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

      - We do not need to kick anything out from the model; we only
        add [D] constraints to the model (in effect) and they are
        fully rewritten by the model, so (K2b) holds

      - A Derived equality can kick out [D] constraints in inert_dicts,
        inert_irreds etc.  Nothing in inert_eqs because there are no
        Derived constraints in inert_eqs (they are in the model)

      - We don't kick out constraints from inert_solved_dicts, and
        inert_solved_funeqs optimistically. But when we lookup we have to
        take the substitution into account

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

    --------------
    addInertSafehask :: InertCans -> Ct -> InertCans
    addInertSafehask ics item@(CDictCan { cc_class = cls, cc_tyargs = tys })
      = ics { inert_safehask = addDict (inert_dicts ics) cls tys item }

    addInertSafehask _ item
      = pprPanic "addInertSafehask: can't happen! Inserting " $ ppr item

    insertSafeOverlapFailureTcS :: Ct -> TcS ()
    -- See Note [Safe Haskell Overlapping Instances Implementation] in TcSimplify
    insertSafeOverlapFailureTcS item
      = updInertCans (\ics -> addInertSafehask ics item)

    getSafeOverlapFailures :: TcS Cts
    -- See Note [Safe Haskell Overlapping Instances Implementation] in TcSimplify
    getSafeOverlapFailures
     = do { IC { inert_safehask = safehask } <- getInertCans
          ; return $ foldDicts consCts safehask emptyCts }

    --------------
    addSolvedDict :: CtEvidence -> Class -> [Type] -> TcS ()
    -- Add a new item in the solved set of the monad
    -- See Note [Solved dictionaries]
    addSolvedDict item cls tys
      | isIPPred (ctEvPred item)    -- Never cache "solved" implicit parameters (not sure why!)
      = return ()
      | otherwise
      = do { traceTcS "updSolvedSetTcs:" $ ppr item
           ; updInertTcS $ \ ics ->
                 ics { inert_solved_dicts = addDict (inert_solved_dicts ics) cls tys item } }

    {- *********************************************************************
    *                                                                      *
                      Other inert-set operations
    *                                                                      *
    ********************************************************************* -}

    updInertTcS :: (InertSet -> InertSet) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertTcS upd_fn
      = do { is_var <- getTcSInertsRef
           ; wrapTcS (do { curr_inert <- TcM.readTcRef is_var
                         ; TcM.writeTcRef is_var (upd_fn curr_inert) }) }

    getInertCans :: TcS InertCans
    getInertCans = do { inerts <- getTcSInerts; return (inert_cans inerts) }

    setInertCans :: InertCans -> TcS ()
    setInertCans ics = updInertTcS $ \ inerts -> inerts { inert_cans = ics }

    takeGivenInsolubles :: TcS Cts
    -- See Note [The inert set after solving Givens]
    takeGivenInsolubles
      = updRetInertCans $ \ cans ->
        ( inert_insols cans
        , cans { inert_insols = emptyBag
               , inert_funeqs = filterFunEqs isGivenCt (inert_funeqs cans) } )

    {- Note [The inert set after solving Givens]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    After solving the Givens we take two things out of the inert set

      a) The insolubles; we return these to report inaccessible code
         We return these separately.  We don't want to leave them in
         the inert set, lest we confuse them with insolubles arising from
         solving wanteds

      b) Any Derived CFunEqCans.  Derived CTyEqCans are in the
         inert_model and do no harm.  In contrast, Derived CFunEqCans
         get mixed up with the Wanteds later and confuse the
         post-solve-wanted unflattening (Trac #10507).
         E.g.  From   [G] 1 <= m, [G] m <= n
               We get [D] 1 <= n, and we must remove it!
             Otherwise we unflatten it more then once, and assign
             to its fmv more than once...disaster.
         It's ok to remove them because they turned not not to
         yield an insoluble, and hence have now done their work.
    -}

    updRetInertCans :: (InertCans -> (a, InertCans)) -> TcS a
    -- Modify the inert set with the supplied function
    updRetInertCans upd_fn
      = do { is_var <- getTcSInertsRef
           ; wrapTcS (do { inerts <- TcM.readTcRef is_var
                         ; let (res, cans') = upd_fn (inert_cans inerts)
                         ; TcM.writeTcRef is_var (inerts { inert_cans = cans' })
                         ; return res }) }

    updInertCans :: (InertCans -> InertCans) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertCans upd_fn
      = updInertTcS $ \ inerts -> inerts { inert_cans = upd_fn (inert_cans inerts) }

    updInertDicts :: (DictMap Ct -> DictMap Ct) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertDicts upd_fn
      = updInertCans $ \ ics -> ics { inert_dicts = upd_fn (inert_dicts ics) }

    updInertSafehask :: (DictMap Ct -> DictMap Ct) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertSafehask upd_fn
      = updInertCans $ \ ics -> ics { inert_safehask = upd_fn (inert_safehask ics) }

    updInertFunEqs :: (FunEqMap Ct -> FunEqMap Ct) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertFunEqs upd_fn
      = updInertCans $ \ ics -> ics { inert_funeqs = upd_fn (inert_funeqs ics) }

    updInertIrreds :: (Cts -> Cts) -> TcS ()
    -- Modify the inert set with the supplied function
    updInertIrreds upd_fn
      = updInertCans $ \ ics -> ics { inert_irreds = upd_fn (inert_irreds ics) }

    getInertEqs :: TcS (TyVarEnv EqualCtList)
    getInertEqs = do { inert <- getInertCans; return (inert_eqs inert) }

    getInertModel :: TcS InertModel
    getInertModel = do { inert <- getInertCans; return (inert_model inert) }

    getInertGivens :: TcS [Ct]
    -- Returns the Given constraints in the inert set,
    -- with type functions *not* unflattened
    getInertGivens
      = do { inerts <- getInertCans
           ; let all_cts = foldDicts (:) (inert_dicts inerts)
                         $ foldFunEqs (:) (inert_funeqs inerts)
                         $ concat (varEnvElts (inert_eqs inerts))
           ; return (filter isGivenCt all_cts) }

    getPendingScDicts :: TcS [Ct]
    -- Find all inert Given dictionaries whose cc_pend_sc flag is True
    -- Set the flag to False in the inert set, and return that Ct
    getPendingScDicts = updRetInertCans get_sc_dicts
      where
        get_sc_dicts ic@(IC { inert_dicts = dicts })
          = (sc_pend_dicts, ic')
          where
            ic' = ic { inert_dicts = foldr add dicts sc_pend_dicts }

            sc_pend_dicts :: [Ct]
            sc_pend_dicts = foldDicts get_pending dicts []

        get_pending :: Ct -> [Ct] -> [Ct]  -- Get dicts with cc_pend_sc = True
                                           -- but flipping the flag
        get_pending dict dicts
            | Just dict' <- isPendingScDict dict = dict' : dicts
            | otherwise                          = dicts

        add :: Ct -> DictMap Ct -> DictMap Ct
        add ct@(CDictCan { cc_class = cls, cc_tyargs = tys }) dicts
            = addDict dicts cls tys ct
        add ct _ = pprPanic "getPendingScDicts" (ppr ct)

    getUnsolvedInerts :: TcS ( Bag Implication
                             , Cts     -- Tyvar eqs: a ~ ty
                             , Cts     -- Fun eqs:   F a ~ ty
                             , Cts     -- Insoluble
                             , Cts )   -- All others
    -- Return all the unsolved [Wanted] or [Derived] constraints
    --
    -- Post-condition: the returned simple constraints are all fully zonked
    --                     (because they come from the inert set)
    --                 the unsolved implics may not be
    getUnsolvedInerts
     = do { IC { inert_eqs    = tv_eqs
               , inert_funeqs = fun_eqs
               , inert_irreds = irreds
               , inert_dicts  = idicts
               , inert_insols = insols
               , inert_model  = model } <- getInertCans
          ; keep_derived <- keepSolvingDeriveds

          ; let der_tv_eqs       = foldVarEnv (add_der_eq keep_derived tv_eqs)
                                              emptyCts model
                unsolved_tv_eqs  = foldTyEqs add_if_unsolved tv_eqs der_tv_eqs
                unsolved_fun_eqs = foldFunEqs add_if_unsolved fun_eqs emptyCts
                unsolved_irreds  = Bag.filterBag is_unsolved irreds
                unsolved_dicts   = foldDicts add_if_unsolved idicts emptyCts
                others           = unsolved_irreds `unionBags` unsolved_dicts

          ; implics <- getWorkListImplics

          ; traceTcS "getUnsolvedInerts" $
            vcat [ text " tv eqs =" <+> ppr unsolved_tv_eqs
                 , text "fun eqs =" <+> ppr unsolved_fun_eqs
                 , text "insols =" <+> ppr insols
                 , text "others =" <+> ppr others
                 , text "implics =" <+> ppr implics ]

          ; return ( implics, unsolved_tv_eqs, unsolved_fun_eqs, insols, others) }
                  -- Keep even the given insolubles
                  -- so that we can report dead GADT pattern match branches
      where
        add_der_eq keep_derived tv_eqs ct cts
           -- See Note [Unsolved Derived equalities]
           | CTyEqCan { cc_tyvar = tv, cc_rhs = rhs } <- ct
           , isMetaTyVar tv || keep_derived
           , not (isInInertEqs tv_eqs tv rhs) = ct `consBag` cts
           | otherwise                        = cts
        add_if_unsolved :: Ct -> Cts -> Cts
        add_if_unsolved ct cts | is_unsolved ct = ct `consCts` cts
                               | otherwise      = cts

        is_unsolved ct = not (isGivenCt ct)   -- Wanted or Derived

    isInInertEqs :: TyVarEnv EqualCtList -> TcTyVar -> TcType -> Bool
    -- True if (a ~N ty) is in the inert set, in either Given or Wanted
    isInInertEqs eqs tv rhs
      = case lookupVarEnv eqs tv of
          Nothing  -> False
          Just cts -> any (same_pred rhs) cts
      where
        same_pred rhs ct
          | CTyEqCan { cc_rhs = rhs2, cc_eq_rel = eq_rel } <- ct
          , NomEq <- eq_rel
          , rhs `eqType` rhs2 = True
          | otherwise         = False

    getNoGivenEqs :: TcLevel     -- TcLevel of this implication
                   -> [TcTyVar]       -- Skolems of this implication
                   -> TcS Bool        -- True <=> definitely no residual given equalities
    -- See Note [When does an implication have given equalities?]
    getNoGivenEqs tclvl skol_tvs
      = do { inerts@(IC { inert_eqs = ieqs, inert_irreds = iirreds, inert_funeqs = funeqs })
                 <- getInertCans
           ; let local_fsks = foldFunEqs add_fsk funeqs emptyVarSet

                 has_given_eqs = foldrBag ((||) . ev_given_here . ctEvidence)  False iirreds
                              || foldVarEnv ((||) . eqs_given_here local_fsks) False ieqs

           ; traceTcS "getNoGivenEqs" (vcat [ppr has_given_eqs, ppr inerts])
           ; return (not has_given_eqs) }
      where
        eqs_given_here :: VarSet -> EqualCtList -> Bool
        eqs_given_here local_fsks [CTyEqCan { cc_tyvar = tv, cc_ev = ev }]
                                  -- Givens are always a sigleton
          = not (skolem_bound_here local_fsks tv) && ev_given_here ev
        eqs_given_here _ _ = False

        ev_given_here :: CtEvidence -> Bool
        -- True for a Given bound by the curent implication,
        -- i.e. the current level
        ev_given_here ev
          =  isGiven ev
          && tclvl == ctLocLevel (ctEvLoc ev)

        add_fsk :: Ct -> VarSet -> VarSet
        add_fsk ct fsks | CFunEqCan { cc_fsk = tv, cc_ev = ev } <- ct
                        , isGiven ev = extendVarSet fsks tv
                        | otherwise  = fsks

        skol_tv_set = mkVarSet skol_tvs
        skolem_bound_here local_fsks tv -- See Note [Let-bound skolems]
          = case tcTyVarDetails tv of
              SkolemTv {} -> tv `elemVarSet` skol_tv_set
              FlatSkol {} -> not (tv `elemVarSet` local_fsks)
              _           -> False

    -- | Returns Given constraints that might,
    -- potentially, match the given pred. This is used when checking to see if a
    -- Given might overlap with an instance. See Note [Instance and Given overlap]
    -- in TcInteract.
    matchableGivens :: CtLoc -> PredType -> InertSet -> Cts
    matchableGivens loc_w pred (IS { inert_cans = inert_cans })
      = filterBag matchable_given all_relevant_givens
      where
        -- just look in class constraints and irreds. matchableGivens does get called
        -- for ~R constraints, but we don't need to look through equalities, because
        -- canonical equalities are used for rewriting. We'll only get caught by
        -- non-canonical -- that is, irreducible -- equalities.
        all_relevant_givens :: Cts
        all_relevant_givens
          | Just (clas, _) <- getClassPredTys_maybe pred
          = findDictsByClass (inert_dicts inert_cans) clas
            `unionBags` inert_irreds inert_cans
          | otherwise
          = inert_irreds inert_cans

        matchable_given :: Ct -> Bool
        matchable_given ct
          | CtGiven { ctev_loc = loc_g } <- ctev
          , Just _ <- tcUnifyTys bind_meta_tv [ctEvPred ctev] [pred]
          , not (prohibitedSuperClassSolve loc_g loc_w)
          = True

          | otherwise
          = False
          where
            ctev = cc_ev ct

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

    prohibitedSuperClassSolve :: CtLoc -> CtLoc -> Bool
    -- See Note [Solving superclass constraints] in TcInstDcls
    prohibitedSuperClassSolve from_loc solve_loc
      | GivenOrigin (InstSC given_size) <- ctLocOrigin from_loc
      , ScOrigin wanted_size <- ctLocOrigin solve_loc
      = given_size >= wanted_size
      | otherwise
      = False

    {- Note [Unsolved Derived equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In getUnsolvedInerts, we return a derived equality from the model
    for two possible reasons:

      * Because it is a candidate for floating out of this implication.
        We only float equalities with a meta-tyvar on the left, so we only
        pull those out here.

      * If we are only solving derived constraints (i.e. tcs_need_derived
        is true; see Note [Solving for Derived constraints]), then we
        those Derived constraints are effectively unsolved, and we need
        them!

    Note [When does an implication have given equalities?]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider an implication
       beta => alpha ~ Int
    where beta is a unification variable that has already been unified
    to () in an outer scope.  Then we can float the (alpha ~ Int) out
    just fine. So when deciding whether the givens contain an equality,
    we should canonicalise first, rather than just looking at the original
    givens (Trac #8644).

    So we simply look at the inert, canonical Givens and see if there are
    any equalities among them, the calculation of has_given_eqs.  There
    are some wrinkles:

     * We must know which ones are bound in *this* implication and which
       are bound further out.  We can find that out from the TcLevel
       of the Given, which is itself recorded in the tcl_tclvl field
       of the TcLclEnv stored in the Given (ev_given_here).

       What about interactions between inner and outer givens?
          - Outer given is rewritten by an inner given, then there must
            have been an inner given equality, hence the “given-eq” flag
            will be true anyway.

          - Inner given rewritten by outer, retains its level (ie. The inner one)

     * We must take account of *potential* equalities, like the one above:
          beta => ...blah...
       If we still don't know what beta is, we conservatively treat it as potentially
       becoming an equality. Hence including 'irreds' in the calculation or has_given_eqs.

     * When flattening givens, we generate Given equalities like
         <F [a]> : F [a] ~ f,
       with Refl evidence, and we *don't* want those to count as an equality
       in the givens!  After all, the entire flattening business is just an
       internal matter, and the evidence does not mention any of the 'givens'
       of this implication.  So we do not treat inert_funeqs as a 'given equality'.

     * See Note [Let-bound skolems] for another wrinkle

     * We do *not* need to worry about representational equalities, because
       these do not affect the ability to float constraints.

    Note [Let-bound skolems]
    ~~~~~~~~~~~~~~~~~~~~~~~~
    If   * the inert set contains a canonical Given CTyEqCan (a ~ ty)
    and  * 'a' is a skolem bound in this very implication, b

    then:
    a) The Given is pretty much a let-binding, like
          f :: (a ~ b->c) => a -> a
       Here the equality constraint is like saying
          let a = b->c in ...
       It is not adding any new, local equality  information,
       and hence can be ignored by has_given_eqs

    b) 'a' will have been completely substituted out in the inert set,
       so we can safely discard it.  Notably, it doesn't need to be
       returned as part of 'fsks'

    For an example, see Trac #9211.
    -}

    removeInertCts :: [Ct] -> InertCans -> InertCans
    -- ^ Remove inert constraints from the 'InertCans', for use when a
    -- typechecker plugin wishes to discard a given.
    removeInertCts cts icans = foldl' removeInertCt icans cts

    removeInertCt :: InertCans -> Ct -> InertCans
    removeInertCt is ct =
      case ct of

        CDictCan  { cc_class = cl, cc_tyargs = tys } ->
          is { inert_dicts = delDict (inert_dicts is) cl tys }

        CFunEqCan { cc_fun  = tf,  cc_tyargs = tys } ->
          is { inert_funeqs = delFunEq (inert_funeqs is) tf tys }

        CTyEqCan  { cc_tyvar = x,  cc_rhs    = ty } ->
          is { inert_eqs    = delTyEq (inert_eqs is) x ty }

        CIrredEvCan {}   -> panic "removeInertCt: CIrredEvCan"
        CNonCanonical {} -> panic "removeInertCt: CNonCanonical"
        CHoleCan {}      -> panic "removeInertCt: CHoleCan"

    lookupFlatCache :: TyCon -> [Type] -> TcS (Maybe (TcCoercion, TcType, CtFlavour))
    lookupFlatCache fam_tc tys
      = do { IS { inert_flat_cache = flat_cache
                , inert_cans = IC { inert_funeqs = inert_funeqs } } <- getTcSInerts
           ; return (firstJusts [lookup_inerts inert_funeqs,
                                 lookup_flats flat_cache]) }
      where
        lookup_inerts inert_funeqs
          | Just (CFunEqCan { cc_ev = ctev, cc_fsk = fsk, cc_tyargs = xis })
               <- findFunEq inert_funeqs fam_tc tys
          , tys `eqTypes` xis   -- the lookup might find a near-match; see
                                -- Note [Use loose types in inert set]
          = Just (ctEvCoercion ctev, mkTyVarTy fsk, ctEvFlavour ctev)
          | otherwise = Nothing

        lookup_flats flat_cache = findExactFunEq flat_cache fam_tc tys

    lookupInInerts :: TcPredType -> TcS (Maybe CtEvidence)
    -- Is this exact predicate type cached in the solved or canonicals of the InertSet?
    lookupInInerts pty
      | ClassPred cls tys <- classifyPredType pty
      = do { inerts <- getTcSInerts
           ; return (lookupSolvedDict inerts cls tys `mplus`
                     lookupInertDict (inert_cans inerts) cls tys) }
      | otherwise -- NB: No caching for equalities, IPs, holes, or errors
      = return Nothing

    -- | Look up a dictionary inert. NB: the returned 'CtEvidence' might not
    -- match the input exactly. Note [Use loose types in inert set].
    lookupInertDict :: InertCans -> Class -> [Type] -> Maybe CtEvidence
    lookupInertDict (IC { inert_dicts = dicts }) cls tys
      = case findDict dicts cls tys of
          Just ct -> Just (ctEvidence ct)
          _       -> Nothing

    -- | Look up a solved inert. NB: the returned 'CtEvidence' might not
    -- match the input exactly. See Note [Use loose types in inert set].
    lookupSolvedDict :: InertSet -> Class -> [Type] -> Maybe CtEvidence
    -- Returns just if exactly this predicate type exists in the solved.
    lookupSolvedDict (IS { inert_solved_dicts = solved }) cls tys
      = case findDict solved cls tys of
          Just ev -> Just ev
          _       -> Nothing

    {- *********************************************************************
    *                                                                      *
                       Irreds
    *                                                                      *
    ********************************************************************* -}

    foldIrreds :: (Ct -> b -> b) -> Cts -> b -> b
    foldIrreds k irreds z = foldrBag k z irreds

    {- *********************************************************************
    *                                                                      *
                       Type equalities
    *                                                                      *
    ********************************************************************* -}

    type EqualCtList = [Ct]

    {- Note [EqualCtList invariants]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        * All are equalities
        * All these equalities have the same LHS
        * The list is never empty
        * No element of the list can rewrite any other

     From the fourth invariant it follows that the list is
       - A single Given, or
       - Any number of Wanteds and/or Deriveds
    -}

    addTyEq :: TyVarEnv EqualCtList -> TcTyVar -> Ct -> TyVarEnv EqualCtList
    addTyEq old_list tv it = extendVarEnv_C (\old_eqs _new_eqs -> it : old_eqs)
                                            old_list tv [it]

    foldTyEqs :: (Ct -> b -> b) -> TyVarEnv EqualCtList -> b -> b
    foldTyEqs k eqs z
      = foldVarEnv (\cts z -> foldr k z cts) z eqs

    findTyEqs :: InertCans -> TyVar -> EqualCtList
    findTyEqs icans tv = lookupVarEnv (inert_eqs icans) tv `orElse` []

    delTyEq :: TyVarEnv EqualCtList -> TcTyVar -> TcType -> TyVarEnv EqualCtList
    delTyEq m tv t = modifyVarEnv (filter (not . isThisOne)) m tv
      where isThisOne (CTyEqCan { cc_rhs = t1 }) = eqType t t1
            isThisOne _                          = False

    {- *********************************************************************
    *                                                                      *
                       TcAppMap
    *                                                                      *
    ************************************************************************

    Note [Use loose types in inert set]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Say we know (Eq (a |> c1)) and we need (Eq (a |> c2)). One is clearly
    solvable from the other. So, we do lookup in the inert set using
    loose types, which omit the kind-check.

    We must be careful when using the result of a lookup because it may
    not match the requsted info exactly!

    -}

    type TcAppMap a = UniqFM (ListMap LooseTypeMap a)
        -- Indexed by tycon then the arg types, using "loose" matching, where
        -- we don't require kind equality. This allows, for example, (a |> co)
        -- to match (a).
        -- See Note [Use loose types in inert set]
        -- Used for types and classes; hence UniqFM

    isEmptyTcAppMap :: TcAppMap a -> Bool
    isEmptyTcAppMap m = isNullUFM m

    emptyTcAppMap :: TcAppMap a
    emptyTcAppMap = emptyUFM

    findTcApp :: TcAppMap a -> Unique -> [Type] -> Maybe a
    findTcApp m u tys = do { tys_map <- lookupUFM m u
                           ; lookupTM tys tys_map }

    delTcApp :: TcAppMap a -> Unique -> [Type] -> TcAppMap a
    delTcApp m cls tys = adjustUFM (deleteTM tys) m cls

    insertTcApp :: TcAppMap a -> Unique -> [Type] -> a -> TcAppMap a
    insertTcApp m cls tys ct = alterUFM alter_tm m cls
      where
        alter_tm mb_tm = Just (insertTM tys ct (mb_tm `orElse` emptyTM))

    -- mapTcApp :: (a->b) -> TcAppMap a -> TcAppMap b
    -- mapTcApp f = mapUFM (mapTM f)

    filterTcAppMap :: (Ct -> Bool) -> TcAppMap Ct -> TcAppMap Ct
    filterTcAppMap f m
      = mapUFM do_tm m
      where
        do_tm tm = foldTM insert_mb tm emptyTM
        insert_mb ct tm
           | f ct      = insertTM tys ct tm
           | otherwise = tm
           where
             tys = case ct of
                    CFunEqCan { cc_tyargs = tys } -> tys
                    CDictCan  { cc_tyargs = tys } -> tys
                    _ -> pprPanic "filterTcAppMap" (ppr ct)

    tcAppMapToBag :: TcAppMap a -> Bag a
    tcAppMapToBag m = foldTcAppMap consBag m emptyBag

    foldTcAppMap :: (a -> b -> b) -> TcAppMap a -> b -> b
    foldTcAppMap k m z = foldUFM (foldTM k) z m

    {- *********************************************************************
    *                                                                      *
                       DictMap
    *                                                                      *
    ********************************************************************* -}

    type DictMap a = TcAppMap a

    emptyDictMap :: DictMap a
    emptyDictMap = emptyTcAppMap

    -- sizeDictMap :: DictMap a -> Int
    -- sizeDictMap m = foldDicts (\ _ x -> x+1) m 0

    findDict :: DictMap a -> Class -> [Type] -> Maybe a
    findDict m cls tys = findTcApp m (getUnique cls) tys

    findDictsByClass :: DictMap a -> Class -> Bag a
    findDictsByClass m cls
      | Just tm <- lookupUFM m cls = foldTM consBag tm emptyBag
      | otherwise                  = emptyBag

    delDict :: DictMap a -> Class -> [Type] -> DictMap a
    delDict m cls tys = delTcApp m (getUnique cls) tys

    addDict :: DictMap a -> Class -> [Type] -> a -> DictMap a
    addDict m cls tys item = insertTcApp m (getUnique cls) tys item

    addDictsByClass :: DictMap Ct -> Class -> Bag Ct -> DictMap Ct
    addDictsByClass m cls items
      = addToUFM m cls (foldrBag add emptyTM items)
      where
        add ct@(CDictCan { cc_tyargs = tys }) tm = insertTM tys ct tm
        add ct _ = pprPanic "addDictsByClass" (ppr ct)

    filterDicts :: (Ct -> Bool) -> DictMap Ct -> DictMap Ct
    filterDicts f m = filterTcAppMap f m

    partitionDicts :: (Ct -> Bool) -> DictMap Ct -> (Bag Ct, DictMap Ct)
    partitionDicts f m = foldTcAppMap k m (emptyBag, emptyDicts)
      where
        k ct (yeses, noes) | f ct      = (ct `consBag` yeses, noes)
                           | otherwise = (yeses,              add ct noes)
        add ct@(CDictCan { cc_class = cls, cc_tyargs = tys }) m
          = addDict m cls tys ct
        add ct _ = pprPanic "partitionDicts" (ppr ct)

    dictsToBag :: DictMap a -> Bag a
    dictsToBag = tcAppMapToBag

    foldDicts :: (a -> b -> b) -> DictMap a -> b -> b
    foldDicts = foldTcAppMap

    emptyDicts :: DictMap a
    emptyDicts = emptyTcAppMap

    {- *********************************************************************
    *                                                                      *
                       FunEqMap
    *                                                                      *
    ********************************************************************* -}

    type FunEqMap a = TcAppMap a  -- A map whose key is a (TyCon, [Type]) pair

    emptyFunEqs :: TcAppMap a
    emptyFunEqs = emptyTcAppMap

    sizeFunEqMap :: FunEqMap a -> Int
    sizeFunEqMap m = foldFunEqs (\ _ x -> x+1) m 0

    findFunEq :: FunEqMap a -> TyCon -> [Type] -> Maybe a
    findFunEq m tc tys = findTcApp m (getUnique tc) tys

    funEqsToBag :: FunEqMap a -> Bag a
    funEqsToBag m = foldTcAppMap consBag m emptyBag

    findFunEqsByTyCon :: FunEqMap a -> TyCon -> [a]
    -- Get inert function equation constraints that have the given tycon
    -- in their head.  Not that the constraints remain in the inert set.
    -- We use this to check for derived interactions with built-in type-function
    -- constructors.
    findFunEqsByTyCon m tc
      | Just tm <- lookupUFM m tc = foldTM (:) tm []
      | otherwise                 = []

    foldFunEqs :: (a -> b -> b) -> FunEqMap a -> b -> b
    foldFunEqs = foldTcAppMap

    -- mapFunEqs :: (a -> b) -> FunEqMap a -> FunEqMap b
    -- mapFunEqs = mapTcApp

    filterFunEqs :: (Ct -> Bool) -> FunEqMap Ct -> FunEqMap Ct
    filterFunEqs = filterTcAppMap

    insertFunEq :: FunEqMap a -> TyCon -> [Type] -> a -> FunEqMap a
    insertFunEq m tc tys val = insertTcApp m (getUnique tc) tys val

    -- insertFunEqCt :: FunEqMap Ct -> Ct -> FunEqMap Ct
    -- insertFunEqCt m ct@(CFunEqCan { cc_fun = tc, cc_tyargs = tys })
    --  = insertFunEq m tc tys ct
    -- insertFunEqCt _ ct = pprPanic "insertFunEqCt" (ppr ct)

    partitionFunEqs :: (Ct -> Bool) -> FunEqMap Ct -> ([Ct], FunEqMap Ct)
    -- Optimise for the case where the predicate is false
    -- partitionFunEqs is called only from kick-out, and kick-out usually
    -- kicks out very few equalities, so we want to optimise for that case
    partitionFunEqs f m = (yeses, foldr del m yeses)
      where
        yeses = foldTcAppMap k m []
        k ct yeses | f ct      = ct : yeses
                   | otherwise = yeses
        del (CFunEqCan { cc_fun = tc, cc_tyargs = tys }) m
            = delFunEq m tc tys
        del ct _ = pprPanic "partitionFunEqs" (ppr ct)

    delFunEq :: FunEqMap a -> TyCon -> [Type] -> FunEqMap a
    delFunEq m tc tys = delTcApp m (getUnique tc) tys

    ------------------------------
    type ExactFunEqMap a = UniqFM (ListMap TypeMap a)

    emptyExactFunEqs :: ExactFunEqMap a
    emptyExactFunEqs = emptyUFM

    findExactFunEq :: ExactFunEqMap a -> TyCon -> [Type] -> Maybe a
    findExactFunEq m tc tys = do { tys_map <- lookupUFM m (getUnique tc)
                                 ; lookupTM tys tys_map }

    insertExactFunEq :: ExactFunEqMap a -> TyCon -> [Type] -> a -> ExactFunEqMap a
    insertExactFunEq m tc tys val = alterUFM alter_tm m (getUnique tc)
      where alter_tm mb_tm = Just (insertTM tys val (mb_tm `orElse` emptyTM))

    {-
    ************************************************************************
    *                                                                      *
    *              The TcS solver monad                                    *
    *                                                                      *
    ************************************************************************

    Note [The TcS monad]
    ~~~~~~~~~~~~~~~~~~~~
    The TcS monad is a weak form of the main Tc monad

    All you can do is
        * fail
        * allocate new variables
        * fill in evidence variables

    Filling in a dictionary evidence variable means to create a binding
    for it, so TcS carries a mutable location where the binding can be
    added.  This is initialised from the innermost implication constraint.

    Note [Solving for Derived constraints]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Sometimes we invoke the solver on a bunch of Derived constraints, not to
    generate any evidence, but just to cause unification side effects or to
    produce a simpler set of constraints.  If that is what we are doing, we
    should do two things differently:
      a) Don't stop when you've solved all the Wanteds; instead keep going
         if there are any Deriveds in the work queue.
      b) In getInertUnsolved, include Derived ones
    -}

    data TcSEnv
      = TcSEnv {
          tcs_ev_binds    :: Maybe EvBindsVar,
              -- this could be Nothing if we can't deal with non-equality
              -- constraints, because, say, we're in a top-level type signature

          tcs_unified     :: IORef Int,
             -- The number of unification variables we have filled
             -- The important thing is whether it is non-zero

          tcs_count     :: IORef Int, -- Global step count

          tcs_inerts    :: IORef InertSet, -- Current inert set

          -- The main work-list and the flattening worklist
          -- See Note [Work list priorities] and
          tcs_worklist  :: IORef WorkList, -- Current worklist

          tcs_used_tcvs :: IORef TyCoVarSet,
            -- these variables were used when filling holes. Don't discard!
            -- See also Note [Tracking redundant constraints] in TcSimplify

          tcs_need_deriveds :: Bool
            -- Keep solving, even if all the unsolved constraints are Derived
            -- See Note [Solving for Derived constraints]
        }

    ---------------
    newtype TcS a = TcS { unTcS :: TcSEnv -> TcM a }

    instance Functor TcS where
      fmap f m = TcS $ fmap f . unTcS m

    instance Applicative TcS where
      pure x = TcS (\_ -> return x)
      (<*>) = ap

    instance Monad TcS where
      return = pure
      fail err  = TcS (\_ -> fail err)
      m >>= k   = TcS (\ebs -> unTcS m ebs >>= \r -> unTcS (k r) ebs)

    #if __GLASGOW_HASKELL__ > 710
    instance MonadFail.MonadFail TcS where
      fail err  = TcS (\_ -> fail err)
    #endif

    instance MonadUnique TcS where
       getUniqueSupplyM = wrapTcS getUniqueSupplyM

    -- Basic functionality
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    wrapTcS :: TcM a -> TcS a
    -- Do not export wrapTcS, because it promotes an arbitrary TcM to TcS,
    -- and TcS is supposed to have limited functionality
    wrapTcS = TcS . const -- a TcM action will not use the TcEvBinds

    wrapErrTcS :: TcM a -> TcS a
    -- The thing wrapped should just fail
    -- There's no static check; it's up to the user
    -- Having a variant for each error message is too painful
    wrapErrTcS = wrapTcS

    wrapWarnTcS :: TcM a -> TcS a
    -- The thing wrapped should just add a warning, or no-op
    -- There's no static check; it's up to the user
    wrapWarnTcS = wrapTcS

    failTcS, panicTcS  :: SDoc -> TcS a
    warnTcS   :: WarningFlag -> SDoc -> TcS ()
    addErrTcS :: SDoc -> TcS ()
    failTcS      = wrapTcS . TcM.failWith
    warnTcS flag = wrapTcS . TcM.addWarn (Reason flag)
    addErrTcS    = wrapTcS . TcM.addErr
    panicTcS doc = pprPanic "TcCanonical" doc

    traceTcS :: String -> SDoc -> TcS ()
    traceTcS herald doc = wrapTcS (TcM.traceTc herald doc)

    runTcPluginTcS :: TcPluginM a -> TcS a
    runTcPluginTcS m = wrapTcS . runTcPluginM m =<< getTcEvBinds

    instance HasDynFlags TcS where
        getDynFlags = wrapTcS getDynFlags

    getGlobalRdrEnvTcS :: TcS GlobalRdrEnv
    getGlobalRdrEnvTcS = wrapTcS TcM.getGlobalRdrEnv

    bumpStepCountTcS :: TcS ()
    bumpStepCountTcS = TcS $ \env -> do { let ref = tcs_count env
                                        ; n <- TcM.readTcRef ref
                                        ; TcM.writeTcRef ref (n+1) }

    -- | Mark variables as used filling a coercion hole
    useVars :: TyCoVarSet -> TcS ()
    useVars vars = TcS $ \env -> do { let ref = tcs_used_tcvs env
                                    ; TcM.updTcRef ref (`unionVarSet` vars) }

    csTraceTcS :: SDoc -> TcS ()
    csTraceTcS doc
      = wrapTcS $ csTraceTcM 1 (return doc)

    traceFireTcS :: CtEvidence -> SDoc -> TcS ()
    -- Dump a rule-firing trace
    traceFireTcS ev doc
      = TcS $ \env -> csTraceTcM 1 $
        do { n <- TcM.readTcRef (tcs_count env)
           ; tclvl <- TcM.getTcLevel
           ; return (hang (int n <> brackets (text "U:" <> ppr tclvl
                                              <> ppr (ctLocDepth (ctEvLoc ev)))
                           <+> doc <> colon)
                         4 (ppr ev)) }

    csTraceTcM :: Int -> TcM SDoc -> TcM ()
    -- Constraint-solver tracing, -ddump-cs-trace
    csTraceTcM trace_level mk_doc
      = do { dflags <- getDynFlags
           ; when (  (dopt Opt_D_dump_cs_trace dflags || dopt Opt_D_dump_tc_trace dflags)
                  && trace_level <= traceLevel dflags ) $
             do { msg <- mk_doc
                ; TcM.traceTcRn Opt_D_dump_cs_trace msg } }

    runTcS :: TcS a                -- What to run
           -> TcM (a, EvBindMap)
    runTcS tcs
      = do { ev_binds_var <- TcM.newTcEvBinds
           ; res <- runTcSWithEvBinds False (Just ev_binds_var) tcs
           ; ev_binds <- TcM.getTcEvBindsMap ev_binds_var
           ; return (res, ev_binds) }

    -- | This variant of 'runTcS' will keep solving, even when only Deriveds
    -- are left around. It also doesn't return any evidence, as callers won't
    -- need it.
    runTcSDeriveds :: TcS a -> TcM a
    runTcSDeriveds tcs
      = do { ev_binds_var <- TcM.newTcEvBinds
           ; runTcSWithEvBinds True (Just ev_binds_var) tcs }

    -- | This can deal only with equality constraints.
    runTcSEqualities :: TcS a -> TcM a
    runTcSEqualities = runTcSWithEvBinds False Nothing

    runTcSWithEvBinds :: Bool  -- ^ keep running even if only Deriveds are left?
                      -> Maybe EvBindsVar
                      -> TcS a
                      -> TcM a
    runTcSWithEvBinds solve_deriveds ev_binds_var tcs
      = do { unified_var <- TcM.newTcRef 0
           ; step_count <- TcM.newTcRef 0
           ; inert_var <- TcM.newTcRef emptyInert
           ; wl_var <- TcM.newTcRef emptyWorkList
           ; used_var <- TcM.newTcRef emptyVarSet -- never read from, but see
                                                  -- nestImplicTcS

           ; let env = TcSEnv { tcs_ev_binds      = ev_binds_var
                              , tcs_unified       = unified_var
                              , tcs_count         = step_count
                              , tcs_inerts        = inert_var
                              , tcs_worklist      = wl_var
                              , tcs_used_tcvs     = used_var
                              , tcs_need_deriveds = solve_deriveds }

                 -- Run the computation
           ; res <- unTcS tcs env

           ; count <- TcM.readTcRef step_count
           ; when (count > 0) $
             csTraceTcM 0 $ return (text "Constraint solver steps =" <+> int count)

    #ifdef DEBUG
           ; whenIsJust ev_binds_var $ \ebv ->
             do { ev_binds <- TcM.getTcEvBinds ebv
                ; checkForCyclicBinds ev_binds }
    #endif

           ; return res }

    #ifdef DEBUG
    checkForCyclicBinds :: Bag EvBind -> TcM ()
    checkForCyclicBinds ev_binds
      | null cycles
      = return ()
      | null coercion_cycles
      = TcM.traceTc "Cycle in evidence binds" $ ppr cycles
      | otherwise
      = pprPanic "Cycle in coercion bindings" $ ppr coercion_cycles
      where
        cycles :: [[EvBind]]
        cycles = [c | CyclicSCC c <- stronglyConnCompFromEdgedVertices edges]

        coercion_cycles = [c | c <- cycles, any is_co_bind c]
        is_co_bind (EvBind { eb_lhs = b }) = isEqPred (varType b)

        edges :: [(EvBind, EvVar, [EvVar])]
        edges = [ (bind, bndr, varSetElems (evVarsOfTerm rhs))
                | bind@(EvBind { eb_lhs = bndr, eb_rhs = rhs}) <- bagToList ev_binds ]
    #endif

    nestImplicTcS :: Maybe EvBindsVar -> TyCoVarSet -- bound in this implication
                  -> TcLevel -> TcS a
                  -> TcS (a, TyCoVarSet)  -- also returns any vars used when filling
                                          -- coercion holes (for redundant-constraint
                                          -- tracking)
    nestImplicTcS m_ref bound_tcvs inner_tclvl (TcS thing_inside)
      = do { (res, used_tcvs) <-
             TcS $ \ TcSEnv { tcs_unified       = unified_var
                            , tcs_inerts        = old_inert_var
                            , tcs_count         = count
                            , tcs_need_deriveds = solve_deriveds
                            } ->
          do { inerts <- TcM.readTcRef old_inert_var
             ; let nest_inert = inerts { inert_flat_cache = emptyExactFunEqs }
                                         -- See Note [Do not inherit the flat cache]
             ; new_inert_var <- TcM.newTcRef nest_inert
             ; new_wl_var    <- TcM.newTcRef emptyWorkList
             ; new_used_var  <- TcM.newTcRef emptyVarSet
             ; let nest_env = TcSEnv { tcs_ev_binds      = m_ref
                                     , tcs_unified       = unified_var
                                     , tcs_count         = count
                                     , tcs_inerts        = new_inert_var
                                     , tcs_worklist      = new_wl_var
                                     , tcs_used_tcvs     = new_used_var
                                     , tcs_need_deriveds = solve_deriveds }
             ; res <- TcM.setTcLevel inner_tclvl $
                      thing_inside nest_env

    #ifdef DEBUG
             -- Perform a check that the thing_inside did not cause cycles
             ; whenIsJust m_ref $ \ ref ->
               do { ev_binds <- TcM.getTcEvBinds ref
                  ; checkForCyclicBinds ev_binds }
    #endif
             ; used_tcvs <- TcM.readTcRef new_used_var
             ; return (res, used_tcvs) }

           ; local_ev_vars <- case m_ref of
               Nothing  -> return emptyVarSet
               Just ref -> do { binds <- wrapTcS $ TcM.getTcEvBinds ref
                              ; return $ mkVarSet $ map evBindVar $ bagToList binds }
           ; let all_locals = bound_tcvs `unionVarSet` local_ev_vars
                 (inner_used_tcvs, outer_used_tcvs)
                   = partitionVarSet (`elemVarSet` all_locals) used_tcvs
           ; useVars outer_used_tcvs

           ; return (res, inner_used_tcvs) }

    {- Note [Do not inherit the flat cache]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We do not want to inherit the flat cache when processing nested
    implications.  Consider
       a ~ F b, forall c. b~Int => blah
    If we have F b ~ fsk in the flat-cache, and we push that into the
    nested implication, we might miss that F b can be rewritten to F Int,
    and hence perhpas solve it.  Moreover, the fsk from outside is
    flattened out after solving the outer level, but and we don't
    do that flattening recursively.
    -}

    nestTcS ::  TcS a -> TcS a
    -- Use the current untouchables, augmenting the current
    -- evidence bindings, and solved dictionaries
    -- But have no effect on the InertCans, or on the inert_flat_cache
    --  (the latter because the thing inside a nestTcS does unflattening)
    nestTcS (TcS thing_inside)
      = TcS $ \ env@(TcSEnv { tcs_inerts = inerts_var }) ->
        do { inerts <- TcM.readTcRef inerts_var
           ; new_inert_var <- TcM.newTcRef inerts
           ; new_wl_var    <- TcM.newTcRef emptyWorkList
           ; let nest_env = env { tcs_inerts   = new_inert_var
                                , tcs_worklist = new_wl_var }

           ; res <- thing_inside nest_env

           ; new_inerts <- TcM.readTcRef new_inert_var

           -- we want to propogate the safe haskell failures
           ; let old_ic = inert_cans inerts
                 new_ic = inert_cans new_inerts
                 nxt_ic = old_ic { inert_safehask = inert_safehask new_ic }

           ; TcM.writeTcRef inerts_var  -- See Note [Propagate the solved dictionaries]
                            (inerts { inert_solved_dicts = inert_solved_dicts new_inerts
                                    , inert_cans = nxt_ic })

           ; return res }

    {-
    Note [Propagate the solved dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's really quite important that nestTcS does not discard the solved
    dictionaries from the thing_inside.
    Consider
       Eq [a]
       forall b. empty =>  Eq [a]
    We solve the simple (Eq [a]), under nestTcS, and then turn our attention to
    the implications.  It's definitely fine to use the solved dictionaries on
    the inner implications, and it can make a signficant performance difference
    if you do so.
    -}

    -- Getters and setters of TcEnv fields
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    -- Getter of inerts and worklist
    getTcSInertsRef :: TcS (IORef InertSet)
    getTcSInertsRef = TcS (return . tcs_inerts)

    getTcSWorkListRef :: TcS (IORef WorkList)
    getTcSWorkListRef = TcS (return . tcs_worklist)

    getTcSInerts :: TcS InertSet
    getTcSInerts = getTcSInertsRef >>= wrapTcS . (TcM.readTcRef)

    setTcSInerts :: InertSet -> TcS ()
    setTcSInerts ics = do { r <- getTcSInertsRef; wrapTcS (TcM.writeTcRef r ics) }

    getWorkListImplics :: TcS (Bag Implication)
    getWorkListImplics
      = do { wl_var <- getTcSWorkListRef
           ; wl_curr <- wrapTcS (TcM.readTcRef wl_var)
           ; return (wl_implics wl_curr) }

    updWorkListTcS :: (WorkList -> WorkList) -> TcS ()
    updWorkListTcS f
      = do { wl_var <- getTcSWorkListRef
           ; wl_curr <- wrapTcS (TcM.readTcRef wl_var)
           ; let new_work = f wl_curr
           ; wrapTcS (TcM.writeTcRef wl_var new_work) }

    -- | Should we keep solving even only deriveds are left?
    keepSolvingDeriveds :: TcS Bool
    keepSolvingDeriveds = TcS (return . tcs_need_deriveds)

    emitWorkNC :: [CtEvidence] -> TcS ()
    emitWorkNC evs
      | null evs
      = return ()
      | otherwise
      = emitWork (map mkNonCanonical evs)

    emitWork :: [Ct] -> TcS ()
    emitWork cts
      = do { traceTcS "Emitting fresh work" (vcat (map ppr cts))
           ; updWorkListTcS (extendWorkListCts cts) }

    emitInsoluble :: Ct -> TcS ()
    -- Emits a non-canonical constraint that will stand for a frozen error in the inerts.
    emitInsoluble ct
      = do { traceTcS "Emit insoluble" (ppr ct $$ pprCtLoc (ctLoc ct))
           ; updInertTcS add_insol }
      where
        this_pred = ctPred ct
        add_insol is@(IS { inert_cans = ics@(IC { inert_insols = old_insols }) })
          | already_there = is
          | otherwise     = is { inert_cans = ics { inert_insols = old_insols `snocCts` ct } }
          where
            already_there = not (isWantedCt ct) && anyBag (tcEqType this_pred . ctPred) old_insols
                 -- See Note [Do not add duplicate derived insolubles]

    newTcRef :: a -> TcS (TcRef a)
    newTcRef x = wrapTcS (TcM.newTcRef x)

    readTcRef :: TcRef a -> TcS a
    readTcRef ref = wrapTcS (TcM.readTcRef ref)

    updTcRef :: TcRef a -> (a->a) -> TcS ()
    updTcRef ref upd_fn = wrapTcS (TcM.updTcRef ref upd_fn)

    getTcEvBinds :: TcS (Maybe EvBindsVar)
    getTcEvBinds = TcS (return . tcs_ev_binds)

    getTcEvBindsFromVar :: EvBindsVar -> TcS (Bag EvBind)
    getTcEvBindsFromVar = wrapTcS . TcM.getTcEvBinds

    getTcLevel :: TcS TcLevel
    getTcLevel = wrapTcS TcM.getTcLevel

    getTcEvBindsMap :: TcS EvBindMap
    getTcEvBindsMap
      = do { ev_binds <- getTcEvBinds
           ; case ev_binds of
               Just (EvBindsVar ev_ref _) -> wrapTcS $ TcM.readTcRef ev_ref
               Nothing                    -> return emptyEvBindMap }

    unifyTyVar :: TcTyVar -> TcType -> TcS ()
    -- Unify a meta-tyvar with a type
    -- We keep track of how many unifications have happened in tcs_unified,
    --
    -- We should never unify the same variable twice!
    unifyTyVar tv ty
      = ASSERT2( isMetaTyVar tv, ppr tv )
        TcS $ \ env ->
        do { TcM.traceTc "unifyTyVar" (ppr tv <+> text ":=" <+> ppr ty)
           ; TcM.writeMetaTyVar tv ty
           ; TcM.updTcRef (tcs_unified env) (+1) }

    unflattenFmv :: TcTyVar -> TcType -> TcS ()
    -- Fill a flatten-meta-var, simply by unifying it.
    -- This does NOT count as a unification in tcs_unified.
    unflattenFmv tv ty
      = ASSERT2( isMetaTyVar tv, ppr tv )
        TcS $ \ _ ->
        do { TcM.traceTc "unflattenFmv" (ppr tv <+> text ":=" <+> ppr ty)
           ; TcM.writeMetaTyVar tv ty }

    reportUnifications :: TcS a -> TcS (Int, a)
    reportUnifications (TcS thing_inside)
      = TcS $ \ env ->
        do { inner_unified <- TcM.newTcRef 0
           ; res <- thing_inside (env { tcs_unified = inner_unified })
           ; n_unifs <- TcM.readTcRef inner_unified
           ; TcM.updTcRef (tcs_unified env) (+ n_unifs)
           ; return (n_unifs, res) }

    getDefaultInfo ::  TcS ([Type], (Bool, Bool))
    getDefaultInfo = wrapTcS TcM.tcGetDefaultTys

    -- Just get some environments needed for instance looking up and matching
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    getInstEnvs :: TcS InstEnvs
    getInstEnvs = wrapTcS $ TcM.tcGetInstEnvs

    getFamInstEnvs :: TcS (FamInstEnv, FamInstEnv)
    getFamInstEnvs = wrapTcS $ FamInst.tcGetFamInstEnvs

    getTopEnv :: TcS HscEnv
    getTopEnv = wrapTcS $ TcM.getTopEnv

    getGblEnv :: TcS TcGblEnv
    getGblEnv = wrapTcS $ TcM.getGblEnv

    getLclEnv :: TcS TcLclEnv
    getLclEnv = wrapTcS $ TcM.getLclEnv

    tcLookupClass :: Name -> TcS Class
    tcLookupClass c = wrapTcS $ TcM.tcLookupClass c

    -- Setting names as used (used in the deriving of Coercible evidence)
    -- Too hackish to expose it to TcS? In that case somehow extract the used
    -- constructors from the result of solveInteract
    addUsedDataCons :: GlobalRdrEnv -> TyCon -> TcS ()
    addUsedDataCons rdr_env tycon = wrapTcS  $ TcM.addUsedDataCons rdr_env tycon

    -- Various smaller utilities [TODO, maybe will be absorbed in the instance matcher]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    checkWellStagedDFun :: PredType -> DFunId -> CtLoc -> TcS ()
    checkWellStagedDFun pred dfun_id loc
      = wrapTcS $ TcM.setCtLocM loc $
        do { use_stage <- TcM.getStage
           ; TcM.checkWellStaged pp_thing bind_lvl (thLevel use_stage) }
      where
        pp_thing = text "instance for" <+> quotes (ppr pred)
        bind_lvl = TcM.topIdLvl dfun_id

    pprEq :: TcType -> TcType -> SDoc
    pprEq ty1 ty2 = pprParendType ty1 <+> char '~' <+> pprParendType ty2

    isTouchableMetaTyVarTcS :: TcTyVar -> TcS Bool
    isTouchableMetaTyVarTcS tv
      = do { tclvl <- getTcLevel
           ; return $ isTouchableMetaTyVar tclvl tv }

    isFilledMetaTyVar_maybe :: TcTyVar -> TcS (Maybe Type)
    isFilledMetaTyVar_maybe tv
     = case tcTyVarDetails tv of
         MetaTv { mtv_ref = ref }
            -> do { cts <- wrapTcS (TcM.readTcRef ref)
                  ; case cts of
                      Indirect ty -> return (Just ty)
                      Flexi       -> return Nothing }
         _ -> return Nothing

    isFilledMetaTyVar :: TcTyVar -> TcS Bool
    isFilledMetaTyVar tv = wrapTcS (TcM.isFilledMetaTyVar tv)

    zonkTyCoVarsAndFV :: TcTyCoVarSet -> TcS TcTyCoVarSet
    zonkTyCoVarsAndFV tvs = wrapTcS (TcM.zonkTyCoVarsAndFV tvs)

    zonkCo :: Coercion -> TcS Coercion
    zonkCo = wrapTcS . TcM.zonkCo

    zonkTcType :: TcType -> TcS TcType
    zonkTcType ty = wrapTcS (TcM.zonkTcType ty)

    zonkTcTypes :: [TcType] -> TcS [TcType]
    zonkTcTypes tys = wrapTcS (TcM.zonkTcTypes tys)

    zonkTcTyVar :: TcTyVar -> TcS TcType
    zonkTcTyVar tv = wrapTcS (TcM.zonkTcTyVar tv)

    zonkSimples :: Cts -> TcS Cts
    zonkSimples cts = wrapTcS (TcM.zonkSimples cts)

    zonkWC :: WantedConstraints -> TcS WantedConstraints
    zonkWC wc = wrapTcS (TcM.zonkWC wc)

    {-
    Note [Do not add duplicate derived insolubles]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    In general we *must* add an insoluble (Int ~ Bool) even if there is
    one such there already, because they may come from distinct call
    sites.  Not only do we want an error message for each, but with
    -fdefer-type-errors we must generate evidence for each.  But for
    *derived* insolubles, we only want to report each one once.  Why?

    (a) A constraint (C r s t) where r -> s, say, may generate the same fundep
        equality many times, as the original constraint is successively rewritten.

    (b) Ditto the successive iterations of the main solver itself, as it traverses
        the constraint tree. See example below.

    Also for *given* insolubles we may get repeated errors, as we
    repeatedly traverse the constraint tree.  These are relatively rare
    anyway, so removing duplicates seems ok.  (Alternatively we could take
    the SrcLoc into account.)

    Note that the test does not need to be particularly efficient because
    it is only used if the program has a type error anyway.

    Example of (b): assume a top-level class and instance declaration:

      class D a b | a -> b
      instance D [a] [a]

    Assume we have started with an implication:

      forall c. Eq c => { wc_simple = D [c] c [W] }

    which we have simplified to:

      forall c. Eq c => { wc_simple = D [c] c [W]
                        , wc_insols = (c ~ [c]) [D] }

    For some reason, e.g. because we floated an equality somewhere else,
    we might try to re-solve this implication. If we do not do a
    dropDerivedWC, then we will end up trying to solve the following
    constraints the second time:

      (D [c] c) [W]
      (c ~ [c]) [D]

    which will result in two Deriveds to end up in the insoluble set:

      wc_simple   = D [c] c [W]
      wc_insols = (c ~ [c]) [D], (c ~ [c]) [D]
    -}

    -- Flatten skolems
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    newFlattenSkolem :: CtFlavour -> CtLoc
                     -> TcType         -- F xis
                     -> TcS (CtEvidence, Coercion, TcTyVar)    -- [W] x:: F xis ~ fsk
    newFlattenSkolem Given loc fam_ty
      = do { fsk <- newFsk fam_ty
           ; let co = mkNomReflCo fam_ty
           ; ev  <- newGivenEvVar loc (mkPrimEqPred fam_ty (mkTyVarTy fsk),
                                       EvCoercion co)
           ; return (ev, co, fsk) }

    newFlattenSkolem Wanted loc fam_ty
      = do { fmv <- newFmv fam_ty
           ; (ev, hole_co) <- newWantedEq loc Nominal fam_ty (mkTyVarTy fmv)
           ; return (ev, hole_co, fmv) }

    newFlattenSkolem Derived loc fam_ty
      = do { fmv <- newFmv fam_ty
           ; ev <- newDerivedNC loc (mkPrimEqPred fam_ty (mkTyVarTy fmv))
           ; return (ev, pprPanic "newFlattenSkolem [D]" (ppr fam_ty), fmv) }

    newFsk, newFmv :: TcType -> TcS TcTyVar
    newFsk fam_ty = wrapTcS (TcM.newFskTyVar fam_ty)
    newFmv fam_ty = wrapTcS (TcM.newFmvTyVar fam_ty)

    extendFlatCache :: TyCon -> [Type] -> (TcCoercion, TcType, CtFlavour) -> TcS ()
    extendFlatCache tc xi_args stuff
      = do { dflags <- getDynFlags
           ; when (gopt Opt_FlatCache dflags) $
             updInertTcS $ \ is@(IS { inert_flat_cache = fc }) ->
                is { inert_flat_cache = insertExactFunEq fc tc xi_args stuff } }

    -- Instantiations
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    instDFunType :: DFunId -> [DFunInstType] -> TcS ([TcType], TcThetaType)
    instDFunType dfun_id inst_tys
      = wrapTcS $ TcM.instDFunType dfun_id inst_tys

    newFlexiTcSTy :: Kind -> TcS TcType
    newFlexiTcSTy knd = wrapTcS (TcM.newFlexiTyVarTy knd)

    cloneMetaTyVar :: TcTyVar -> TcS TcTyVar
    cloneMetaTyVar tv = wrapTcS (TcM.cloneMetaTyVar tv)

    demoteUnfilledFmv :: TcTyVar -> TcS ()
    -- If a flatten-meta-var is still un-filled,
    -- turn it into an ordinary meta-var
    demoteUnfilledFmv fmv
      = wrapTcS $ do { is_filled <- TcM.isFilledMetaTyVar fmv
                     ; unless is_filled $
                       do { tv_ty <- TcM.newFlexiTyVarTy (tyVarKind fmv)
                          ; TcM.writeMetaTyVar fmv tv_ty } }

    instFlexiTcS :: [TKVar] -> TcS (TCvSubst, [TcType])
    instFlexiTcS tvs = wrapTcS (mapAccumLM inst_one emptyTCvSubst tvs)
      where
         inst_one subst tv
             = do { ty' <- instFlexiTcSHelper (tyVarName tv)
                                              (substTyUnchecked subst (tyVarKind tv))
                  ; return (extendTvSubst subst tv ty', ty') }

    instFlexiTcSHelper :: Name -> Kind -> TcM TcType
    instFlexiTcSHelper tvname kind
      = do { uniq <- TcM.newUnique
           ; details <- TcM.newMetaDetails TauTv
           ; let name = setNameUnique tvname uniq
           ; return (mkTyVarTy (mkTcTyVar name kind details)) }

    -- Creating and setting evidence variables and CtFlavors
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    data MaybeNew = Fresh CtEvidence | Cached EvTerm

    isFresh :: MaybeNew -> Bool
    isFresh (Fresh {})  = True
    isFresh (Cached {}) = False

    freshGoals :: [MaybeNew] -> [CtEvidence]
    freshGoals mns = [ ctev | Fresh ctev <- mns ]

    getEvTerm :: MaybeNew -> EvTerm
    getEvTerm (Fresh ctev) = ctEvTerm ctev
    getEvTerm (Cached evt) = evt

    setEvBind :: EvBind -> TcS ()
    setEvBind ev_bind
      = do { tc_evbinds <- getTcEvBinds
           ; case tc_evbinds of
               Just evb -> wrapTcS $ TcM.addTcEvBind evb ev_bind
               Nothing  -> pprPanic "setEvBind" (ppr ev_bind) }

    -- | Equalities only
    setWantedEq :: TcEvDest -> Coercion -> TcS ()
    setWantedEq (HoleDest hole) co
      = do { useVars (tyCoVarsOfCo co)
           ; wrapTcS $ TcM.fillCoercionHole hole co }
    setWantedEq (EvVarDest ev) _ = pprPanic "setWantedEq" (ppr ev)

    -- | Equalities only
    setEqIfWanted :: CtEvidence -> Coercion -> TcS ()
    setEqIfWanted (CtWanted { ctev_dest = dest }) co = setWantedEq dest co
    setEqIfWanted _ _ = return ()

    -- | Good for equalities and non-equalities
    setWantedEvTerm :: TcEvDest -> EvTerm -> TcS ()
    setWantedEvTerm (HoleDest hole) tm
      = do { let co = evTermCoercion tm
           ; useVars (tyCoVarsOfCo co)
           ; wrapTcS $ TcM.fillCoercionHole hole co }
    setWantedEvTerm (EvVarDest ev) tm = setWantedEvBind ev tm

    setWantedEvBind :: EvVar -> EvTerm -> TcS ()
    setWantedEvBind ev_id tm = setEvBind (mkWantedEvBind ev_id tm)

    setEvBindIfWanted :: CtEvidence -> EvTerm -> TcS ()
    setEvBindIfWanted ev tm
      = case ev of
          CtWanted { ctev_dest = dest }
            -> setWantedEvTerm dest tm
          _ -> return ()

    newTcEvBinds :: TcS EvBindsVar
    newTcEvBinds = wrapTcS TcM.newTcEvBinds

    newEvVar :: TcPredType -> TcS EvVar
    newEvVar pred = wrapTcS (TcM.newEvVar pred)

    newGivenEvVar :: CtLoc -> (TcPredType, EvTerm) -> TcS CtEvidence
    -- Make a new variable of the given PredType,
    -- immediately bind it to the given term
    -- and return its CtEvidence
    -- See Note [Bind new Givens immediately] in TcRnTypes
    newGivenEvVar loc (pred, rhs)
      = do { new_ev <- newBoundEvVarId pred rhs
           ; return (CtGiven { ctev_pred = pred, ctev_evar = new_ev, ctev_loc = loc }) }

    -- | Make a new 'Id' of the given type, bound (in the monad's EvBinds) to the
    -- given term
    newBoundEvVarId :: TcPredType -> EvTerm -> TcS EvVar
    newBoundEvVarId pred rhs
      = do { new_ev <- newEvVar pred
           ; setEvBind (mkGivenEvBind new_ev rhs)
           ; return new_ev }

    newGivenEvVars :: CtLoc -> [(TcPredType, EvTerm)] -> TcS [CtEvidence]
    newGivenEvVars loc pts = mapM (newGivenEvVar loc) pts

    -- | Make a new equality CtEvidence
    newWantedEq :: CtLoc -> Role -> TcType -> TcType -> TcS (CtEvidence, Coercion)
    newWantedEq loc role ty1 ty2
      = do { hole <- wrapTcS $ TcM.newCoercionHole
           ; traceTcS "Emitting new coercion hole" (ppr hole <+> dcolon <+> ppr pty)
           ; return ( CtWanted { ctev_pred = pty, ctev_dest = HoleDest hole
                               , ctev_loc = loc}
                    , mkHoleCo hole role ty1 ty2 ) }
      where
        pty = mkPrimEqPredRole role ty1 ty2

    -- no equalities here. Use newWantedEqNC instead
    newWantedEvVarNC :: CtLoc -> TcPredType -> TcS CtEvidence
    -- Don't look up in the solved/inerts; we know it's not there
    newWantedEvVarNC loc pty
      = do { -- checkReductionDepth loc pty
           ; new_ev <- newEvVar pty
           ; traceTcS "Emitting new wanted" (ppr new_ev <+> dcolon <+> ppr pty $$
                                             pprCtLoc loc)
           ; return (CtWanted { ctev_pred = pty, ctev_dest = EvVarDest new_ev
                              , ctev_loc = loc })}

    newWantedEvVar :: CtLoc -> TcPredType -> TcS MaybeNew
    -- For anything except ClassPred, this is the same as newWantedEvVarNC
    newWantedEvVar loc pty
      = do { mb_ct <- lookupInInerts pty
           ; case mb_ct of
                Just ctev
                  | not (isDerived ctev)
                  -> do { traceTcS "newWantedEvVar/cache hit" $ ppr ctev
                        ; return $ Cached (ctEvTerm ctev) }
                _ -> do { ctev <- newWantedEvVarNC loc pty
                        ; return (Fresh ctev) } }

    -- deals with both equalities and non equalities. Tries to look
    -- up non-equalities in the cache
    newWanted :: CtLoc -> PredType -> TcS MaybeNew
    newWanted loc pty
      | Just (role, ty1, ty2) <- getEqPredTys_maybe pty
      = Fresh . fst <$> newWantedEq loc role ty1 ty2
      | otherwise
      = newWantedEvVar loc pty

    emitNewDerived :: CtLoc -> TcPredType -> TcS ()
    emitNewDerived loc pred
      = do { ev <- newDerivedNC loc pred
           ; traceTcS "Emitting new derived" (ppr ev)
           ; updWorkListTcS (extendWorkListDerived loc ev) }

    emitNewDeriveds :: CtLoc -> [TcPredType] -> TcS ()
    emitNewDeriveds loc preds
      | null preds
      = return ()
      | otherwise
      = do { evs <- mapM (newDerivedNC loc) preds
           ; traceTcS "Emitting new deriveds" (ppr evs)
           ; updWorkListTcS (extendWorkListDeriveds loc evs) }

    emitNewDerivedEq :: CtLoc -> Role -> TcType -> TcType -> TcS ()
    -- Create new equality Derived and put it in the work list
    -- There's no caching, no lookupInInerts
    emitNewDerivedEq loc role ty1 ty2
      = do { ev <- newDerivedNC loc (mkPrimEqPredRole role ty1 ty2)
           ; traceTcS "Emitting new derived equality" (ppr ev $$ pprCtLoc loc)
           ; updWorkListTcS (extendWorkListDerived loc ev) }

    newDerivedNC :: CtLoc -> TcPredType -> TcS CtEvidence
    newDerivedNC loc pred
      = do { -- checkReductionDepth loc pred
           ; return (CtDerived { ctev_pred = pred, ctev_loc = loc }) }

    -- --------- Check done in TcInteract.selectNewWorkItem???? ---------
    -- | Checks if the depth of the given location is too much. Fails if
    -- it's too big, with an appropriate error message.
    checkReductionDepth :: CtLoc -> TcType   -- ^ type being reduced
                        -> TcS ()
    checkReductionDepth loc ty
      = do { dflags <- getDynFlags
           ; when (subGoalDepthExceeded dflags (ctLocDepth loc)) $
             wrapErrTcS $
             solverDepthErrorTcS loc ty }

    matchFam :: TyCon -> [Type] -> TcS (Maybe (Coercion, TcType))
    matchFam tycon args = wrapTcS $ matchFamTcM tycon args

    matchFamTcM :: TyCon -> [Type] -> TcM (Maybe (Coercion, TcType))
    -- Given (F tys) return (ty, co), where co :: F tys ~ ty
    matchFamTcM tycon args
      = do { fam_envs <- FamInst.tcGetFamInstEnvs
           ; return $ reduceTyFamApp_maybe fam_envs Nominal tycon args }

    {-
    Note [Residual implications]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The wl_implics in the WorkList are the residual implication
    constraints that are generated while solving or canonicalising the
    current worklist.  Specifically, when canonicalising
       (forall a. t1 ~ forall a. t2)
    from which we get the implication
       (forall a. t1 ~ t2)
    See TcSMonad.deferTcSForAllEq
    -}

    -- Deferring forall equalities as implications
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    deferTcSForAllEq :: Role -- Nominal or Representational
                     -> CtLoc  -- Original wanted equality flavor
                     -> [Coercion]        -- among the kinds of the binders
                     -> ([TyBinder],TcType)   -- ForAll tvs1 body1
                     -> ([TyBinder],TcType)   -- ForAll tvs2 body2
                     -> TcS Coercion
    deferTcSForAllEq role loc kind_cos (bndrs1,body1) (bndrs2,body2)
     = do { let tvs1'  = zipWithEqual "deferTcSForAllEq"
                           mkCastTy (mkTyVarTys tvs1) kind_cos
                body2' = substTyWithUnchecked tvs2 tvs1' body2
          ; (subst, skol_tvs) <- wrapTcS $ TcM.tcInstSkolTyVars tvs1
          ; let phi1  = Type.substTyUnchecked subst body1
                phi2  = Type.substTyUnchecked subst body2'
                skol_info = UnifyForAllSkol phi1

          ; (ctev, hole_co) <- newWantedEq loc role phi1 phi2
          ; env <- getLclEnv
          ; let new_tclvl = pushTcLevel (tcl_tclvl env)
                wc        = WC { wc_simple = singleCt (mkNonCanonical ctev)
                               , wc_impl   = emptyBag
                               , wc_insol  = emptyCts }
                imp       = Implic { ic_tclvl  = new_tclvl
                                   , ic_skols  = skol_tvs
                                   , ic_no_eqs = True
                                   , ic_given  = []
                                   , ic_wanted = wc
                                   , ic_status = IC_Unsolved
                                   , ic_binds  = Nothing -- no place to put binds
                                   , ic_env    = env
                                   , ic_info   = skol_info }
          ; updWorkListTcS (extendWorkListImplic imp)
          ; let cobndrs    = zip skol_tvs kind_cos
          ; return $ mkForAllCos cobndrs hole_co }
       where
         tvs1 = map (binderVar "deferTcSForAllEq") bndrs1
         tvs2 = map (binderVar "deferTcSForAllEq") bndrs2