    {-# LANGUAGE DerivingStrategies #-}
    {-# LANGUAGE RankNTypes #-}
    {-# LANGUAGE TypeApplications #-}

    {-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-}

    module GHC.Tc.Solver.InertSet (
        -- * The work list
        WorkList(..), isEmptyWorkList, emptyWorkList,
        extendWorkListNonEq, extendWorkListCt,
        extendWorkListCts, extendWorkListCtList,
        extendWorkListEq, extendWorkListEqs,
        appendWorkList, extendWorkListImplic,
        workListSize,
        selectWorkItem,

        -- * The inert set
        InertSet(..),
        InertCans(..),
        emptyInert,

        noMatchableGivenDicts,
        noGivenNewtypeReprEqs, updGivenEqs,
        mightEqualLater,
        prohibitedSuperClassSolve,

        -- * Inert equalities
        InertEqs,
        foldTyEqs, delEq, findEq,
        partitionInertEqs, partitionFunEqs,
        foldFunEqs, addEqToCans,

        -- * Inert Dicts
        updDicts, delDict, addDict, filterDicts, partitionDicts,
        addSolvedDict,

        -- * Inert Irreds
        InertIrreds, delIrred, addIrreds, addIrred, foldIrreds,
        findMatchingIrreds, updIrreds, addIrredToCans,

        -- * Kick-out
        KickOutSpec(..), kickOutRewritableLHS,

        -- * Cycle breaker vars
        CycleBreakerVarStack,
        pushCycleBreakerVarStack,
        addCycleBreakerBindings,
        forAllCycleBreakerBindings_,

        -- * Solving one from another
        InteractResult(..), solveOneFromTheOther

      ) where

    import GHC.Prelude

    import GHC.Tc.Types.Constraint
    import GHC.Tc.Types.Origin
    import GHC.Tc.Types.CtLoc( CtLoc, ctLocOrigin, ctLocSpan, ctLocLevel )
    import GHC.Tc.Solver.Types
    import GHC.Tc.Utils.TcType

    import GHC.Types.Var
    import GHC.Types.Var.Env
    import GHC.Types.Var.Set
    import GHC.Types.Basic( SwapFlag(..) )

    import GHC.Core.Reduction
    import GHC.Core.Predicate
    import GHC.Core.TyCo.FVs
    import qualified GHC.Core.TyCo.Rep as Rep
    import GHC.Core.Class( Class )
    import GHC.Core.TyCon
    import GHC.Core.Class( classTyCon )
    import GHC.Core.Unify

    import GHC.Utils.Misc       ( partitionWith )
    import GHC.Utils.Outputable
    import GHC.Utils.Panic
    import GHC.Data.Maybe
    import GHC.Data.Bag

    import Data.List.NonEmpty ( NonEmpty(..), (<|) )
    import qualified Data.List.NonEmpty as NE
    import Data.Function ( on )

    import Control.Monad      ( forM_ )

    {-
    ************************************************************************
    *                                                                      *
    *                            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 flavours).
    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); see Note [Prioritise equalities]
    * all the rest (wl_rest)

    Note [Prioritise equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    It's very important to process equalities over class constraints:

    * (Efficiency)  The general reason to do so is that if we process a
      class constraint first, we may end up putting it into the inert set
      and then kicking it out later.  That's extra work compared to just
      doing the equality first.

    * (Avoiding fundep iteration) As #14723 showed, it's possible to
      get non-termination if we
          - Emit the fundep equalities for a class constraint,
            generating some fresh unification variables.
          - That leads to some unification
          - Which kicks out the class constraint
          - Which isn't solved (because there are still some more
            equalities in the work-list), but generates yet more fundeps
      Solution: prioritise equalities over class constraints

    * (Class equalities) We need to prioritise equalities even if they
      are hidden inside a class constraint; see Note [Prioritise class equalities]

    * (Kick-out) We want to apply this priority scheme to kicked-out
      constraints too (see the call to extendWorkListCt in kick_out_rewritable)
      E.g. a CIrredCan can be a hetero-kinded (t1 ~ t2), which may become
      homo-kinded when kicked out, and hence we want to prioritise it.

    Further refinements:

    * Among the equalities we prioritise ones with an empty rewriter set;
      see Note [Wanteds rewrite Wanteds] in GHC.Tc.Types.Constraint, wrinkle (W1).

    * Among equalities with an empty rewriter set, we prioritise nominal equalities.
       * They have more rewriting power, so doing them first is better.
       * Prioritising them ameliorates the incompleteness of newtype
         solving: see (Ex2) in Note [Decomposing newtype equalities] in
         GHC.Tc.Solver.Equality.

    Note [Prioritise class equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We prioritise equalities in the solver (see selectWorkItem). But class
    constraints like (a ~ b) and (a ~~ b) are actually equalities too;
    see Note [The equality types story] in GHC.Builtin.Types.Prim.

    Failing to prioritise these is inefficient (more kick-outs etc).
    But, worse, it can prevent us spotting a "recursive knot" among
    Wanted constraints.  See comment:10 of #12734 for a worked-out
    example.

    So we arrange to put these particular class constraints in the wl_eqs.

      NB: since we do not currently apply the substitution to the
      inert_solved_dicts, the knot-tying still seems a bit fragile.
      But this makes it better.

    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 GHC.Tc.Solver.Monad.deferTcSForAllEq

    -}

    -- See Note [WorkList priorities]
    data WorkList
      = WL { WorkList -> [Ct]
    wl_eqs_N :: [Ct]  -- /Nominal/ equalities (s ~#N t), (s ~ t), (s ~~ t)
                               -- with empty rewriter set
           , WorkList -> [Ct]
    wl_eqs_X :: [Ct]  -- CEqCan, CDictCan, CIrredCan
                               -- with empty rewriter set
               -- All other equalities: contains both equality constraints and
               -- their class-level variants (a~b) and (a~~b);
               -- See Note [Prioritise equalities]
               -- See Note [Prioritise class equalities]

           , WorkList -> [Ct]
    wl_rw_eqs  :: [Ct]  -- Like wl_eqs, but ones that have a non-empty
                                 -- rewriter set; or, more precisely, did when
                                 -- added to the WorkList
             -- We prioritise wl_eqs over wl_rw_eqs;
             -- see Note [Prioritise Wanteds with empty RewriterSet]
             -- in GHC.Tc.Types.Constraint for more details.

           , WorkList -> [Ct]
    wl_rest :: [Ct]

           , WorkList -> Bag Implication
    wl_implics :: Bag Implication  -- See Note [Residual implications]
        }

    appendWorkList :: WorkList -> WorkList -> WorkList
    appendWorkList :: WorkList -> WorkList -> WorkList
    appendWorkList
        (WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs1_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs1_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs1
            , wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest1, wl_implics :: WorkList -> Bag Implication
    wl_implics = Bag Implication
    implics1 })
        (WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs2_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs2_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs2
            , wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest2, wl_implics :: WorkList -> Bag Implication
    wl_implics = Bag Implication
    implics2 })
       = WL { wl_eqs_N :: [Ct]
    wl_eqs_N   = [Ct]
    eqs1_N   [Ct] -> [Ct] -> [Ct]
    forall a. [a] -> [a] -> [a]
    ++ [Ct]
    eqs2_N
            , wl_eqs_X :: [Ct]
    wl_eqs_X   = [Ct]
    eqs1_X   [Ct] -> [Ct] -> [Ct]
    forall a. [a] -> [a] -> [a]
    ++ [Ct]
    eqs2_X
            , wl_rw_eqs :: [Ct]
    wl_rw_eqs  = [Ct]
    rw_eqs1  [Ct] -> [Ct] -> [Ct]
    forall a. [a] -> [a] -> [a]
    ++ [Ct]
    rw_eqs2
            , wl_rest :: [Ct]
    wl_rest    = [Ct]
    rest1    [Ct] -> [Ct] -> [Ct]
    forall a. [a] -> [a] -> [a]
    ++ [Ct]
    rest2
            , wl_implics :: Bag Implication
    wl_implics = Bag Implication
    implics1 Bag Implication -> Bag Implication -> Bag Implication
    forall a. Bag a -> Bag a -> Bag a
    `unionBags`   Bag Implication
    implics2 }

    workListSize :: WorkList -> Int
    workListSize :: WorkList -> ScDepth
    workListSize (WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs, wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest })
      = [Ct] -> ScDepth
    forall a. [a] -> ScDepth
    forall (t :: * -> *) a. Foldable t => t a -> ScDepth
    length [Ct]
    eqs_N ScDepth -> ScDepth -> ScDepth
    forall a. Num a => a -> a -> a
    + [Ct] -> ScDepth
    forall a. [a] -> ScDepth
    forall (t :: * -> *) a. Foldable t => t a -> ScDepth
    length [Ct]
    eqs_X ScDepth -> ScDepth -> ScDepth
    forall a. Num a => a -> a -> a
    + [Ct] -> ScDepth
    forall a. [a] -> ScDepth
    forall (t :: * -> *) a. Foldable t => t a -> ScDepth
    length [Ct]
    rw_eqs ScDepth -> ScDepth -> ScDepth
    forall a. Num a => a -> a -> a
    + [Ct] -> ScDepth
    forall a. [a] -> ScDepth
    forall (t :: * -> *) a. Foldable t => t a -> ScDepth
    length [Ct]
    rest

    extendWorkListEq :: RewriterSet -> Ct -> WorkList -> WorkList
    extendWorkListEq :: RewriterSet -> Ct -> WorkList -> WorkList
    extendWorkListEq RewriterSet
    rewriters Ct
    ct
        wl :: WorkList
    wl@(WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs })
      | RewriterSet -> Bool
    isEmptyRewriterSet RewriterSet
    rewriters      -- A wanted that has not been rewritten
        -- isEmptyRewriterSet: see Note [Prioritise Wanteds with empty RewriterSet]
        --                         in GHC.Tc.Types.Constraint
      = if Type -> Bool
    isNomEqPred (Ct -> Type
    ctPred Ct
    ct)
        then WorkList
    wl { wl_eqs_N = ct : eqs_N }
        else WorkList
    wl { wl_eqs_X = ct : eqs_X }

      | Bool
    otherwise
      = WorkList
    wl { wl_rw_eqs = ct : rw_eqs }

    extendWorkListEqs :: RewriterSet -> Bag Ct -> WorkList -> WorkList
    -- Add [eq1,...,eqn] to the work-list
    -- They all have the same rewriter set
    -- The constraints will be solved in left-to-right order:
    --   see Note [Work-list ordering] in GHC.Tc.Solver.Equality
    --
    -- Precondition: new_eqs is non-empty
    extendWorkListEqs :: RewriterSet -> Bag Ct -> WorkList -> WorkList
    extendWorkListEqs RewriterSet
    rewriters Bag Ct
    new_eqs
        wl :: WorkList
    wl@(WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs })
      | RewriterSet -> Bool
    isEmptyRewriterSet RewriterSet
    rewriters
        -- isEmptyRewriterSet: see Note [Prioritise Wanteds with empty RewriterSet]
        --                         in GHC.Tc.Types.Constraint
      = case (Ct -> Bool) -> Bag Ct -> (Bag Ct, Bag Ct)
    forall a. (a -> Bool) -> Bag a -> (Bag a, Bag a)
    partitionBag Ct -> Bool
    is_nominal Bag Ct
    new_eqs of
           (Bag Ct
    new_eqs_N, Bag Ct
    new_eqs_X)
              | Bag Ct -> Bool
    forall a. Bag a -> Bool
    isEmptyBag Bag Ct
    new_eqs_N -> WorkList
    wl { wl_eqs_X = new_eqs_X `push_on_front` eqs_X }
              | Bag Ct -> Bool
    forall a. Bag a -> Bool
    isEmptyBag Bag Ct
    new_eqs_X -> WorkList
    wl { wl_eqs_N = new_eqs_N `push_on_front` eqs_N }
              | Bool
    otherwise            -> WorkList
    wl { wl_eqs_N = new_eqs_N `push_on_front` eqs_N
                                           , wl_eqs_X = new_eqs_X `push_on_front` eqs_X }
              -- These isEmptyBag tests are just trying
              -- to avoid creating unnecessary thunks

      | Bool
    otherwise
      = WorkList
    wl { wl_rw_eqs = new_eqs `push_on_front` rw_eqs }
      where
        push_on_front :: Bag Ct -> [Ct] -> [Ct]
        -- push_on_front puts the new equlities on the front of the queue
        push_on_front :: Bag Ct -> [Ct] -> [Ct]
    push_on_front Bag Ct
    new_eqs [Ct]
    eqs = (Ct -> [Ct] -> [Ct]) -> [Ct] -> Bag Ct -> [Ct]
    forall a b. (a -> b -> b) -> b -> Bag a -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr (:) [Ct]
    eqs Bag Ct
    new_eqs

        is_nominal :: Ct -> Bool
    is_nominal Ct
    ct = Type -> Bool
    isNomEqPred (Ct -> Type
    ctPred Ct
    ct)

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

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

    extendWorkListCt :: Ct -> WorkList -> WorkList
    -- Agnostic about what kind of constraint
    extendWorkListCt :: Ct -> WorkList -> WorkList
    extendWorkListCt Ct
    ct WorkList
    wl
     = case Type -> Pred
    classifyPredType (CtEvidence -> Type
    ctEvPred CtEvidence
    ev) of
         EqPred {}
           -> RewriterSet -> Ct -> WorkList -> WorkList
    extendWorkListEq RewriterSet
    rewriters Ct
    ct WorkList
    wl

         ClassPred Class
    cls [Type]
    _  -- See Note [Prioritise class equalities]
           |  Class -> Bool
    isEqualityClass Class
    cls
           -> RewriterSet -> Ct -> WorkList -> WorkList
    extendWorkListEq RewriterSet
    rewriters Ct
    ct WorkList
    wl

         Pred
    _ -> Ct -> WorkList -> WorkList
    extendWorkListNonEq Ct
    ct WorkList
    wl
      where
        ev :: CtEvidence
    ev = Ct -> CtEvidence
    ctEvidence Ct
    ct
        rewriters :: RewriterSet
    rewriters = CtEvidence -> RewriterSet
    ctEvRewriters CtEvidence
    ev

    extendWorkListCtList :: [Ct] -> WorkList -> WorkList
    extendWorkListCtList :: [Ct] -> WorkList -> WorkList
    extendWorkListCtList [Ct]
    cts WorkList
    wl = (Ct -> WorkList -> WorkList) -> WorkList -> [Ct] -> WorkList
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr Ct -> WorkList -> WorkList
    extendWorkListCt WorkList
    wl [Ct]
    cts

    extendWorkListCts :: Cts -> WorkList -> WorkList
    extendWorkListCts :: Bag Ct -> WorkList -> WorkList
    extendWorkListCts Bag Ct
    cts WorkList
    wl = (Ct -> WorkList -> WorkList) -> WorkList -> Bag Ct -> WorkList
    forall a b. (a -> b -> b) -> b -> Bag a -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr Ct -> WorkList -> WorkList
    extendWorkListCt WorkList
    wl Bag Ct
    cts

    isEmptyWorkList :: WorkList -> Bool
    isEmptyWorkList :: WorkList -> Bool
    isEmptyWorkList (WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X
                        , wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest, wl_implics :: WorkList -> Bag Implication
    wl_implics = Bag Implication
    implics })
      = [Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    eqs_N Bool -> Bool -> Bool
    && [Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    eqs_X Bool -> Bool -> Bool
    && [Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    rest Bool -> Bool -> Bool
    && Bag Implication -> Bool
    forall a. Bag a -> Bool
    isEmptyBag Bag Implication
    implics

    emptyWorkList :: WorkList
    emptyWorkList :: WorkList
    emptyWorkList = WL { wl_eqs_N :: [Ct]
    wl_eqs_N = [], wl_eqs_X :: [Ct]
    wl_eqs_X = []
                       , wl_rw_eqs :: [Ct]
    wl_rw_eqs = [], wl_rest :: [Ct]
    wl_rest = [], wl_implics :: Bag Implication
    wl_implics = Bag Implication
    forall a. Bag a
    emptyBag }

    selectWorkItem :: WorkList -> Maybe (Ct, WorkList)
    -- See Note [Prioritise equalities]
    selectWorkItem :: WorkList -> Maybe (Ct, WorkList)
    selectWorkItem wl :: WorkList
    wl@(WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X
                          , wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs, wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest })
      | Ct
    ct:[Ct]
    cts <- [Ct]
    eqs_N  = (Ct, WorkList) -> Maybe (Ct, WorkList)
    forall a. a -> Maybe a
    Just (Ct
    ct, WorkList
    wl { wl_eqs_N  = cts })
      | Ct
    ct:[Ct]
    cts <- [Ct]
    eqs_X  = (Ct, WorkList) -> Maybe (Ct, WorkList)
    forall a. a -> Maybe a
    Just (Ct
    ct, WorkList
    wl { wl_eqs_X  = cts })
      | Ct
    ct:[Ct]
    cts <- [Ct]
    rw_eqs = (Ct, WorkList) -> Maybe (Ct, WorkList)
    forall a. a -> Maybe a
    Just (Ct
    ct, WorkList
    wl { wl_rw_eqs = cts })
      | Ct
    ct:[Ct]
    cts <- [Ct]
    rest   = (Ct, WorkList) -> Maybe (Ct, WorkList)
    forall a. a -> Maybe a
    Just (Ct
    ct, WorkList
    wl { wl_rest   = cts })
      | Bool
    otherwise        = Maybe (Ct, WorkList)
    forall a. Maybe a
    Nothing

    -- Pretty printing
    instance Outputable WorkList where
      ppr :: WorkList -> SDoc
    ppr (WL { wl_eqs_N :: WorkList -> [Ct]
    wl_eqs_N = [Ct]
    eqs_N, wl_eqs_X :: WorkList -> [Ct]
    wl_eqs_X = [Ct]
    eqs_X, wl_rw_eqs :: WorkList -> [Ct]
    wl_rw_eqs = [Ct]
    rw_eqs
              , wl_rest :: WorkList -> [Ct]
    wl_rest = [Ct]
    rest, wl_implics :: WorkList -> Bag Implication
    wl_implics = Bag Implication
    implics })
       = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "WL" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> (SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    braces (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
         [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat [ Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    eqs_N) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Eqs_N =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((Ct -> SDoc) -> [Ct] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map Ct -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Ct]
    eqs_N)
              , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    eqs_X) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Eqs_X =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((Ct -> SDoc) -> [Ct] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map Ct -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Ct]
    eqs_X)
              , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    rw_eqs) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "RwEqs =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((Ct -> SDoc) -> [Ct] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map Ct -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Ct]
    rw_eqs)
              , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([Ct] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [Ct]
    rest) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Non-eqs =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((Ct -> SDoc) -> [Ct] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map Ct -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [Ct]
    rest)
              , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (Bag Implication -> Bool
    forall a. Bag a -> Bool
    isEmptyBag Bag Implication
    implics) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                SDoc -> SDoc -> SDoc
    forall doc. IsOutput doc => doc -> doc -> doc
    ifPprDebug (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Implics =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((Implication -> SDoc) -> [Implication] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map Implication -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr (Bag Implication -> [Implication]
    forall a. Bag a -> [a]
    bagToList Bag Implication
    implics)))
                           (String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "(Implics omitted)")
              ])

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

    type CycleBreakerVarStack = NonEmpty (Bag (TcTyVar, TcType))
       -- ^ a stack of (CycleBreakerTv, original family applications) lists
       -- first element in the stack corresponds to current implication;
       --   later elements correspond to outer implications
       -- used to undo the cycle-breaking needed to handle
       -- Note [Type equality cycles] in GHC.Tc.Solver.Equality
       -- Why store the outer implications? For the use in mightEqualLater (only)
       --
       -- Why NonEmpty? So there is always a top element to add to

    data InertSet
      = IS { InertSet -> InertCans
    inert_cans :: InertCans
                  -- Canonical Given, Wanted
                  -- Sometimes called "the inert set"

           , InertSet -> CycleBreakerVarStack
    inert_cycle_breakers :: CycleBreakerVarStack

           , InertSet -> FunEqMap Reduction
    inert_famapp_cache :: FunEqMap Reduction
                  -- Just a hash-cons cache for use when reducing family applications
                  -- only
                  --
                  -- If    F tys :-> (co, rhs, flav),
                  -- then  co :: F tys ~N rhs
                  -- all evidence is from instances or Givens; no coercion holes here
                  -- (We have no way of "kicking out" from the cache, so putting
                  --  wanteds here means we can end up solving a Wanted with itself. Bad)

           , InertSet -> DictMap DictCt
    inert_solved_dicts :: DictMap DictCt
                  -- All Wanteds, of form (C t1 .. tn)
                  -- Always a dictionary solved by an instance decl; never an implict parameter
                  -- See Note [Solved dictionaries]
                  -- and Note [Do not add superclasses of solved dictionaries]
           }

    instance Outputable InertSet where
      ppr :: InertSet -> SDoc
    ppr (IS { inert_cans :: InertSet -> InertCans
    inert_cans = InertCans
    ics
              , inert_solved_dicts :: InertSet -> DictMap DictCt
    inert_solved_dicts = DictMap DictCt
    solved_dicts })
          = [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat [ InertCans -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr InertCans
    ics
                 , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([DictCt] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [DictCt]
    dicts) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
                   String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Solved dicts =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((DictCt -> SDoc) -> [DictCt] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map DictCt -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [DictCt]
    dicts) ]
             where
               dicts :: [DictCt]
    dicts = Bag DictCt -> [DictCt]
    forall a. Bag a -> [a]
    bagToList (DictMap DictCt -> Bag DictCt
    forall a. DictMap a -> Bag a
    dictsToBag DictMap DictCt
    solved_dicts)

    emptyInertCans :: InertCans
    emptyInertCans :: InertCans
    emptyInertCans
      = IC { inert_eqs :: InertEqs
    inert_eqs          = InertEqs
    emptyTyEqs
           , inert_funeqs :: InertFunEqs
    inert_funeqs       = InertFunEqs
    forall a. TcAppMap a
    emptyFunEqs
           , inert_given_eq_lvl :: TcLevel
    inert_given_eq_lvl = TcLevel
    topTcLevel
           , inert_given_eqs :: Bool
    inert_given_eqs    = Bool
    False
           , inert_dicts :: DictMap DictCt
    inert_dicts        = DictMap DictCt
    forall a. TcAppMap a
    emptyDictMap
           , inert_safehask :: DictMap DictCt
    inert_safehask     = DictMap DictCt
    forall a. TcAppMap a
    emptyDictMap
           , inert_insts :: [QCInst]
    inert_insts        = []
           , inert_irreds :: InertIrreds
    inert_irreds       = InertIrreds
    forall a. Bag a
    emptyBag }

    emptyInert :: InertSet
    emptyInert :: InertSet
    emptyInert
      = IS { inert_cans :: InertCans
    inert_cans           = InertCans
    emptyInertCans
           , inert_cycle_breakers :: CycleBreakerVarStack
    inert_cycle_breakers = Bag (TcTyVar, Type)
    forall a. Bag a
    emptyBag Bag (TcTyVar, Type)
    -> [Bag (TcTyVar, Type)] -> CycleBreakerVarStack
    forall a. a -> [a] -> NonEmpty a
    :| []
           , inert_famapp_cache :: FunEqMap Reduction
    inert_famapp_cache   = FunEqMap Reduction
    forall a. TcAppMap a
    emptyFunEqs
           , inert_solved_dicts :: DictMap DictCt
    inert_solved_dicts   = DictMap DictCt
    forall a. TcAppMap a
    emptyDictMap }

    {- Note [Solved dictionaries]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When we apply a top-level instance declaration, 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* dictionaries.
    The simplest, degenerate 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]

    VERY IMPORTANT INVARIANT:

     (Solved Dictionary Invariant)
        Every member of the inert_solved_dicts is the result
        of applying an instance declaration that "takes a step"

        An instance "takes a step" if it has the form
            dfunDList d1 d2 = MkD (...) (...) (...)
        That is, the dfun is lazy in its arguments, and guarantees to
        immediately return a dictionary constructor.  NB: all dictionary
        data constructors are lazy in their arguments.

        This property is crucial to ensure that all dictionaries are
        non-bottom, which in turn ensures that the whole "recursive
        dictionary" idea works at all, even if we get something like
            rec { d = dfunDList d dx }
        See Note [Recursive superclasses] in GHC.Tc.TyCl.Instance.

     Reason:
       - All instances, except two exceptions listed below, "take a step"
         in the above sense

       - Exception 1: local quantified constraints have no such guarantee;
         indeed, adding a "solved dictionary" when applying a quantified
         constraint led to the ability to define unsafeCoerce
         in #17267.

       - Exception 2: the magic built-in instance for (~) has no
         such guarantee.  It behaves as if we had
             class    (a ~# b) => (a ~ b) where {}
             instance (a ~# b) => (a ~ b) where {}
         The "dfun" for the instance is strict in the coercion.
         Anyway there's no point in recording a "solved dict" for
         (t1 ~ t2); it's not going to allow a recursive dictionary
         to be constructed.  Ditto (~~) and Coercible.

    THEREFORE we only add a "solved dictionary"
      - when applying an instance declaration
      - subject to Exceptions 1 and 2 above

    In implementation terms
      - GHC.Tc.Solver.Monad.addSolvedDict adds a new solved dictionary,
        conditional on the kind of instance

      - It is only called when applying an instance decl,
        in GHC.Tc.Solver.Dict.tryInstances

      - ClsInst.InstanceWhat says what kind of instance was
        used to solve the constraint.  In particular
          * LocalInstance identifies quantified constraints
          * BuiltinEqInstance identifies the strange built-in
            instances for equality.

      - ClsInst.instanceReturnsDictCon says which kind of
        instance guarantees to return a dictionary constructor

    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.

    * The inert_solved_dicts are all Wanteds, never givens

    * We only cache dictionaries from top-level instances, not from
      local quantified constraints.  Reason: if we cached the latter
      we'd need to purge the cache when bringing new quantified
      constraints into scope, because quantified constraints "shadow"
      top-level instances.

    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
    *                                                                      *
    *                                                                      *
    ********************************************************************* -}

    {- Note [Tracking Given equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    For reasons described in (UNTOUCHABLE) in GHC.Tc.Utils.Unify
    Note [Unification preconditions], we can't unify
       alpha[2] ~ Int
    under a level-4 implication if there are any Given equalities
    bound by the implications at level 3 of 4.  To that end, the
    InertCans tracks

      inert_given_eq_lvl :: TcLevel
         -- The TcLevel of the innermost implication that has a Given
         -- equality of the sort that make a unification variable untouchable
         -- (see Note [Unification preconditions] in GHC.Tc.Utils.Unify).

    We update inert_given_eq_lvl whenever we add a Given to the
    inert set, in updGivenEqs.

    Then a unification variable alpha[n] is untouchable iff
        n < inert_given_eq_lvl
    that is, if the unification variable was born outside an
    enclosing Given equality.

    Exactly which constraints should trigger (UNTOUCHABLE), and hence
    should update inert_given_eq_lvl?

    (TGE1) We do /not/ need to worry about let-bound skolems, such as
         forall[2] a. a ~ [b] => blah
      See Note [Let-bound skolems] and the isOuterTyVar tests in `updGivenEqs`

    (TGE2) However, solely to support better error messages (see Note [HasGivenEqs] in
       GHC.Tc.Types.Constraint) we also track these "local" equalities in the
       boolean inert_given_eqs field.  This field is used only subsequntly (see
       `getHasGivenEqs`), to set the ic_given_eqs field to LocalGivenEqs.

    (TGE3) Consider an implication
          forall[2]. beta[1] => alpha[1] ~ Int
      where beta is a unification variable that has already been unified
      to () in an outer scope.  Then alpha[1] is perfectly touchable and
      we can unify alpha := Int. So when deciding whether the givens contain
      an equality, we should canonicalise first, rather than just looking at
      the /original/ givens (#8644).

    (TGE4) However, we must take account of *potential* equalities. Consider the
       same example again, but this time we have /not/ yet unified beta:
          forall[2] beta[1] => ...blah...

       Because beta might turn into an equality, updGivenEqs conservatively
       treats it as a potential equality, and updates inert_give_eq_lvl

    (TGE5) We should not look at the equality relation involved (nominal vs
       representational), because representational equalities can still
       imply nominal ones. For example, if (G a ~R G b) and G's argument's
       role is nominal, then we can deduce a ~N b.

    Historical note: prior to #24938 we also ignored Given equalities that
    did not mention an "outer" type variable.  But that is wrong, as #24938
    showed. Another example is immortalised in test LocalGivenEqs2
       data T where
          MkT :: F a ~ G b => a -> b -> T
       f (MkT _ _) = True
    We should not infer the type for `f`; let-bound-skolems does not apply.

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

    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.

    For an example, see #9211.

    The actual test is in `isLetBoundSkolemCt`

    Wrinkles:

    (LBS1) See GHC.Tc.Utils.Unify Note [Deeper level on the left] for how we ensure
           that the correct variable is on the left of the equality when both are
           tyvars.

    (LBS2) We also want this to work for
                forall a. [G] F b ~ a   (CEqCt with TyFamLHS)
       Here the Given will have a TyFamLHS, with the skolem-bound tyvar on the RHS.
       See tests T24938a, and LocalGivenEqs.

    (LBS3) Happily (LBS2) also makes cycle-breakers work. Suppose we have
                forall a. [G] (F a) Int ~ a
      where F has arity 1, and `a` is the locally-bound skolem.  Then, as
      Note [Type equality cycles] explains, we split into
               [G] F a ~ cbv, [G] cbv Int ~ a
      where `cbv` is the cycle breaker variable.  But cbv has the same level
      as `a`, so `isOuterTyVar` (called in `isLetBoundSkolemCt`) will return False.

      This actually matters occasionally: see test LocalGivenEqs.

    You might wonder whether the skolem really needs to be bound "in the
    very same implication" as the equality constraint.
    Consider this (c.f. #15009):

      data S a where
        MkS :: (a ~ Int) => S a

      g :: forall a. S a -> a -> blah
      g x y = let h = \z. ( z :: Int
                          , case x of
                               MkS -> [y,z])
              in ...

    From the type signature for `g`, we get `y::a` .  Then when we
    encounter the `\z`, we'll assign `z :: alpha[1]`, say.  Next, from the
    body of the lambda we'll get

      [W] alpha[1] ~ Int                             -- From z::Int
      [W] forall[2]. (a ~ Int) => [W] alpha[1] ~ a   -- From [y,z]

    Now, unify alpha := a.  Now we are stuck with an unsolved alpha~Int!
    So we must treat alpha as untouchable under the forall[2] implication.

    Possible future improvements.  The current test just looks to see whether one
    side of an equality is a locally-bound skolem.  But actually we could, in
    theory, do better: if one side (or both sides, actually) of an equality
    ineluctably mentions a local skolem, then the equality cannot possibly impact
    types outside of the implication (because doing to would cause those types to be
    ill-scoped). The problem is the "ineluctably": this means that no expansion,
    other solving, etc., could possibly get rid of the variable. This is hard,
    perhaps impossible, to know for sure, especially when we think about type family
    interactions. (And it's a user-visible property so we don't want it to be hard
    to predict.) So we keep the existing check, looking for one lone variable,
    because we're sure that variable isn't going anywhere.

    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-CEqCan constraints are fully rewritten with respect
        to the CEqCan equalities (modulo eqCanRewrite of course;
        eg a wanted cannot rewrite a given)

      * CEqCan equalities: see Note [inert_eqs: the inert equalities]
        Also see documentation in Constraint.Ct for a list of invariants

    Note [inert_eqs: the inert equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Our main invariant:
       the EqCts in inert_eqs should be a
            terminating generalised substitution

    -------------- 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
      (See Note [Why R2?].)

    Lemma (L0). 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 (lhs -f-> t), where
      - lhs is a type variable or an exactly-saturated type family application
                      (that is, lhs is a CanEqLHS)
      - t is a type
      - f is a flavour

    such that

      (WF1) if (lhs1 -f1-> t1) in S
               (lhs2 -f2-> t2) in S
            then (f1 >= f2) implies that lhs1 does not appear within lhs2

      (WF2) if (lhs -f-> t) is in S, then t /= lhs

      (WF3) No LHS in S is rewritable in an RHS in S,
            in the argument of a type family application (F ty1..tyn)
            where F heads a LHS in S

    --------- Definition [Applying a generalised substitution] ----------
    If S is a generalised substitution
       S(f,lhs)      = rhs,             if (lhs -fs-> rhs) in S, and fs >= f
       S(f,T t1..tn) = T S(f1,t1)..S(fn,tn)
       S(f,t1 t2)    = S(f,t1) S(f_N,t2)
       S(f,t)        = t
    Here f1..fn are obtained from f and T using the roles of T, and f_N is
    the nominal version of f.  See Note [Flavours with roles].

    Notation: repeated application.
      S^0(f,t)     = t
      S^(n+1)(f,t) = S(f, S^n(t))
      S*(f,t) is the result of applying S until you reach a fixpoint

    ---------  Definition [Terminating generalised substitution] ---------
    A generalised substitution S is *terminating* iff

      (IG1) for every f,t, there is an n such that
                 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.
    --------- End of definitions ------------------------------------

    Rationale for (WF1)-(WF3)
    -------------------------
    * (WF1) guarantees that S is well-defined /as a function/;
      see Theorem (S is a function)

       Theorem (S is a function): S(f,t0) is well defined as a function.
       Proof: Suppose (lhs -f1-> t1) and (lhs -f2-> t2) are both in S,
                   and  f1 >= f and f2 >= f
              Then by (R2) f1 >= f2 or f2 >= f1, which contradicts (WF1)
       Note: this argument isn't quite right.  WF1 ensures that lhs1 does
       not appear inside lhs2, and that guarantees confluence. But I can't quite
       see how to make that argument precise.

    * (WF2) is a bit trivial.  It means that if S is terminating, so that
      S^(n+1)(f,t) = S^n(f,t), then there is no LHS of S in S^n(f,t).  We
      never get a silly infinite sequence a -> a -> a -> a  .... which is
      technically a fixed point but would still go on for ever.

    * (WF3) is need for the termination proof.

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

    Note [Why R2?]
    ~~~~~~~~~~~~~~
    R2 states that, if we have f1 >= f and f2 >= f, then either f1 >= f2 or f2 >=
    f1. If we do not have R2, we will easily fall into a loop.

    To see why, imagine we have f1 >= f, f2 >= f, and that's it. Then, let our
    inert set S = {a -f1-> b, b -f2-> a}. Computing S(f,a) does not terminate. And
    yet, we have a hard time noticing an occurs-check problem when building S, as
    the two equalities cannot rewrite one another.

    R2 actually restricts our ability to accept user-written programs. See
    Note [Avoiding rewriting cycles] in GHC.Tc.Types.Constraint for an example.

    Note [Rewritable]
    ~~~~~~~~~~~~~~~~~
    Definition. A CanEqLHS lhs is *rewritable* in a type t if the
    lhs tree appears as a subtree within t without traversing any of the following
    components of t:
      * coercions (whether they appear in casts CastTy or as arguments CoercionTy)
      * kinds of variable occurrences
    The check for rewritability *does* look in kinds of the bound variable of a
    ForAllTy.

    The reason for this definition is that the rewriter does not rewrite in coercions
    or variables' kinds. In turn, the rewriter does not need to rewrite there because
    those places are never used for controlling the behaviour of the solver: these
    places are not used in matching instances or in decomposing equalities.

    This definition is used by the anyRewritableXXX family of functions and is meant
    to model the actual behaviour in GHC.Tc.Solver.Rewrite.

    Goal: If lhs is not rewritable in t, then t is a fixpoint of the generalised
    substitution containing only {lhs -f*-> t'}, where f* is a flavour such that f* >= f
    for all f.

    Wrinkles

    * Taking roles into account: we must consider a rewrite at a given role. That is,
      a rewrite arises from some equality, and that equality has a role associated
      with it. As we traverse a type, we track what role we are allowed to rewrite with.

      For example, suppose we have an inert [G] b ~R# Int. Then b is rewritable in
      Maybe b but not in F b, where F is a type function. This role-aware logic is
      present in both the anyRewritableXXX functions and in the rewriter.
      See also Note [anyRewritableTyVar must be role-aware] in GHC.Tc.Utils.TcType.

    * There is one exception to the claim that non-rewritable parts of the tree do
      not affect the solver: we sometimes do an occurs-check to decide e.g. how to
      orient an equality. (See the comments on GHC.Tc.Solver.Equality.canEqTyVarFunEq.)
      Accordingly, the presence of a variable in a kind or coercion just might
      influence the solver. Here is an example:

        type family Const x y where
          Const x y = x

        AxConst :: forall x y. Const x y ~# x

        alpha :: Const Type Nat
        [W] alpha ~ Int |> (sym (AxConst Type alpha) ;;
                            AxConst Type alpha ;;
                            sym (AxConst Type Nat))

      The cast is clearly ludicrous (it ties together a cast and its symmetric
      version), but we can't quite rule it out. (See (EQ1) from Note [Respecting
      definitional equality] in GHC.Core.TyCo.Rep to see why we need the Const Type
      Nat bit.) And yet this cast will (quite rightly) prevent alpha from unifying
      with the RHS. I (Richard E) don't have an example of where this problem can
      arise from a Haskell program, but we don't have an air-tight argument for why
      the definition of *rewritable* given here is correct.

    Note [Extending the inert equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Main Theorem [Stability under extension]
       GIVEN a "work item" [lhs_w -fw-> rhs_w]
             and a terminating generalised substitution S,

       SUCH THAT
          (T1) S(fw,lhs_w) = lhs_w   -- LHS of work-item is a fixpoint of S(fw,_)
          (T2) S(fw,rhs_w) = rhs_w   -- RHS of work-item is a fixpoint of S(fw,_)
          (T3) lhs_w not in rhs_w    -- No occurs check in the work item
                 -- If lhs is a type family application, we require only that
                 -- lhs is not *rewritable* in rhs_w. See Note [Rewritable] and
                 -- Note [EqCt occurs check] in GHC.Tc.Types.Constraint.
          (T4) no [lhs_s -fs-> rhs_s] in S meets [The KickOut Criteria]
               (i.e. we already kicked any such items out!)

       THEN the extended substitution T = S+(lhs_w -fw-> rhs_w)
            is a terminating generalised substitution

    How do we establish these conditions?

      * (T1) and (T2) are guaranteed by exhaustively rewriting the work-item
        with S(fw,_).

      * (T3) is guaranteed by an occurs-check on the work item.
        This is done during canonicalisation, in checkTypeEq; invariant
        (TyEq:OC) of CEqCan. See also Note [EqCt occurs check] in GHC.Tc.Types.Constraint.

      * (T4) is established by GHC.Tc.Solver.Monad.kickOutRewritable.  If the inert
        set contains a triple that meets the KickOut Criteria, we kick it out and
        add it to the work list for later re-examination.  See
        Note [The KickOut Criteria]

    Theorem: T (defined in "THEN" above) is a generalised substitution;
      that is, it satisfies (WF1)-(WF3)
    Proof:
      (WF1) Suppose we are adding [lhs_w -fw-> rhs_w], and [lhs_s -fs-> rhs_s] is in S.
            Then:
              - by (T1)  if fs>=fw, lhs_s does not occur within lhs_w.
              - by (KK1) if fw>=fs, lhs_w is not rewritable in lhs_s, or we'd have
                kicked out the stable constraint.

      (WF2) is directly guaranteed by (T3)

      (WF3) No lhs_s in S is rewritable in rhs_w at all, because of (T2)
            And (KK2) guarantees that lhs_w is not rewritable under a type
            family in rhs_s

    Note [The KickOut Criteria]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Kicking out is a Bad Thing:
    * It means we have to re-process a constraint.  The less we kick out, the better.
    * In the limit, kicking can lead to non-termination: imagine that we /always/
      kick out the entire inert set!
    * Because (mid 2024) we don't support sharing in constraints, excessive kicking out
      can lead to exponentially big constraints (#24984).

    So we seek to do as little kicking out as possible.  For example, consider this,
    which happens a lot:

       Inert:  g1: a ~ Maybe b
       Work:   g2: b ~ Int

    We do /not/ kick out g1 when adding g2.  The new substitution S' = {g1,g2} is still
    /terminating/ but it is not /idmempotent/.  To apply S' to, say, (Tree a), we may
    need to apply it twice:  Tree a --> Tree (Maybe b) --> Tree (Maybe Int)

    Here are the KickOut Criteria:

        When adding [lhs_w -fw-> rhs_w] to a well-formed terminating substitution S,
        element [lhs_s -fs-> rhs_s] in S meets the KickOut Criteria if:

        (KK0) fw >= fs    AND   any of (KK1), (KK2) or (KK3) hold

        * (KK1: satisfy WF1) `lhs_w` is rewritable in `lhs_s`.

        * (KK2: termination) `lhs_w` is rewritable in `rhs_s` in these positions:
            If not(fs>=fw)
            then (KK2a) anywhere
            else (KK2b) look only in the argument of type family applications,
                        whose type family heads some LHS in `S`

        * (KK3: completeness)
          If not(fs >= fw)   -- If fs can rewrite fw, kick-out is redundant/harmful
          * (KK3a) If the role of `fs` is Nominal:
               kick out if `rhs_s = lhs_w`
          * (KK3b) If the role of `fs` is Representational:
               kick out if `rhs_s` is of form `(lhs_w t1 .. tn)`

    Rationale

    * (KK0) kick out only if `fw` can rewrite `fs`.
      Reason: suppose we kick out (lhs1 -fs-> s), and add (lhs -fw-> t) to the ineart
      set. The latter can't rewrite the former, so the kick-out achieved nothing

    * (KK1) `lhs_w` is rewritable in `lhs_s`.
      Reason: needed to guarantee (WF1).  See Theorem: T is well formed

    * (KK2) see Note [KK2: termination of the extended substitution]

    * (KK3) see Note [KK3: completeness of solving]

    The above story is a bit vague wrt roles, but the code is not.
    See Note [Flavours with roles]

    Note [KK2: termination of the extended substitution]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Proving termination of the extended substitution T is surprisingly tricky.

    * Reason for (KK2a).  Consider
          Work:  [G] b ~ a
          Inert: [W] a ~ b
      If we don't kick out the inert, then we get a loop on e.g. [W] a ~ Int.
      But if both were Wanted we really should not kick out (the substitution does not
      have to be idempotent). So we only look everywhere for the `lhs_w` if
      not (fs>=fw), that is the inert item cannot rewrite the work item.  So in the
      above example we will kick out; but if both were Wanted we won't.

    * Reason for (KK2b).  Consider the case where (fs >= fw)
          Work:  [G] a ~ Int
          Inert: [G] F Int ~ F a
      If we just added the work item, the substitution would loop on type (F Int).
      So we must kick out the inert item, even though (fs>=fw). (KK2b) does this
      by looking for lhs_w under type family applications in rhs_s.

      (KK2b) makes kick-out less aggressive by looking only under type-family applications,
      in the case where (fs >= fw), and that made a /huge/ difference to #24944.

    Tricky examples in: #19042, #17672, #24984. The last (#24984) is particular subtle:

      Inert:   [W] g1: F a0 ~ F a1
               [W] g2: F a2 ~ F a1
               [W] g3: F a3 ~ F a1

    Now we add [W] g4: F a1 ~ F a7.  Should we kick out g1,g2,g3?  No!  The
    substitution doesn't need to be idempotent, merely terminating.  And in #24984
    it turned out that we kept adding one new constraint and kicking out all the
    previous inert ones (and that rewriting led to exponentially big constraints due
    to lack of contraint sharing.)  So we only want to look /under/ type family applications.

    The proof is hard. We start by ignoring flavours. Suppose that:
    * We are adding [lhs_w -fw-> rhs_w] to a well-formed, terminating substitution S.
    * None of the constraints in S meet the KickOut Criteria.
    * Define T = S+[lhs_w -fw-> rhs_w]
    * `f` is an arbitrary flavour

    Lemma 1: for any lhs_s in S, T*(f,lhs_s) terminates.
      Proof.
      * We know that r1 = S*(f,lhs_s) terminates.
      * Moreover, we know there are no occurrences of lhs_w under a type family (which
        is the head of a LHS) in r1 (KK2)+(WF3).  We need (WF3) because you might wonder
        what if rhs_s is (F a), and [a --> lhs_w] was in S.  But (WF3) prevents that.
      * Define r2 = r1{rhs_w/lhs_w}.  We know that rhs_w has no occurrences of any lhs in S,
        nor of lhs_w.
      * Since any occurrence of lhs_w does not occur under a type family, the substitution
        won't make any F t1..tn ~ s in S match.
      * So r2 is a fixed point of T.

    Lemma 2: T*(f,lhs_w) teminates.
      Proof: no occurrences of any LHS in rhs_w.

    Theorem. For any type r, T*(r) terminates.
      Proof:
      1. Consider any sub-term of r, which is a LHS of T.
         - Rewrite it with T*; this terminates (Lemma 1).
         - Do this simultaneously to all sub-terms that match a LHS of T, yielding r1.
      2. Could this new r1 have a sub-term that is an LHS of T?  Yes, but only if r has a
         sub-term F w, and w rewrote in Step 1 to w' and F w' matches a LHS in T.
      3. Very well: apply step 1 again, but note that /doing so consumes one of the family
         applications in the original r/.
      4. After Step 1 either we have reached a fixed point, or we repeat Step 1 consuming at
         least one family application of r.
      5. There are only a finite number of family applications in r, so this process terminates.

    Example:

    Inert set:   gs : F Int ~ b
    Work item:   gw : b ~ Int

    F (F (F b)) --[gw]--> F (F (F Int)) --[gs]--> F (F b)
                --[gw]--> F (F Int)     --[gs]--> F b
                --[gw]--> F Int         --[gs]--> b
                --[gw]--> Int

    Notice that each iteration of Step 1 strips off one of the layers of F, all
    of which were in the original r.

    The argument is even more tricky when flavours are involved, and we have not
    fleshed it out in detail.

    Note [KK3: completeness of solving]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    (KK3) is not necessary for the extended substitution
    to be terminating.  In fact (KK0) could be made stronger by saying
       ... then (not (fw >= fs) or not (fs >= fs))
    But it's not enough for S to be /terminating/; 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 (KK3) to the kick-out criteria:

        * (KK3: completeness)
          If not(fs >= fw)   (KK3a)
          * (KK3b) If the role of `fs` is Nominal:
               kick out if `rhs_s = lhs_w`
          * (KK3c) If the role of `fs` is Representational:
               kick out if `rhs_s` is of form `(lhs_w t1 .. tn)`

    Wrinkles:

    * (KK3a) All this can only happen if the work-item can rewrite the inert
      one, /but not vice versa/; that is not(fs >= fw).  It is useless to kick
      out if (fs >= fw) becuase then the work-item is already fully rewritten
      by the inert item.  And too much kick-out is positively harmful.
      (Historical example #14363.)

    * (KK3b) addresses teh main example above for KK3. Another way to understand
      (KK3b) 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.

    * (KK3c) When considering roles, we also need the second clause (KK3b). Consider
          work-item    c -G/N-> a
          inert-item   a -W/R-> b c
      The work-item doesn't get rewritten by the inert, because (>=) doesn't hold.
      But we don't kick out the inert item because not (W/R >= W/R).  So we just
      add the work item. But then, consider if we hit the following:
          work-item    b -G/N-> Id
          inert-items  a -W/R-> b c
                     c -G/N-> a
        where
          newtype Id x = Id x

      For similar reasons, if we only had (KK3a), 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 lhs of a
      work item is "exposed", where exposed means being at the head of the top-level
      application chain (lhs t1 .. tn).  See head_is_new_lhs. This is encoded in
      (KK3c)).

    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, 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 [inert_eqs: the inert equalities] may
    need to be revisited, but we don't think that the end conclusion is wrong.
    -}

    data InertCans   -- See Note [Detailed InertCans Invariants] for more
      = IC { InertCans -> InertEqs
    inert_eqs :: InertEqs
                  -- See Note [inert_eqs: the inert equalities]
                  -- All EqCt with a TyVarLHS; index is the LHS tyvar
                  -- Domain = skolems and untouchables; a touchable would be unified

           , InertCans -> InertFunEqs
    inert_funeqs :: InertFunEqs
                  -- All EqCt with a TyFamLHS; index is the whole family head type.
                  -- LHS is fully rewritten (modulo eqCanRewrite constraints)
                  --     wrt inert_eqs
                  -- Can include both [G] and [W]

           , InertCans -> DictMap DictCt
    inert_dicts :: DictMap DictCt
                  -- Dictionaries only
                  -- All fully rewritten (modulo flavour constraints)
                  --     wrt inert_eqs

           , InertCans -> [QCInst]
    inert_insts :: [QCInst]

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

           , InertCans -> InertIrreds
    inert_irreds :: InertIrreds
                  -- Irreducible predicates that cannot be made canonical,
                  --     and which don't interact with others (e.g.  (c a))
                  -- and insoluble predicates (e.g.  Int ~ Bool, or a ~ [a])

           , InertCans -> TcLevel
    inert_given_eq_lvl :: TcLevel
                  -- The TcLevel of the innermost implication that has a Given
                  -- equality of the sort that make a unification variable untouchable
                  -- (see Note [Unification preconditions] in GHC.Tc.Utils.Unify).
                  -- See Note [Tracking Given equalities]

           , InertCans -> Bool
    inert_given_eqs :: Bool
                  -- True <=> The inert Givens *at this level* (tcl_tclvl)
                  --          could includes at least one equality /other than/ a
                  --          let-bound skolem equality.
                  -- Reason: report these givens when reporting a failed equality
                  -- See Note [Tracking Given equalities]
           }

    type InertEqs    = DTyVarEnv EqualCtList
    type InertFunEqs = FunEqMap  EqualCtList
    type InertIrreds = Bag IrredCt

    instance Outputable InertCans where
      ppr :: InertCans -> SDoc
    ppr (IC { inert_eqs :: InertCans -> InertEqs
    inert_eqs = InertEqs
    eqs
              , inert_funeqs :: InertCans -> InertFunEqs
    inert_funeqs = InertFunEqs
    funeqs
              , inert_dicts :: InertCans -> DictMap DictCt
    inert_dicts = DictMap DictCt
    dicts
              , inert_safehask :: InertCans -> DictMap DictCt
    inert_safehask = DictMap DictCt
    safehask
              , inert_irreds :: InertCans -> InertIrreds
    inert_irreds = InertIrreds
    irreds
              , inert_given_eq_lvl :: InertCans -> TcLevel
    inert_given_eq_lvl = TcLevel
    ge_lvl
              , inert_given_eqs :: InertCans -> Bool
    inert_given_eqs = Bool
    given_eqs
              , inert_insts :: InertCans -> [QCInst]
    inert_insts = [QCInst]
    insts })

        = SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    braces (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $ [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat
          [ Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (InertEqs -> Bool
    forall a. DVarEnv a -> Bool
    isEmptyDVarEnv InertEqs
    eqs) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Equalities ="
              SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Bag EqCt -> SDoc
    forall a. Outputable a => Bag a -> SDoc
    pprBag ((EqCt -> Bag EqCt -> Bag EqCt) -> InertEqs -> Bag EqCt -> Bag EqCt
    forall b. (EqCt -> b -> b) -> InertEqs -> b -> b
    foldTyEqs EqCt -> Bag EqCt -> Bag EqCt
    forall a. a -> Bag a -> Bag a
    consBag InertEqs
    eqs Bag EqCt
    forall a. Bag a
    emptyBag)
          , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (InertFunEqs -> Bool
    forall a. TcAppMap a -> Bool
    isEmptyTcAppMap InertFunEqs
    funeqs) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Type-function equalities ="
              SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Bag EqCt -> SDoc
    forall a. Outputable a => Bag a -> SDoc
    pprBag ((EqCt -> Bag EqCt -> Bag EqCt)
    -> InertFunEqs -> Bag EqCt -> Bag EqCt
    forall b. (EqCt -> b -> b) -> InertFunEqs -> b -> b
    foldFunEqs EqCt -> Bag EqCt -> Bag EqCt
    forall a. a -> Bag a -> Bag a
    consBag InertFunEqs
    funeqs Bag EqCt
    forall a. Bag a
    emptyBag)
          , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (DictMap DictCt -> Bool
    forall a. TcAppMap a -> Bool
    isEmptyTcAppMap DictMap DictCt
    dicts) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Dictionaries =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Bag DictCt -> SDoc
    forall a. Outputable a => Bag a -> SDoc
    pprBag (DictMap DictCt -> Bag DictCt
    forall a. DictMap a -> Bag a
    dictsToBag DictMap DictCt
    dicts)
          , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (DictMap DictCt -> Bool
    forall a. TcAppMap a -> Bool
    isEmptyTcAppMap DictMap DictCt
    safehask) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Safe Haskell unsafe overlap =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Bag DictCt -> SDoc
    forall a. Outputable a => Bag a -> SDoc
    pprBag (DictMap DictCt -> Bag DictCt
    forall a. DictMap a -> Bag a
    dictsToBag DictMap DictCt
    safehask)
          , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless (InertIrreds -> Bool
    forall a. Bag a -> Bool
    isEmptyBag InertIrreds
    irreds) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Irreds =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> InertIrreds -> SDoc
    forall a. Outputable a => Bag a -> SDoc
    pprBag InertIrreds
    irreds
          , Bool -> SDoc -> SDoc
    forall doc. IsOutput doc => Bool -> doc -> doc
    ppUnless ([QCInst] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [QCInst]
    insts) (SDoc -> SDoc) -> SDoc -> SDoc
    forall a b. (a -> b) -> a -> b
    $
            String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Given instances =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> [SDoc] -> SDoc
    forall doc. IsDoc doc => [doc] -> doc
    vcat ((QCInst -> SDoc) -> [QCInst] -> [SDoc]
    forall a b. (a -> b) -> [a] -> [b]
    map QCInst -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr [QCInst]
    insts)
          , String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Innermost given equalities =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> TcLevel -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TcLevel
    ge_lvl
          , String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "Given eqs at this level =" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> Bool -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Bool
    given_eqs
          ]

    {- *********************************************************************
    *                                                                      *
                       Inert equalities
    *                                                                      *
    ********************************************************************* -}

    emptyTyEqs :: InertEqs
    emptyTyEqs :: InertEqs
    emptyTyEqs = InertEqs
    forall a. DVarEnv a
    emptyDVarEnv

    addEqToCans :: TcLevel -> EqCt -> InertCans -> InertCans
    addEqToCans :: TcLevel -> EqCt -> InertCans -> InertCans
    addEqToCans TcLevel
    tc_lvl eq_ct :: EqCt
    eq_ct@(EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = CanEqLHS
    lhs })
                ics :: InertCans
    ics@(IC { inert_funeqs :: InertCans -> InertFunEqs
    inert_funeqs = InertFunEqs
    funeqs, inert_eqs :: InertCans -> InertEqs
    inert_eqs = InertEqs
    eqs })
      = TcLevel -> Ct -> InertCans -> InertCans
    updGivenEqs TcLevel
    tc_lvl (EqCt -> Ct
    CEqCan EqCt
    eq_ct) (InertCans -> InertCans) -> InertCans -> InertCans
    forall a b. (a -> b) -> a -> b
    $
        case CanEqLHS
    lhs of
           TyFamLHS TyCon
    tc [Type]
    tys -> InertCans
    ics { inert_funeqs = addCanFunEq funeqs tc tys eq_ct }
           TyVarLHS TcTyVar
    tv     -> InertCans
    ics { inert_eqs    = addTyEq eqs tv eq_ct }

    addTyEq :: InertEqs -> TcTyVar -> EqCt -> InertEqs
    addTyEq :: InertEqs -> TcTyVar -> EqCt -> InertEqs
    addTyEq InertEqs
    old_eqs TcTyVar
    tv EqCt
    ct
      = (EqualCtList -> EqualCtList -> EqualCtList)
    -> InertEqs -> TcTyVar -> EqualCtList -> InertEqs
    forall a. (a -> a -> a) -> DVarEnv a -> TcTyVar -> a -> DVarEnv a
    extendDVarEnv_C EqualCtList -> EqualCtList -> EqualCtList
    add_eq InertEqs
    old_eqs TcTyVar
    tv [EqCt
    ct]
      where
        add_eq :: EqualCtList -> EqualCtList -> EqualCtList
    add_eq EqualCtList
    old_eqs EqualCtList
    _ = EqCt -> EqualCtList -> EqualCtList
    addToEqualCtList EqCt
    ct EqualCtList
    old_eqs

    foldTyEqs :: (EqCt -> b -> b) -> InertEqs -> b -> b
    foldTyEqs :: forall b. (EqCt -> b -> b) -> InertEqs -> b -> b
    foldTyEqs EqCt -> b -> b
    k InertEqs
    eqs b
    z
      = (EqualCtList -> b -> b) -> b -> InertEqs -> b
    forall a b. (a -> b -> b) -> b -> DVarEnv a -> b
    foldDVarEnv (\EqualCtList
    cts b
    z -> (EqCt -> b -> b) -> b -> EqualCtList -> b
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr EqCt -> b -> b
    k b
    z EqualCtList
    cts) b
    z InertEqs
    eqs

    findTyEqs :: InertCans -> TyVar -> [EqCt]
    findTyEqs :: InertCans -> TcTyVar -> EqualCtList
    findTyEqs InertCans
    icans TcTyVar
    tv = forall (t :: * -> *) a. Foldable t => t [a] -> [a]
    concat @Maybe (InertEqs -> TcTyVar -> Maybe EqualCtList
    forall a. DVarEnv a -> TcTyVar -> Maybe a
    lookupDVarEnv (InertCans -> InertEqs
    inert_eqs InertCans
    icans) TcTyVar
    tv)

    delEq :: EqCt -> InertCans -> InertCans
    delEq :: EqCt -> InertCans -> InertCans
    delEq (EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = CanEqLHS
    lhs, eq_rhs :: EqCt -> Type
    eq_rhs = Type
    rhs }) InertCans
    ic = case CanEqLHS
    lhs of
        TyVarLHS TcTyVar
    tv
          -> InertCans
    ic { inert_eqs = alterDVarEnv upd (inert_eqs ic) tv }
        TyFamLHS TyCon
    tf [Type]
    args
          -> InertCans
    ic { inert_funeqs = alterTcApp (inert_funeqs ic) tf args upd }
      where
        isThisOne :: EqCt -> Bool
        isThisOne :: EqCt -> Bool
    isThisOne (EqCt { eq_rhs :: EqCt -> Type
    eq_rhs = Type
    t1 }) = Type -> Type -> Bool
    tcEqTypeNoKindCheck Type
    rhs Type
    t1

        upd :: Maybe EqualCtList -> Maybe EqualCtList
        upd :: Maybe EqualCtList -> Maybe EqualCtList
    upd (Just EqualCtList
    eq_ct_list) = (EqCt -> Bool) -> EqualCtList -> Maybe EqualCtList
    filterEqualCtList (Bool -> Bool
    not (Bool -> Bool) -> (EqCt -> Bool) -> EqCt -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . EqCt -> Bool
    isThisOne) EqualCtList
    eq_ct_list
        upd Maybe EqualCtList
    Nothing           = Maybe EqualCtList
    forall a. Maybe a
    Nothing

    findEq :: InertCans -> CanEqLHS -> [EqCt]
    findEq :: InertCans -> CanEqLHS -> EqualCtList
    findEq InertCans
    icans (TyVarLHS TcTyVar
    tv) = InertCans -> TcTyVar -> EqualCtList
    findTyEqs InertCans
    icans TcTyVar
    tv
    findEq InertCans
    icans (TyFamLHS TyCon
    fun_tc [Type]
    fun_args)
      = forall (t :: * -> *) a. Foldable t => t [a] -> [a]
    concat @Maybe (InertFunEqs -> TyCon -> [Type] -> Maybe EqualCtList
    forall a. FunEqMap a -> TyCon -> [Type] -> Maybe a
    findFunEq (InertCans -> InertFunEqs
    inert_funeqs InertCans
    icans) TyCon
    fun_tc [Type]
    fun_args)

    {-# INLINE partition_eqs_container #-}
    partition_eqs_container
      :: forall container
       . container    -- empty container
      -> (forall b. (EqCt -> b -> b) ->  container -> b -> b) -- folder
      -> (EqCt -> container -> container)  -- extender
      -> (EqCt -> Bool)
      -> container
      -> ([EqCt], container)
    partition_eqs_container :: forall container.
    container
    -> (forall b. (EqCt -> b -> b) -> container -> b -> b)
    -> (EqCt -> container -> container)
    -> (EqCt -> Bool)
    -> container
    -> (EqualCtList, container)
    partition_eqs_container container
    empty_container forall b. (EqCt -> b -> b) -> container -> b -> b
    fold_container EqCt -> container -> container
    extend_container EqCt -> Bool
    pred container
    orig_inerts
      = (EqCt -> (EqualCtList, container) -> (EqualCtList, container))
    -> container
    -> (EqualCtList, container)
    -> (EqualCtList, container)
    forall b. (EqCt -> b -> b) -> container -> b -> b
    fold_container EqCt -> (EqualCtList, container) -> (EqualCtList, container)
    folder container
    orig_inerts ([], container
    empty_container)
      where
        folder :: EqCt -> ([EqCt], container) -> ([EqCt], container)
        folder :: EqCt -> (EqualCtList, container) -> (EqualCtList, container)
    folder EqCt
    eq_ct (EqualCtList
    acc_true, container
    acc_false)
          | EqCt -> Bool
    pred EqCt
    eq_ct = (EqCt
    eq_ct EqCt -> EqualCtList -> EqualCtList
    forall a. a -> [a] -> [a]
    : EqualCtList
    acc_true, container
    acc_false)
          | Bool
    otherwise  = (EqualCtList
    acc_true,         EqCt -> container -> container
    extend_container EqCt
    eq_ct container
    acc_false)

    partitionInertEqs :: (EqCt -> Bool)   -- EqCt will always have a TyVarLHS
                      -> InertEqs
                      -> ([EqCt], InertEqs)
    partitionInertEqs :: (EqCt -> Bool) -> InertEqs -> (EqualCtList, InertEqs)
    partitionInertEqs = InertEqs
    -> (forall b. (EqCt -> b -> b) -> InertEqs -> b -> b)
    -> (EqCt -> InertEqs -> InertEqs)
    -> (EqCt -> Bool)
    -> InertEqs
    -> (EqualCtList, InertEqs)
    forall container.
    container
    -> (forall b. (EqCt -> b -> b) -> container -> b -> b)
    -> (EqCt -> container -> container)
    -> (EqCt -> Bool)
    -> container
    -> (EqualCtList, container)
    partition_eqs_container InertEqs
    emptyTyEqs (EqCt -> b -> b) -> InertEqs -> b -> b
    forall b. (EqCt -> b -> b) -> InertEqs -> b -> b
    foldTyEqs EqCt -> InertEqs -> InertEqs
    addInertEqs

    addInertEqs :: EqCt -> InertEqs -> InertEqs
    -- Precondition: CanEqLHS is a TyVarLHS
    addInertEqs :: EqCt -> InertEqs -> InertEqs
    addInertEqs eq_ct :: EqCt
    eq_ct@(EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = TyVarLHS TcTyVar
    tv }) InertEqs
    eqs = InertEqs -> TcTyVar -> EqCt -> InertEqs
    addTyEq InertEqs
    eqs TcTyVar
    tv EqCt
    eq_ct
    addInertEqs EqCt
    other InertEqs
    _ = String -> SDoc -> InertEqs
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "extendInertEqs" (EqCt -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr EqCt
    other)

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

    addCanFunEq :: InertFunEqs -> TyCon -> [TcType] -> EqCt -> InertFunEqs
    addCanFunEq :: InertFunEqs -> TyCon -> [Type] -> EqCt -> InertFunEqs
    addCanFunEq InertFunEqs
    old_eqs TyCon
    fun_tc [Type]
    fun_args EqCt
    ct
      = InertFunEqs
    -> TyCon
    -> [Type]
    -> (Maybe EqualCtList -> Maybe EqualCtList)
    -> InertFunEqs
    forall a. TcAppMap a -> TyCon -> [Type] -> XT a -> TcAppMap a
    alterTcApp InertFunEqs
    old_eqs TyCon
    fun_tc [Type]
    fun_args Maybe EqualCtList -> Maybe EqualCtList
    upd
      where
        upd :: Maybe EqualCtList -> Maybe EqualCtList
    upd (Just EqualCtList
    old_equal_ct_list) = EqualCtList -> Maybe EqualCtList
    forall a. a -> Maybe a
    Just (EqualCtList -> Maybe EqualCtList)
    -> EqualCtList -> Maybe EqualCtList
    forall a b. (a -> b) -> a -> b
    $ EqCt -> EqualCtList -> EqualCtList
    addToEqualCtList EqCt
    ct EqualCtList
    old_equal_ct_list
        upd Maybe EqualCtList
    Nothing                  = EqualCtList -> Maybe EqualCtList
    forall a. a -> Maybe a
    Just [EqCt
    ct]

    foldFunEqs :: (EqCt -> b -> b) -> FunEqMap EqualCtList -> b -> b
    foldFunEqs :: forall b. (EqCt -> b -> b) -> InertFunEqs -> b -> b
    foldFunEqs EqCt -> b -> b
    k InertFunEqs
    fun_eqs b
    z = (EqualCtList -> b -> b) -> InertFunEqs -> b -> b
    forall a b. (a -> b -> b) -> TcAppMap a -> b -> b
    foldTcAppMap (\EqualCtList
    eqs b
    z -> (EqCt -> b -> b) -> b -> EqualCtList -> b
    forall a b. (a -> b -> b) -> b -> [a] -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr EqCt -> b -> b
    k b
    z EqualCtList
    eqs) InertFunEqs
    fun_eqs b
    z

    partitionFunEqs :: (EqCt -> Bool)    -- EqCt will have a TyFamLHS
                    -> InertFunEqs
                    -> ([EqCt], InertFunEqs)
    partitionFunEqs :: (EqCt -> Bool) -> InertFunEqs -> (EqualCtList, InertFunEqs)
    partitionFunEqs = InertFunEqs
    -> (forall b. (EqCt -> b -> b) -> InertFunEqs -> b -> b)
    -> (EqCt -> InertFunEqs -> InertFunEqs)
    -> (EqCt -> Bool)
    -> InertFunEqs
    -> (EqualCtList, InertFunEqs)
    forall container.
    container
    -> (forall b. (EqCt -> b -> b) -> container -> b -> b)
    -> (EqCt -> container -> container)
    -> (EqCt -> Bool)
    -> container
    -> (EqualCtList, container)
    partition_eqs_container InertFunEqs
    forall a. TcAppMap a
    emptyFunEqs (EqCt -> b -> b) -> InertFunEqs -> b -> b
    forall b. (EqCt -> b -> b) -> InertFunEqs -> b -> b
    foldFunEqs EqCt -> InertFunEqs -> InertFunEqs
    addFunEqs

    addFunEqs :: EqCt -> InertFunEqs -> InertFunEqs
    -- Precondition: EqCt is a TyFamLHS
    addFunEqs :: EqCt -> InertFunEqs -> InertFunEqs
    addFunEqs eq_ct :: EqCt
    eq_ct@(EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = TyFamLHS TyCon
    tc [Type]
    args }) InertFunEqs
    fun_eqs
      = InertFunEqs -> TyCon -> [Type] -> EqCt -> InertFunEqs
    addCanFunEq InertFunEqs
    fun_eqs TyCon
    tc [Type]
    args EqCt
    eq_ct
    addFunEqs EqCt
    other InertFunEqs
    _ = String -> SDoc -> InertFunEqs
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "extendFunEqs" (EqCt -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr EqCt
    other)

    {- *********************************************************************
    *                                                                      *
                       Inert Dicts
    *                                                                      *
    ********************************************************************* -}

    updDicts :: (DictMap DictCt -> DictMap DictCt) -> InertCans -> InertCans
    updDicts :: (DictMap DictCt -> DictMap DictCt) -> InertCans -> InertCans
    updDicts DictMap DictCt -> DictMap DictCt
    upd InertCans
    ics = InertCans
    ics { inert_dicts = upd (inert_dicts ics) }

    delDict :: DictCt -> DictMap a -> DictMap a
    delDict :: forall a. DictCt -> DictMap a -> DictMap a
    delDict (DictCt { di_cls :: DictCt -> Class
    di_cls = Class
    cls, di_tys :: DictCt -> [Type]
    di_tys = [Type]
    tys }) DictMap a
    m
      = DictMap a -> TyCon -> [Type] -> DictMap a
    forall a. TcAppMap a -> TyCon -> [Type] -> TcAppMap a
    delTcApp DictMap a
    m (Class -> TyCon
    classTyCon Class
    cls) [Type]
    tys

    addDict :: DictCt -> DictMap DictCt -> DictMap DictCt
    addDict :: DictCt -> DictMap DictCt -> DictMap DictCt
    addDict item :: DictCt
    item@(DictCt { di_cls :: DictCt -> Class
    di_cls = Class
    cls, di_tys :: DictCt -> [Type]
    di_tys = [Type]
    tys }) DictMap DictCt
    dm
      = DictMap DictCt -> TyCon -> [Type] -> DictCt -> DictMap DictCt
    forall a. TcAppMap a -> TyCon -> [Type] -> a -> TcAppMap a
    insertTcApp DictMap DictCt
    dm (Class -> TyCon
    classTyCon Class
    cls) [Type]
    tys DictCt
    item

    addSolvedDict :: DictCt -> DictMap DictCt -> DictMap DictCt
    addSolvedDict :: DictCt -> DictMap DictCt -> DictMap DictCt
    addSolvedDict item :: DictCt
    item@(DictCt { di_cls :: DictCt -> Class
    di_cls = Class
    cls, di_tys :: DictCt -> [Type]
    di_tys = [Type]
    tys }) DictMap DictCt
    dm
      = DictMap DictCt -> TyCon -> [Type] -> DictCt -> DictMap DictCt
    forall a. TcAppMap a -> TyCon -> [Type] -> a -> TcAppMap a
    insertTcApp DictMap DictCt
    dm (Class -> TyCon
    classTyCon Class
    cls) [Type]
    tys DictCt
    item

    filterDicts :: (DictCt -> Bool) -> DictMap DictCt -> DictMap DictCt
    filterDicts :: (DictCt -> Bool) -> DictMap DictCt -> DictMap DictCt
    filterDicts DictCt -> Bool
    f DictMap DictCt
    m = (DictCt -> Bool) -> DictMap DictCt -> DictMap DictCt
    forall a. (a -> Bool) -> TcAppMap a -> TcAppMap a
    filterTcAppMap DictCt -> Bool
    f DictMap DictCt
    m

    partitionDicts :: (DictCt -> Bool) -> DictMap DictCt -> (Bag DictCt, DictMap DictCt)
    partitionDicts :: (DictCt -> Bool) -> DictMap DictCt -> (Bag DictCt, DictMap DictCt)
    partitionDicts DictCt -> Bool
    f DictMap DictCt
    m = (DictCt
     -> (Bag DictCt, DictMap DictCt) -> (Bag DictCt, DictMap DictCt))
    -> DictMap DictCt
    -> (Bag DictCt, DictMap DictCt)
    -> (Bag DictCt, DictMap DictCt)
    forall a b. (a -> b -> b) -> TcAppMap a -> b -> b
    foldTcAppMap DictCt
    -> (Bag DictCt, DictMap DictCt) -> (Bag DictCt, DictMap DictCt)
    k DictMap DictCt
    m (Bag DictCt
    forall a. Bag a
    emptyBag, DictMap DictCt
    forall a. TcAppMap a
    emptyDictMap)
      where
        k :: DictCt
    -> (Bag DictCt, DictMap DictCt) -> (Bag DictCt, DictMap DictCt)
    k DictCt
    ct (Bag DictCt
    yeses, DictMap DictCt
    noes) | DictCt -> Bool
    f DictCt
    ct      = (DictCt
    ct DictCt -> Bag DictCt -> Bag DictCt
    forall a. a -> Bag a -> Bag a
    `consBag` Bag DictCt
    yeses, DictMap DictCt
    noes)
                           | Bool
    otherwise = (Bag DictCt
    yeses,              DictCt -> DictMap DictCt -> DictMap DictCt
    addDict DictCt
    ct DictMap DictCt
    noes)

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

    addIrredToCans :: TcLevel -> IrredCt -> InertCans -> InertCans
    addIrredToCans :: TcLevel -> IrredCt -> InertCans -> InertCans
    addIrredToCans TcLevel
    tc_lvl IrredCt
    irred InertCans
    ics
      = TcLevel -> Ct -> InertCans -> InertCans
    updGivenEqs TcLevel
    tc_lvl (IrredCt -> Ct
    CIrredCan IrredCt
    irred) (InertCans -> InertCans) -> InertCans -> InertCans
    forall a b. (a -> b) -> a -> b
    $
        (InertIrreds -> InertIrreds) -> InertCans -> InertCans
    updIrreds (IrredCt -> InertIrreds -> InertIrreds
    addIrred IrredCt
    irred) InertCans
    ics

    addIrreds :: [IrredCt] -> InertIrreds -> InertIrreds
    addIrreds :: [IrredCt] -> InertIrreds -> InertIrreds
    addIrreds [IrredCt]
    extras InertIrreds
    irreds
      | [IrredCt] -> Bool
    forall a. [a] -> Bool
    forall (t :: * -> *) a. Foldable t => t a -> Bool
    null [IrredCt]
    extras = InertIrreds
    irreds
      | Bool
    otherwise   = InertIrreds
    irreds InertIrreds -> InertIrreds -> InertIrreds
    forall a. Bag a -> Bag a -> Bag a
    `unionBags` [IrredCt] -> InertIrreds
    forall a. [a] -> Bag a
    listToBag [IrredCt]
    extras

    addIrred :: IrredCt -> InertIrreds -> InertIrreds
    addIrred :: IrredCt -> InertIrreds -> InertIrreds
    addIrred IrredCt
    extra InertIrreds
    irreds = InertIrreds
    irreds InertIrreds -> IrredCt -> InertIrreds
    forall a. Bag a -> a -> Bag a
    `snocBag` IrredCt
    extra

    updIrreds :: (InertIrreds -> InertIrreds) -> InertCans -> InertCans
    updIrreds :: (InertIrreds -> InertIrreds) -> InertCans -> InertCans
    updIrreds InertIrreds -> InertIrreds
    upd InertCans
    ics = InertCans
    ics { inert_irreds = upd (inert_irreds ics) }

    delIrred :: IrredCt -> InertCans -> InertCans
    -- Remove a particular (Given) Irred, on the instructions of a plugin
    -- For some reason this is done vis the evidence Id, not the type
    -- Compare delEq.  I have not idea why
    delIrred :: IrredCt -> InertCans -> InertCans
    delIrred (IrredCt { ir_ev :: IrredCt -> CtEvidence
    ir_ev = CtEvidence
    ev }) InertCans
    ics
      = (InertIrreds -> InertIrreds) -> InertCans -> InertCans
    updIrreds ((IrredCt -> Bool) -> InertIrreds -> InertIrreds
    forall a. (a -> Bool) -> Bag a -> Bag a
    filterBag IrredCt -> Bool
    keep) InertCans
    ics
      where
        ev_id :: TcTyVar
    ev_id = CtEvidence -> TcTyVar
    ctEvEvId CtEvidence
    ev
        keep :: IrredCt -> Bool
    keep (IrredCt { ir_ev :: IrredCt -> CtEvidence
    ir_ev = CtEvidence
    ev' }) = TcTyVar
    ev_id TcTyVar -> TcTyVar -> Bool
    forall a. Eq a => a -> a -> Bool
    /= CtEvidence -> TcTyVar
    ctEvEvId CtEvidence
    ev'

    foldIrreds :: (IrredCt -> b -> b) -> InertIrreds -> b -> b
    foldIrreds :: forall b. (IrredCt -> b -> b) -> InertIrreds -> b -> b
    foldIrreds IrredCt -> b -> b
    k InertIrreds
    irreds b
    z = (IrredCt -> b -> b) -> b -> InertIrreds -> b
    forall a b. (a -> b -> b) -> b -> Bag a -> b
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr IrredCt -> b -> b
    k b
    z InertIrreds
    irreds

    findMatchingIrreds :: InertIrreds -> CtEvidence
                       -> (Bag (IrredCt, SwapFlag), InertIrreds)
    findMatchingIrreds :: InertIrreds -> CtEvidence -> (Bag (IrredCt, SwapFlag), InertIrreds)
    findMatchingIrreds InertIrreds
    irreds CtEvidence
    ev
      | EqPred EqRel
    eq_rel1 Type
    lty1 Type
    rty1 <- Type -> Pred
    classifyPredType Type
    pred
        -- See Note [Solving irreducible equalities]
      = (IrredCt -> Either (IrredCt, SwapFlag) IrredCt)
    -> InertIrreds -> (Bag (IrredCt, SwapFlag), InertIrreds)
    forall a b c. (a -> Either b c) -> Bag a -> (Bag b, Bag c)
    partitionBagWith (EqRel
    -> Type -> Type -> IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    match_eq EqRel
    eq_rel1 Type
    lty1 Type
    rty1) InertIrreds
    irreds
      | Bool
    otherwise
      = (IrredCt -> Either (IrredCt, SwapFlag) IrredCt)
    -> InertIrreds -> (Bag (IrredCt, SwapFlag), InertIrreds)
    forall a b c. (a -> Either b c) -> Bag a -> (Bag b, Bag c)
    partitionBagWith IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    match_non_eq InertIrreds
    irreds
      where
        pred :: Type
    pred = CtEvidence -> Type
    ctEvPred CtEvidence
    ev
        match_non_eq :: IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    match_non_eq IrredCt
    irred
          | IrredCt -> Type
    irredCtPred IrredCt
    irred HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    pred = (IrredCt, SwapFlag) -> Either (IrredCt, SwapFlag) IrredCt
    forall a b. a -> Either a b
    Left (IrredCt
    irred, SwapFlag
    NotSwapped)
          | Bool
    otherwise                         = IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    forall a b. b -> Either a b
    Right IrredCt
    irred

        match_eq :: EqRel
    -> Type -> Type -> IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    match_eq EqRel
    eq_rel1 Type
    lty1 Type
    rty1 IrredCt
    irred
          | EqPred EqRel
    eq_rel2 Type
    lty2 Type
    rty2 <- Type -> Pred
    classifyPredType (IrredCt -> Type
    irredCtPred IrredCt
    irred)
          , EqRel
    eq_rel1 EqRel -> EqRel -> Bool
    forall a. Eq a => a -> a -> Bool
    == EqRel
    eq_rel2
          , Just SwapFlag
    swap <- Type -> Type -> Type -> Type -> Maybe SwapFlag
    match_eq_help Type
    lty1 Type
    rty1 Type
    lty2 Type
    rty2
          = (IrredCt, SwapFlag) -> Either (IrredCt, SwapFlag) IrredCt
    forall a b. a -> Either a b
    Left (IrredCt
    irred, SwapFlag
    swap)
          | Bool
    otherwise
          = IrredCt -> Either (IrredCt, SwapFlag) IrredCt
    forall a b. b -> Either a b
    Right IrredCt
    irred

        match_eq_help :: Type -> Type -> Type -> Type -> Maybe SwapFlag
    match_eq_help Type
    lty1 Type
    rty1 Type
    lty2 Type
    rty2
          | Type
    lty1 HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    lty2, Type
    rty1 HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    rty2
          = SwapFlag -> Maybe SwapFlag
    forall a. a -> Maybe a
    Just SwapFlag
    NotSwapped
          | Type
    lty1 HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    rty2, Type
    rty1 HasDebugCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `tcEqType` Type
    lty2
          = SwapFlag -> Maybe SwapFlag
    forall a. a -> Maybe a
    Just SwapFlag
    IsSwapped
          | Bool
    otherwise
          = Maybe SwapFlag
    forall a. Maybe a
    Nothing

    {- Note [Solving irreducible equalities]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider (#14333)
      [G] a b ~R# c d
      [W] c d ~R# a b
    Clearly we should be able to solve this! Even though the constraints are
    not decomposable. We solve this when looking up the work-item in the
    irreducible constraints to look for an identical one.  When doing this
    lookup, findMatchingIrreds spots the equality case, and matches either
    way around. It has to return a swap-flag so we can generate evidence
    that is the right way round too.
    -}

    {- *********************************************************************
    *                                                                      *
                    Adding to and removing from the inert set
    *                                                                      *
    *                                                                      *
    ********************************************************************* -}

    updGivenEqs :: TcLevel -> Ct -> InertCans -> InertCans
    -- Set the inert_given_eq_level to the current level (tclvl)
    -- if the constraint is a given equality that should prevent
    -- filling in an outer unification variable.
    -- See Note [Tracking Given equalities]
    --
    -- Precondition: Ct is either CEqCan or CIrredCan
    updGivenEqs :: TcLevel -> Ct -> InertCans -> InertCans
    updGivenEqs TcLevel
    tclvl Ct
    ct InertCans
    inerts
      | Bool -> Bool
    not (Ct -> Bool
    isGivenCt Ct
    ct) = InertCans
    inerts

      -- See Note [Let-bound skolems]
      | TcLevel -> Ct -> Bool
    isLetBoundSkolemCt TcLevel
    tclvl Ct
    ct = InertCans
    inerts { inert_given_eqs = True }

      -- At this point we are left with a constraint that either
      -- is an equality (F a ~ ty), or /might/ be, like (c a)
      | Bool
    otherwise = InertCans
    inerts { inert_given_eq_lvl = tclvl
                           , inert_given_eqs    = True }

    isLetBoundSkolemCt :: TcLevel -> Ct -> Bool
    -- See Note [Let-bound skolems]
    isLetBoundSkolemCt :: TcLevel -> Ct -> Bool
    isLetBoundSkolemCt TcLevel
    tclvl (CEqCan (EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = CanEqLHS
    lhs, eq_rhs :: EqCt -> Type
    eq_rhs = Type
    rhs }))
      = case CanEqLHS
    lhs of
          TyVarLHS TcTyVar
    tv -> Bool -> Bool
    not (TcLevel -> TcTyVar -> Bool
    isOuterTyVar TcLevel
    tclvl TcTyVar
    tv)
          TyFamLHS {} -> case Type -> Maybe TcTyVar
    getTyVar_maybe Type
    rhs of
                           Just TcTyVar
    tv -> Bool -> Bool
    not (TcLevel -> TcTyVar -> Bool
    isOuterTyVar TcLevel
    tclvl TcTyVar
    tv)
                           Maybe TcTyVar
    Nothing -> Bool
    False
    isLetBoundSkolemCt TcLevel
    _ Ct
    _ = Bool
    False

    data KickOutSpec -- See Note [KickOutSpec]
      = KOAfterUnify  TcTyVarSet   -- We have unified these tyvars
      | KOAfterAdding CanEqLHS     -- We are adding to the inert set a canonical equality
                                   -- constraint with this LHS

    instance Outputable KickOutSpec where
      ppr :: KickOutSpec -> SDoc
    ppr (KOAfterUnify TcTyVarSet
    tvs)  = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "KOAfterUnify" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> TcTyVarSet -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TcTyVarSet
    tvs
      ppr (KOAfterAdding CanEqLHS
    lhs) = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "KOAfterAdding" SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc
    parens (CanEqLHS -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr CanEqLHS
    lhs)

    {- Note [KickOutSpec]
    ~~~~~~~~~~~~~~~~~~~~~~
    KickOutSpec explains why we are kicking out.

    Important property:
      KOAfterAdding (TyVarLHS tv) should behave exactly like
      KOAfterUnifying (unitVarSet tv)

    The main reasons for treating the two separately are
    * More efficient in the single-tyvar case
    * The code is far more perspicuous
    -}

    data WhereToLook = LookEverywhere | LookOnlyUnderFamApps
                       deriving( WhereToLook -> WhereToLook -> Bool
    (WhereToLook -> WhereToLook -> Bool)
    -> (WhereToLook -> WhereToLook -> Bool) -> Eq WhereToLook
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: WhereToLook -> WhereToLook -> Bool
    == :: WhereToLook -> WhereToLook -> Bool
    $c/= :: WhereToLook -> WhereToLook -> Bool
    /= :: WhereToLook -> WhereToLook -> Bool
    Eq )

    kickOutRewritableLHS :: KickOutSpec -> CtFlavourRole -> InertCans -> (Cts, InertCans)
    -- See Note [kickOutRewritable]
    kickOutRewritableLHS :: KickOutSpec -> CtFlavourRole -> InertCans -> (Bag Ct, InertCans)
    kickOutRewritableLHS KickOutSpec
    ko_spec new_fr :: CtFlavourRole
    new_fr@(CtFlavour
    _, EqRel
    new_role)
                         ics :: InertCans
    ics@(IC { inert_eqs :: InertCans -> InertEqs
    inert_eqs      = InertEqs
    tv_eqs
                                 , inert_dicts :: InertCans -> DictMap DictCt
    inert_dicts    = DictMap DictCt
    dictmap
                                 , inert_funeqs :: InertCans -> InertFunEqs
    inert_funeqs   = InertFunEqs
    funeqmap
                                 , inert_irreds :: InertCans -> InertIrreds
    inert_irreds   = InertIrreds
    irreds
                                 , inert_insts :: InertCans -> [QCInst]
    inert_insts    = [QCInst]
    old_insts })
      = (Bag Ct
    kicked_out, InertCans
    inert_cans_in)
      where
        -- inert_safehask stays unchanged; is that right?
        inert_cans_in :: InertCans
    inert_cans_in = InertCans
    ics { inert_eqs      = tv_eqs_in
                            , inert_dicts    = dicts_in
                            , inert_funeqs   = feqs_in
                            , inert_irreds   = irs_in
                            , inert_insts    = insts_in }

        kicked_out :: Cts
        kicked_out :: Bag Ct
    kicked_out = ((DictCt -> Ct) -> Bag DictCt -> Bag Ct
    forall a b. (a -> b) -> Bag a -> Bag b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap DictCt -> Ct
    CDictCan Bag DictCt
    dicts_out Bag Ct -> Bag Ct -> Bag Ct
    `andCts` (IrredCt -> Ct) -> InertIrreds -> Bag Ct
    forall a b. (a -> b) -> Bag a -> Bag b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap IrredCt -> Ct
    CIrredCan InertIrreds
    irs_out)
                      Bag Ct -> [Ct] -> Bag Ct
    `extendCtsList` [Ct]
    insts_out
                      Bag Ct -> [Ct] -> Bag Ct
    `extendCtsList` (EqCt -> Ct) -> EqualCtList -> [Ct]
    forall a b. (a -> b) -> [a] -> [b]
    map EqCt -> Ct
    CEqCan EqualCtList
    tv_eqs_out
                      Bag Ct -> [Ct] -> Bag Ct
    `extendCtsList` (EqCt -> Ct) -> EqualCtList -> [Ct]
    forall a b. (a -> b) -> [a] -> [b]
    map EqCt -> Ct
    CEqCan EqualCtList
    feqs_out

        (EqualCtList
    tv_eqs_out, InertEqs
    tv_eqs_in) = (EqCt -> Bool) -> InertEqs -> (EqualCtList, InertEqs)
    partitionInertEqs EqCt -> Bool
    kick_out_eq InertEqs
    tv_eqs
        (EqualCtList
    feqs_out,   InertFunEqs
    feqs_in)   = (EqCt -> Bool) -> InertFunEqs -> (EqualCtList, InertFunEqs)
    partitionFunEqs   EqCt -> Bool
    kick_out_eq InertFunEqs
    funeqmap
        (Bag DictCt
    dicts_out,  DictMap DictCt
    dicts_in)  = (DictCt -> Bool) -> DictMap DictCt -> (Bag DictCt, DictMap DictCt)
    partitionDicts    DictCt -> Bool
    kick_out_dict DictMap DictCt
    dictmap
        (InertIrreds
    irs_out,    InertIrreds
    irs_in)    = (IrredCt -> Bool) -> InertIrreds -> (InertIrreds, InertIrreds)
    forall a. (a -> Bool) -> Bag a -> (Bag a, Bag a)
    partitionBag      IrredCt -> Bool
    kick_out_irred InertIrreds
    irreds
          -- Kick out even insolubles: See Note [Rewrite insolubles]
          -- Of course we must kick out irreducibles like (c a), in case
          -- we can rewrite 'c' to something more useful

        -- Kick-out for inert instances
        -- See Note [Quantified constraints] in GHC.Tc.Solver.Solve
        insts_out :: [Ct]
        insts_in  :: [QCInst]
        ([Ct]
    insts_out, [QCInst]
    insts_in)
           | CtFlavourRole -> Bool
    fr_may_rewrite (CtFlavour
    Given, EqRel
    NomEq)  -- All the insts are Givens
           = (QCInst -> Either Ct QCInst) -> [QCInst] -> ([Ct], [QCInst])
    forall a b c. (a -> Either b c) -> [a] -> ([b], [c])
    partitionWith QCInst -> Either Ct QCInst
    kick_out_qci [QCInst]
    old_insts
           | Bool
    otherwise
           = ([], [QCInst]
    old_insts)
        kick_out_qci :: QCInst -> Either Ct QCInst
    kick_out_qci QCInst
    qci
          | let ev :: CtEvidence
    ev = QCInst -> CtEvidence
    qci_ev QCInst
    qci
          , WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    LookEverywhere EqRel
    NomEq (CtEvidence -> Type
    ctEvPred (QCInst -> CtEvidence
    qci_ev QCInst
    qci))
          = Ct -> Either Ct QCInst
    forall a b. a -> Either a b
    Left (CtEvidence -> Ct
    mkNonCanonical CtEvidence
    ev)
          | Bool
    otherwise
          = QCInst -> Either Ct QCInst
    forall a b. b -> Either a b
    Right QCInst
    qci

        fr_tv_can_rewrite_ty :: WhereToLook -> (TyVar -> Bool) -> EqRel -> Type -> Bool
        fr_tv_can_rewrite_ty :: WhereToLook -> (TcTyVar -> Bool) -> EqRel -> Type -> Bool
    fr_tv_can_rewrite_ty WhereToLook
    where_to_look TcTyVar -> Bool
    check_tv EqRel
    role Type
    ty
          = EqRel -> (Bool -> EqRel -> TcTyVar -> Bool) -> Type -> Bool
    anyRewritableTyVar EqRel
    role Bool -> EqRel -> TcTyVar -> Bool
    can_rewrite Type
    ty
          where
            can_rewrite :: UnderFam -> EqRel -> TyVar -> Bool
            can_rewrite :: Bool -> EqRel -> TcTyVar -> Bool
    can_rewrite Bool
    is_under_famapp EqRel
    old_role TcTyVar
    tv
               = (WhereToLook
    where_to_look WhereToLook -> WhereToLook -> Bool
    forall a. Eq a => a -> a -> Bool
    == WhereToLook
    LookEverywhere Bool -> Bool -> Bool
    || Bool
    is_under_famapp) Bool -> Bool -> Bool
    &&
                 EqRel
    new_role EqRel -> EqRel -> Bool
    `eqCanRewrite` EqRel
    old_role Bool -> Bool -> Bool
    && TcTyVar -> Bool
    check_tv TcTyVar
    tv

        fr_tf_can_rewrite_ty :: WhereToLook -> TyCon -> [TcType] -> EqRel -> Type -> Bool
        fr_tf_can_rewrite_ty :: WhereToLook -> TyCon -> [Type] -> EqRel -> Type -> Bool
    fr_tf_can_rewrite_ty WhereToLook
    where_to_look TyCon
    new_tf [Type]
    new_tf_args EqRel
    role Type
    ty
          = EqRel -> (Bool -> EqRel -> TyCon -> [Type] -> Bool) -> Type -> Bool
    anyRewritableTyFamApp EqRel
    role Bool -> EqRel -> TyCon -> [Type] -> Bool
    can_rewrite Type
    ty
          where
            can_rewrite :: UnderFam -> EqRel -> TyCon -> [TcType] -> Bool
            can_rewrite :: Bool -> EqRel -> TyCon -> [Type] -> Bool
    can_rewrite Bool
    is_under_famapp EqRel
    old_role TyCon
    old_tf [Type]
    old_tf_args
              = (WhereToLook
    where_to_look WhereToLook -> WhereToLook -> Bool
    forall a. Eq a => a -> a -> Bool
    == WhereToLook
    LookEverywhere Bool -> Bool -> Bool
    || Bool
    is_under_famapp) Bool -> Bool -> Bool
    &&
                EqRel
    new_role EqRel -> EqRel -> Bool
    `eqCanRewrite` EqRel
    old_role Bool -> Bool -> Bool
    &&
                TyCon -> [Type] -> TyCon -> [Type] -> Bool
    tcEqTyConApps TyCon
    new_tf [Type]
    new_tf_args TyCon
    old_tf [Type]
    old_tf_args
                  -- it's possible for old_tf_args to have too many. This is fine;
                  -- we'll only check what we need to.

        fr_can_rewrite_ty :: WhereToLook -> EqRel -> Type -> Bool
        -- UnderFam = True <=> look only under type-family applications
        fr_can_rewrite_ty :: WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    uf = case KickOutSpec
    ko_spec of  -- See Note [KickOutSpec]
          KOAfterUnify TcTyVarSet
    tvs                    -> WhereToLook -> (TcTyVar -> Bool) -> EqRel -> Type -> Bool
    fr_tv_can_rewrite_ty WhereToLook
    uf (TcTyVar -> TcTyVarSet -> Bool
    `elemVarSet` TcTyVarSet
    tvs)
          KOAfterAdding (TyVarLHS TcTyVar
    tv)         -> WhereToLook -> (TcTyVar -> Bool) -> EqRel -> Type -> Bool
    fr_tv_can_rewrite_ty WhereToLook
    uf (TcTyVar -> TcTyVar -> Bool
    forall a. Eq a => a -> a -> Bool
    == TcTyVar
    tv)
          KOAfterAdding (TyFamLHS TyCon
    tf [Type]
    tf_args) -> WhereToLook -> TyCon -> [Type] -> EqRel -> Type -> Bool
    fr_tf_can_rewrite_ty WhereToLook
    uf TyCon
    tf [Type]
    tf_args

        fr_may_rewrite :: CtFlavourRole -> Bool
        fr_may_rewrite :: CtFlavourRole -> Bool
    fr_may_rewrite CtFlavourRole
    fs = CtFlavourRole
    new_fr CtFlavourRole -> CtFlavourRole -> Bool
    `eqCanRewriteFR` CtFlavourRole
    fs
            -- Can the new item rewrite the inert item?

        kick_out_dict :: DictCt -> Bool
        -- Kick it out if the new CEqCan can rewrite the inert one
        -- See Note [kickOutRewritable]
        kick_out_dict :: DictCt -> Bool
    kick_out_dict (DictCt { di_tys :: DictCt -> [Type]
    di_tys = [Type]
    tys, di_ev :: DictCt -> CtEvidence
    di_ev = CtEvidence
    ev })
          =  CtFlavourRole -> Bool
    fr_may_rewrite (CtEvidence -> CtFlavour
    ctEvFlavour CtEvidence
    ev, EqRel
    NomEq)
          Bool -> Bool -> Bool
    && (Type -> Bool) -> [Type] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    any (WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    LookEverywhere EqRel
    NomEq) [Type]
    tys

        kick_out_irred :: IrredCt -> Bool
        kick_out_irred :: IrredCt -> Bool
    kick_out_irred (IrredCt { ir_ev :: IrredCt -> CtEvidence
    ir_ev = CtEvidence
    ev })
          =  CtFlavourRole -> Bool
    fr_may_rewrite (CtEvidence -> CtFlavour
    ctEvFlavour CtEvidence
    ev, EqRel
    eq_rel)
          Bool -> Bool -> Bool
    && WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    LookEverywhere EqRel
    eq_rel Type
    pred
          where
           pred :: Type
    pred   = CtEvidence -> Type
    ctEvPred CtEvidence
    ev
           eq_rel :: EqRel
    eq_rel = Type -> EqRel
    predTypeEqRel Type
    pred

        -- Implements criteria K1-K3 in Note [Extending the inert equalities]
        kick_out_eq :: EqCt -> Bool
        kick_out_eq :: EqCt -> Bool
    kick_out_eq (EqCt { eq_lhs :: EqCt -> CanEqLHS
    eq_lhs = CanEqLHS
    lhs, eq_rhs :: EqCt -> Type
    eq_rhs = Type
    rhs_ty
                          , eq_ev :: EqCt -> CtEvidence
    eq_ev = CtEvidence
    ev, eq_eq_rel :: EqCt -> EqRel
    eq_eq_rel = EqRel
    eq_rel })

          -- (KK0) Keep it in the inert set if the new thing can't rewrite it
          | Bool -> Bool
    not (CtFlavourRole -> Bool
    fr_may_rewrite CtFlavourRole
    fs)
          = Bool
    False

          -- Below here (fr_may_rewrite fs) is True

          -- (KK1)
          | WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    LookEverywhere EqRel
    eq_rel (CanEqLHS -> Type
    canEqLHSType CanEqLHS
    lhs)
          = Bool
    True   -- (KK1)
             -- The above check redundantly checks the role & flavour,
             -- but it's very convenient

          -- (KK2)
          | let where_to_look :: WhereToLook
    where_to_look | Bool
    fs_can_rewrite_fr = WhereToLook
    LookOnlyUnderFamApps
                              | Bool
    otherwise         = WhereToLook
    LookEverywhere
          , WhereToLook -> EqRel -> Type -> Bool
    fr_can_rewrite_ty WhereToLook
    where_to_look EqRel
    eq_rel Type
    rhs_ty
          = Bool
    True

          -- (KK3)
          | Bool -> Bool
    not Bool
    fs_can_rewrite_fr                    -- (KK3a)
          , case EqRel
    eq_rel of
                  EqRel
    NomEq  -> Type -> Bool
    is_new_lhs      Type
    rhs_ty   -- (KK3b)
                  EqRel
    ReprEq -> Type -> Bool
    head_is_new_lhs Type
    rhs_ty   -- (KK3c)
          = Bool
    True

          | Bool
    otherwise = Bool
    False

          where
            fs_can_rewrite_fr :: Bool
    fs_can_rewrite_fr = CtFlavourRole
    fs CtFlavourRole -> CtFlavourRole -> Bool
    `eqCanRewriteFR` CtFlavourRole
    new_fr
            fs :: CtFlavourRole
    fs = (CtEvidence -> CtFlavour
    ctEvFlavour CtEvidence
    ev, EqRel
    eq_rel)

        is_new_lhs :: Type -> Bool
        is_new_lhs :: Type -> Bool
    is_new_lhs = case KickOutSpec
    ko_spec of   -- See Note [KickOutSpec]
              KOAfterUnify TcTyVarSet
    tvs  -> TcTyVarSet -> Type -> Bool
    is_tyvar_ty_for TcTyVarSet
    tvs
              KOAfterAdding CanEqLHS
    lhs -> (HasCallStack => Type -> Type -> Bool
    Type -> Type -> Bool
    `eqType` CanEqLHS -> Type
    canEqLHSType CanEqLHS
    lhs)

        is_tyvar_ty_for :: TcTyVarSet -> Type -> Bool
        -- True if the type is equal to one of the tyvars
        is_tyvar_ty_for :: TcTyVarSet -> Type -> Bool
    is_tyvar_ty_for TcTyVarSet
    tvs Type
    ty
          = case Type -> Maybe TcTyVar
    getTyVar_maybe Type
    ty of
              Maybe TcTyVar
    Nothing -> Bool
    False
              Just TcTyVar
    tv -> TcTyVar
    tv TcTyVar -> TcTyVarSet -> Bool
    `elemVarSet` TcTyVarSet
    tvs

        head_is_new_lhs :: Type -> Bool
        head_is_new_lhs :: Type -> Bool
    head_is_new_lhs = case KickOutSpec
    ko_spec of   -- See Note [KickOutSpec]
              KOAfterUnify TcTyVarSet
    tvs                    -> (TcTyVar -> Bool) -> Type -> Bool
    tv_at_head (TcTyVar -> TcTyVarSet -> Bool
    `elemVarSet` TcTyVarSet
    tvs)
              KOAfterAdding (TyVarLHS TcTyVar
    tv)         -> (TcTyVar -> Bool) -> Type -> Bool
    tv_at_head (TcTyVar -> TcTyVar -> Bool
    forall a. Eq a => a -> a -> Bool
    == TcTyVar
    tv)
              KOAfterAdding (TyFamLHS TyCon
    tf [Type]
    tf_args) -> TyCon -> [Type] -> Type -> Bool
    fam_at_head TyCon
    tf [Type]
    tf_args

        tv_at_head :: (TyVar -> Bool) -> Type -> Bool
        tv_at_head :: (TcTyVar -> Bool) -> Type -> Bool
    tv_at_head TcTyVar -> Bool
    is_tv = Type -> Bool
    go
          where
            go :: Type -> Bool
    go (Rep.TyVarTy TcTyVar
    tv)    = TcTyVar -> Bool
    is_tv TcTyVar
    tv
            go (Rep.AppTy Type
    fun Type
    _)   = Type -> Bool
    go Type
    fun
            go (Rep.CastTy Type
    ty KindCoercion
    _)   = Type -> Bool
    go Type
    ty
            go (Rep.TyConApp {})   = Bool
    False
            go (Rep.LitTy {})      = Bool
    False
            go (Rep.ForAllTy {})   = Bool
    False
            go (Rep.FunTy {})      = Bool
    False
            go (Rep.CoercionTy {}) = Bool
    False

        fam_at_head :: TyCon -> [Type] -> Type -> Bool
        fam_at_head :: TyCon -> [Type] -> Type -> Bool
    fam_at_head TyCon
    fun_tc [Type]
    fun_args = Type -> Bool
    go
          where
            go :: Type -> Bool
    go (Rep.TyVarTy {})       = Bool
    False
            go (Rep.AppTy {})         = Bool
    False  -- no TyConApp to the left of an AppTy
            go (Rep.CastTy Type
    ty KindCoercion
    _)      = Type -> Bool
    go Type
    ty
            go (Rep.TyConApp TyCon
    tc [Type]
    args) = TyCon -> [Type] -> TyCon -> [Type] -> Bool
    tcEqTyConApps TyCon
    fun_tc [Type]
    fun_args TyCon
    tc [Type]
    args
            go (Rep.LitTy {})         = Bool
    False
            go (Rep.ForAllTy {})      = Bool
    False
            go (Rep.FunTy {})         = Bool
    False
            go (Rep.CoercionTy {})    = Bool
    False

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

    When we add a new inert equality (lhs ~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) 'lhs' is free in the inert constraint (so that it *will*)
           rewrite it if we kick it out.

        For (b) we use anyRewritableCanLHS, which examines the types /and
        kinds/ 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 LHS!

      - 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

    NB: we could in principle avoid kick-out:
      a) When unifying a meta-tyvar from an outer level, because
         then the entire implication will be iterated; see
         Note [The Unification Level Flag] in GHC.Tc.Solver.Monad.

      b) For Givens, after a unification.  By (GivenInv) in GHC.Tc.Utils.TcType
         Note [TcLevel invariants], a Given can't include a meta-tyvar from
         its own level, so it falls under (a).  Of course, we must still
         kick out Givens when adding a new non-unification Given.

    But kicking out more vigorously may lead to earlier unification and fewer
    iterations, so we don't take advantage of these possibilities.

    Note [Rewrite 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.

    Hence:
     * In the main simplifier loops in GHC.Tc.Solver (solveWanteds,
       simpl_loop), we feed the insolubles in solveSimpleWanteds,
       so that they get rewritten (albeit not solved).

     * We kick insolubles out of the inert set, if they can be
       rewritten (see GHC.Tc.Solver.Monad.kick_out_rewritable)

     * We rewrite those insolubles in GHC.Tc.Solver.Equality
       See Note [Make sure that insolubles are fully rewritten]
       in GHC.Tc.Solver.Equality
    -}

    {- *********************************************************************
    *                                                                      *
                     Queries
    *                                                                      *
    *                                                                      *
    ********************************************************************* -}

    isOuterTyVar :: TcLevel -> TyCoVar -> Bool
    -- True of a type variable that comes from a
    -- shallower level than the ambient level (tclvl)
    isOuterTyVar :: TcLevel -> TcTyVar -> Bool
    isOuterTyVar TcLevel
    tclvl TcTyVar
    tv
      | TcTyVar -> Bool
    isTyVar TcTyVar
    tv = Bool -> SDoc -> Bool -> Bool
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (Bool -> Bool
    not (TcLevel -> TcTyVar -> Bool
    isTouchableMetaTyVar TcLevel
    tclvl TcTyVar
    tv)) (TcTyVar -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TcTyVar
    tv SDoc -> SDoc -> SDoc
    forall doc. IsLine doc => doc -> doc -> doc
    <+> TcLevel -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TcLevel
    tclvl) (Bool -> Bool) -> Bool -> Bool
    forall a b. (a -> b) -> a -> b
    $
                     TcLevel
    tclvl TcLevel -> TcLevel -> Bool
    `strictlyDeeperThan` TcTyVar -> TcLevel
    tcTyVarLevel TcTyVar
    tv
        -- ASSERT: we are dealing with Givens here, and invariant (GivenInv) from
        -- Note Note [TcLevel invariants] in GHC.Tc.Utils.TcType ensures that there can't
        -- be a touchable meta tyvar.   If this wasn't true, you might worry that,
        -- at level 3, a meta-tv alpha[3] gets unified with skolem b[2], and thereby
        -- becomes "outer" even though its level numbers says it isn't.
      | Bool
    otherwise  = Bool
    False  -- Coercion variables; doesn't much matter

    noGivenNewtypeReprEqs :: TyCon -> InertSet -> Bool
    -- True <=> there is no Irred looking like (N tys1 ~ N tys2)
    -- See Note [Decomposing newtype equalities] (EX2) in GHC.Tc.Solver.Equality
    --     This is the only call site.
    noGivenNewtypeReprEqs :: TyCon -> InertSet -> Bool
    noGivenNewtypeReprEqs TyCon
    tc InertSet
    inerts
      = Bool -> Bool
    not ((IrredCt -> Bool) -> InertIrreds -> Bool
    forall a. (a -> Bool) -> Bag a -> Bool
    anyBag IrredCt -> Bool
    might_help (InertCans -> InertIrreds
    inert_irreds (InertSet -> InertCans
    inert_cans InertSet
    inerts)))
      where
        might_help :: IrredCt -> Bool
    might_help IrredCt
    irred
          = case Type -> Pred
    classifyPredType (CtEvidence -> Type
    ctEvPred (IrredCt -> CtEvidence
    irredCtEvidence IrredCt
    irred)) of
              EqPred EqRel
    ReprEq Type
    t1 Type
    t2
                 | Just (TyCon
    tc1,[Type]
    _) <- HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    t1
                 , TyCon
    tc TyCon -> TyCon -> Bool
    forall a. Eq a => a -> a -> Bool
    == TyCon
    tc1
                 , Just (TyCon
    tc2,[Type]
    _) <- HasDebugCallStack => Type -> Maybe (TyCon, [Type])
    Type -> Maybe (TyCon, [Type])
    tcSplitTyConApp_maybe Type
    t2
                 , TyCon
    tc TyCon -> TyCon -> Bool
    forall a. Eq a => a -> a -> Bool
    == TyCon
    tc2
                 -> Bool
    True
              Pred
    _  -> Bool
    False

    -- | Returns True iff there are no Given constraints that might,
    -- potentially, match the given class constraint. This is used when checking to see if a
    -- Given might overlap with an instance. See Note [Instance and Given overlap]
    -- in GHC.Tc.Solver.Dict
    noMatchableGivenDicts :: InertSet -> CtLoc -> Class -> [TcType] -> Bool
    noMatchableGivenDicts :: InertSet -> CtLoc -> Class -> [Type] -> Bool
    noMatchableGivenDicts inerts :: InertSet
    inerts@(IS { inert_cans :: InertSet -> InertCans
    inert_cans = InertCans
    inert_cans }) CtLoc
    loc_w Class
    clas [Type]
    tys
      = Bool -> Bool
    not (Bool -> Bool) -> Bool -> Bool
    forall a b. (a -> b) -> a -> b
    $ (DictCt -> Bool) -> Bag DictCt -> Bool
    forall a. (a -> Bool) -> Bag a -> Bool
    anyBag DictCt -> Bool
    matchable_given (Bag DictCt -> Bool) -> Bag DictCt -> Bool
    forall a b. (a -> b) -> a -> b
    $
        DictMap DictCt -> Class -> Bag DictCt
    forall a. DictMap a -> Class -> Bag a
    findDictsByClass (InertCans -> DictMap DictCt
    inert_dicts InertCans
    inert_cans) Class
    clas
      where
        pred_w :: Type
    pred_w = Class -> [Type] -> Type
    mkClassPred Class
    clas [Type]
    tys

        matchable_given :: DictCt -> Bool
        matchable_given :: DictCt -> Bool
    matchable_given (DictCt { di_ev :: DictCt -> CtEvidence
    di_ev = CtEvidence
    ev })
          | CtGiven { ctev_loc :: CtEvidence -> CtLoc
    ctev_loc = CtLoc
    loc_g, ctev_pred :: CtEvidence -> Type
    ctev_pred = Type
    pred_g } <- CtEvidence
    ev
          = Maybe Subst -> Bool
    forall a. Maybe a -> Bool
    isJust (Maybe Subst -> Bool) -> Maybe Subst -> Bool
    forall a b. (a -> b) -> a -> b
    $ InertSet -> Type -> CtLoc -> Type -> CtLoc -> Maybe Subst
    mightEqualLater InertSet
    inerts Type
    pred_g CtLoc
    loc_g Type
    pred_w CtLoc
    loc_w

          | Bool
    otherwise
          = Bool
    False

    mightEqualLater :: InertSet -> TcPredType -> CtLoc -> TcPredType -> CtLoc -> Maybe Subst
    -- See Note [What might equal later?]
    -- Used to implement logic in Note [Instance and Given overlap] in GHC.Tc.Solver.Dict
    mightEqualLater :: InertSet -> Type -> CtLoc -> Type -> CtLoc -> Maybe Subst
    mightEqualLater InertSet
    inert_set Type
    given_pred CtLoc
    given_loc Type
    wanted_pred CtLoc
    wanted_loc
      | CtLoc -> CtLoc -> Bool
    prohibitedSuperClassSolve CtLoc
    given_loc CtLoc
    wanted_loc
      = Maybe Subst
    forall a. Maybe a
    Nothing

      | Bool
    otherwise
      = case BindFun -> [Type] -> [Type] -> UnifyResult
    tcUnifyTysFG BindFun
    bind_fun [Type
    flattened_given] [Type
    flattened_wanted] of
          Unifiable Subst
    subst
            -> Subst -> Maybe Subst
    forall a. a -> Maybe a
    Just Subst
    subst
          MaybeApart MaybeApartReason
    reason Subst
    subst
            | MaybeApartReason
    MARInfinite <- MaybeApartReason
    reason -- see Example 7 in the Note.
            -> Maybe Subst
    forall a. Maybe a
    Nothing
            | Bool
    otherwise
            -> Subst -> Maybe Subst
    forall a. a -> Maybe a
    Just Subst
    subst
          UnifyResult
    SurelyApart -> Maybe Subst
    forall a. Maybe a
    Nothing

      where
        in_scope :: InScopeSet
    in_scope  = TcTyVarSet -> InScopeSet
    mkInScopeSet (TcTyVarSet -> InScopeSet) -> TcTyVarSet -> InScopeSet
    forall a b. (a -> b) -> a -> b
    $ [Type] -> TcTyVarSet
    tyCoVarsOfTypes [Type
    given_pred, Type
    wanted_pred]

        -- NB: flatten both at the same time, so that we can share mappings
        -- from type family applications to variables, and also to guarantee
        -- that the fresh variables are really fresh between the given and
        -- the wanted. Flattening both at the same time is needed to get
        -- Example 10 from the Note.
        ([Type
    flattened_given, Type
    flattened_wanted], TyVarEnv (TyCon, [Type])
    var_mapping)
          = InScopeSet -> [Type] -> ([Type], TyVarEnv (TyCon, [Type]))
    flattenTysX InScopeSet
    in_scope [Type
    given_pred, Type
    wanted_pred]

        bind_fun :: BindFun
        bind_fun :: BindFun
    bind_fun TcTyVar
    tv Type
    rhs_ty
          | TcTyVar -> Bool
    isMetaTyVar TcTyVar
    tv
          , TcTyVar -> MetaInfo -> Type -> Bool
    can_unify TcTyVar
    tv (TcTyVar -> MetaInfo
    metaTyVarInfo TcTyVar
    tv) Type
    rhs_ty
             -- this checks for CycleBreakerTvs and TyVarTvs; forgetting
             -- the latter was #19106.
          = BindFlag
    BindMe

             -- See Examples 4, 5, and 6 from the Note
          | Just (TyCon
    _fam_tc, [Type]
    fam_args) <- TyVarEnv (TyCon, [Type]) -> TcTyVar -> Maybe (TyCon, [Type])
    forall a. VarEnv a -> TcTyVar -> Maybe a
    lookupVarEnv TyVarEnv (TyCon, [Type])
    var_mapping TcTyVar
    tv
          , (TcTyVar -> Bool) -> [Type] -> Bool
    anyFreeVarsOfTypes TcTyVar -> Bool
    mentions_meta_ty_var [Type]
    fam_args
          = BindFlag
    BindMe

          | Bool
    otherwise
          = BindFlag
    Apart

        -- True for TauTv and TyVarTv (and RuntimeUnkTv) meta-tyvars
        -- (as they can be unified)
        -- and also for CycleBreakerTvs that mentions meta-tyvars
        mentions_meta_ty_var :: TyVar -> Bool
        mentions_meta_ty_var :: TcTyVar -> Bool
    mentions_meta_ty_var TcTyVar
    tv
          | TcTyVar -> Bool
    isMetaTyVar TcTyVar
    tv
          = case TcTyVar -> MetaInfo
    metaTyVarInfo TcTyVar
    tv of
              -- See Examples 8 and 9 in the Note
              MetaInfo
    CycleBreakerTv
                -> (TcTyVar -> Bool) -> Type -> Bool
    anyFreeVarsOfType TcTyVar -> Bool
    mentions_meta_ty_var
                     (TcTyVar -> InertSet -> Type
    lookupCycleBreakerVar TcTyVar
    tv InertSet
    inert_set)
              MetaInfo
    _ -> Bool
    True
          | Bool
    otherwise
          = Bool
    False

        -- Like checkTopShape, but allows cbv variables to unify
        can_unify :: TcTyVar -> MetaInfo -> Type -> Bool
        can_unify :: TcTyVar -> MetaInfo -> Type -> Bool
    can_unify TcTyVar
    _lhs_tv MetaInfo
    TyVarTv Type
    rhs_ty  -- see Example 3 from the Note
          | Just TcTyVar
    rhs_tv <- Type -> Maybe TcTyVar
    getTyVar_maybe Type
    rhs_ty
          = case TcTyVar -> TcTyVarDetails
    tcTyVarDetails TcTyVar
    rhs_tv of
              MetaTv { mtv_info :: TcTyVarDetails -> MetaInfo
    mtv_info = MetaInfo
    TyVarTv } -> Bool
    True
              MetaTv {}                     -> Bool
    False  -- Could unify with anything
              SkolemTv {}                   -> Bool
    True
              TcTyVarDetails
    RuntimeUnk                    -> Bool
    True
          | Bool
    otherwise  -- not a var on the RHS
          = Bool
    False
        can_unify TcTyVar
    lhs_tv MetaInfo
    _other Type
    _rhs_ty = TcTyVar -> Bool
    mentions_meta_ty_var TcTyVar
    lhs_tv

    -- | Is it (potentially) loopy to use the first @ct1@ to solve @ct2@?
    --
    -- Necessary (but not sufficient) conditions for this function to return @True@:
    --
    --   - @ct1@ and @ct2@ both arise from superclass expansion,
    --   - @ct1@ is a Given and @ct2@ is a Wanted.
    --
    -- See Note [Solving superclass constraints] in GHC.Tc.TyCl.Instance, (sc2).
    prohibitedSuperClassSolve :: CtLoc -- ^ is it loopy to use this one ...
                              -> CtLoc -- ^ ... to solve this one?
                              -> Bool  -- ^ True ==> don't solve it
    prohibitedSuperClassSolve :: CtLoc -> CtLoc -> Bool
    prohibitedSuperClassSolve CtLoc
    given_loc CtLoc
    wanted_loc
      | GivenSCOrigin SkolemInfoAnon
    _ ScDepth
    _ Bool
    blocked <- CtLoc -> CtOrigin
    ctLocOrigin CtLoc
    given_loc
      , Bool
    blocked
      , ScOrigin ClsInstOrQC
    _ NakedScFlag
    NakedSc <- CtLoc -> CtOrigin
    ctLocOrigin CtLoc
    wanted_loc
      = Bool
    True    -- Prohibited if the Wanted is a superclass
                -- and the Given has come via a superclass selection from
                -- a predicate bigger than the head
      | Bool
    otherwise
      = Bool
    False

    {- Note [What might equal later?]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We must determine whether a Given might later equal a Wanted. We
    definitely need to account for the possibility that any metavariable
    might be arbitrarily instantiated. Yet we do *not* want
    to allow skolems in to be instantiated, as we've already rewritten
    with respect to any Givens. (We're solving a Wanted here, and so
    all Givens have already been processed.)

    This is best understood by example.

    1. C alpha  ~?  C Int

       That given certainly might match later.

    2. C a  ~?  C Int

       No. No new givens are going to arise that will get the `a` to rewrite
       to Int.

    3. C alpha[tv]   ~?  C Int

       That alpha[tv] is a TyVarTv, unifiable only with other type variables.
       It cannot equal later.

    4. C (F alpha)   ~?   C Int

       Sure -- that can equal later, if we learn something useful about alpha.

    5. C (F alpha[tv])  ~?  C Int

       This, too, might equal later. Perhaps we have [G] F b ~ Int elsewhere.
       Or maybe we have C (F alpha[tv] beta[tv]), these unify with each other,
       and F x x = Int. Remember: returning True doesn't commit ourselves to
       anything.

    6. C (F a)  ~?  C a

       No, this won't match later. If we could rewrite (F a) or a, we would
       have by now. But see also Red Herring below.

    7. C (Maybe alpha)  ~?  C alpha

       We say this cannot equal later, because it would require
       alpha := Maybe (Maybe (Maybe ...)). While such a type can be contrived,
       we choose not to worry about it. See Note [Infinitary substitution in lookup]
       in GHC.Core.InstEnv. Getting this wrong let to #19107, tested in
       typecheck/should_compile/T19107.

    8. C cbv   ~?  C Int
       where cbv = F a

       The cbv is a cycle-breaker var which stands for F a. See
       Note [Type equality cycles] in GHC.Tc.Solver.Equality
       This is just like case 6, and we say "no". Saying "no" here is
       essential in getting the parser to type-check, with its use of DisambECP.

    9. C cbv   ~?   C Int
       where cbv = F alpha

       Here, we might indeed equal later. Distinguishing between
       this case and Example 8 is why we need the InertSet in mightEqualLater.

    10. C (F alpha, Int)  ~?  C (Bool, F alpha)

       This cannot equal later, because F a would have to equal both Bool and
       Int.

    To deal with type family applications, we use the Core flattener. See
    Note [Flattening type-family applications when matching instances] in GHC.Core.Unify.
    The Core flattener replaces all type family applications with
    fresh variables. The next question: should we allow these fresh
    variables in the domain of a unifying substitution?

    A type family application that mentions only skolems (example 6) is settled:
    any skolems would have been rewritten w.r.t. Givens by now. These type family
    applications match only themselves. A type family application that mentions
    metavariables, on the other hand, can match anything. So, if the original type
    family application contains a metavariable, we use BindMe to tell the unifier
    to allow it in the substitution. On the other hand, a type family application
    with only skolems is considered rigid.

    This treatment fixes #18910 and is tested in
    typecheck/should_compile/InstanceGivenOverlap{,2}

    Red Herring
    ~~~~~~~~~~~
    In #21208, we have this scenario:

    instance forall b. C b
    [G] C a[sk]
    [W] C (F a[sk])

    What should we do with that wanted? According to the logic above, the Given
    cannot match later (this is example 6), and so we use the global instance.
    But wait, you say: What if we learn later (say by a future type instance F a = a)
    that F a unifies with a? That looks like the Given might really match later!

    This mechanism described in this Note is *not* about this kind of situation, however.
    It is all asking whether a Given might match the Wanted *in this run of the solver*.
    It is *not* about whether a variable might be instantiated so that the Given matches,
    or whether a type instance introduced in a downstream module might make the Given match.
    The reason we care about what might match later is only about avoiding order-dependence.
    That is, we don't want to commit to a course of action that depends on seeing constraints
    in a certain order. But an instantiation of a variable and a later type instance
    don't introduce order dependency in this way, and so mightMatchLater is right to ignore
    these possibilities.

    Here is an example, with no type families, that is perhaps clearer:

    instance forall b. C (Maybe b)
    [G] C (Maybe Int)
    [W] C (Maybe a)

    What to do? We *might* say that the Given could match later and should thus block
    us from using the global instance. But we don't do this. Instead, we rely on class
    coherence to say that choosing the global instance is just fine, even if later we
    call a function with (a := Int). After all, in this run of the solver, [G] C (Maybe Int)
    will definitely never match [W] C (Maybe a). (Recall that we process Givens before
    Wanteds, so there is no [G] a ~ Int hanging about unseen.)

    Interestingly, in the first case (from #21208), the behavior changed between
    GHC 8.10.7 and GHC 9.2, with the latter behaving correctly and the former
    reporting overlapping instances.

    Test case: typecheck/should_compile/T21208.

    -}

    {- *********************************************************************
    *                                                                      *
        Cycle breakers
    *                                                                      *
    ********************************************************************* -}

    -- | Return the type family application a CycleBreakerTv maps to.
    lookupCycleBreakerVar :: TcTyVar    -- ^ cbv, must be a CycleBreakerTv
                          -> InertSet
                          -> TcType     -- ^ type family application the cbv maps to
    lookupCycleBreakerVar :: TcTyVar -> InertSet -> Type
    lookupCycleBreakerVar TcTyVar
    cbv (IS { inert_cycle_breakers :: InertSet -> CycleBreakerVarStack
    inert_cycle_breakers = CycleBreakerVarStack
    cbvs_stack })
    -- This function looks at every environment in the stack. This is necessary
    -- to avoid #20231. This function (and its one usage site) is the only reason
    -- that we store a stack instead of just the top environment.
      | Just Type
    tyfam_app <- Bool -> Maybe Type -> Maybe Type
    forall a. HasCallStack => Bool -> a -> a
    assert (TcTyVar -> Bool
    isCycleBreakerTyVar TcTyVar
    cbv) (Maybe Type -> Maybe Type) -> Maybe Type -> Maybe Type
    forall a b. (a -> b) -> a -> b
    $
                          NonEmpty (Maybe Type) -> Maybe Type
    forall (f :: * -> *) a. Foldable f => f (Maybe a) -> Maybe a
    firstJusts ((Bag (TcTyVar, Type) -> Maybe Type)
    -> CycleBreakerVarStack -> NonEmpty (Maybe Type)
    forall a b. (a -> b) -> NonEmpty a -> NonEmpty b
    NE.map (TcTyVar -> Bag (TcTyVar, Type) -> Maybe Type
    forall a b. Eq a => a -> Bag (a, b) -> Maybe b
    lookupBag TcTyVar
    cbv) CycleBreakerVarStack
    cbvs_stack)
      = Type
    tyfam_app
      | Bool
    otherwise
      = String -> SDoc -> Type
    forall a. HasCallStack => String -> SDoc -> a
    pprPanic String
    "lookupCycleBreakerVar found an unbound cycle breaker" (TcTyVar -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr TcTyVar
    cbv SDoc -> SDoc -> SDoc
    forall doc. IsDoc doc => doc -> doc -> doc
    $$ CycleBreakerVarStack -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr CycleBreakerVarStack
    cbvs_stack)

    -- | Push a fresh environment onto the cycle-breaker var stack. Useful
    -- when entering a nested implication.
    pushCycleBreakerVarStack :: CycleBreakerVarStack -> CycleBreakerVarStack
    pushCycleBreakerVarStack :: CycleBreakerVarStack -> CycleBreakerVarStack
    pushCycleBreakerVarStack = (Bag (TcTyVar, Type)
    forall a. Bag a
    emptyBag Bag (TcTyVar, Type) -> CycleBreakerVarStack -> CycleBreakerVarStack
    forall a. a -> NonEmpty a -> NonEmpty a
    <|)

    -- | Add a new cycle-breaker binding to the top environment on the stack.
    addCycleBreakerBindings :: Bag (TcTyVar, Type)   -- ^ (cbv,expansion) pairs
                            -> InertSet -> InertSet
    addCycleBreakerBindings :: Bag (TcTyVar, Type) -> InertSet -> InertSet
    addCycleBreakerBindings Bag (TcTyVar, Type)
    prs InertSet
    ics
      = Bool -> SDoc -> InertSet -> InertSet
    forall a. HasCallStack => Bool -> SDoc -> a -> a
    assertPpr (((TcTyVar, Type) -> Bool) -> Bag (TcTyVar, Type) -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all (TcTyVar -> Bool
    isCycleBreakerTyVar (TcTyVar -> Bool)
    -> ((TcTyVar, Type) -> TcTyVar) -> (TcTyVar, Type) -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (TcTyVar, Type) -> TcTyVar
    forall a b. (a, b) -> a
    fst) Bag (TcTyVar, Type)
    prs) (Bag (TcTyVar, Type) -> SDoc
    forall a. Outputable a => a -> SDoc
    ppr Bag (TcTyVar, Type)
    prs) (InertSet -> InertSet) -> InertSet -> InertSet
    forall a b. (a -> b) -> a -> b
    $
        InertSet
    ics { inert_cycle_breakers = add_to (inert_cycle_breakers ics) }
      where
        add_to :: CycleBreakerVarStack -> CycleBreakerVarStack
    add_to (Bag (TcTyVar, Type)
    top_env :| [Bag (TcTyVar, Type)]
    rest_envs) = (Bag (TcTyVar, Type)
    prs Bag (TcTyVar, Type) -> Bag (TcTyVar, Type) -> Bag (TcTyVar, Type)
    forall a. Bag a -> Bag a -> Bag a
    `unionBags` Bag (TcTyVar, Type)
    top_env) Bag (TcTyVar, Type)
    -> [Bag (TcTyVar, Type)] -> CycleBreakerVarStack
    forall a. a -> [a] -> NonEmpty a
    :| [Bag (TcTyVar, Type)]
    rest_envs

    -- | Perform a monadic operation on all pairs in the top environment
    -- in the stack.
    forAllCycleBreakerBindings_ :: Monad m
                                => CycleBreakerVarStack
                                -> (TcTyVar -> TcType -> m ()) -> m ()
    forAllCycleBreakerBindings_ :: forall (m :: * -> *).
    Monad m =>
    CycleBreakerVarStack -> (TcTyVar -> Type -> m ()) -> m ()
    forAllCycleBreakerBindings_ (Bag (TcTyVar, Type)
    top_env :| [Bag (TcTyVar, Type)]
    _rest_envs) TcTyVar -> Type -> m ()
    action
      = Bag (TcTyVar, Type) -> ((TcTyVar, Type) -> m ()) -> m ()
    forall (t :: * -> *) (m :: * -> *) a b.
    (Foldable t, Monad m) =>
    t a -> (a -> m b) -> m ()
    forM_ Bag (TcTyVar, Type)
    top_env ((TcTyVar -> Type -> m ()) -> (TcTyVar, Type) -> m ()
    forall a b c. (a -> b -> c) -> (a, b) -> c
    uncurry TcTyVar -> Type -> m ()
    action)
    {-# INLINABLE forAllCycleBreakerBindings_ #-}  -- to allow SPECIALISE later

    {- *********************************************************************
    *                                                                      *
             Solving one from another
    *                                                                      *
    ********************************************************************* -}

    data InteractResult
       = KeepInert   -- Keep the inert item, and solve the work item from it
                     -- (if the latter is Wanted; just discard it if not)
       | KeepWork    -- Keep the work item, and solve the inert item from it

    instance Outputable InteractResult where
      ppr :: InteractResult -> SDoc
    ppr InteractResult
    KeepInert = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "keep inert"
      ppr InteractResult
    KeepWork  = String -> SDoc
    forall doc. IsLine doc => String -> doc
    text String
    "keep work-item"

    solveOneFromTheOther :: Ct  -- Inert    (Dict or Irred)
                         -> Ct  -- WorkItem (same predicate as inert)
                         -> InteractResult
    -- Precondition:
    -- * inert and work item represent evidence for the /same/ predicate
    -- * Both are CDictCan or CIrredCan
    --
    -- We can always solve one from the other: even if both are wanted,
    -- although we don't rewrite wanteds with wanteds, we can combine
    -- two wanteds into one by solving one from the other

    solveOneFromTheOther :: Ct -> Ct -> InteractResult
    solveOneFromTheOther Ct
    ct_i Ct
    ct_w
      | CtWanted { ctev_loc :: CtEvidence -> CtLoc
    ctev_loc = CtLoc
    loc_w } <- CtEvidence
    ev_w
      , CtLoc -> CtLoc -> Bool
    prohibitedSuperClassSolve CtLoc
    loc_i CtLoc
    loc_w
      -- See Note [Solving superclass constraints] in GHC.Tc.TyCl.Instance
      = -- Inert must be Given
        InteractResult
    KeepWork

      | CtWanted {} <- CtEvidence
    ev_w
      = -- Inert is Given or Wanted
        case CtEvidence
    ev_i of
          CtGiven {} -> InteractResult
    KeepInert
            -- work is Wanted; inert is Given: easy choice.

          CtWanted {} -- Both are Wanted
            -- If only one has no pending superclasses, use it
            -- Otherwise we can get infinite superclass expansion (#22516)
            -- in silly cases like   class C T b => C a b where ...
            | Bool -> Bool
    not Bool
    is_psc_i, Bool
    is_psc_w     -> InteractResult
    KeepInert
            | Bool
    is_psc_i,     Bool -> Bool
    not Bool
    is_psc_w -> InteractResult
    KeepWork

            -- If only one is a WantedSuperclassOrigin (arising from expanding
            -- a Wanted class constraint), keep the other: wanted superclasses
            -- may be unexpected by users
            | Bool -> Bool
    not Bool
    is_wsc_orig_i, Bool
    is_wsc_orig_w     -> InteractResult
    KeepInert
            | Bool
    is_wsc_orig_i,     Bool -> Bool
    not Bool
    is_wsc_orig_w -> InteractResult
    KeepWork

            -- otherwise, just choose the lower span
            -- reason: if we have something like (abs 1) (where the
            -- Num constraint cannot be satisfied), it's better to
            -- get an error about abs than about 1.
            -- This test might become more elaborate if we see an
            -- opportunity to improve the error messages
            | (RealSrcSpan -> RealSrcSpan -> Bool
    forall a. Ord a => a -> a -> Bool
    (<) (RealSrcSpan -> RealSrcSpan -> Bool)
    -> (CtLoc -> RealSrcSpan) -> CtLoc -> CtLoc -> Bool
    forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
    `on` CtLoc -> RealSrcSpan
    ctLocSpan) CtLoc
    loc_i CtLoc
    loc_w -> InteractResult
    KeepInert
            | Bool
    otherwise                        -> InteractResult
    KeepWork

      -- From here on the work-item is Given

      | CtWanted { ctev_loc :: CtEvidence -> CtLoc
    ctev_loc = CtLoc
    loc_i } <- CtEvidence
    ev_i
      , CtLoc -> CtLoc -> Bool
    prohibitedSuperClassSolve CtLoc
    loc_w CtLoc
    loc_i
      = InteractResult
    KeepInert   -- Just discard the un-usable Given
                    -- This never actually happens because
                    -- Givens get processed first

      | CtWanted {} <- CtEvidence
    ev_i
      = InteractResult
    KeepWork

      -- From here on both are Given
      -- See Note [Replacement vs keeping]

      | TcLevel
    lvl_i TcLevel -> TcLevel -> Bool
    `sameDepthAs` TcLevel
    lvl_w
      = InteractResult
    same_level_strategy

      | Bool
    otherwise   -- Both are Given, levels differ
      = InteractResult
    different_level_strategy
      where
         ev_i :: CtEvidence
    ev_i  = Ct -> CtEvidence
    ctEvidence Ct
    ct_i
         ev_w :: CtEvidence
    ev_w  = Ct -> CtEvidence
    ctEvidence Ct
    ct_w

         pred :: Type
    pred  = CtEvidence -> Type
    ctEvPred CtEvidence
    ev_i

         loc_i :: CtLoc
    loc_i  = CtEvidence -> CtLoc
    ctEvLoc CtEvidence
    ev_i
         loc_w :: CtLoc
    loc_w  = CtEvidence -> CtLoc
    ctEvLoc CtEvidence
    ev_w
         orig_i :: CtOrigin
    orig_i = CtLoc -> CtOrigin
    ctLocOrigin CtLoc
    loc_i
         orig_w :: CtOrigin
    orig_w = CtLoc -> CtOrigin
    ctLocOrigin CtLoc
    loc_w
         lvl_i :: TcLevel
    lvl_i  = CtLoc -> TcLevel
    ctLocLevel CtLoc
    loc_i
         lvl_w :: TcLevel
    lvl_w  = CtLoc -> TcLevel
    ctLocLevel CtLoc
    loc_w

         is_psc_w :: Bool
    is_psc_w = Ct -> Bool
    isPendingScDict Ct
    ct_w
         is_psc_i :: Bool
    is_psc_i = Ct -> Bool
    isPendingScDict Ct
    ct_i

         is_wsc_orig_i :: Bool
    is_wsc_orig_i = CtOrigin -> Bool
    isWantedSuperclassOrigin CtOrigin
    orig_i
         is_wsc_orig_w :: Bool
    is_wsc_orig_w = CtOrigin -> Bool
    isWantedSuperclassOrigin CtOrigin
    orig_w

         different_level_strategy :: InteractResult
    different_level_strategy  -- Both Given
           | Type -> Bool
    isIPLikePred Type
    pred = if TcLevel
    lvl_w TcLevel -> TcLevel -> Bool
    `strictlyDeeperThan` TcLevel
    lvl_i then InteractResult
    KeepWork  else InteractResult
    KeepInert
           | Bool
    otherwise         = if TcLevel
    lvl_w TcLevel -> TcLevel -> Bool
    `strictlyDeeperThan` TcLevel
    lvl_i then InteractResult
    KeepInert else InteractResult
    KeepWork
           -- See Note [Replacement vs keeping] part (1)
           -- For the isIPLikePred case see Note [Shadowing of implicit parameters]
           --                               in GHC.Tc.Solver.Dict

         same_level_strategy :: InteractResult
    same_level_strategy -- Both Given
           = case (CtOrigin
    orig_i, CtOrigin
    orig_w) of

               (GivenSCOrigin SkolemInfoAnon
    _ ScDepth
    depth_i Bool
    blocked_i, GivenSCOrigin SkolemInfoAnon
    _ ScDepth
    depth_w Bool
    blocked_w)
                 | Bool
    blocked_i, Bool -> Bool
    not Bool
    blocked_w -> InteractResult
    KeepWork  -- Case 2(a) from
                 | Bool -> Bool
    not Bool
    blocked_i, Bool
    blocked_w -> InteractResult
    KeepInert -- Note [Replacement vs keeping]

                 -- Both blocked or both not blocked

                 | ScDepth
    depth_w ScDepth -> ScDepth -> Bool
    forall a. Ord a => a -> a -> Bool
    < ScDepth
    depth_i -> InteractResult
    KeepWork   -- Case 2(c) from
                 | Bool
    otherwise         -> InteractResult
    KeepInert  -- Note [Replacement vs keeping]

               (GivenSCOrigin {}, CtOrigin
    _) -> InteractResult
    KeepWork  -- Case 2(b) from Note [Replacement vs keeping]

               (CtOrigin, CtOrigin)
    _ -> InteractResult
    KeepInert  -- Case 2(d) from Note [Replacement vs keeping]

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

      1) Constraints come from different levels (different_level_strategy)

          - For implicit parameters we want to keep the innermost (deepest)
            one, so that it overrides the outer one.
            See Note [Shadowing of implicit parameters] in GHC.Tc.Solver.Dict

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

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

      2) Constraints coming from the same level (i.e. same implication)

           (a) If both are GivenSCOrigin, choose the one that is unblocked if possible
               according to Note [Solving superclass constraints] in GHC.Tc.TyCl.Instance.

           (b) Prefer constraints that are not superclass selections. Example:

                 f :: (Eq a, Ord a) => a -> Bool
                 f x = x == x

               Eager superclass expansion gives us two [G] Eq a constraints. We
               want to keep the one from the user-written Eq a, not the superclass
               selection. This means we report the Ord a as redundant with
               -Wredundant-constraints, not the Eq a.

               Getting this wrong was #20602. See also
               Note [Tracking redundant constraints] in GHC.Tc.Solver.

           (c) If both are GivenSCOrigin, chooose the one with the shallower
               superclass-selection depth, in the hope of identifying more correct
               redundant constraints. This is really a generalization of point (b),
               because the superclass depth of a non-superclass constraint is 0.

               (If the levels differ, we definitely won't have both with GivenSCOrigin.)

           (d) Finally, when there is still a choice, use KeepInert rather than
               KeepWork, for two reasons:
                 - to avoid unnecessary munging of the inert set.
                 - to cut off superclass loops; see Note [Superclass loops] in GHC.Tc.Solver.Dict

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

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

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

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