TcInteract.lhs 87.3 KB
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\begin{code}
module TcInteract ( 
     solveInteract, AtomicInert, 
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     InertSet, emptyInert, updInertSet, extractUnsolved, solveOne 
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  ) where  

#include "HsVersions.h"

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import BasicTypes 
import TcCanonical
import VarSet
import Type
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import TypeRep 
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import Id 
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import VarEnv
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import Var

import TcType
import HsBinds 

import InstEnv 
import Class 
import TyCon 
import Name

import FunDeps

import Control.Monad ( when ) 

import Coercion
import Outputable

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

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import Control.Monad( zipWithM, unless )
import FastString ( sLit ) 
import DynFlags
\end{code}

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Note [InertSet invariants]
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~~~~~~~~~~~~~~~~~~~~~~~~~~~

An InertSet is a bag of canonical constraints, with the following invariants:

  1 No two constraints react with each other. 
    
    A tricky case is when there exists a given (solved) dictionary 
    constraint and a wanted identical constraint in the inert set, but do 
    not react because reaction would create loopy dictionary evidence for 
    the wanted. See note [Recursive dictionaries]

  2 Given equalities form an idempotent substitution [none of the
    given LHS's occur in any of the given RHS's or reactant parts]

  3 Wanted equalities also form an idempotent substitution
  4 The entire set of equalities is acyclic.

  5 Wanted dictionaries are inert with the top-level axiom set 

  6 Equalities of the form tv1 ~ tv2 always have a touchable variable
    on the left (if possible).
  7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints 
    will be marked as solved right before being pushed into the inert set. 
    See note [Touchables and givens].
 
Note that 6 and 7 are /not/ enforced by canonicalization but rather by 
insertion in the inert list, ie by TcInteract. 

During the process of solving, the inert set will contain some
previously given constraints, some wanted constraints, and some given
constraints which have arisen from solving wanted constraints. For
now we do not distinguish between given and solved constraints.

Note that we must switch wanted inert items to given when going under an
implication constraint (when in top-level inference mode).

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Note [InertSet FlattenSkolemEqClass] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The inert_fsks field of the inert set contains an "inverse map" of all the 
flatten skolem equalities in the inert set. For instance, if inert_cts looks
like this: 
 
    fsk1 ~ fsk2 
    fsk3 ~ fsk2 
    fsk4 ~ fsk5 

Then, the inert_fsks fields holds the following map: 
    fsk2 |-> { fsk1, fsk3 } 
    fsk5 |-> { fsk4 } 
Along with the necessary coercions to convert fsk1 and fsk3 back to fsk2 
and fsk4 back to fsk5. Hence, the invariants of the inert_fsks field are: 
  
   (a) All TcTyVars in the domain and range of inert_fsks are flatten skolems
   (b) All TcTyVars in the domain of inert_fsk occur naked as rhs in some 
       equalities of inert_cts 
   (c) For every mapping  fsk1 |-> { (fsk2,co), ... } it must be: 
         co : fsk2 ~ fsk1 

The role of the inert_fsks is to make it easy to maintain the equivalence
class of each flatten skolem, which is much needed to correctly do spontaneous
solving. See Note [Loopy Spontaneous Solving] 
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\begin{code}

-- See Note [InertSet invariants]
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data InertSet 
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  = IS { inert_eqs  :: Bag.Bag CanonicalCt   -- Equalities only **CTyEqCan** 
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       , inert_cts  :: Bag.Bag CanonicalCt   -- Other constraints 
       , inert_fds  :: FDImprovements        -- List of pairwise improvements that have kicked in already
                                             -- and reside either in the worklist or in the inerts 
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       , inert_fsks :: Map.Map TcTyVar [(TcTyVar,Coercion)] }
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       -- See Note [InertSet FlattenSkolemEqClass] 
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type FDImprovement  = (PredType,PredType) 
type FDImprovements = [(PredType,PredType)] 

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instance Outputable InertSet where
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  ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
                , vcat (map ppr (Bag.bagToList $ inert_cts is))
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                , vcat (map (\(v,rest) -> ppr v <+> text "|->" <+> hsep (map (ppr.fst) rest)) 
                       (Map.toList $ inert_fsks is)
                       )
                ]
                       
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emptyInert :: InertSet
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emptyInert = IS { inert_eqs = Bag.emptyBag
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                , inert_cts = Bag.emptyBag, inert_fsks = Map.empty, inert_fds = [] }
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updInertSet :: InertSet -> AtomicInert -> InertSet 
-- Introduces an element in the inert set for the first time 
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updInertSet (IS { inert_eqs = eqs, inert_cts = cts, inert_fsks = fsks, inert_fds = fdis })  
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            item@(CTyEqCan { cc_id    = cv
                           , cc_tyvar = tv1 
                           , cc_rhs   = xi })
  | Just tv2 <- tcGetTyVar_maybe xi,
    FlatSkol {} <- tcTyVarDetails tv1, 
    FlatSkol {} <- tcTyVarDetails tv2 
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  = let eqs'  = eqs `Bag.snocBag` item 
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        fsks' = Map.insertWith (++) tv2 [(tv1, mkCoVarCoercion cv)] fsks
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        -- See Note [InertSet FlattenSkolemEqClass] 
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    in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks', inert_fds = fdis }
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updInertSet (IS { inert_eqs = eqs, inert_cts = cts
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                , inert_fsks = fsks, inert_fds = fdis }) item 
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  | isTyEqCCan item 
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  = let eqs' = eqs `Bag.snocBag` item 
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    in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks, inert_fds = fdis } 
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  | otherwise 
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  = let cts' = cts `Bag.snocBag` item
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    in IS { inert_eqs = eqs, inert_cts = cts', inert_fsks = fsks, inert_fds = fdis } 

updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet 
updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is } 
updInertSetFDImprs is Nothing    = is 
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foldISEqCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a 
-- Fold over the equalities of the inerts
foldISEqCtsM k z IS { inert_eqs = eqs } 
  = Bag.foldlBagM k z eqs 

foldISOtherCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a 
-- Fold over other constraints in the inerts 
foldISOtherCtsM k z IS { inert_cts = cts } 
  = Bag.foldlBagM k z cts 
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extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
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extractUnsolved is@(IS {inert_eqs = eqs, inert_cts = cts, inert_fds = fdis }) 
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  = let is_init  = is { inert_eqs = emptyCCan 
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                      , inert_cts = solved_cts, inert_fsks = Map.empty, inert_fds = fdis }
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        is_final = Bag.foldlBag updInertSet is_init solved_eqs -- Add equalities carefully
    in (is_final, unsolved) 
  where (unsolved_cts, solved_cts) = Bag.partitionBag isWantedCt cts
        (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs
        unsolved                   = unsolved_cts `unionBags` unsolved_eqs
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getFskEqClass :: InertSet -> TcTyVar -> [(TcTyVar,Coercion)] 
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-- Precondition: tv is a FlatSkol. See Note [InertSet FlattenSkolemEqClass] 
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getFskEqClass (IS { inert_cts = cts, inert_fsks = fsks }) tv 
  = case lkpTyEqCanByLhs of
      Nothing  -> fromMaybe [] (Map.lookup tv fsks)  
      Just ceq -> 
        case tcGetTyVar_maybe (cc_rhs ceq) of 
          Just tv_rhs | FlatSkol {} <- tcTyVarDetails tv_rhs
            -> let ceq_co = mkSymCoercion $ mkCoVarCoercion (cc_id ceq)
                   mk_co (v,c) = (v, mkTransCoercion c ceq_co)
               in (tv_rhs, ceq_co): map mk_co (fromMaybe [] $ Map.lookup tv fsks) 
          _ -> []
  where lkpTyEqCanByLhs = Bag.foldlBag lkp Nothing cts 
        lkp :: Maybe CanonicalCt -> CanonicalCt -> Maybe CanonicalCt 
        lkp Nothing ct@(CTyEqCan {cc_tyvar = tv'}) | tv' == tv = Just ct 
        lkp other _ct = other 

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haveBeenImproved :: FDImprovements -> PredType -> PredType -> Bool 
haveBeenImproved [] _ _ = False 
haveBeenImproved ((pty1,pty2):fdimprs) pty1' pty2' 
 | tcEqPred pty1 pty1' && tcEqPred pty2 pty2' 
 = True 
 | tcEqPred pty1 pty2' && tcEqPred pty2 pty1'
 = True 
 | otherwise 
 = haveBeenImproved fdimprs pty1' pty2' 

getFDImprovements :: InertSet -> FDImprovements 
-- Return a list of the improvements that have kicked in so far 
getFDImprovements = inert_fds 

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isWantedCt :: CanonicalCt -> Bool 
isWantedCt ct = isWanted (cc_flavor ct)
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{- TODO: Later ...
data Inert = IS { class_inerts :: FiniteMap Class Atomics
     	          ip_inerts    :: FiniteMap Class Atomics
     	          tyfun_inerts :: FiniteMap TyCon Atomics
		  tyvar_inerts :: FiniteMap TyVar Atomics
                }

Later should we also separate out givens and wanteds?
-}

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\end{code}

Note [Touchables and givens]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Touchable variables will never show up in givens which are inputs to
the solver.  However, touchables may show up in givens generated by the flattener.  
For example,

  axioms:
    G Int ~ Char
    F Char ~ Int

  wanted:
    F (G alpha) ~w Int
  
canonicalises to

  G alpha ~g b
  F b ~w Int

which can be put in the inert set.  Suppose we also have a wanted

  alpha ~w Int

We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
Int.  Instead, after reacting alpha ~w Int with the whole inert set,
we observe that we can solve it by unifying alpha with Int, so we mark
it as solved and put it back in the *work list*. [We also immediately unify
alpha := Int, without telling anyone, see trySpontaneousSolve function, to 
avoid doing this in the end.]

Later, because it is solved (given, in effect), we can use it to rewrite 
G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually, 
we will dispatch the remaining wanted constraints using the top-level axioms.

Finally, note that after reacting a wanted equality with the entire inert set
we may end up with something like

  b ~w alpha

which we should flip around to generate the solved constraint alpha ~s b.

%*********************************************************************
%*                                                                   * 
*                      Main Interaction Solver                       *
*                                                                    *
**********************************************************************

Note [Basic plan] 
~~~~~~~~~~~~~~~~~
1. Canonicalise (unary)
2. Pairwise interaction (binary)
    * Take one from work list 
    * Try all pair-wise interactions with each constraint in inert
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   As an optimisation, we prioritize the equalities both in the 
   worklist and in the inerts. 

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3. Try to solve spontaneously for equalities involving touchables 
4. Top-level interaction (binary wrt top-level)
   Superclass decomposition belongs in (4), see note [Superclasses]

\begin{code}
type AtomicInert = CanonicalCt     -- constraint pulled from InertSet
type WorkItem    = CanonicalCt     -- constraint pulled from WorkList

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-- A mixture of Given, Wanted, and Derived constraints. 
-- We split between equalities and the rest to process equalities first. 
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type WorkList = CanonicalCts
type SWorkList = WorkList        -- A worklist of solved 
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unionWorkLists :: WorkList -> WorkList -> WorkList 
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unionWorkLists = andCCan
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isEmptyWorkList :: WorkList -> Bool 
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isEmptyWorkList = isEmptyCCan 
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emptyWorkList :: WorkList
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emptyWorkList = emptyCCan
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workListFromCCan :: CanonicalCt -> WorkList 
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workListFromCCan = singleCCan
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------------------------
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data StopOrContinue 
  = Stop			-- Work item is consumed
  | ContinueWith WorkItem	-- Not consumed

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

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

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

type SimplifierStage = WorkItem -> InertSet -> TcS StageResult 

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

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

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

Example 1:
  Inert:   {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
  Reagent: a ~ [b] (given)

React with (c~d)     ==> IR (ContinueWith (a~[b]))  True    []
React with (F a ~ t) ==> IR (ContinueWith (a~[b]))  False   [F [b] ~ t]
React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True    []

Example 2:
  Inert:  {c ~w d, F a ~g t, b ~w Int, a ~w ty}
  Reagent: a ~w [b]

React with (c ~w d)   ==> IR (ContinueWith (a~[b]))  True    []
React with (F a ~g t) ==> IR (ContinueWith (a~[b]))  True    []    (can't rewrite given with wanted!)
etc.

Example 3:
  Inert:  {a ~ Int, F Int ~ b} (given)
  Reagent: F a ~ b (wanted)

React with (a ~ Int)   ==> IR (ContinueWith (F Int ~ b)) True []
React with (F Int ~ b) ==> IR Stop True []    -- after substituting we re-canonicalize and get nothing

\begin{code}
-- Main interaction solver: we fully solve the worklist 'in one go', 
-- returning an extended inert set.
--
-- See Note [Touchables and givens].
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solveInteract :: InertSet -> CanonicalCts -> TcS InertSet
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solveInteract inert ws 
  = do { dyn_flags <- getDynFlags
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       ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert ws
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       }
solveOne :: InertSet -> WorkItem -> TcS InertSet 
solveOne inerts workItem 
  = do { dyn_flags <- getDynFlags
       ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
       }

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

  | n > max_depth 
  = solverDepthErrorTcS n stack

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

	      -- Solve equalities first
       ; let (eqs, non_eqs) = Bag.partitionBag isTyEqCCan ws
       ; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
       ; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
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------------------
-- Fully interact the given work item with an inert set, and return a
-- new inert set which has assimilated the new information.
solveOneWithDepth :: (Int, Int, [WorkItem])
                  -> InertSet -> WorkItem -> TcS InertSet
solveOneWithDepth (max_depth, n, stack) inert work
  = do { traceTcS0 (indent ++ "Solving {") (ppr work)
       ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
         
       ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)

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

       ; traceTcS0 (indent ++ "Done }") (ppr work) 
       ; return res_inert }
  where
    indent = replicate (2*n) ' '

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

*********************************************************************************
*                                                                               * 
                       The spontaneous-solve Stage
*                                                                               *
*********************************************************************************

\begin{code}
spontaneousSolveStage :: SimplifierStage 
spontaneousSolveStage workItem inerts 
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  = do { mSolve <- trySpontaneousSolve workItem inerts
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       ; case mSolve of 
           Nothing -> -- no spontaneous solution for him, keep going
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               return $ SR { sr_new_work   = emptyWorkList
                           , sr_inerts     = inerts
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                           , sr_stop       = ContinueWith workItem }

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           Just workList' -> -- He has been solved; workList' are all givens
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               return $ SR { sr_new_work = workList'
                           , sr_inerts   = inerts 
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                           , sr_stop     = Stop }
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       }
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-- @trySpontaneousSolve wi@ solves equalities where one side is a
-- touchable unification variable. Returns:
--   * Nothing if we were not able to solve it
--   * Just wi' if we solved it, wi' (now a "given") should be put in the work list.
--     	    See Note [Touchables and givens] 
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-- NB: just passing the inerts through for the skolem equivalence classes
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trySpontaneousSolve :: WorkItem -> InertSet -> TcS (Maybe SWorkList)
trySpontaneousSolve (CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi }) inerts 
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  | isGiven gw
  = return Nothing
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  | Just tv2 <- tcGetTyVar_maybe xi
  = do { tch1 <- isTouchableMetaTyVar tv1
       ; tch2 <- isTouchableMetaTyVar tv2
       ; case (tch1, tch2) of
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           (True,  True)  -> trySpontaneousEqTwoWay inerts cv gw tv1 tv2
           (True,  False) -> trySpontaneousEqOneWay inerts cv gw tv1 xi
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           (False, True)  -> trySpontaneousEqOneWay inerts cv gw tv2 (mkTyVarTy tv1)
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	   _ -> return Nothing }
  | otherwise
  = do { tch1 <- isTouchableMetaTyVar tv1
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       ; if tch1 then trySpontaneousEqOneWay inerts cv gw tv1 xi
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                 else return Nothing }

  -- No need for 
  --      trySpontaneousSolve (CFunEqCan ...) = ...
  -- See Note [No touchables as FunEq RHS] in TcSMonad
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trySpontaneousSolve _ _ = return Nothing 
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----------------
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trySpontaneousEqOneWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi
                       -> TcS (Maybe SWorkList)
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-- tv is a MetaTyVar, not untouchable
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trySpontaneousEqOneWay inerts cv gw tv xi	
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  | not (isSigTyVar tv) || isTyVarTy xi 
  = if typeKind xi `isSubKind` tyVarKind tv then
        solveWithIdentity inerts cv gw tv xi
    else if tyVarKind tv `isSubKind` typeKind xi then 
             return Nothing -- kinds are compatible but we can't solveWithIdentity this way
                            -- This case covers the  a_touchable :: * ~ b_untouchable :: ?? 
                            -- which has to be deferred or floated out for someone else to solve 
                            -- it in a scope where 'b' is no longer untouchable. 
         else kindErrorTcS gw (mkTyVarTy tv) xi -- See Note [Kind errors]

  | otherwise -- Still can't solve, sig tyvar and non-variable rhs
  = return Nothing 
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----------------
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trySpontaneousEqTwoWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> TcTyVar
                       -> TcS (Maybe SWorkList)
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-- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
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trySpontaneousEqTwoWay inerts cv gw tv1 tv2
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  | k1 `isSubKind` k2
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  , nicer_to_update_tv2 = solveWithIdentity inerts cv gw tv2 (mkTyVarTy tv1)
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  | k2 `isSubKind` k1 
  = solveWithIdentity inerts cv gw tv1 (mkTyVarTy tv2) 
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  | otherwise -- None is a subkind of the other, but they are both touchable! 
  = kindErrorTcS gw (mkTyVarTy tv1) (mkTyVarTy tv2) -- See Note [Kind errors]
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  where
    k1 = tyVarKind tv1
    k2 = tyVarKind tv2
    nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
\end{code}

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Note [Kind errors] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the wanted problem: 
      alpha ~ (# Int, Int #) 
where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint, 
but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay' 
simply returns @Nothing@ then that wanted constraint is going to propagate all the way and 
get quantified over in inference mode. That's bad because we do know at this point that the 
constraint is insoluble. Instead, we call 'kindErrorTcS' here, which immediately fails. 

The same applies in canonicalization code in case of kind errors in the givens. 
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Note [Spontaneous solving and kind compatibility] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note that our canonical constraints insist that only *given* equalities (tv ~ xi) 
or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds. 

  - We have to require this because: 
        Given equalities can be freely used to rewrite inside 
        other types or constraints.
  - We do not have to do the same for wanteds because:
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        First, wanted equations (tv ~ xi) where tv is a touchable
        unification variable may have kinds that do not agree (the
        kind of xi must be a sub kind of the kind of tv).  Second, any
        potential kind mismatch will result in the constraint not
        being soluble, which will be reported anyway. This is the
        reason that @trySpontaneousOneWay@ and @trySpontaneousTwoWay@
        will perform a kind compatibility check, and only then will
        they proceed to @solveWithIdentity@.
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Caveat: 
  - Givens from higher-rank, such as: 
          type family T b :: * -> * -> * 
          type instance T Bool = (->) 

          f :: forall a. ((T a ~ (->)) => ...) -> a -> ... 
          flop = f (...) True 
     Whereas we would be able to apply the type instance, we would not be able to 
     use the given (T Bool ~ (->)) in the body of 'flop' 

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Note [Loopy spontaneous solving] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the original wanted: 
   wanted :  Maybe (E alpha) ~ alpha 
where E is a type family, such that E (T x) = x. After canonicalization, 
as a result of flattening, we will get: 
   given  : E alpha ~ fsk 
   wanted : alpha ~ Maybe fsk
where (fsk := E alpha, on the side). Now, if we spontaneously *solve* 
(alpha := Maybe fsk) we are in trouble! Instead, we should refrain from solving 
it and keep it as wanted.  In inference mode we'll end up quantifying over
   (alpha ~ Maybe (E alpha))
Hence, 'solveWithIdentity' performs a small occurs check before
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actually solving. But this occurs check *must look through* flatten skolems.

However, it may be the case that the flatten skolem in hand is equal to some other 
flatten skolem whith *does not* mention our unification variable. Here's a typical example:

Original wanteds: 
   g: F alpha ~ F beta 
   w: alpha ~ F alpha 
After canonicalization: 
   g: F beta ~ f1 
   g: F alpha ~ f1 
   w: alpha ~ f2 
   g: F alpha ~ f2 
After some reactions: 
   g: f1 ~ f2 
   g: F beta ~ f1 
   w: alpha ~ f2 
   g: F alpha ~ f2 
At this point, we will try to spontaneously solve (alpha ~ f2) which remains as yet unsolved.
We will look inside f2, which immediately mentions (F alpha), so it's not good to unify! However
by looking at the equivalence class of the flatten skolems, we can see that it is fine to 
unify (alpha ~ f1) which solves our goals! 

A similar problem happens because of other spontaneous solving. Suppose we have the 
following wanteds, arriving in this exact order:
  (first)  w: beta ~ alpha 
  (second) w: alpha ~ fsk 
  (third)  g: F beta ~ fsk
Then, we first spontaneously solve the first constraint, making (beta := alpha), and having
(beta ~ alpha) as given. *Then* we encounter the second wanted (alpha ~ fsk). "fsk" does not 
obviously mention alpha, so naively we can also spontaneously solve (alpha := fsk). But 
that is wrong since fsk mentions beta, which has already secretly been unified to alpha! 

To avoid this problem, the same occurs check must unveil rewritings that can happen because 
of spontaneously having solved other constraints. 

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Note [Avoid double unifications] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The spontaneous solver has to return a given which mentions the unified unification
variable *on the left* of the equality. Here is what happens if not: 
  Original wanted:  (a ~ alpha),  (alpha ~ Int) 
We spontaneously solve the first wanted, without changing the order! 
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      given : a ~ alpha      [having unified alpha := a] 
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Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
At the end we spontaneously solve that guy, *reunifying*  [alpha := Int] 

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We avoid this problem by orienting the given so that the unification
variable is on the left.  [Note that alternatively we could attempt to
enforce this at canonicalization]
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See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
double unifications is the main reason we disallow touchable
unification variables as RHS of type family equations: F xis ~ alpha.
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\begin{code}
----------------
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solveWithIdentity :: InertSet 
                  -> CoVar -> CtFlavor -> TcTyVar -> Xi 
                  -> TcS (Maybe SWorkList)
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-- Solve with the identity coercion 
-- Precondition: kind(xi) is a sub-kind of kind(tv)
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-- Precondition: CtFlavor is Wanted or Derived
-- See [New Wanted Superclass Work] to see why solveWithIdentity 
--     must work for Derived as well as Wanted
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solveWithIdentity inerts cv gw tv xi 
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  = do { tybnds <- getTcSTyBindsMap
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       ; case occurCheck tybnds inerts tv xi of 
           Nothing              -> return Nothing 
           Just (xi_unflat,coi) -> solve_with xi_unflat coi }
  where
    solve_with xi_unflat coi  -- coi : xi_unflat ~ xi  
      = do { traceTcS "Sneaky unification:" $ 
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                       vcat [text "Coercion variable:  " <+> ppr gw, 
                             text "Coercion:           " <+> pprEq (mkTyVarTy tv) xi,
                             text "Left  Kind is     : " <+> ppr (typeKind (mkTyVarTy tv)),
                             text "Right Kind is     : " <+> ppr (typeKind xi)
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                  ]
           ; setWantedTyBind tv xi_unflat        -- Set tv := xi_unflat
           ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat
           ; let flav = mkGivenFlavor gw UnkSkol 
           ; (cts, co) <- case coi of 
               ACo co  -> do { can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi_unflat
                             ; return (can_eqs, co) }
               IdCo co -> return $ 
                          (singleCCan (CTyEqCan { cc_id = cv_given 
                                                , cc_flavor = mkGivenFlavor gw UnkSkol
                                                , cc_tyvar = tv, cc_rhs = xi }
                                                -- xi, *not* xi_unflat because 
                                                -- xi_unflat may require flattening!
                                      ), co)
           ; case gw of 
               Wanted  {} -> setWantedCoBind  cv co
               Derived {} -> setDerivedCoBind cv co 
               _          -> pprPanic "Can't spontaneously solve *given*" empty 
	              -- See Note [Avoid double unifications] 
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           ; return $ Just cts }
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occurCheck :: VarEnv (TcTyVar, TcType) -> InertSet
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           -> TcTyVar -> TcType -> Maybe (TcType,CoercionI) 
-- Traverse @ty@ to make sure that @tv@ does not appear under some flatten skolem. 
-- If it appears under some flatten skolem look in that flatten skolem equivalence class 
-- (see Note [InertSet FlattenSkolemEqClass], [Loopy Spontaneous Solving]) to see if you 
-- can find a different flatten skolem to use, that is, one that does not mention @tv@.
-- 
-- Postcondition: Just (ty', coi) = occurCheck binds inerts tv ty 
--       coi :: ty' ~ ty 
-- NB: The returned type ty' may not be flat!

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occurCheck ty_binds inerts the_tv the_ty
  = ok emptyVarSet the_ty 
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  where 
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    -- If (fsk `elem` bad) then tv occurs in any rendering
    -- of the type under the expansion of fsk
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    ok bad this_ty@(TyConApp tc tys) 
      | Just tys_cois <- allMaybes (map (ok bad) tys) 
      , (tys',cois') <- unzip tys_cois
      = Just (TyConApp tc tys', mkTyConAppCoI tc cois') 
      | isSynTyCon tc, Just ty_expanded <- tcView this_ty
      = ok bad ty_expanded   -- See Note [Type synonyms and the occur check] in TcUnify
    ok bad (PredTy sty) 
      | Just (sty',coi) <- ok_pred bad sty 
      = Just (PredTy sty', coi) 
    ok bad (FunTy arg res) 
      | Just (arg', coiarg) <- ok bad arg, Just (res', coires) <- ok bad res
      = Just (FunTy arg' res', mkFunTyCoI coiarg coires) 
    ok bad (AppTy fun arg) 
      | Just (fun', coifun) <- ok bad fun, Just (arg', coiarg) <- ok bad arg 
      = Just (AppTy fun' arg', mkAppTyCoI coifun coiarg) 
    ok bad (ForAllTy tv1 ty1) 
    -- WARNING: What if it is a (t1 ~ t2) => t3? It's not handled properly at the moment. 
      | Just (ty1', coi) <- ok bad ty1 
      = Just (ForAllTy tv1 ty1', mkForAllTyCoI tv1 coi) 

    -- Variable cases 
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    ok bad this_ty@(TyVarTy tv) 
      | tv == the_tv           		        = Nothing             -- Occurs check error
      | not (isTcTyVar tv) 		        = Just (this_ty, IdCo this_ty) -- Bound var
      | FlatSkol zty <- tcTyVarDetails tv       = ok_fsk bad tv zty
      | Just (_,ty) <- lookupVarEnv ty_binds tv = ok bad ty 
      | otherwise                               = Just (this_ty, IdCo this_ty)
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    -- Check if there exists a ty bind already, as a result of sneaky unification. 
    -- Fall through
    ok _bad _ty = Nothing 

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    -----------
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    ok_pred bad (ClassP cn tys)
      | Just tys_cois <- allMaybes $ map (ok bad) tys 
      = let (tys', cois') = unzip tys_cois 
        in Just (ClassP cn tys', mkClassPPredCoI cn cois')
    ok_pred bad (IParam nm ty)   
      | Just (ty',co') <- ok bad ty 
      = Just (IParam nm ty', mkIParamPredCoI nm co') 
    ok_pred bad (EqPred ty1 ty2) 
      | Just (ty1',coi1) <- ok bad ty1, Just (ty2',coi2) <- ok bad ty2
      = Just (EqPred ty1' ty2', mkEqPredCoI coi1 coi2) 
    ok_pred _ _ = Nothing 

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    -----------
    ok_fsk bad fsk zty
      | fsk `elemVarSet` bad 
            -- We are already trying to find a rendering of fsk, 
	    -- and to do that it seems we need a rendering, so fail
      = Nothing
      | otherwise 
      = firstJusts (ok new_bad zty : map (go_under_fsk new_bad) fsk_equivs)
      where
        fsk_equivs = getFskEqClass inerts fsk 
        new_bad    = bad `extendVarSetList` (fsk : map fst fsk_equivs)

    -----------
    go_under_fsk bad_tvs (fsk,co)
      | FlatSkol zty <- tcTyVarDetails fsk
      = case ok bad_tvs zty of
           Nothing        -> Nothing
           Just (ty,coi') -> Just (ty, mkTransCoI coi' (ACo co)) 
      | otherwise = pprPanic "go_down_equiv" (ppr fsk)
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\end{code}


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

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

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

        , ir_new_work     :: WorkList
            -- new work items to add to the WorkList
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        , ir_improvement  :: Maybe FDImprovement -- In case improvement kicked in
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        }

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

mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
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mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing 
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mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
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mkIRStop keep newWork = return $ IR Stop keep newWork Nothing

mkIRStop_RecordImprovement :: Monad m => InertAction -> WorkList -> FDImprovement -> m InteractResult 
mkIRStop_RecordImprovement keep newWork fdimpr = return $ IR Stop keep newWork (Just fdimpr) 

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dischargeWorkItem :: Monad m => m InteractResult
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dischargeWorkItem = mkIRStop KeepInert emptyWorkList
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noInteraction :: Monad m => WorkItem -> m InteractResult
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noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
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data WhichComesFromInert = LeftComesFromInert | RightComesFromInert 
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---------------------------------------------------
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-- Interact a single WorkItem with the equalities of an inert set as far as possible, i.e. until we 
-- get a Stop result from an individual reaction (i.e. when the WorkItem is consumed), or until we've 
-- interact the WorkItem with the entire equalities of the InertSet

interactWithInertEqsStage :: SimplifierStage 
interactWithInertEqsStage workItem inert
  = foldISEqCtsM interactNext initITR inert 
  where initITR = SR { sr_inerts   = IS { inert_eqs  = emptyCCan -- We will fold over the equalities
                                        , inert_fsks = Map.empty -- which will generate those two again
                                        , inert_cts  = inert_cts inert
                                        , inert_fds  = inert_fds inert
                                        }
                     , sr_new_work = emptyWorkList
                     , sr_stop     = ContinueWith workItem }

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---------------------------------------------------
-- Interact a single WorkItem with *non-equality* constraints in the inert set. 
-- Precondition: equality interactions must have already happened, hence we have 
-- to pick up some information from the incoming inert, before folding over the 
-- "Other" constraints it contains! 
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interactWithInertsStage :: SimplifierStage
interactWithInertsStage workItem inert
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  = foldISOtherCtsM interactNext initITR inert
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  where 
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    initITR = SR { -- Pick up: (1) equations, (2) FD improvements, (3) FlatSkol equiv. classes
                   sr_inerts   = IS { inert_eqs  = inert_eqs inert 
                                    , inert_cts  = emptyCCan      
                                    , inert_fds  = inert_fds inert 
                                    , inert_fsks = inert_fsks inert }
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                 , sr_new_work = emptyWorkList
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                 , sr_stop     = ContinueWith workItem }

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interactNext :: StageResult -> AtomicInert -> TcS StageResult 
interactNext it inert  
  | ContinueWith workItem <- sr_stop it
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  = do { let inerts      = sr_inerts it 
             fdimprs_old = getFDImprovements inerts 

       ; ir <- interactWithInert fdimprs_old inert workItem 

       -- New inerts depend on whether we KeepInert or not and must 
       -- be updated with FD improvement information from the interaction result (ir) 
       ; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir) 
             upd_inert  = if ir_inert_action ir == KeepInert 
                          then inerts `updInertSet` inert else inerts

       ; return $ SR { sr_inerts   = inerts_new
                     , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
                     , sr_stop     = ir_stop ir } }
  | otherwise 
  = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
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-- Do a single interaction of two constraints.
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interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
interactWithInert fdimprs inert workitem 
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  =  do { ctxt <- getTcSContext
        ; let is_allowed  = allowedInteraction (simplEqsOnly ctxt) inert workitem 
              inert_ev    = cc_id inert 
              work_ev     = cc_id workitem 

        -- Never interact a wanted and a derived where the derived's evidence 
        -- mentions the wanted evidence in an unguarded way. 
        -- See Note [Superclasses and recursive dictionaries] 
        -- and Note [New Wanted Superclass Work] 
        -- We don't have to do this for givens, as we fully know the evidence for them. 
        ; rec_ev_ok <- 
            case (cc_flavor inert, cc_flavor workitem) of 
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              (Wanted loc, Derived {}) -> isGoodRecEv work_ev  (WantedEvVar inert_ev loc)
              (Derived {}, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
              _                        -> return True 
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        ; if is_allowed && rec_ev_ok then 
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              doInteractWithInert fdimprs inert workitem 
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          else 
              noInteraction workitem 
        }

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

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

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

  | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
  = 	 -- See Note [When improvement happens]
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    do { let pty1 = ClassP cls1 tys1 
             pty2 = ClassP cls2 tys2 
             work_item_pred_loc = (pty2, ppr d2)
             inert_pred_loc     = (pty1, ppr d1)
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	     loc                = combineCtLoc fl1 fl2
             eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc         
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       ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs 
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       ; fd_work <- canWanteds wevvars 
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              	 -- See Note [Generating extra equalities]
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       ; traceTcS "Checking if improvements existed." (ppr fdimprs) 
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       ; if isEmptyWorkList fd_work || haveBeenImproved fdimprs pty1 pty2 then
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             -- Must keep going
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             mkIRContinue workItem KeepInert fd_work 
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         else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
                 ; mkIRStop_RecordImprovement KeepInert 
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                      (fd_work `unionWorkLists` workListFromCCan workItem) (pty1,pty2)
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                 }
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         -- See Note [FunDep Reactions] 
       }

-- Class constraint and given equality: use the equality to rewrite
-- the class constraint. 
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doInteractWithInert _fdimprs
                    (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi }) 
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                    (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis }) 
  | ifl `canRewrite` wfl 
  , tv `elemVarSet` tyVarsOfTypes xis
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  = if isDerivedSC wfl then 
        mkIRStop KeepInert $ emptyWorkList -- See Note [Adding Derived Superclasses]
    else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
            -- Continue with rewritten Dictionary because we can only be in the 
            -- interactWithEqsStage, so the dictionary is inert. 
            ; mkIRContinue rewritten_dict KeepInert emptyWorkList }
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doInteractWithInert _fdimprs 
                    (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis }) 
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           workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
  | wfl `canRewrite` ifl
  , tv `elemVarSet` tyVarsOfTypes xis
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  = if isDerivedSC ifl then
        mkIRContinue workItem DropInert emptyWorkList -- No need to do any rewriting, 
                                                      -- see Note [Adding Derived Superclasses]
    else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis) 
            ; mkIRContinue workItem DropInert (workListFromCCan rewritten_dict) }
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-- Class constraint and given equality: use the equality to rewrite
-- the class constraint.
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doInteractWithInert _fdimprs 
                    (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi }) 
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                    (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty }) 
  | ifl `canRewrite` wfl
  , tv `elemVarSet` tyVarsOfType ty 
  = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty) 
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       ; mkIRContinue rewritten_ip KeepInert emptyWorkList } 
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doInteractWithInert _fdimprs 
                    (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty }) 
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           workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
  | wfl `canRewrite` ifl
  , tv `elemVarSet` tyVarsOfType ty
  = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty) 
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       ; mkIRContinue workItem DropInert (workListFromCCan rewritten_ip) }
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-- Two implicit parameter constraints.  If the names are the same,
-- but their types are not, we generate a wanted type equality 
-- that equates the type (this is "improvement").  
-- However, we don't actually need the coercion evidence,
-- so we just generate a fresh coercion variable that isn't used anywhere.
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doInteractWithInert _fdimprs 
                    (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 }) 
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           workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
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  | nm1 == nm2 && isGiven wfl && isGiven ifl
  = 	-- See Note [Overriding implicit parameters]
        -- Dump the inert item, override totally with the new one
	-- Do not require type equality
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    mkIRContinue workItem DropInert emptyWorkList
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  | nm1 == nm2 && ty1 `tcEqType` ty2 
  = solveOneFromTheOther (id1,ifl) workItem 

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  | nm1 == nm2
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  =  	-- See Note [When improvement happens]
    do { co_var <- newWantedCoVar ty1 ty2 
       ; let flav = Wanted (combineCtLoc ifl wfl) 
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       ; cans <- mkCanonical flav co_var 
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       ; mkIRContinue workItem KeepInert cans }
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-- Inert: equality, work item: function equality

-- Never rewrite a given with a wanted equality, and a type function
-- equality can never rewrite an equality.  Note also that if we have
-- F x1 ~ x2 and a ~ x3, and a occurs in x2, we don't rewrite it.  We
-- can wait until F x1 ~ x2 matches another F x1 ~ x4, and only then
-- we will ``expose'' x2 and x4 to rewriting.

-- Otherwise, we can try rewriting the type function equality with the equality.
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doInteractWithInert _fdimprs
                    (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 }) 
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                    (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
                               , cc_tyargs = args, cc_rhs = xi2 })
  | ifl `canRewrite` wfl 
  , tv `elemVarSet` tyVarsOfTypes args
  = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2) 
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       ; mkIRStop KeepInert (workListFromCCan rewritten_funeq) } 
         -- must Stop here, because we may no longer be inert after the rewritting.
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-- Inert: function equality, work item: equality
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doInteractWithInert _fdimprs
                    (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
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                              , cc_tyargs = args, cc_rhs = xi1 }) 
           workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
  | wfl `canRewrite` ifl
  , tv `elemVarSet` tyVarsOfTypes args
  = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1) 
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       ; mkIRContinue workItem DropInert (workListFromCCan rewritten_funeq) } 
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doInteractWithInert _fdimprs
                    (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
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                               , cc_tyargs = args1, cc_rhs = xi1 }) 
           workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
                               , cc_tyargs = args2, cc_rhs = xi2 })
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  | fl1 `canSolve` fl2 && lhss_match
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  = do { cans <- rewriteEqLHS LeftComesFromInert  (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2) 
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       ; mkIRStop KeepInert cans } 
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  | fl2 `canSolve` fl1 && lhss_match
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  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1) 
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       ; mkIRContinue workItem DropInert cans }
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  where
    lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2) 

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doInteractWithInert _fdimprs 
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           inert@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 }) 
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           workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
-- Check for matching LHS 
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  | fl1 `canSolve` fl2 && tv1 == tv2 
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  = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2) 
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       ; mkIRStop KeepInert cans } 
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  | fl2 `canSolve` fl1 && tv1 == tv2 
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  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1) 
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       ; mkIRContinue workItem DropInert cans } 
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-- Check for rewriting RHS 
  | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2 
  = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2) 
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       ; mkIRStop KeepInert rewritten_eq }
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  | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
  = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1) 
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       ; mkIRContinue workItem DropInert rewritten_eq } 
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-- Finally, if workitem is a Flatten Equivalence Class constraint and the 
-- inert is a wanted constraint, even when the workitem cannot rewrite the 
-- inert, drop the inert out because you may have to reconsider solving the 
-- inert *using* the equivalence class you created. See note [Loopy Spontaneous Solving]
-- and [InertSet FlattenSkolemEqClass] 
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  | not $ isGiven fl1,                  -- The inert is wanted or derived
    isMetaTyVar tv1,                    -- and has a unification variable lhs
    FlatSkol {} <- tcTyVarDetails tv2,  -- And workitem is a flatten skolem equality
    Just tv2'   <- tcGetTyVar_maybe xi2, FlatSkol {} <- tcTyVarDetails tv2' 
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  = mkIRContinue workItem DropInert (workListFromCCan inert)   
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-- Fall-through case for all other situations
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doInteractWithInert _fdimprs _ workItem = noInteraction workItem
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-------------------------
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-- Equational Rewriting 
rewriteDict  :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
rewriteDict (cv,tv,xi) (dv,gw,cl,xis) 
  = do { let cos  = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
             args = substTysWith [tv] [xi] xis
             con  = classTyCon cl 
             dict_co = mkTyConCoercion con cos 
       ; dv' <- newDictVar cl args 
       ; case gw of 
           Wanted {}         -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
           _given_or_derived -> setDictBind dv' (EvCast dv dict_co) 
       ; return (CDictCan { cc_id = dv'
                          , cc_flavor = gw 
                          , cc_class = cl 
                          , cc_tyargs = args }) } 

rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt 
rewriteIP (cv,tv,xi) (ipid,gw,nm,ty) 
  = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty     -- ty[tv] ~ t[xi] 
             ty'   = substTyWith [tv] [xi] ty
       ; ipid' <- newIPVar nm ty' 
       ; case gw of 
           Wanted {}         -> setIPBind ipid  (EvCast ipid' (mkSymCoercion ip_co))
           _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co) 
       ; return (CIPCan { cc_id = ipid'
                        , cc_flavor = gw
                        , cc_ip_nm = nm
                        , cc_ip_ty = ty' }) }
   
rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) 
  = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args 
             args'   = substTysWith [tv] [xi1] args 
             fun_co  = mkTyConCoercion tc arg_cos 
       ; cv2' <- case gw of 
                   Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2 
                                   ; setWantedCoBind cv2 $ 
                                     mkTransCoercion fun_co (mkCoVarCoercion cv2') 
                                   ; return cv2' } 
                   _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2 $
                                  mkTransCoercion (mkSymCoercion fun_co) (mkCoVarCoercion cv2) 
       ; return (CFunEqCan { cc_id = cv2'
                           , cc_flavor = gw
                           , cc_tyargs = args'
                           , cc_fun = tc 
                           , cc_rhs = xi2 }) }


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

       ; xi2'' <- canOccursCheck gw tv2 xi2' -- we know xi2' is *not* tv2 
       ; return (singleCCan $ CTyEqCan { cc_id = cv2' 
                                       , cc_flavor = gw 
                                       , cc_tyvar = tv2 
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                                       , cc_rhs   = xi2'' })
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       }
  where 
    xi2' = substTyWith [tv1] [xi1] xi2 
    co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2  -- xi2 ~ xi2[xi1/tv1]

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rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
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-- Used to ineract two equalities of the following form: 
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-- First Equality:   co1: (XXX ~ xi1)  
-- Second Equality:  cv2: (XXX ~ xi2) 
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-- Where the cv1 `canSolve` cv2 equality 
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-- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1). This 
-- depends on whether the left or the right equality comes from the inert set. 
-- We must:  
--     prefer to create (xi2 ~ xi1) if the first comes from the inert 
--     prefer to create (xi1 ~ xi2) if the second comes from the inert 
rewriteEqLHS which (co1,xi1) (cv2,gw,xi2) 
  = do { cv2' <- case (isWanted gw, which) of 
                   (True,LeftComesFromInert) ->
                       do { cv2' <- newWantedCoVar xi2 xi1 
                          ; setWantedCoBind cv2 $ 
                            co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
                          ; return cv2' } 
                   (True,RightComesFromInert) -> 
                       do { cv2' <- newWantedCoVar xi1 xi2 
                          ; setWantedCoBind cv2 $ 
                            co1 `mkTransCoercion` mkCoVarCoercion cv2'
                          ; return cv2' } 
                   (False,LeftComesFromInert) ->
                       newGivOrDerCoVar xi2 xi1 $ 
                       mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1 
                   (False,RightComesFromInert) -> 
                        newGivOrDerCoVar xi1 xi2 $ 
                        mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
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       ; mkCanonical gw cv2'
       }
                                           
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solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult 
-- First argument inert, second argument workitem. They both represent 
-- wanted/given/derived evidence for the *same* predicate so we try here to 
-- discharge one directly from the other. 
--
-- Precondition: value evidence only (implicit parameters, classes) 
--               not coercion
solveOneFromTheOther (iid,ifl) workItem 
      -- Both derived needs a special case. You might think that we do not need
      -- two evidence terms for the same claim. But, since the evidence is partial, 
      -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
      -- See also Example 3 in Note [Superclasses and recursive dictionaries] 
  | isDerived ifl && isDerived wfl 
  = noInteraction workItem 

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  | ifl `canSolve` wfl
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  = do { unless (isGiven wfl) $ setEvBind wid (EvId iid) 
           -- Overwrite the binding, if one exists
	   -- For Givens, which are lambda-bound, nothing to overwrite,
       ; dischargeWorkItem }

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  | otherwise  -- wfl `canSolve` ifl 
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  = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
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       ; mkIRContinue workItem DropInert emptyWorkList }
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  where 
     wfl = cc_flavor workItem
     wid = cc_id workItem
\end{code}

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

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

When we simplify a wanted constraint, if we first see a matching
instance, we may produce new wanted work. To (1) avoid doing this work 
twice in the future and (2) to handle recursive dictionaries we may ``cache'' 
this item as solved (in effect, given) into our inert set and with that add 
its superclass constraints (as given) in our worklist. 

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

Example 1: 

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

and wanted (Foo [t] t). We are first going to see that the instance matches 
and create an inert set that includes the solved (Foo [t] t) and its 
superclasses. 
       d1 :_g Foo [t] t                 d1 := EvDFunApp fooDFun d3 
       d2 :_g Eq t                      d2 := EvSuperClass d1 0 
Our work list is going to contain a new *wanted* goal
       d3 :_w Eq t 
It is wrong to react the wanted (Eq t) with the given (Eq t) because that would 
construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert. 

OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries, 
at all? Consider

Example 2:

    data D r = ZeroD | SuccD (r (D r));
    
    instance (Eq (r (D r))) => Eq (D r) where
        ZeroD     == ZeroD     = True
        (SuccD a) == (SuccD b) = a == b
        _         == _         = False;
    
    equalDC :: D [] -> D [] -> Bool;
    equalDC = (==);

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

	d1 :_w Eq (D [])

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

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

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

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


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

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

    class Data Maybe a => Foo a    

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

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

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

So our problem is this
    d0 :_g Foo t
    d1 :_w Data Maybe [t] 

We may add the given in the inert set, along with its superclasses
[assuming we don't fail because there is a matching instance, see 
 tryTopReact, given case ]
  Inert:
    d0 :_g Foo t 
  WorkList 
    d01 :_g Data Maybe t  -- d2 := EvDictSuperClass d0 0 
    d1 :_w Data Maybe [t] 
Then d2 can readily enter the inert, and we also do solving of the wanted
  Inert: 
    d0 :_g Foo t 
    d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3 
  WorkList
    d2 :_w Sat (Maybe [t])          
    d3 :_w Data Maybe t
    d01 :_g Data Maybe t 
Now, we may simplify d2 more: 
  Inert:
      d0 :_g Foo t 
      d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3 
      d1 :_g Data Maybe [t] 
      d2 :_g Sat (Maybe [t])          d2 := dfunSat d4 
  WorkList: 
      d3 :_w Data Maybe t 
      d4 :_w Foo [t] 
      d01 :_g Data Maybe t 

Now, we can just solve d3.
  Inert
      d0 :_g Foo t 
      d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3 
      d2 :_g Sat (Maybe [t])          d2 := dfunSat d4 
  WorkList
      d4 :_w Foo [t] 
      d01 :_g Data Maybe t 
And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
  Inert
      d0 :_g Foo t 
      d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3 
      d2 :_g Sat (Maybe [t])          d2 := dfunSat d4 
      d4 :_g Foo [t]                  d4 := dfunFoo2 d5 
  WorkList:
      d5 :_w Foo t 
      d6 :_g Data Maybe [t]           d6 := EvDictSuperClass d4 0
      d01 :_g Data Maybe t 
Now, d5 can be solved! (and its superclass enter scope) 
  Inert
      d0 :_g Foo t 
      d1 :_s Data Maybe [t]           d1 := dfunData2 d2 d3 
      d2 :_g Sat (Maybe [t])          d2 := dfunSat d4 
      d4 :_g Foo [t]                  d4 := dfunFoo2 d5 
      d5 :_g Foo t                    d5 := dfunFoo1 d7
  WorkList:
      d7 :_w Data Maybe t
      d6 :_g Data Maybe [t]
      d8 :_g Data Maybe t            d8 := EvDictSuperClass d5 0
      d01 :_g Data Maybe t 

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

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

      So, no interaction happens there. Then we meet d01 and there is no recursion 
      problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01! 
             
Note [SUPERCLASS-LOOP 1]
~~~~~~~~~~~~~~~~~~~~~~~~
We have to be very, very careful when generating superclasses, lest we
accidentally build a loop. Here's an example:

  class S a

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

    class Data Maybe a => Foo a

    instance Foo t => Sat (Maybe t)

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

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

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

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

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

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

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

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


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

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


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