\begin{code}
{-# OPTIONS -fno-warn-tabs #-}
-- The above warning supression flag is a temporary kludge.
-- While working on this module you are encouraged to remove it and
-- detab the module (please do the detabbing in a separate patch). See
-- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#TabsvsSpaces
-- for details
module TcInteract (
solveInteractGiven, -- Solves [EvVar],GivenLoc
solveInteractCts, -- Solves [Cts]
) where
#include "HsVersions.h"
import BasicTypes ()
import TcCanonical
import VarSet
import Type
import Unify
import FamInstEnv
import Coercion( mkAxInstRHS )
import Var
import TcType
import PrelNames (singIClassName)
import Class
import TyCon
import Name
import IParam
import FunDeps
import TcEvidence
import Outputable
import TcMType ( zonkTcPredType )
import TcRnTypes
import TcErrors
import TcSMonad
import Maybes( orElse )
import Bag
import Control.Monad ( foldM )
import VarEnv
import qualified Data.Traversable as Traversable
import Data.Maybe ( isJust )
import Control.Monad( when, unless )
import Pair ()
import UniqFM
import FastString ( sLit )
import DynFlags
import Util
\end{code}
**********************************************************************
* *
* Main Interaction Solver *
* *
**********************************************************************
Note [Basic Simplifier Plan]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. Pick an element from the WorkList if there exists one with depth
less thanour context-stack depth.
2. Run it down the 'stage' pipeline. Stages are:
- canonicalization
- inert reactions
- spontaneous reactions
- top-level intreactions
Each stage returns a StopOrContinue and may have sideffected
the inerts or worklist.
The threading of the stages is as follows:
- If (Stop) is returned by a stage then we start again from Step 1.
- If (ContinueWith ct) is returned by a stage, we feed 'ct' on to
the next stage in the pipeline.
4. If the element has survived (i.e. ContinueWith x) the last stage
then we add him in the inerts and jump back to Step 1.
If in Step 1 no such element exists, we have exceeded our context-stack
depth and will simply fail.
\begin{code}
solveInteractCts :: [Ct] -> TcS (Bag Implication)
-- Returns a bag of residual implications that have arisen while solving
-- this particular worklist.
solveInteractCts cts
= do { traceTcS "solveInteractCtS" (vcat [ text "cts =" <+> ppr cts ])
; updWorkListTcS (appendWorkListCt cts) >> solveInteract
; impls <- getTcSImplics
; updTcSImplics (const emptyBag) -- Nullify residual implications
; return impls }
solveInteractGiven :: GivenLoc -> [EvVar] -> TcS (Bag Implication)
-- In principle the givens can kick out some wanteds from the inert
-- resulting in solving some more wanted goals here which could emit
-- implications. That's why I return a bag of implications. Not sure
-- if this can happen in practice though.
solveInteractGiven gloc evs
= solveInteractCts (map mk_noncan evs)
where
mk_noncan ev = CNonCanonical { cc_ev = Given { ctev_gloc = gloc
, ctev_evtm = EvId ev
, ctev_pred = evVarPred ev }
, cc_depth = 0 }
-- The main solver loop implements Note [Basic Simplifier Plan]
---------------------------------------------------------------
solveInteract :: TcS ()
-- Returns the final InertSet in TcS, WorkList will be eventually empty.
solveInteract
= {-# SCC "solveInteract" #-}
do { dyn_flags <- getDynFlags
; let max_depth = ctxtStkDepth dyn_flags
solve_loop
= {-# SCC "solve_loop" #-}
do { sel <- selectNextWorkItem max_depth
; case sel of
NoWorkRemaining -- Done, successfuly (modulo frozen)
-> return ()
MaxDepthExceeded ct -- Failure, depth exceeded
-> wrapErrTcS $ solverDepthErrorTcS (cc_depth ct) [ct]
NextWorkItem ct -- More work, loop around!
-> runSolverPipeline thePipeline ct >> solve_loop }
; solve_loop }
type WorkItem = Ct
type SimplifierStage = WorkItem -> TcS StopOrContinue
continueWith :: WorkItem -> TcS StopOrContinue
continueWith work_item = return (ContinueWith work_item)
data SelectWorkItem
= NoWorkRemaining -- No more work left (effectively we're done!)
| MaxDepthExceeded Ct -- More work left to do but this constraint has exceeded
-- the max subgoal depth and we must stop
| NextWorkItem Ct -- More work left, here's the next item to look at
selectNextWorkItem :: SubGoalDepth -- Max depth allowed
-> TcS SelectWorkItem
selectNextWorkItem max_depth
= updWorkListTcS_return pick_next
where
pick_next :: WorkList -> (SelectWorkItem, WorkList)
pick_next wl = case selectWorkItem wl of
(Nothing,_)
-> (NoWorkRemaining,wl) -- No more work
(Just ct, new_wl)
| cc_depth ct > max_depth -- Depth exceeded
-> (MaxDepthExceeded ct,new_wl)
(Just ct, new_wl)
-> (NextWorkItem ct, new_wl) -- New workitem and worklist
runSolverPipeline :: [(String,SimplifierStage)] -- The pipeline
-> WorkItem -- The work item
-> TcS ()
-- Run this item down the pipeline, leaving behind new work and inerts
runSolverPipeline pipeline workItem
= do { initial_is <- getTcSInerts
; traceTcS "Start solver pipeline {" $
vcat [ ptext (sLit "work item = ") <+> ppr workItem
, ptext (sLit "inerts = ") <+> ppr initial_is]
; final_res <- run_pipeline pipeline (ContinueWith workItem)
; final_is <- getTcSInerts
; case final_res of
Stop -> do { traceTcS "End solver pipeline (discharged) }"
(ptext (sLit "inerts = ") <+> ppr final_is)
; return () }
ContinueWith ct -> do { traceTcS "End solver pipeline (not discharged) }" $
vcat [ ptext (sLit "final_item = ") <+> ppr ct
, ptext (sLit "inerts = ") <+> ppr final_is]
; updInertSetTcS ct }
}
where run_pipeline :: [(String,SimplifierStage)] -> StopOrContinue -> TcS StopOrContinue
run_pipeline [] res = return res
run_pipeline _ Stop = return Stop
run_pipeline ((stg_name,stg):stgs) (ContinueWith ct)
= do { traceTcS ("runStage " ++ stg_name ++ " {")
(text "workitem = " <+> ppr ct)
; res <- stg ct
; traceTcS ("end stage " ++ stg_name ++ " }") empty
; run_pipeline stgs res
}
\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}
thePipeline :: [(String,SimplifierStage)]
thePipeline = [ ("lookup-in-inerts", lookupInInertsStage)
, ("canonicalization", canonicalizationStage)
, ("spontaneous solve", spontaneousSolveStage)
, ("interact with inerts", interactWithInertsStage)
, ("top-level reactions", topReactionsStage) ]
\end{code}
\begin{code}
-- A quick lookup everywhere to see if we know about this constraint
--------------------------------------------------------------------
lookupInInertsStage :: SimplifierStage
lookupInInertsStage ct
| Wanted { ctev_evar = ev_id, ctev_pred = pred } <- cc_ev ct
= do { is <- getTcSInerts
; case lookupInInerts is pred of
Just ctev
| not (isDerived ctev)
-> do { setEvBind ev_id (ctEvTerm ctev)
; return Stop }
_ -> continueWith ct }
| otherwise -- I could do something like that for givens
-- as well I suppose but it is not a big deal
= continueWith ct
-- The canonicalization stage, see TcCanonical for details
----------------------------------------------------------
canonicalizationStage :: SimplifierStage
canonicalizationStage = TcCanonical.canonicalize
\end{code}
*********************************************************************************
* *
The spontaneous-solve Stage
* *
*********************************************************************************
Note [Efficient Orientation]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There are two cases where we have to be careful about
orienting equalities to get better efficiency.
Case 1: In Rewriting Equalities (function rewriteEqLHS)
When rewriting two equalities with the same LHS:
(a) (tv ~ xi1)
(b) (tv ~ xi2)
We have a choice of producing work (xi1 ~ xi2) (up-to the
canonicalization invariants) However, to prevent the inert items
from getting kicked out of the inerts first, we prefer to
canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
~ xi1) if (a) comes from the inert set.
Case 2: Functional Dependencies
Again, we should prefer, if possible, the inert variables on the RHS
Case 3: IP improvement work
We must always rewrite so that the inert type is on the right.
\begin{code}
spontaneousSolveStage :: SimplifierStage
spontaneousSolveStage workItem
= do { mSolve <- trySpontaneousSolve workItem
; spont_solve mSolve }
where spont_solve SPCantSolve
| isCTyEqCan workItem -- Unsolved equality
= do { kickOutRewritableInerts workItem -- NB: will add workItem in inerts
; return Stop }
| otherwise
= continueWith workItem
spont_solve (SPSolved workItem') -- Post: workItem' must be equality
= do { bumpStepCountTcS
; traceFireTcS (cc_depth workItem) $
ptext (sLit "Spontaneous:") <+> ppr workItem
-- NB: will add the item in the inerts
; kickOutRewritableInerts workItem'
-- .. and Stop
; return Stop }
kickOutRewritableInerts :: Ct -> TcS ()
-- Pre: ct is a CTyEqCan
-- Post: The TcS monad is left with the thinner non-rewritable inerts; but which
-- contains the new constraint.
-- The rewritable end up in the worklist
kickOutRewritableInerts ct
= {-# SCC "kickOutRewritableInerts" #-}
do { traceTcS "kickOutRewritableInerts" $ text "workitem = " <+> ppr ct
; (wl,ieqs) <- {-# SCC "kick_out_rewritable" #-}
modifyInertTcS (kick_out_rewritable ct)
; traceTcS "Kicked out the following constraints" $ ppr wl
; is <- getTcSInerts
; traceTcS "Remaining inerts are" $ ppr is
-- Step 1: Rewrite as many of the inert_eqs on the spot!
-- NB: if it is a given constraint just use the cached evidence
-- to optimize e.g. mkRefl coercions from spontaneously solved cts.
; bnds <- getTcEvBindsMap
; let ct_coercion = getCtCoercion bnds ct
; new_ieqs <- {-# SCC "rewriteInertEqsFromInertEq" #-}
rewriteInertEqsFromInertEq (cc_tyvar ct,
ct_coercion,cc_ev ct) ieqs
; let upd_eqs is = is { inert_cans = new_ics }
where ics = inert_cans is
new_ics = ics { inert_eqs = new_ieqs }
; modifyInertTcS (\is -> ((), upd_eqs is))
; is <- getTcSInerts
; traceTcS "Final inerts are" $ ppr is
-- Step 2: Add the new guy in
; updInertSetTcS ct
; traceTcS "Kick out" (ppr ct $$ ppr wl)
; updWorkListTcS (unionWorkList wl) }
rewriteInertEqsFromInertEq :: (TcTyVar, TcCoercion, CtEvidence) -- A new substitution
-> TyVarEnv Ct -- All the inert equalities
-> TcS (TyVarEnv Ct) -- The new inert equalities
rewriteInertEqsFromInertEq (subst_tv, _subst_co, subst_fl) ieqs
-- The goal: traverse the inert equalities and throw some of them back to the worklist
-- if you have to rewrite and recheck them for occurs check errors.
-- To see which ones we must throw out see Note [Delicate equality kick-out]
= do { mieqs <- Traversable.mapM do_one ieqs
; traceTcS "Original inert equalities:" (ppr ieqs)
; let flatten_justs elem venv
| Just act <- elem = extendVarEnv venv (cc_tyvar act) act
| otherwise = venv
final_ieqs = foldVarEnv flatten_justs emptyVarEnv mieqs
; traceTcS "Remaining inert equalities:" (ppr final_ieqs)
; return final_ieqs }
where do_one ct
| subst_fl `canRewrite` fl && (subst_tv `elemVarSet` tyVarsOfCt ct)
= if fl `canRewrite` subst_fl then
-- If also the inert can rewrite the subst then there is no danger of
-- occurs check errors sor keep it there. No need to rewrite the inert equality
-- (as we did in the past) because of point (8) of
-- Note [Detailed InertCans Invariants] and
return (Just ct)
-- used to be: rewrite_on_the_spot ct >>= ( return . Just )
else -- We have to throw inert back to worklist for occurs checks
updWorkListTcS (extendWorkListEq ct) >> return Nothing
| otherwise -- Just keep it there
= return (Just ct)
where
fl = cc_ev ct
kick_out_rewritable :: Ct
-> InertSet
-> ((WorkList, TyVarEnv Ct),InertSet)
-- Post: returns ALL inert equalities, to be dealt with later
--
kick_out_rewritable ct is@(IS { inert_cans =
IC { inert_eqs = eqmap
, inert_eq_tvs = inscope
, inert_dicts = dictmap
, inert_ips = ipmap
, inert_funeqs = funeqmap
, inert_irreds = irreds }
, inert_frozen = frozen })
= ((kicked_out,eqmap), remaining)
where
rest_out = fro_out `andCts` dicts_out
`andCts` ips_out `andCts` irs_out
kicked_out = WorkList { wl_eqs = []
, wl_funeqs = bagToList feqs_out
, wl_rest = bagToList rest_out }
remaining = is { inert_cans = IC { inert_eqs = emptyVarEnv
, inert_eq_tvs = inscope
-- keep the same, safe and cheap
, inert_dicts = dicts_in
, inert_ips = ips_in
, inert_funeqs = feqs_in
, inert_irreds = irs_in }
, inert_frozen = fro_in }
-- NB: Notice that don't rewrite
-- inert_solved, inert_flat_cache and inert_solved_funeqs
-- optimistically. But when we lookup we have to take the
-- subsitution into account
fl = cc_ev ct
tv = cc_tyvar ct
(ips_out, ips_in) = partitionCCanMap rewritable ipmap
(feqs_out, feqs_in) = partCtFamHeadMap rewritable funeqmap
(dicts_out, dicts_in) = partitionCCanMap rewritable dictmap
(irs_out, irs_in) = partitionBag rewritable irreds
(fro_out, fro_in) = partitionBag rewritable frozen
rewritable ct = (fl `canRewrite` cc_ev ct) &&
(tv `elemVarSet` tyVarsOfCt ct)
-- NB: tyVarsOfCt will return the type
-- variables /and the kind variables/ that are
-- directly visible in the type. Hence we will
-- have exposed all the rewriting we care about
-- to make the most precise kinds visible for
-- matching classes etc. No need to kick out
-- constraints that mention type variables whose
-- kinds could contain this variable!
\end{code}
Note [Delicate equality kick-out]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Delicate:
When kicking out rewritable constraints, it would be safe to simply
kick out all rewritable equalities, but instead we only kick out those
that, when rewritten, may result in occur-check errors. Example:
WorkItem = [G] a ~ b
Inerts = { [W] b ~ [a] }
Now at this point the work item cannot be further rewritten by the
inert (due to the weaker inert flavor). Instead the workitem can
rewrite the inert leading to potential occur check errors. So we must
kick the inert out. On the other hand, if the inert flavor was as
powerful or more powerful than the workitem flavor, the work-item could
not have reached this stage (because it would have already been
rewritten by the inert).
The coclusion is: we kick out the 'dangerous' equalities that may
require recanonicalization (occurs checks) and the rest we keep
there in the inerts without further checks.
In the past we used to rewrite-on-the-spot those equalities that we keep in,
but this is no longer necessary see Note [Non-idempotent inert substitution].
\begin{code}
data SPSolveResult = SPCantSolve
| SPSolved WorkItem
-- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
-- SPSolved workItem' gives us a new *given* to go on
-- @trySpontaneousSolve wi@ solves equalities where one side is a
-- touchable unification variable.
-- See Note [Touchables and givens]
trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
trySpontaneousSolve workItem@(CTyEqCan { cc_ev = gw
, cc_tyvar = tv1, cc_rhs = xi, cc_depth = d })
| isGiven gw
= return SPCantSolve
| Just tv2 <- tcGetTyVar_maybe xi
= do { tch1 <- isTouchableMetaTyVar tv1
; tch2 <- isTouchableMetaTyVar tv2
; case (tch1, tch2) of
(True, True) -> trySpontaneousEqTwoWay d gw tv1 tv2
(True, False) -> trySpontaneousEqOneWay d gw tv1 xi
(False, True) -> trySpontaneousEqOneWay d gw tv2 (mkTyVarTy tv1)
_ -> return SPCantSolve }
| otherwise
= do { tch1 <- isTouchableMetaTyVar tv1
; if tch1 then trySpontaneousEqOneWay d gw tv1 xi
else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:" $
ppr workItem
; return SPCantSolve }
}
-- No need for
-- trySpontaneousSolve (CFunEqCan ...) = ...
-- See Note [No touchables as FunEq RHS] in TcSMonad
trySpontaneousSolve _ = return SPCantSolve
----------------
trySpontaneousEqOneWay :: SubGoalDepth
-> CtEvidence -> TcTyVar -> Xi -> TcS SPSolveResult
-- tv is a MetaTyVar, not untouchable
trySpontaneousEqOneWay d gw tv xi
| not (isSigTyVar tv) || isTyVarTy xi
= solveWithIdentity d gw tv xi
| otherwise -- Still can't solve, sig tyvar and non-variable rhs
= return SPCantSolve
----------------
trySpontaneousEqTwoWay :: SubGoalDepth
-> CtEvidence -> TcTyVar -> TcTyVar -> TcS SPSolveResult
-- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
trySpontaneousEqTwoWay d gw tv1 tv2
= do { let k1_sub_k2 = k1 `tcIsSubKind` k2
; if k1_sub_k2 && nicer_to_update_tv2
then solveWithIdentity d gw tv2 (mkTyVarTy tv1)
else solveWithIdentity d gw tv1 (mkTyVarTy tv2) }
where
k1 = tyVarKind tv1
k2 = tyVarKind tv2
nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
\end{code}
Note [Kind errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the wanted problem:
alpha ~ (# Int, Int #)
where alpha :: ArgKind and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
get quantified over in inference mode. That's bad because we do know at this point that the
constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
The same applies in canonicalization code in case of kind errors in the givens.
However, when we canonicalize givens we only check for compatibility (@compatKind@).
If there were a kind error in the givens, this means some form of inconsistency or dead code.
You may think that when we spontaneously solve wanteds we may have to look through the
bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
@alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
so this situation can't happen.
Note [Spontaneous solving and kind compatibility]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that our canonical constraints insist that *all* equalities (tv ~
xi) or (F xis ~ rhs) require the LHS and the RHS to have *compatible*
the same kinds. ("compatible" means one is a subKind of the other.)
- It can't be *equal* kinds, because
b) wanted constraints don't necessarily have identical kinds
eg alpha::? ~ Int
b) a solved wanted constraint becomes a given
- SPJ thinks that *given* constraints (tv ~ tau) always have that
tau has a sub-kind of tv; and when solving wanted constraints
in trySpontaneousEqTwoWay we re-orient to achieve this.
- Note that the kind invariant is maintained by rewriting.
Eg wanted1 rewrites wanted2; if both were compatible kinds before,
wanted2 will be afterwards. Similarly givens.
Caveat:
- Givens from higher-rank, such as:
type family T b :: * -> * -> *
type instance T Bool = (->)
f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
flop = f (...) True
Whereas we would be able to apply the type instance, we would not be able to
use the given (T Bool ~ (->)) in the body of 'flop'
Note [Avoid double unifications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The spontaneous solver has to return a given which mentions the unified unification
variable *on the left* of the equality. Here is what happens if not:
Original wanted: (a ~ alpha), (alpha ~ Int)
We spontaneously solve the first wanted, without changing the order!
given : a ~ alpha [having unified alpha := a]
Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
We avoid this problem by orienting the resulting given so that the unification
variable is on the left. [Note that alternatively we could attempt to
enforce this at canonicalization]
See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
double unifications is the main reason we disallow touchable
unification variables as RHS of type family equations: F xis ~ alpha.
\begin{code}
----------------
solveWithIdentity :: SubGoalDepth
-> CtEvidence -> TcTyVar -> Xi -> TcS SPSolveResult
-- Solve with the identity coercion
-- Precondition: kind(xi) is a sub-kind of kind(tv)
-- Precondition: CtEvidence is Wanted or Derived
-- See [New Wanted Superclass Work] to see why solveWithIdentity
-- must work for Derived as well as Wanted
-- Returns: workItem where
-- workItem = the new Given constraint
--
-- NB: No need for an occurs check here, because solveWithIdentity always
-- arises from a CTyEqCan, a *canonical* constraint. Its invariants
-- say that in (a ~ xi), the type variable a does not appear in xi.
-- See TcRnTypes.Ct invariants.
solveWithIdentity d wd tv xi
= do { let tv_ty = mkTyVarTy tv
; traceTcS "Sneaky unification:" $
vcat [text "Constraint:" <+> ppr wd,
text "Coercion:" <+> pprEq tv_ty xi,
text "Left Kind is:" <+> ppr (typeKind tv_ty),
text "Right Kind is:" <+> ppr (typeKind xi) ]
; let xi' = defaultKind xi
-- We only instantiate kind unification variables
-- with simple kinds like *, not OpenKind or ArgKind
-- cf TcUnify.uUnboundKVar
; setWantedTyBind tv xi'
; let refl_evtm = EvCoercion (mkTcReflCo xi')
refl_pred = mkTcEqPred tv_ty xi'
; when (isWanted wd) $
setEvBind (ctev_evar wd) refl_evtm
; let given_fl = Given { ctev_gloc = mkGivenLoc (ctev_wloc wd) UnkSkol
, ctev_pred = refl_pred
, ctev_evtm = refl_evtm }
; return $
SPSolved (CTyEqCan { cc_ev = given_fl
, cc_tyvar = tv, cc_rhs = xi', cc_depth = d }) }
\end{code}
*********************************************************************************
* *
The interact-with-inert Stage
* *
*********************************************************************************
Note [The Solver Invariant]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
We always add Givens first. So you might think that the solver has
the invariant
If the work-item is Given,
then the inert item must Given
But this isn't quite true. Suppose we have,
c1: [W] beta ~ [alpha], c2 : [W] blah, c3 :[W] alpha ~ Int
After processing the first two, we get
c1: [G] beta ~ [alpha], c2 : [W] blah
Now, c3 does not interact with the the given c1, so when we spontaneously
solve c3, we must re-react it with the inert set. So we can attempt a
reaction between inert c2 [W] and work-item c3 [G].
It *is* true that [Solver Invariant]
If the work-item is Given,
AND there is a reaction
then the inert item must Given
or, equivalently,
If the work-item is Given,
and the inert item is Wanted/Derived
then there is no reaction
\begin{code}
-- Interaction result of WorkItem <~> Ct
data InteractResult
= IRWorkItemConsumed { ir_fire :: String }
| IRInertConsumed { ir_fire :: String }
| IRKeepGoing { ir_fire :: String }
irWorkItemConsumed :: String -> TcS InteractResult
irWorkItemConsumed str = return (IRWorkItemConsumed str)
irInertConsumed :: String -> TcS InteractResult
irInertConsumed str = return (IRInertConsumed str)
irKeepGoing :: String -> TcS InteractResult
irKeepGoing str = return (IRKeepGoing str)
-- You can't discard neither workitem or inert, but you must keep
-- going. It's possible that new work is waiting in the TcS worklist.
interactWithInertsStage :: WorkItem -> TcS StopOrContinue
-- Precondition: if the workitem is a CTyEqCan then it will not be able to
-- react with anything at this stage.
interactWithInertsStage wi
= do { traceTcS "interactWithInerts" $ text "workitem = " <+> ppr wi
; rels <- extractRelevantInerts wi
; traceTcS "relevant inerts are:" $ ppr rels
; foldlBagM interact_next (ContinueWith wi) rels }
where interact_next Stop atomic_inert
= updInertSetTcS atomic_inert >> return Stop
interact_next (ContinueWith wi) atomic_inert
= do { ir <- doInteractWithInert atomic_inert wi
; let mk_msg rule keep_doc
= vcat [ text rule <+> keep_doc
, ptext (sLit "InertItem =") <+> ppr atomic_inert
, ptext (sLit "WorkItem =") <+> ppr wi ]
; case ir of
IRWorkItemConsumed { ir_fire = rule }
-> do { bumpStepCountTcS
; traceFireTcS (cc_depth wi)
(mk_msg rule (text "WorkItemConsumed"))
; updInertSetTcS atomic_inert
; return Stop }
IRInertConsumed { ir_fire = rule }
-> do { bumpStepCountTcS
; traceFireTcS (cc_depth atomic_inert)
(mk_msg rule (text "InertItemConsumed"))
; return (ContinueWith wi) }
IRKeepGoing {} -- Should we do a bumpStepCountTcS? No for now.
-> do { updInertSetTcS atomic_inert
; return (ContinueWith wi) }
}
\end{code}
\begin{code}
--------------------------------------------
doInteractWithInert :: Ct -> Ct -> TcS InteractResult
-- Identical class constraints.
doInteractWithInert
inertItem@(CDictCan { cc_ev = fl1, cc_class = cls1, cc_tyargs = tys1 })
workItem@(CDictCan { cc_ev = fl2, cc_class = cls2, cc_tyargs = tys2 })
| cls1 == cls2
= do { let pty1 = mkClassPred cls1 tys1
pty2 = mkClassPred cls2 tys2
inert_pred_loc = (pty1, pprFlavorArising fl1)
work_item_pred_loc = (pty2, pprFlavorArising fl2)
; traceTcS "doInteractWithInert" (vcat [ text "inertItem = " <+> ppr inertItem
, text "workItem = " <+> ppr workItem ])
; any_fundeps
<- if isGiven fl1 && isGiven fl2 then return Nothing
-- NB: We don't create fds for given (and even solved), have not seen a useful
-- situation for these and even if we did we'd have to be very careful to only
-- create Derived's and not Wanteds.
else do { let fd_eqns = improveFromAnother inert_pred_loc work_item_pred_loc
wloc = getWantedLoc fl2
; rewriteWithFunDeps fd_eqns tys2 wloc }
-- See Note [Efficient Orientation], [When improvement happens]
; case any_fundeps of
-- No Functional Dependencies
Nothing
| eqTypes tys1 tys2 -> solveOneFromTheOther "Cls/Cls" fl1 workItem
| otherwise -> irKeepGoing "NOP"
-- Actual Functional Dependencies
Just (_rewritten_tys2, fd_work)
-- Standard thing: create derived fds and keep on going. Importantly we don't
-- throw workitem back in the worklist because this can cause loops. See #5236.
-> do { emitFDWorkAsDerived fd_work (cc_depth workItem)
; irKeepGoing "Cls/Cls (new fundeps)" } -- Just keep going without droping the inert
}
-- Two pieces of irreducible evidence: if their types are *exactly identical*
-- we can rewrite them. We can never improve using this:
-- if we want ty1 :: Constraint and have ty2 :: Constraint it clearly does not
-- mean that (ty1 ~ ty2)
doInteractWithInert (CIrredEvCan { cc_ev = ifl, cc_ty = ty1 })
workItem@(CIrredEvCan { cc_ty = ty2 })
| ty1 `eqType` ty2
= solveOneFromTheOther "Irred/Irred" ifl workItem
-- Two implicit parameter constraints. If the names are the same,
-- but their types are not, we generate a wanted type equality
-- that equates the type (this is "improvement").
-- However, we don't actually need the coercion evidence,
-- so we just generate a fresh coercion variable that isn't used anywhere.
doInteractWithInert (CIPCan { cc_ev = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
workItem@(CIPCan { cc_ev = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
| nm1 == nm2 && isGiven wfl && isGiven ifl
= -- See Note [Overriding implicit parameters]
-- Dump the inert item, override totally with the new one
-- Do not require type equality
-- For example, given let ?x::Int = 3 in let ?x::Bool = True in ...
-- we must *override* the outer one with the inner one
irInertConsumed "IP/IP (override inert)"
| nm1 == nm2 && ty1 `eqType` ty2
= solveOneFromTheOther "IP/IP" ifl workItem
| nm1 == nm2
= -- See Note [When improvement happens]
do { mb_eqv <- newWantedEvVar new_wloc (mkEqPred ty2 ty1)
-- co :: ty2 ~ ty1, see Note [Efficient orientation]
; cv <- case mb_eqv of
Fresh eqv ->
do { updWorkListTcS $ extendWorkListEq $
CNonCanonical { cc_ev = eqv
, cc_depth = cc_depth workItem }
; return (ctEvTerm eqv) }
Cached eqv -> return eqv
; case wfl of
Wanted { ctev_evar = ev_id } ->
let ip_co = mkTcTyConAppCo (ipTyCon nm1) [evTermCoercion cv]
in do { setEvBind ev_id $
mkEvCast (ctEvTerm ifl) (mkTcSymCo ip_co)
; irWorkItemConsumed "IP/IP (solved by rewriting)" }
_ -> pprPanic "Unexpected IP constraint" (ppr workItem) }
where
new_wloc | isGiven wfl = getWantedLoc ifl
| otherwise = getWantedLoc wfl
doInteractWithInert ii@(CFunEqCan { cc_ev = fl1, cc_fun = tc1
, cc_tyargs = args1, cc_rhs = xi1, cc_depth = d1 })
wi@(CFunEqCan { cc_ev = fl2, cc_fun = tc2
, cc_tyargs = args2, cc_rhs = xi2, cc_depth = d2 })
{- ToDo: Check with Dimitrios
| lhss_match
, isSolved fl1 -- Inert is solved and we can simply ignore it
-- when workitem is given/solved
, isGiven fl2
= irInertConsumed "FunEq/FunEq"
| lhss_match
, isSolved fl2 -- Workitem is solved and we can ignore it when
-- the inert is given/solved
, isGiven fl1
= irWorkItemConsumed "FunEq/FunEq"
-}
| fl1 `canSolve` fl2 && lhss_match
= do { traceTcS "interact with inerts: FunEq/FunEq" $
vcat [ text "workItem =" <+> ppr wi
, text "inertItem=" <+> ppr ii ]
; let xev = XEvTerm xcomp xdecomp
-- xcomp : [(xi2 ~ xi1)] -> (F args ~ xi2)
xcomp [x] = EvCoercion (co1 `mkTcTransCo` mk_sym_co x)
xcomp _ = panic "No more goals!"
-- xdecomp : (F args ~ xi2) -> [(xi2 ~ xi1)]
xdecomp x = [EvCoercion (mk_sym_co x `mkTcTransCo` co1)]
; ctevs <- xCtFlavor_cache False fl2 [mkTcEqPred xi2 xi1] xev
-- Why not simply xCtFlavor? See Note [Cache-caused loops]
-- Why not (mkTcEqPred xi1 xi2)? See Note [Efficient orientation]
; add_to_work d2 ctevs
; irWorkItemConsumed "FunEq/FunEq" }
| fl2 `canSolve` fl1 && lhss_match
= do { traceTcS "interact with inerts: FunEq/FunEq" $
vcat [ text "workItem =" <+> ppr wi
, text "inertItem=" <+> ppr ii ]
; let xev = XEvTerm xcomp xdecomp
-- xcomp : [(xi2 ~ xi1)] -> [(F args ~ xi1)]
xcomp [x] = EvCoercion (co2 `mkTcTransCo` evTermCoercion x)
xcomp _ = panic "No more goals!"
-- xdecomp : (F args ~ xi1) -> [(xi2 ~ xi1)]
xdecomp x = [EvCoercion (mkTcSymCo co2 `mkTcTransCo` evTermCoercion x)]
; ctevs <- xCtFlavor_cache False fl1 [mkTcEqPred xi2 xi1] xev
-- Why not simply xCtFlavor? See Note [Cache-caused loops]
-- Why not (mkTcEqPred xi1 xi2)? See Note [Efficient orientation]
; add_to_work d1 ctevs
; irInertConsumed "FunEq/FunEq"}
where
add_to_work d [ctev] = updWorkListTcS $ extendWorkListEq $
CNonCanonical {cc_ev = ctev, cc_depth = d}
add_to_work _ _ = return ()
lhss_match = tc1 == tc2 && eqTypes args1 args2
co1 = evTermCoercion $ ctEvTerm fl1
co2 = evTermCoercion $ ctEvTerm fl2
mk_sym_co x = mkTcSymCo (evTermCoercion x)
doInteractWithInert _ _ = irKeepGoing "NOP"
\end{code}
Note [Cache-caused loops]
~~~~~~~~~~~~~~~~~~~~~~~~~
It is very dangerous to cache a rewritten wanted family equation as 'solved' in our
solved cache (which is the default behaviour or xCtFlavor), because the interaction
may not be contributing towards a solution. Here is an example:
Initial inert set:
[W] g1 : F a ~ beta1
Work item:
[W] g2 : F a ~ beta2
The work item will react with the inert yielding the _same_ inert set plus:
i) Will set g2 := g1 `cast` g3
ii) Will add to our solved cache that [S] g2 : F a ~ beta2
iii) Will emit [W] g3 : beta1 ~ beta2
Now, the g3 work item will be spontaneously solved to [G] g3 : beta1 ~ beta2
and then it will react the item in the inert ([W] g1 : F a ~ beta1). So it
will set
g1 := g ; sym g3
and what is g? Well it would ideally be a new goal of type (F a ~ beta2) but
remember that we have this in our solved cache, and it is ... g2! In short we
created the evidence loop:
g2 := g1 ; g3
g3 := refl
g1 := g2 ; sym g3
To avoid this situation we do not cache as solved any workitems (or inert)
which did not really made a 'step' towards proving some goal. Solved's are
just an optimization so we don't lose anything in terms of completeness of
solving.
\begin{code}
solveOneFromTheOther :: String -- Info
-> CtEvidence -- Inert
-> Ct -- WorkItem
-> TcS InteractResult
-- Preconditions:
-- 1) inert and work item represent evidence for the /same/ predicate
-- 2) ip/class/irred evidence (no coercions) only
solveOneFromTheOther info ifl workItem
| isDerived wfl
= irWorkItemConsumed ("Solved[DW] " ++ info)
| isDerived ifl -- The inert item is Derived, we can just throw it away,
-- The workItem is inert wrt earlier inert-set items,
-- so it's safe to continue on from this point
= irInertConsumed ("Solved[DI] " ++ info)
{- ToDo: Check with Dimitrios
| isSolved ifl, isGiven wfl
-- Same if the inert is a GivenSolved -- just get rid of it
= irInertConsumed ("Solved[SI] " ++ info)
-}
| otherwise
= ASSERT( ifl `canSolve` wfl )
-- Because of Note [The Solver Invariant], plus Derived dealt with
do { case wfl of
Wanted { ctev_evar = ev_id } -> setEvBind ev_id (ctEvTerm ifl)
_ -> return ()
-- Overwrite the binding, if one exists
-- If both are Given, we already have evidence; no need to duplicate
; irWorkItemConsumed ("Solved " ++ info) }
where
wfl = cc_ev workItem
\end{code}
Note [Superclasses and recursive dictionaries]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Overlaps with Note [SUPERCLASS-LOOP 1]
Note [SUPERCLASS-LOOP 2]
Note [Recursive instances and superclases]
ToDo: check overlap and delete redundant stuff
Right before adding a given into the inert set, we must
produce some more work, that will bring the superclasses
of the given into scope. The superclass constraints go into
our worklist.
When we simplify a wanted constraint, if we first see a matching
instance, we may produce new wanted work. To (1) avoid doing this work
twice in the future and (2) to handle recursive dictionaries we may ``cache''
this item as given into our inert set WITHOUT adding its superclass constraints,
otherwise we'd be in danger of creating a loop [In fact this was the exact reason
for doing the isGoodRecEv check in an older version of the type checker].
But now we have added partially solved constraints to the worklist which may
interact with other wanteds. Consider the example:
Example 1:
class Eq b => Foo a b --- 0-th selector
instance Eq a => Foo [a] a --- fooDFun
and wanted (Foo [t] t). We are first going to see that the instance matches
and create an inert set that includes the solved (Foo [t] t) but not its superclasses:
d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
Our work list is going to contain a new *wanted* goal
d3 :_w Eq t
Ok, so how do we get recursive dictionaries, at all:
Example 2:
data D r = ZeroD | SuccD (r (D r));
instance (Eq (r (D r))) => Eq (D r) where
ZeroD == ZeroD = True
(SuccD a) == (SuccD b) = a == b
_ == _ = False;
equalDC :: D [] -> D [] -> Bool;
equalDC = (==);
We need to prove (Eq (D [])). Here's how we go:
d1 :_w Eq (D [])
by instance decl, holds if
d2 :_w Eq [D []]
where d1 = dfEqD d2
*BUT* we have an inert set which gives us (no superclasses):
d1 :_g Eq (D [])
By the instance declaration of Eq we can show the 'd2' goal if
d3 :_w Eq (D [])
where d2 = dfEqList d3
d1 = dfEqD d2
Now, however this wanted can interact with our inert d1 to set:
d3 := d1
and solve the goal. Why was this interaction OK? Because, if we chase the
evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
are really setting
d3 := dfEqD2 (dfEqList d3)
which is FINE because the use of d3 is protected by the instance function
applications.
So, our strategy is to try to put solved wanted dictionaries into the
inert set along with their superclasses (when this is meaningful,
i.e. when new wanted goals are generated) but solve a wanted dictionary
from a given only in the case where the evidence variable of the
wanted is mentioned in the evidence of the given (recursively through
the evidence binds) in a protected way: more instance function applications
than superclass selectors.
Here are some more examples from GHC's previous type checker
Example 3:
This code arises in the context of "Scrap Your Boilerplate with Class"
class Sat a
class Data ctx a
instance Sat (ctx Char) => Data ctx Char -- dfunData1
instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
class Data Maybe a => Foo a
instance Foo t => Sat (Maybe t) -- dfunSat
instance Data Maybe a => Foo a -- dfunFoo1
instance Foo a => Foo [a] -- dfunFoo2
instance Foo [Char] -- dfunFoo3
Consider generating the superclasses of the instance declaration
instance Foo a => Foo [a]
So our problem is this
d0 :_g Foo t
d1 :_w Data Maybe [t]
We may add the given in the inert set, along with its superclasses
[assuming we don't fail because there is a matching instance, see
tryTopReact, given case ]
Inert:
d0 :_g Foo t
WorkList
d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
d1 :_w Data Maybe [t]
Then d2 can readily enter the inert, and we also do solving of the wanted
Inert:
d0 :_g Foo t
d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
WorkList
d2 :_w Sat (Maybe [t])
d3 :_w Data Maybe t
d01 :_g Data Maybe t
Now, we may simplify d2 more:
Inert:
d0 :_g Foo t
d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
d1 :_g Data Maybe [t]
d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
WorkList:
d3 :_w Data Maybe t
d4 :_w Foo [t]
d01 :_g Data Maybe t
Now, we can just solve d3.
Inert
d0 :_g Foo t
d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
WorkList
d4 :_w Foo [t]
d01 :_g Data Maybe t
And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
Inert
d0 :_g Foo t
d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
d4 :_g Foo [t] d4 := dfunFoo2 d5
WorkList:
d5 :_w Foo t
d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
d01 :_g Data Maybe t
Now, d5 can be solved! (and its superclass enter scope)
Inert
d0 :_g Foo t
d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
d4 :_g Foo [t] d4 := dfunFoo2 d5
d5 :_g Foo t d5 := dfunFoo1 d7
WorkList:
d7 :_w Data Maybe t
d6 :_g Data Maybe [t]
d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
d01 :_g Data Maybe t
Now, two problems:
[1] Suppose we pick d8 and we react him with d01. Which of the two givens should
we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
that must not be used (look at case interactInert where both inert and workitem
are givens). So we have several options:
- Drop the workitem always (this will drop d8)
This feels very unsafe -- what if the work item was the "good" one
that should be used later to solve another wanted?
- Don't drop anyone: the inert set may contain multiple givens!
[This is currently implemented]
The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
[2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
d7. Now the [isRecDictEv] function in the ineration solver
[case inert-given workitem-wanted] will prevent us from interacting d7 := d8
precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
So, no interaction happens there. Then we meet d01 and there is no recursion
problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
Note [SUPERCLASS-LOOP 1]
~~~~~~~~~~~~~~~~~~~~~~~~
We have to be very, very careful when generating superclasses, lest we
accidentally build a loop. Here's an example:
class S a
class S a => C a where { opc :: a -> a }
class S b => D b where { opd :: b -> b }
instance C Int where
opc = opd
instance D Int where
opd = opc
From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
Simplifying, we may well get:
$dfCInt = :C ds1 (opd dd)
dd = $dfDInt
ds1 = $p1 dd
Notice that we spot that we can extract ds1 from dd.
Alas! Alack! We can do the same for (instance D Int):
$dfDInt = :D ds2 (opc dc)
dc = $dfCInt
ds2 = $p1 dc
And now we've defined the superclass in terms of itself.
Two more nasty cases are in
tcrun021
tcrun033
Solution:
- Satisfy the superclass context *all by itself*
(tcSimplifySuperClasses)
- And do so completely; i.e. no left-over constraints
to mix with the constraints arising from method declarations
Note [SUPERCLASS-LOOP 2]
~~~~~~~~~~~~~~~~~~~~~~~~
We need to be careful when adding "the constaint we are trying to prove".
Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
class Ord a => C a where
instance Ord [a] => C [a] where ...
Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
superclasses of C [a] to avails. But we must not overwrite the binding
for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
build a loop!
Here's another variant, immortalised in tcrun020
class Monad m => C1 m
class C1 m => C2 m x
instance C2 Maybe Bool
For the instance decl we need to build (C1 Maybe), and it's no good if
we run around and add (C2 Maybe Bool) and its superclasses to the avails
before we search for C1 Maybe.
Here's another example
class Eq b => Foo a b
instance Eq a => Foo [a] a
If we are reducing
(Foo [t] t)
we'll first deduce that it holds (via the instance decl). We must not
then overwrite the Eq t constraint with a superclass selection!
At first I had a gross hack, whereby I simply did not add superclass constraints
in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
becuase it lost legitimate superclass sharing, and it still didn't do the job:
I found a very obscure program (now tcrun021) in which improvement meant the
simplifier got two bites a the cherry... so something seemed to be an Stop
first time, but reducible next time.
Now we implement the Right Solution, which is to check for loops directly
when adding superclasses. It's a bit like the occurs check in unification.
Note [Recursive instances and superclases]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider this code, which arises in the context of "Scrap Your
Boilerplate with Class".
class Sat a
class Data ctx a
instance Sat (ctx Char) => Data ctx Char
instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
class Data Maybe a => Foo a
instance Foo t => Sat (Maybe t)
instance Data Maybe a => Foo a
instance Foo a => Foo [a]
instance Foo [Char]
In the instance for Foo [a], when generating evidence for the superclasses
(ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
Using the instance for Data, we therefore need
(Sat (Maybe [a], Data Maybe a)
But we are given (Foo a), and hence its superclass (Data Maybe a).
So that leaves (Sat (Maybe [a])). Using the instance for Sat means
we need (Foo [a]). And that is the very dictionary we are bulding
an instance for! So we must put that in the "givens". So in this
case we have
Given: Foo a, Foo [a]
Wanted: Data Maybe [a]
BUT we must *not not not* put the *superclasses* of (Foo [a]) in
the givens, which is what 'addGiven' would normally do. Why? Because
(Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
by selecting a superclass from Foo [a], which simply makes a loop.
On the other hand we *must* put the superclasses of (Foo a) in
the givens, as you can see from the derivation described above.
Conclusion: in the very special case of tcSimplifySuperClasses
we have one 'given' (namely the "this" dictionary) whose superclasses
must not be added to 'givens' by addGiven.
There is a complication though. Suppose there are equalities
instance (Eq a, a~b) => Num (a,b)
Then we normalise the 'givens' wrt the equalities, so the original
given "this" dictionary is cast to one of a different type. So it's a
bit trickier than before to identify the "special" dictionary whose
superclasses must not be added. See test
indexed-types/should_run/EqInInstance
We need a persistent property of the dictionary to record this
special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
but cool), which is maintained by dictionary normalisation.
Specifically, the InstLocOrigin is
NoScOrigin
then the no-superclass thing kicks in. WATCH OUT if you fiddle
with InstLocOrigin!
Note [MATCHING-SYNONYMS]
~~~~~~~~~~~~~~~~~~~~~~~~
When trying to match a dictionary (D tau) to a top-level instance, or a
type family equation (F taus_1 ~ tau_2) to a top-level family instance,
we do *not* need to expand type synonyms because the matcher will do that for us.
Note [RHS-FAMILY-SYNONYMS]
~~~~~~~~~~~~~~~~~~~~~~~~~~
The RHS of a family instance is represented as yet another constructor which is
like a type synonym for the real RHS the programmer declared. Eg:
type instance F (a,a) = [a]
Becomes:
:R32 a = [a] -- internal type synonym introduced
F (a,a) ~ :R32 a -- instance
When we react a family instance with a type family equation in the work list
we keep the synonym-using RHS without expansion.
%************************************************************************
%* *
%* Functional dependencies, instantiation of equations
%* *
%************************************************************************
When we spot an equality arising from a functional dependency,
we now use that equality (a "wanted") to rewrite the work-item
constraint right away. This avoids two dangers
Danger 1: If we send the original constraint on down the pipeline
it may react with an instance declaration, and in delicate
situations (when a Given overlaps with an instance) that
may produce new insoluble goals: see Trac #4952
Danger 2: If we don't rewrite the constraint, it may re-react
with the same thing later, and produce the same equality
again --> termination worries.
To achieve this required some refactoring of FunDeps.lhs (nicer
now!).
\begin{code}
rewriteWithFunDeps :: [Equation]
-> [Xi]
-> WantedLoc
-> TcS (Maybe ([Xi], [CtEvidence]))
-- Not quite a WantedEvVar unfortunately
-- Because our intention could be to make
-- it derived at the end of the day
-- NB: The flavor of the returned EvVars will be decided by the caller
-- Post: returns no trivial equalities (identities) and all EvVars returned are fresh
rewriteWithFunDeps eqn_pred_locs xis wloc
= do { fd_ev_poss <- mapM (instFunDepEqn wloc) eqn_pred_locs
; let fd_ev_pos :: [(Int,CtEvidence)]
fd_ev_pos = concat fd_ev_poss
rewritten_xis = rewriteDictParams fd_ev_pos xis
; if null fd_ev_pos then return Nothing
else return (Just (rewritten_xis, map snd fd_ev_pos)) }
instFunDepEqn :: WantedLoc -> Equation -> TcS [(Int,CtEvidence)]
-- Post: Returns the position index as well as the corresponding FunDep equality
instFunDepEqn wl (FDEqn { fd_qtvs = tvs, fd_eqs = eqs
, fd_pred1 = d1, fd_pred2 = d2 })
= do { (subst, _) <- instFlexiTcS tvs -- Takes account of kind substitution
; foldM (do_one subst) [] eqs }
where
do_one subst ievs (FDEq { fd_pos = i, fd_ty_left = ty1, fd_ty_right = ty2 })
= let sty1 = Type.substTy subst ty1
sty2 = Type.substTy subst ty2
in if eqType sty1 sty2 then return ievs -- Return no trivial equalities
else do { mb_eqv <- newDerived (push_ctx wl) (mkTcEqPred sty1 sty2)
; case mb_eqv of
Just ctev -> return $ (i,ctev):ievs
Nothing -> return ievs }
-- We are eventually going to emit FD work back in the work list so
-- it is important that we only return the /freshly created/ and not
-- some existing equality!
push_ctx :: WantedLoc -> WantedLoc
push_ctx loc = pushErrCtxt FunDepOrigin (False, mkEqnMsg d1 d2) loc
mkEqnMsg :: (TcPredType, SDoc)
-> (TcPredType, SDoc) -> TidyEnv -> TcM (TidyEnv, SDoc)
mkEqnMsg (pred1,from1) (pred2,from2) tidy_env
= do { zpred1 <- zonkTcPredType pred1
; zpred2 <- zonkTcPredType pred2
; let { tpred1 = tidyType tidy_env zpred1
; tpred2 = tidyType tidy_env zpred2 }
; let msg = vcat [ptext (sLit "When using functional dependencies to combine"),
nest 2 (sep [ppr tpred1 <> comma, nest 2 from1]),
nest 2 (sep [ppr tpred2 <> comma, nest 2 from2])]
; return (tidy_env, msg) }
rewriteDictParams :: [(Int,CtEvidence)] -- A set of coercions : (pos, ty' ~ ty)
-> [Type] -- A sequence of types: tys
-> [Type]
rewriteDictParams param_eqs tys
= zipWith do_one tys [0..]
where
do_one :: Type -> Int -> Type
do_one ty n = case lookup n param_eqs of
Just wev -> get_fst_ty wev
Nothing -> ty
get_fst_ty ctev
| Just (ty1, _) <- getEqPredTys_maybe (ctEvPred ctev)
= ty1
| otherwise
= panic "rewriteDictParams: non equality fundep!?"
emitFDWorkAsDerived :: [CtEvidence] -- All Derived
-> SubGoalDepth -> TcS ()
emitFDWorkAsDerived evlocs d
= updWorkListTcS $ appendWorkListEqs (map mk_fd_ct evlocs)
where
mk_fd_ct der_ev = CNonCanonical { cc_ev = der_ev, cc_depth = d }
\end{code}
*********************************************************************************
* *
The top-reaction Stage
* *
*********************************************************************************
\begin{code}
topReactionsStage :: SimplifierStage
topReactionsStage workItem
= tryTopReact workItem
tryTopReact :: WorkItem -> TcS StopOrContinue
tryTopReact wi
= do { inerts <- getTcSInerts
; tir <- doTopReact inerts wi
; case tir of
NoTopInt
-> return (ContinueWith wi)
SomeTopInt rule what_next
-> do { bumpStepCountTcS
; traceFireTcS (cc_depth wi) $
vcat [ ptext (sLit "Top react:") <+> text rule
, text "WorkItem =" <+> ppr wi ]
; return what_next }
}
data TopInteractResult
= NoTopInt
| SomeTopInt { tir_rule :: String, tir_new_item :: StopOrContinue }
doTopReact :: InertSet -> WorkItem -> TcS TopInteractResult
-- The work item does not react with the inert set, so try interaction
-- with top-level instances
-- NB: The place to add superclasses in *not*
-- in doTopReact stage. Instead superclasses are added in the worklist
-- as part of the canonicalisation process. See Note [Adding superclasses].
-- Given dictionary
-- See Note [Given constraint that matches an instance declaration]
doTopReact _inerts (CDictCan { cc_ev = Given {} })
= return NoTopInt -- NB: Superclasses already added since it's canonical
-- Derived dictionary: just look for functional dependencies
doTopReact _inerts workItem@(CDictCan { cc_ev = Derived loc _pty
, cc_class = cls, cc_tyargs = xis })
= do { instEnvs <- getInstEnvs
; let fd_eqns = improveFromInstEnv instEnvs
(mkClassPred cls xis, pprArisingAt loc)
; m <- rewriteWithFunDeps fd_eqns xis loc
; case m of
Nothing -> return NoTopInt
Just (xis', fd_work) ->
let workItem' = workItem { cc_tyargs = xis' }
-- Deriveds are not supposed to have identity
in do { emitFDWorkAsDerived fd_work (cc_depth workItem)
; return $
SomeTopInt { tir_rule = "Derived Cls fundeps"
, tir_new_item = ContinueWith workItem' } }
}
-- Wanted dictionary
doTopReact inerts workItem@(CDictCan { cc_ev = fl@(Wanted { ctev_wloc = loc, ctev_evar = dict_id })
, cc_class = cls, cc_tyargs = xis
, cc_depth = depth })
-- See Note [MATCHING-SYNONYMS]
= do { traceTcS "doTopReact" (ppr workItem)
; instEnvs <- getInstEnvs
; let fd_eqns = improveFromInstEnv instEnvs
(mkClassPred cls xis, pprArisingAt loc)
; traceTcS "improve" (vcat [ppr cls <+> ppr xis, vcat (map pprEquation fd_eqns), ppr (snd instEnvs)])
; any_fundeps <- rewriteWithFunDeps fd_eqns xis loc
; case any_fundeps of
-- No Functional Dependencies
Nothing ->
do { lkup_inst_res <- matchClassInst inerts cls xis loc
; case lkup_inst_res of
GenInst wtvs ev_term -> do { addToSolved fl
; doSolveFromInstance wtvs ev_term }
NoInstance -> return NoTopInt
}
-- Actual Functional Dependencies
Just (_xis', fd_work) ->
do { emitFDWorkAsDerived fd_work (cc_depth workItem)
; return SomeTopInt { tir_rule = "Dict/Top (fundeps)"
, tir_new_item = ContinueWith workItem } } }
where
doSolveFromInstance :: [CtEvidence] -> EvTerm -> TcS TopInteractResult
-- Precondition: evidence term matches the predicate workItem
doSolveFromInstance evs ev_term
| null evs
= do { traceTcS "doTopReact/found nullary instance for" $
ppr dict_id
; setEvBind dict_id ev_term
; return $
SomeTopInt { tir_rule = "Dict/Top (solved, no new work)"
, tir_new_item = Stop } }
| otherwise
= do { traceTcS "doTopReact/found non-nullary instance for" $
ppr dict_id
; setEvBind dict_id ev_term
; let mk_new_wanted ev
= CNonCanonical { cc_ev = ev
, cc_depth = depth + 1 }
; updWorkListTcS (appendWorkListCt (map mk_new_wanted evs))
; return $
SomeTopInt { tir_rule = "Dict/Top (solved, more work)"
, tir_new_item = Stop }
}
-- Type functions
{- ToDo: Check with Dimitrios
doTopReact _inerts (CFunEqCan { cc_ev = fl })
| isSolved fl
= return NoTopInt -- If Solved, no more interactions should happen
-}
-- Otherwise, it's a Given, Derived, or Wanted
doTopReact _inerts workItem@(CFunEqCan { cc_ev = fl, cc_depth = d
, cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
= ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
; case match_res of
Nothing -> return NoTopInt
Just (famInst, rep_tys)
-> do { mb_already_solved <- lkpSolvedFunEqCache (mkTyConApp tc args)
; traceTcS "doTopReact: Family instance matches" $
vcat [ text "solved-fun-cache" <+> if isJust mb_already_solved then text "hit" else text "miss"
, text "workItem =" <+> ppr workItem ]
; let (coe,rhs_ty)
| Just ctev <- mb_already_solved
, not (isDerived ctev)
= ASSERT( isEqPred (ctEvPred ctev) )
(evTermCoercion (ctEvTerm ctev), snd (getEqPredTys (ctEvPred ctev)))
| otherwise
= let coe_ax = famInstAxiom famInst
in (mkTcAxInstCo coe_ax rep_tys,
mkAxInstRHS coe_ax rep_tys)
xdecomp x = [EvCoercion (mkTcSymCo coe `mkTcTransCo` evTermCoercion x)]
xcomp [x] = EvCoercion (coe `mkTcTransCo` evTermCoercion x)
xcomp _ = panic "No more goals!"
xev = XEvTerm xcomp xdecomp
; ctevs <- xCtFlavor fl [mkTcEqPred rhs_ty xi] xev
; case ctevs of
[ctev] -> updWorkListTcS $ extendWorkListEq $
CNonCanonical { cc_ev = ctev
, cc_depth = d+1 }
ctevs -> -- No subgoal (because it's cached)
ASSERT( null ctevs) return ()
; unless (isDerived fl) $
do { addSolvedFunEq fl
; addToSolved fl }
; return $ SomeTopInt { tir_rule = "Fun/Top"
, tir_new_item = Stop } } }
-- Any other work item does not react with any top-level equations
doTopReact _inerts _workItem = return NoTopInt
lkpSolvedFunEqCache :: TcType -> TcS (Maybe CtEvidence)
lkpSolvedFunEqCache fam_head
= do { (_subst,_inscope) <- getInertEqs
; fun_cache <- getTcSInerts >>= (return . inert_solved_funeqs)
; traceTcS "lkpFunEqCache" $ vcat [ text "fam_head =" <+> ppr fam_head
, text "funeq cache =" <+> ppr fun_cache ]
; return (lookupFamHead fun_cache fam_head) }
{- ToDo; talk to Dimitrios. I have no idea what is happening here
; rewrite_cached (lookupFamHead fun_cache fam_head) }
-- The two different calls do not seem to make a significant difference in
-- terms of hit/miss rate for many memory-critical/performance tests but the
-- latter blows up the space on the heap somehow ... It maybe the niFixTvSubst.
-- So, I am simply disabling it for now, until we investigate a bit more.
-- lookupTypeMap_mod subst cc_rhs fam_head (unCtFamHeadMap fun_cache) }
where rewrite_cached Nothing = return Nothing
rewrite_cached (Just ct@(CFunEqCan { cc_ev = fl, cc_depth = d
, cc_fun = tc, cc_tyargs = xis
, cc_rhs = xi}))
= do { (xis_subst,cos) <- flattenMany d FMFullFlatten fl xis
-- cos :: xis_subst ~ xis
; (xi_subst,co) <- flatten d FMFullFlatten fl xi
-- co :: xi_subst ~ xi
; let flat_fam_head = mkTyConApp tc xis_subst
; unless (flat_fam_head `eqType` fam_head) $
pprPanic "lkpFunEqCache" (vcat [ text "Cached (solved) constraint =" <+> ppr ct
, text "Flattened constr. head =" <+> ppr flat_fam_head ])
; traceTcS "lkpFunEqCache" $ text "Flattened constr. rhs = " <+> ppr xi_subst
; let new_pty = mkTcEqPred (mkTyConApp tc xis_subst) xi_subst
new_co = mkTcTyConAppCo eqTyCon [ mkTcReflCo (defaultKind $ typeKind xi_subst)
, mkTcTyConAppCo tc cos
, co ]
-- new_co :: (F xis_subst ~ xi_subst) ~ (F xis ~ xi)
-- new_co = (~) (F cos) co
; new_fl <- rewriteCtFlavor fl new_pty new_co
; case new_fl of
Nothing
-> return Nothing -- Strange: cached?
Just fl'
-> return $
Just (CFunEqCan { cc_ev = fl'
, cc_depth = d
, cc_fun = tc
, cc_tyargs = xis_subst
, cc_rhs = xi_subst }) }
rewrite_cached (Just other_ct)
= pprPanic "lkpFunEqCache:not family equation!" $ ppr other_ct
-}
\end{code}
Note [FunDep and implicit parameter reactions]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Currently, our story of interacting two dictionaries (or a dictionary
and top-level instances) for functional dependencies, and implicit
paramters, is that we simply produce new wanted equalities. So for example
class D a b | a -> b where ...
Inert:
d1 :g D Int Bool
WorkItem:
d2 :w D Int alpha
We generate the extra work item
cv :w alpha ~ Bool
where 'cv' is currently unused. However, this new item reacts with d2,
discharging it in favour of a new constraint d2' thus:
d2' :w D Int Bool
d2 := d2' |> D Int cv
Now d2' can be discharged from d1
We could be more aggressive and try to *immediately* solve the dictionary
using those extra equalities. With the same inert set and work item we
might dischard d2 directly:
cv :w alpha ~ Bool
d2 := d1 |> D Int cv
But in general it's a bit painful to figure out the necessary coercion,
so we just take the first approach. Here is a better example. Consider:
class C a b c | a -> b
And:
[Given] d1 : C T Int Char
[Wanted] d2 : C T beta Int
In this case, it's *not even possible* to solve the wanted immediately.
So we should simply output the functional dependency and add this guy
[but NOT its superclasses] back in the worklist. Even worse:
[Given] d1 : C T Int beta
[Wanted] d2: C T beta Int
Then it is solvable, but its very hard to detect this on the spot.
It's exactly the same with implicit parameters, except that the
"aggressive" approach would be much easier to implement.
Note [When improvement happens]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We fire an improvement rule when
* Two constraints match (modulo the fundep)
e.g. C t1 t2, C t1 t3 where C a b | a->b
The two match because the first arg is identical
* At least one is not Given. If they are both given, we don't fire
the reaction because we have no way of constructing evidence for a
new equality nor does it seem right to create a new wanted goal
(because the goal will most likely contain untouchables, which
can't be solved anyway)!
Note that we *do* fire the improvement if one is Given and one is Derived.
The latter can be a superclass of a wanted goal. Example (tcfail138)
class L a b | a -> b
class (G a, L a b) => C a b
instance C a b' => G (Maybe a)
instance C a b => C (Maybe a) a
instance L (Maybe a) a
When solving the superclasses of the (C (Maybe a) a) instance, we get
Given: C a b ... and hance by superclasses, (G a, L a b)
Wanted: G (Maybe a)
Use the instance decl to get
Wanted: C a b'
The (C a b') is inert, so we generate its Derived superclasses (L a b'),
and now we need improvement between that derived superclass an the Given (L a b)
Note [Overriding implicit parameters]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
f :: (?x::a) -> Bool -> a
g v = let ?x::Int = 3
in (f v, let ?x::Bool = True in f v)
This should probably be well typed, with
g :: Bool -> (Int, Bool)
So the inner binding for ?x::Bool *overrides* the outer one.
Hence a work-item Given overrides an inert-item Given.
Note [Given constraint that matches an instance declaration]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What should we do when we discover that one (or more) top-level
instances match a given (or solved) class constraint? We have
two possibilities:
1. Reject the program. The reason is that there may not be a unique
best strategy for the solver. Example, from the OutsideIn(X) paper:
instance P x => Q [x]
instance (x ~ y) => R [x] y
wob :: forall a b. (Q [b], R b a) => a -> Int
g :: forall a. Q [a] => [a] -> Int
g x = wob x
will generate the impliation constraint:
Q [a] => (Q [beta], R beta [a])
If we react (Q [beta]) with its top-level axiom, we end up with a
(P beta), which we have no way of discharging. On the other hand,
if we react R beta [a] with the top-level we get (beta ~ a), which
is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
now solvable by the given Q [a].
However, this option is restrictive, for instance [Example 3] from
Note [Recursive instances and superclases] will fail to work.
2. Ignore the problem, hoping that the situations where there exist indeed
such multiple strategies are rare: Indeed the cause of the previous
problem is that (R [x] y) yields the new work (x ~ y) which can be
*spontaneously* solved, not using the givens.
We are choosing option 2 below but we might consider having a flag as well.
Note [New Wanted Superclass Work]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Even in the case of wanted constraints, we may add some superclasses
as new given work. The reason is:
To allow FD-like improvement for type families. Assume that
we have a class
class C a b | a -> b
and we have to solve the implication constraint:
C a b => C a beta
Then, FD improvement can help us to produce a new wanted (beta ~ b)
We want to have the same effect with the type family encoding of
functional dependencies. Namely, consider:
class (F a ~ b) => C a b
Now suppose that we have:
given: C a b
wanted: C a beta
By interacting the given we will get given (F a ~ b) which is not
enough by itself to make us discharge (C a beta). However, we
may create a new derived equality from the super-class of the
wanted constraint (C a beta), namely derived (F a ~ beta).
Now we may interact this with given (F a ~ b) to get:
derived : beta ~ b
But 'beta' is a touchable unification variable, and hence OK to
unify it with 'b', replacing the derived evidence with the identity.
This requires trySpontaneousSolve to solve *derived*
equalities that have a touchable in their RHS, *in addition*
to solving wanted equalities.
We also need to somehow use the superclasses to quantify over a minimal,
constraint see note [Minimize by Superclasses] in TcSimplify.
Finally, here is another example where this is useful.
Example 1:
----------
class (F a ~ b) => C a b
And we are given the wanteds:
w1 : C a b
w2 : C a c
w3 : b ~ c
We surely do *not* want to quantify over (b ~ c), since if someone provides
dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
Step 1: We will get new *given* superclass work,
provisionally to our solving of w1 and w2
g1: F a ~ b, g2 : F a ~ c,
w1 : C a b, w2 : C a c, w3 : b ~ c
The evidence for g1 and g2 is a superclass evidence term:
g1 := sc w1, g2 := sc w2
Step 2: The givens will solve the wanted w3, so that
w3 := sym (sc w1) ; sc w2
Step 3: Now, one may naively assume that then w2 can be solve from w1
after rewriting with the (now solved equality) (b ~ c).
But this rewriting is ruled out by the isGoodRectDict!
Conclusion, we will (correctly) end up with the unsolved goals
(C a b, C a c)
NB: The desugarer needs be more clever to deal with equalities
that participate in recursive dictionary bindings.
\begin{code}
data LookupInstResult
= NoInstance
| GenInst [CtEvidence] EvTerm
matchClassInst :: InertSet -> Class -> [Type] -> WantedLoc -> TcS LookupInstResult
matchClassInst _ clas [ _, ty ] _
| className clas == singIClassName
, Just n <- isNumLitTy ty = return $ GenInst [] $ EvLit $ EvNum n
| className clas == singIClassName
, Just s <- isStrLitTy ty = return $ GenInst [] $ EvLit $ EvStr s
matchClassInst inerts clas tys loc
= do { dflags <- getDynFlags
; let pred = mkClassPred clas tys
incoherent_ok = xopt Opt_IncoherentInstances dflags
; mb_result <- matchClass clas tys
; untch <- getUntouchables
; traceTcS "matchClassInst" $ vcat [ text "pred =" <+> ppr pred
, text "inerts=" <+> ppr inerts
, text "untouchables=" <+> ppr untch ]
; case mb_result of
MatchInstNo -> return NoInstance
MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
-- we learn more about the reagent
MatchInstSingle (_,_)
| not incoherent_ok && given_overlap untch
-> -- see Note [Instance and Given overlap]
do { traceTcS "Delaying instance application" $
vcat [ text "Workitem=" <+> pprType (mkClassPred clas tys)
, text "Relevant given dictionaries=" <+> ppr givens_for_this_clas ]
; return NoInstance
}
MatchInstSingle (dfun_id, mb_inst_tys) ->
do { checkWellStagedDFun pred dfun_id loc
-- mb_inst_tys :: Maybe TcType
-- See Note [DFunInstType: instantiating types] in InstEnv
; (tys, dfun_phi) <- instDFunType dfun_id mb_inst_tys
; let (theta, _) = tcSplitPhiTy dfun_phi
; if null theta then
return (GenInst [] (EvDFunApp dfun_id tys []))
else do
{ evc_vars <- instDFunConstraints loc theta
; let new_ev_vars = freshGoals evc_vars
-- new_ev_vars are only the real new variables that can be emitted
dfun_app = EvDFunApp dfun_id tys (getEvTerms evc_vars)
; return $ GenInst new_ev_vars dfun_app } }
}
where
givens_for_this_clas :: Cts
givens_for_this_clas
= lookupUFM (cts_given (inert_dicts $ inert_cans inerts)) clas
`orElse` emptyCts
given_overlap :: TcsUntouchables -> Bool
given_overlap untch = anyBag (matchable untch) givens_for_this_clas
matchable untch (CDictCan { cc_class = clas_g, cc_tyargs = sys
, cc_ev = fl })
| isGiven fl
= ASSERT( clas_g == clas )
case tcUnifyTys (\tv -> if isTouchableMetaTyVar_InRange untch tv &&
tv `elemVarSet` tyVarsOfTypes tys
then BindMe else Skolem) tys sys of
-- We can't learn anything more about any variable at this point, so the only
-- cause of overlap can be by an instantiation of a touchable unification
-- variable. Hence we only bind touchable unification variables. In addition,
-- we use tcUnifyTys instead of tcMatchTys to rule out cyclic substitutions.
Nothing -> False
Just _ -> True
| otherwise = False -- No overlap with a solved, already been taken care of
-- by the overlap check with the instance environment.
matchable _tys ct = pprPanic "Expecting dictionary!" (ppr ct)
\end{code}
Note [Instance and Given overlap]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assume that we have an inert set that looks as follows:
[Given] D [Int]
And an instance declaration:
instance C a => D [a]
A new wanted comes along of the form:
[Wanted] D [alpha]
One possibility is to apply the instance declaration which will leave us
with an unsolvable goal (C alpha). However, later on a new constraint may
arise (for instance due to a functional dependency between two later dictionaries),
that will add the equality (alpha ~ Int), in which case our ([Wanted] D [alpha])
will be transformed to [Wanted] D [Int], which could have been discharged by the given.
The solution is that in matchClassInst and eventually in topReact, we get back with
a matching instance, only when there is no Given in the inerts which is unifiable to
this particular dictionary.
The end effect is that, much as we do for overlapping instances, we delay choosing a
class instance if there is a possibility of another instance OR a given to match our
constraint later on. This fixes bugs #4981 and #5002.
This is arguably not easy to appear in practice due to our aggressive prioritization
of equality solving over other constraints, but it is possible. I've added a test case
in typecheck/should-compile/GivenOverlapping.hs
We ignore the overlap problem if -XIncoherentInstances is in force: see
Trac #6002 for a worked-out example where this makes a difference.
Moreover notice that our goals here are different than the goals of the top-level
overlapping checks. There we are interested in validating the following principle:
If we inline a function f at a site where the same global instance environment
is available as the instance environment at the definition site of f then we
should get the same behaviour.
But for the Given Overlap check our goal is just related to completeness of
constraint solving.