\begin{code}
module TcInteract (
solveInteract, AtomicInert,
InertSet, emptyInert, updInertSet, extractUnsolved, solveOne, foldISEqCts
) where
#include "HsVersions.h"
import BasicTypes
import TcCanonical
import VarSet
import Type
import Id
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
import Bag
import qualified Data.Map as Map
import Control.Monad( zipWithM, unless )
import FastString ( sLit )
import DynFlags
\end{code}
Note [InertSet invariants]
~~~~~~~~~~~~~~~~~~~~~~~~~~~
An InertSet is a bag of canonical constraints, with the following invariants:
1 No two constraints react with each other.
A tricky case is when there exists a given (solved) dictionary
constraint and a wanted identical constraint in the inert set, but do
not react because reaction would create loopy dictionary evidence for
the wanted. See note [Recursive dictionaries]
2 Given equalities form an idempotent substitution [none of the
given LHS's occur in any of the given RHS's or reactant parts]
3 Wanted equalities also form an idempotent substitution
4 The entire set of equalities is acyclic.
5 Wanted dictionaries are inert with the toplevel axiom set
6 Equalities of the form tv1 ~ tv2 always have a touchable variable
on the left (if possible).
7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
will be marked as solved right before being pushed into the inert set.
See note [Touchables and givens].
8 No Given constraint mentions a touchable unification variable,
except if the
Note that 6 and 7 are /not/ enforced by canonicalization but rather by
insertion in the inert list, ie by TcInteract.
During the process of solving, the inert set will contain some
previously given constraints, some wanted constraints, and some given
constraints which have arisen from solving wanted constraints. For
now we do not distinguish between given and solved constraints.
Note that we must switch wanted inert items to given when going under an
implication constraint (when in toplevel inference mode).
\begin{code}
data CCanMap a = CCanMap { cts_givder :: Map.Map a CanonicalCts
, cts_wanted :: Map.Map a CanonicalCts }
cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts
cCanMapToBag cmap = Map.fold unionBags rest_cts (cts_givder cmap)
where rest_cts = Map.fold unionBags emptyCCan (cts_wanted cmap)
emptyCCanMap :: CCanMap a
emptyCCanMap = CCanMap { cts_givder = Map.empty, cts_wanted = Map.empty }
updCCanMap:: Ord a => (a,CanonicalCt) -> CCanMap a -> CCanMap a
updCCanMap (a,ct) cmap
= case cc_flavor ct of
Wanted {}
-> cmap { cts_wanted = Map.insertWith unionBags a this_ct (cts_wanted cmap) }
_
-> cmap { cts_givder = Map.insertWith unionBags a this_ct (cts_givder cmap) }
where this_ct = singleCCan ct
getRelevantCts :: Ord a => a -> CCanMap a -> (CanonicalCts, CCanMap a)
getRelevantCts a cmap
= let relevant = unionBags (Map.findWithDefault emptyCCan a (cts_wanted cmap))
(Map.findWithDefault emptyCCan a (cts_givder cmap))
residual_map = cmap { cts_wanted = Map.delete a (cts_wanted cmap)
, cts_givder = Map.delete a (cts_givder cmap) }
in (relevant, residual_map)
extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a)
extractUnsolvedCMap cmap =
let unsolved = Map.fold unionBags emptyCCan (cts_wanted cmap)
in (unsolved, cmap { cts_wanted = Map.empty})
data InertSet
= IS { inert_eqs :: CanonicalCts
, inert_dicts :: CCanMap Class
, inert_ips :: CCanMap (IPName Name)
, inert_funeqs :: CCanMap TyCon
, inert_fds :: FDImprovements
}
type FDImprovement = (PredType,PredType)
type FDImprovements = [(PredType,PredType)]
instance Outputable InertSet where
ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
, vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is)))
, vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is)))
, vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
]
emptyInert :: InertSet
emptyInert = IS { inert_eqs = Bag.emptyBag
, inert_dicts = emptyCCanMap
, inert_ips = emptyCCanMap
, inert_funeqs = emptyCCanMap
, inert_fds = [] }
updInertSet :: InertSet -> AtomicInert -> InertSet
updInertSet is item
| isCTyEqCan item
= let eqs' = inert_eqs is `Bag.snocBag` item
in is { inert_eqs = eqs' }
| Just cls <- isCDictCan_Maybe item
= is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) }
| Just x <- isCIPCan_Maybe item
= is { inert_ips = updCCanMap (x,item) (inert_ips is) }
| Just tc <- isCFunEqCan_Maybe item
= is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
| otherwise
= pprPanic "Unknown form of constraint!" (ppr item)
updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet
updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is }
updInertSetFDImprs is Nothing = is
foldISEqCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
foldISEqCtsM k z IS { inert_eqs = eqs }
= Bag.foldlBagM k z eqs
foldISEqCts :: (a -> AtomicInert -> a) -> a -> InertSet -> a
foldISEqCts k z IS { inert_eqs = eqs }
= Bag.foldlBag k z eqs
extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
extractUnsolved is@(IS {inert_eqs = eqs})
= let is_solved = is { inert_eqs = solved_eqs
, inert_dicts = solved_dicts
, inert_ips = solved_ips
, inert_funeqs = solved_funeqs }
in (is_solved, unsolved)
where (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs
(unsolved_ips, solved_ips) = extractUnsolvedCMap (inert_ips is)
(unsolved_dicts, solved_dicts) = extractUnsolvedCMap (inert_dicts is)
(unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is)
unsolved = unsolved_eqs `unionBags`
unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs
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
getFDImprovements = inert_fds
\end{code}
%*********************************************************************
%* *
* Main Interaction Solver *
* *
**********************************************************************
Note [Basic plan]
~~~~~~~~~~~~~~~~~
1. Canonicalise (unary)
2. Pairwise interaction (binary)
* Take one from work list
* Try all pairwise interactions with each constraint in inert
As an optimisation, we prioritize the equalities both in the
worklist and in the inerts.
3. Try to solve spontaneously for equalities involving touchables
4. Toplevel interaction (binary wrt toplevel)
Superclass decomposition belongs in (4), see note [Superclasses]
\begin{code}
type AtomicInert = CanonicalCt
type WorkItem = CanonicalCt
type WorkList = CanonicalCts
unionWorkLists :: WorkList -> WorkList -> WorkList
unionWorkLists = andCCan
isEmptyWorkList :: WorkList -> Bool
isEmptyWorkList = isEmptyCCan
emptyWorkList :: WorkList
emptyWorkList = emptyCCan
workListFromCCan :: CanonicalCt -> WorkList
workListFromCCan = singleCCan
data StopOrContinue
= Stop
| ContinueWith WorkItem
instance Outputable StopOrContinue where
ppr Stop = ptext (sLit "Stop")
ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
data StageResult
= SR { sr_inerts :: InertSet
, sr_new_work :: WorkList
, 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
runSolverPipeline :: [(String, SimplifierStage)]
-> InertSet -> WorkItem
-> TcS (InertSet, WorkList)
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
ContinueWith item -> sr_inerts itr_out `updInertSet` item
; return (new_inert, sr_new_work itr_out) }
where
run_pipeline :: [(String, SimplifierStage)]
-> StageResult -> TcS StageResult
run_pipeline [] itr = return itr
run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
run_pipeline ((name,stage):stages)
(SR { sr_new_work = accum_work
, sr_inerts = inerts
, sr_stop = ContinueWith work_item })
= do { itr <- stage work_item inerts
; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
; run_pipeline stages itr' }
\end{code}
Example 1:
Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
Reagent: a ~ [b] (given)
React with (c~d) ==> IR (ContinueWith (a~[b])) True []
React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
Example 2:
Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
Reagent: a ~w [b]
React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
etc.
Example 3:
Inert: {a ~ Int, F Int ~ b} (given)
Reagent: F a ~ b (wanted)
React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
React with (F Int ~ b) ==> IR Stop True []
\begin{code}
solveInteract :: InertSet -> CanonicalCts -> TcS InertSet
solveInteract inert ws
= do { dyn_flags <- getDynFlags
; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert ws
}
solveOne :: InertSet -> WorkItem -> TcS InertSet
solveOne inerts workItem
= do { dyn_flags <- getDynFlags
; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
}
solveInteractWithDepth :: (Int, Int, [WorkItem])
-> InertSet -> WorkList -> TcS InertSet
solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws
| isEmptyWorkList ws
= return inert
| n > max_depth
= solverDepthErrorTcS n stack
| otherwise
= do { traceTcS "solveInteractWithDepth" $
vcat [ text "Current depth =" <+> ppr n
, text "Max depth =" <+> ppr max_depth ]
; let (eqs, non_eqs) = Bag.partitionBag isCTyEqCan ws
; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
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)
; 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)]
thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
, ("interact with inerts", interactWithInertsStage)
, ("spontaneous solve", spontaneousSolveStage)
, ("top-level reactions", topReactionsStage) ]
\end{code}
*********************************************************************************
* *
The spontaneoussolve 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) (upto the
canonicalization invariants) However, to prevent the inert items
from getting kicked out of the inerts first, we prefer to
canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
~ xi1) if (a) comes from the inert set.
This choice is implemented using the WhichComesFromInert flag.
Case 2: Functional Dependencies
Again, we should prefer, if possible, the inert variables on the RHS
Case 3: IP improvement work
We must always rewrite so that the inert type is on the right.
\begin{code}
spontaneousSolveStage :: SimplifierStage
spontaneousSolveStage workItem inerts
= do { mSolve <- trySpontaneousSolve workItem
; case mSolve of
SPCantSolve ->
return $ SR { sr_new_work = emptyWorkList
, sr_inerts = inerts
, sr_stop = ContinueWith workItem }
SPSolved workItem'
| not (isGivenCt workItem)
-> do { (new_inert, new_work) <- runSolverPipeline
[ ("recursive interact with inert eqs", interactWithInertEqsStage)
, ("recursive interact with inerts", interactWithInertsStage)
] inerts workItem'
; return $ SR { sr_new_work = new_work
, sr_inerts = new_inert
, sr_stop = Stop }
}
| otherwise
->
return $ SR { sr_new_work = emptyWorkList
, sr_inerts = inerts `updInertSet` workItem'
, sr_stop = Stop }
SPError ->
return $ SR { sr_new_work = emptyWorkList
, sr_inerts = inerts
, sr_stop = Stop }
}
data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
| isGiven gw
= return SPCantSolve
| Just tv2 <- tcGetTyVar_maybe xi
= do { tch1 <- isTouchableMetaTyVar tv1
; tch2 <- isTouchableMetaTyVar tv2
; case (tch1, tch2) of
(True, True) -> trySpontaneousEqTwoWay cv gw tv1 tv2
(True, False) -> trySpontaneousEqOneWay cv gw tv1 xi
(False, True) -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
_ -> return SPCantSolve }
| otherwise
= do { tch1 <- isTouchableMetaTyVar tv1
; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:" (ppr workItem)
; return SPCantSolve }
}
trySpontaneousSolve _ = return SPCantSolve
trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
trySpontaneousEqOneWay cv gw tv xi
| not (isSigTyVar tv) || isTyVarTy xi
= do { let kxi = typeKind xi
; if kxi `isSubKind` tyVarKind tv then
solveWithIdentity cv gw tv xi
else if tyVarKind tv `isSubKind` kxi then
return SPCantSolve
else do { addErrorTcS KindError gw (mkTyVarTy tv) xi
; return SPError }
}
| otherwise
= return SPCantSolve
trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
trySpontaneousEqTwoWay cv gw tv1 tv2
| k1 `isSubKind` k2
, nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
| k2 `isSubKind` k1
= solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
| otherwise
= do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
; return SPError }
where
k1 = tyVarKind tv1
k2 = tyVarKind tv2
nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
\end{code}
Note [Kind errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the wanted problem:
alpha ~ (# Int, Int #)
where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
get quantified over in inference mode. That's bad because we do know at this point that the
constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
The same applies in canonicalization code in case of kind errors in the givens.
However, when we canonicalize givens we only check for compatibility (@compatKind@).
If there were a kind error in the givens, this means some form of inconsistency or dead code.
You may think that when we spontaneously solve wanteds we may have to look through the
bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
@alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
so this situation can't happen.
Note [Spontaneous solving and kind compatibility]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that our canonical constraints insist that 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:
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@.
Caveat:
Givens from higherrank, such as:
type family T b :: * -> * -> *
type instance T Bool = (->)
f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
flop = f (...) True
Whereas we would be able to apply the type instance, we would not be able to
use the given (T Bool ~ (->)) in the body of 'flop'
Note [Avoid double unifications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The spontaneous solver has to return a given which mentions the unified unification
variable *on the left* of the equality. Here is what happens if not:
Original wanted: (a ~ alpha), (alpha ~ Int)
We spontaneously solve the first wanted, without changing the order!
given : a ~ alpha [having unified alpha := a]
Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
We avoid this problem by orienting the resulting given so that the unification
variable is on the left. [Note that alternatively we could attempt to
enforce this at canonicalization]
See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
double unifications is the main reason we disallow touchable
unification variables as RHS of type family equations: F xis ~ alpha.
\begin{code}
solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
solveWithIdentity cv wd tv xi
= do { traceTcS "Sneaky unification:" $
vcat [text "Coercion variable: " <+> ppr wd,
text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
text "Right Kind is : " <+> ppr (typeKind xi)
]
; setWantedTyBind tv xi
; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi xi
; case wd of Wanted {} -> setWantedCoBind cv xi
Derived {} -> setDerivedCoBind cv xi
_ -> pprPanic "Can't spontaneously solve given!" empty
; return $ SPSolved (CTyEqCan { cc_id = cv_given
, cc_flavor = mkGivenFlavor wd UnkSkol
, cc_tyvar = tv, cc_rhs = xi })
}
\end{code}
*********************************************************************************
* *
The interactwithinert Stage
* *
*********************************************************************************
\begin{code}
data InteractResult
= IR { ir_stop :: StopOrContinue
, ir_inert_action :: InertAction
, ir_new_work :: WorkList
, ir_improvement :: Maybe FDImprovement
}
data InertAction = KeepInert
| DropInert
| KeepTransformedInert CanonicalCt
mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing
mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
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)
dischargeWorkItem :: Monad m => m InteractResult
dischargeWorkItem = mkIRStop KeepInert emptyWorkList
noInteraction :: Monad m => WorkItem -> m InteractResult
noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
interactWithInertEqsStage :: SimplifierStage
interactWithInertEqsStage workItem inert
= foldISEqCtsM interactNext initITR inert
where initITR = SR { sr_inerts = IS { inert_eqs = emptyCCan
, inert_dicts = inert_dicts inert
, inert_ips = inert_ips inert
, inert_funeqs = inert_funeqs inert
, inert_fds = inert_fds inert
}
, sr_new_work = emptyWorkList
, sr_stop = ContinueWith workItem }
interactWithInertsStage :: SimplifierStage
interactWithInertsStage workItem inert
= let (relevant, inert_residual) = getISRelevant workItem inert
initITR = SR { sr_inerts = inert_residual
, sr_new_work = emptyWorkList
, sr_stop = ContinueWith workItem }
in Bag.foldlBagM interactNext initITR relevant
where
getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
getISRelevant (CDictCan { cc_class = cls } ) is
= let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
in (relevant, is { inert_dicts = residual_map })
getISRelevant (CFunEqCan { cc_fun = tc } ) is
= let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
in (relevant, is { inert_funeqs = residual_map })
getISRelevant (CIPCan { cc_ip_nm = nm }) is
= let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
in (relevant, is { inert_ips = residual_map })
getISRelevant _eq_ct is
= let cts = cCanMapToBag (inert_ips is) `unionBags`
cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
in (cts, is { inert_dicts = emptyCCanMap
, inert_ips = emptyCCanMap
, inert_funeqs = emptyCCanMap })
interactNext :: StageResult -> AtomicInert -> TcS StageResult
interactNext it inert
| ContinueWith workItem <- sr_stop it
= do { let inerts = sr_inerts it
fdimprs_old = getFDImprovements inerts
; ir <- interactWithInert fdimprs_old inert workItem
; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir)
upd_inert = case ir_inert_action ir of
KeepInert -> inerts `updInertSet` inert
DropInert -> inerts
KeepTransformedInert inert' -> inerts `updInertSet` inert'
; 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 }
interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
interactWithInert fdimprs inert workitem
= do { ctxt <- getTcSContext
; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem
inert_ev = cc_id inert
work_ev = cc_id workitem
; rec_ev_ok <-
case (cc_flavor inert, cc_flavor workitem) of
(Wanted loc, Derived {}) -> isGoodRecEv work_ev (WantedEvVar inert_ev loc)
(Derived {}, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
_ -> return True
; if is_allowed && rec_ev_ok then
doInteractWithInert fdimprs inert workitem
else
noInteraction workitem
}
allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
allowedInteraction _ _ _ = True
doInteractWithInert :: FDImprovements -> CanonicalCt -> CanonicalCt -> TcS InteractResult
doInteractWithInert fdimprs
(CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
workItem@(CDictCan { 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))
=
do { let pty1 = ClassP cls1 tys1
pty2 = ClassP cls2 tys2
work_item_pred_loc = (pty2, pprFlavorArising fl2)
inert_pred_loc = (pty1, pprFlavorArising fl1)
loc = combineCtLoc fl1 fl2
eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
; fd_work <- canWanteds wevvars
; traceTcS "Checking if improvements existed." (ppr fdimprs)
; if isEmptyWorkList fd_work || haveBeenImproved fdimprs pty1 pty2 then
mkIRContinue workItem KeepInert fd_work
else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
; mkIRStop_RecordImprovement KeepInert
(fd_work `unionWorkLists` workListFromCCan workItem) (pty1,pty2)
}
}
doInteractWithInert _fdimprs
(CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
(CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
| ifl `canRewrite` wfl
, tv `elemVarSet` tyVarsOfTypes xis
= if isDerivedSC wfl then
mkIRStop KeepInert $ emptyWorkList
else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
; mkIRContinue rewritten_dict KeepInert emptyWorkList }
doInteractWithInert _fdimprs
(CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
| wfl `canRewrite` ifl
, tv `elemVarSet` tyVarsOfTypes xis
= if isDerivedSC ifl then
mkIRContinue workItem DropInert emptyWorkList
else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
; mkIRContinue workItem DropInert (workListFromCCan rewritten_dict) }
doInteractWithInert _fdimprs
(CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
(CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
| ifl `canRewrite` wfl
, tv `elemVarSet` tyVarsOfType ty
= do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
; mkIRContinue rewritten_ip KeepInert emptyWorkList }
doInteractWithInert _fdimprs
(CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
| wfl `canRewrite` ifl
, tv `elemVarSet` tyVarsOfType ty
= do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
; mkIRContinue workItem DropInert (workListFromCCan rewritten_ip) }
doInteractWithInert _fdimprs
(CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
| nm1 == nm2 && isGiven wfl && isGiven ifl
=
mkIRContinue workItem DropInert emptyWorkList
| nm1 == nm2 && ty1 `tcEqType` ty2
= solveOneFromTheOther (id1,ifl) workItem
| nm1 == nm2
=
do { co_var <- newWantedCoVar ty2 ty1
; let flav = Wanted (combineCtLoc ifl wfl)
; cans <- mkCanonical flav co_var
; mkIRContinue workItem KeepInert cans }
doInteractWithInert _fdimprs
(CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
(CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
, cc_tyargs = args, cc_rhs = xi2 })
| ifl `canRewrite` wfl
, tv `elemVarSet` tyVarsOfTypes (xi2:args)
= do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
; mkIRStop KeepInert (workListFromCCan rewritten_funeq) }
doInteractWithInert _fdimprs
(CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
, cc_tyargs = args, cc_rhs = xi1 })
workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
| wfl `canRewrite` ifl
, tv `elemVarSet` tyVarsOfTypes (xi1:args)
= do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
; mkIRContinue workItem DropInert (workListFromCCan rewritten_funeq) }
doInteractWithInert _fdimprs
(CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
, cc_tyargs = args1, cc_rhs = xi1 })
workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
, cc_tyargs = args2, cc_rhs = xi2 })
| fl1 `canSolve` fl2 && lhss_match
= do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
; mkIRStop KeepInert cans }
| fl2 `canSolve` fl1 && lhss_match
= do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
; mkIRContinue workItem DropInert cans }
where
lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
doInteractWithInert _fdimprs
(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
| fl1 `canSolve` fl2 && tv1 == tv2
= do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
; mkIRStop KeepInert cans }
| fl2 `canSolve` fl1 && tv1 == tv2
= do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
; mkIRContinue workItem DropInert cans }
| fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
= do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
; mkIRStop KeepInert rewritten_eq }
| fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
= do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
; mkIRContinue workItem DropInert rewritten_eq }
doInteractWithInert _fdimprs _ workItem = noInteraction workItem
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
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' = 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
xi2' = substTyWith [tv] [xi1] xi2
xi2_co = substTyWith [tv] [mkCoVarCoercion cv1] xi2
; cv2' <- case gw of
Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2'
; setWantedCoBind cv2 $
fun_co `mkTransCoercion`
mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion xi2_co
; return cv2' }
_giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2' $
mkSymCoercion fun_co `mkTransCoercion`
mkCoVarCoercion cv2 `mkTransCoercion` xi2_co
; return (CFunEqCan { cc_id = cv2'
, cc_flavor = gw
, cc_tyargs = args'
, cc_fun = tc
, cc_rhs = xi2' }) }
rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
| Just tv2' <- tcGetTyVar_maybe xi2'
, 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'
; canEq gw cv2' (mkTyVarTy tv2) xi2'
}
where
xi2' = substTyWith [tv1] [xi1] xi2
co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2
rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
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
; mkCanonical gw cv2'
}
solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult
solveOneFromTheOther (iid,ifl) workItem
| isDerived ifl && isDerived wfl
= noInteraction workItem
| ifl `canSolve` wfl
= do { unless (isGiven wfl) $ setEvBind wid (EvId iid)
; dischargeWorkItem }
| otherwise
= do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
; mkIRContinue workItem DropInert emptyWorkList }
where
wfl = cc_flavor workItem
wid = cc_id workItem
\end{code}
Note [Superclasses and recursive dictionaries]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Overlaps with Note [SUPERCLASSLOOP 1]
Note [SUPERCLASSLOOP 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
instance Eq a => Foo [a] a
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
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]
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
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
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 inertgiven workitemwanted] 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 [SUPERCLASSLOOP 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 leftover constraints
to mix with the constraints arising from method declarations
Note [SUPERCLASSLOOP 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 suboptimal,
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
indexedtypes/should_run/EqInInstance
We need a persistent property of the dictionary to record this
specialness. 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 nosuperclass thing kicks in. WATCH OUT if you fiddle
with InstLocOrigin!
Note [MATCHINGSYNONYMS]
~~~~~~~~~~~~~~~~~~~~~~~~
When trying to match a dictionary (D tau) to a toplevel instance, or a
type family equation (F taus_1 ~ tau_2) to a toplevel family instance,
we do *not* need to expand type synonyms because the matcher will do that for us.
Note [RHSFAMILYSYNONYMS]
~~~~~~~~~~~~~~~~~~~~~~~~~~
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]
F (a,a) ~ :R32 a
When we react a family instance with a type family equation in the work list
we keep the synonymusing RHS without expansion.
*********************************************************************************
* *
The topreaction Stage
* *
*********************************************************************************
\begin{code}
data TopInteractResult
= NoTopInt
| SomeTopInt
{ tir_new_work :: WorkList
, tir_new_inert :: StopOrContinue
}
topReactionsStage :: SimplifierStage
topReactionsStage workItem inerts
= do { tir <- tryTopReact workItem
; case tir of
NoTopInt ->
return $ SR { sr_inerts = inerts
, sr_new_work = emptyWorkList
, sr_stop = ContinueWith workItem }
SomeTopInt tir_new_work tir_new_inert ->
return $ SR { sr_inerts = inerts
, sr_new_work = tir_new_work
, sr_stop = tir_new_inert
}
}
tryTopReact :: WorkItem -> TcS TopInteractResult
tryTopReact workitem
= do {
ctxt <- getTcSContext
; if allowedTopReaction (simplEqsOnly ctxt) workitem
then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
; doTopReact workitem }
else return NoTopInt
}
allowedTopReaction :: Bool -> WorkItem -> Bool
allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
allowedTopReaction _ _ = True
doTopReact :: WorkItem -> TcS TopInteractResult
doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Given loc
, cc_class = cls, cc_tyargs = xis })
= do { sc_work <- newGivenSCWork dv loc cls xis
; return $ SomeTopInt sc_work (ContinueWith workItem) }
doTopReact workItem@(CDictCan { cc_flavor = Derived loc _
, cc_class = cls, cc_tyargs = xis })
= do { fd_work <- findClassFunDeps cls xis loc
; if isEmptyWorkList fd_work then
return NoTopInt
else return $ SomeTopInt { tir_new_work = fd_work
, tir_new_inert = ContinueWith workItem } }
doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc
, cc_class = cls, cc_tyargs = xis })
= do {
; lkp_inst_res <- matchClassInst cls xis loc
; case lkp_inst_res of
NoInstance ->
do { traceTcS "doTopReact/ no class instance for" (ppr dv)
; fd_work <- findClassFunDeps cls xis loc
; if isEmptyWorkList fd_work then
do { sc_work <- newDerivedSCWork dv loc cls xis
; return $ SomeTopInt
{ tir_new_work = fd_work `unionWorkLists` sc_work
, tir_new_inert = ContinueWith workItem } }
else
return $ SomeTopInt
{ tir_new_work = fd_work `unionWorkLists`
workListFromCCan workItem
, tir_new_inert = Stop } }
GenInst wtvs ev_term ->
do { traceTcS "doTopReact/ found class instance for" (ppr dv)
; setDictBind dv ev_term
; inst_work <- canWanteds wtvs
; if null wtvs
then return $ SomeTopInt { tir_new_work = emptyWorkList
, tir_new_inert = Stop }
else do { let solved = makeSolvedByInst workItem
; sc_work <- newDerivedSCWork dv loc cls xis
; return $ SomeTopInt
{ tir_new_work = inst_work `unionWorkLists` sc_work
, tir_new_inert = ContinueWith solved } }
} }
doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
, cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
= ASSERT (isSynFamilyTyCon tc)
do { match_res <- matchFam tc args
; case match_res of
MatchInstNo
-> return NoTopInt
MatchInstSingle (rep_tc, rep_tys)
-> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
coe = mkTyConApp coe_tc rep_tys
; cv' <- case fl of
Wanted {} -> do { cv' <- newWantedCoVar rhs_ty xi
; setWantedCoBind cv $
coe `mkTransCoercion`
mkCoVarCoercion cv'
; return cv' }
_ -> newGivOrDerCoVar xi rhs_ty $
mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
; can_cts <- mkCanonical fl cv'
; return $ SomeTopInt can_cts Stop }
_
-> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
}
doTopReact _workItem = return NoTopInt
findClassFunDeps :: Class -> [Xi] -> WantedLoc -> TcS WorkList
findClassFunDeps cls xis loc
= do { instEnvs <- getInstEnvs
; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs)
(ClassP cls xis, pprArisingAt loc)
; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
; canWanteds wevvars }
\end{code}
Note [Adding Derived Superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Generally speaking, we want to be able to add derived superclasses of
unsolved wanteds, and wanteds that have been partially being solved
via an instance. This is important to be able to simplify the inferred
constraints more (and to allow for recursive dictionaries, less
importantly). Example:
Inferred wanted constraint is (Eq a, Ord a), but we'd only like to
quantify over Ord a, hence we would like to be able to add the
superclass of Ord a as Derived and use it to solve the wanted Eq a.
Hence we will add Derived superclasses in the following two cases:
(1) When we meet an unsolved wanted in toplevel reactions
(2) When we partially solve a wanted in toplevel reactions using an instance decl.
At that point, we have two options:
(1) Add transitively add *ALL* of the superclasses of the Derived
(2) Add only the immediate ones, but whenever we meet a Derived in
the future, add its own superclasses as Derived.
Option (2) is terrible, because deriveds may be rewritten or kicked
out of the inert set, which will result in slightly rewritten
superclasses being reintroduced in the worklist and the inert set. Eg:
class C a => B a
instance Foo a => B [a]
Original constraints:
[Wanted] d : B [a]
[Given] co : a ~ Int
We apply the instance to the wanted and put it and its superclasses as
as Deriveds in the inerts:
[Derived] d : B [a]
[Derived] (sel d) : C [a]
The work is now:
[Given] co : a ~ Int
[Wanted] d' : Foo a
Now, suppose that we interact the Derived with the Given equality, and
kick him out of the inert, the next time around a superclass C [Int]
will be produced
will anyway get rewritten to C [Int].
So we choose (1), and *never* introduce any more superclass work from
Deriveds. This enables yet another optimisation: If we ever meet an
equality that can rewrite a Derived, if that Derived is a superclass
derived (like C [a] above), i.e. not a partially solved one (like B
[a]) above, we may simply completely *discard* that Derived. The
reason is because somewhere in the inert lies the original wanted, or
partially solved constraint that gave rise to that superclass, and
that constraint *will* be kicked out, and *will* result in the
rewritten superclass to be added in the inerts later on, anyway.
Note [FunDep and implicit parameter reactions]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Currently, our story of interacting two dictionaries (or a dictionary
and toplevel 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 workitem Given overrides an inertitem Given.
Note [Given constraint that matches an instance declaration]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What should we do when we discover that one (or more) toplevel
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 toplevel 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 toplevel we get (beta ~ a), which
is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
now solvable by the given Q [a].
However, this option is restrictive, for instance [Example 3] from
Note [Recursive dictionaries] will fail to work.
2. Ignore the problem, hoping that the situations where there exist indeed
such multiple strategies are rare: Indeed the cause of the previous
problem is that (R [x] y) yields the new work (x ~ y) which can be
*spontaneously* solved, not using the givens.
We are choosing option 2 below but we might consider having a flag as well.
Note [New Wanted Superclass Work]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Even in the case of wanted constraints, we add all of its superclasses as
new given work. There are several reasons for this:
a) to minimise error messages;
eg suppose we have wanted (Eq a, Ord a)
then we report only (Ord a) unsoluble
b) to make the smallest number of constraints when *inferring* a type
(same Eq/Ord example)
c) for recursive dictionaries we *must* add the superclasses
so that we can use them when solving a subproblem
d) To allow FDlike 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 superclass 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.
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}
newGivenSCWork :: EvVar -> GivenLoc -> Class -> [Xi] -> TcS WorkList
newGivenSCWork ev loc cls xis
| NoScSkol <- ctLocOrigin loc
= return emptyWorkList
| otherwise
= newImmSCWorkFromFlavored ev (Given loc) cls xis >>= return
newDerivedSCWork :: EvVar -> WantedLoc -> Class -> [Xi] -> TcS WorkList
newDerivedSCWork ev loc cls xis
= do { ims <- newImmSCWorkFromFlavored ev flavor cls xis
; rec_sc_work ims }
where
rec_sc_work :: CanonicalCts -> TcS CanonicalCts
rec_sc_work cts
= do { bg <- mapBagM (\c -> do { ims <- imm_sc_work c
; recs_ims <- rec_sc_work ims
; return $ consBag c recs_ims }) cts
; return $ concatBag bg }
imm_sc_work (CDictCan { cc_id = dv, cc_flavor = fl, cc_class = cls, cc_tyargs = xis })
= newImmSCWorkFromFlavored dv fl cls xis
imm_sc_work _ct = return emptyCCan
flavor = Derived loc DerSC
newImmSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS WorkList
newImmSCWorkFromFlavored ev flavor cls xis
= do { let (tyvars, sc_theta, _, _) = classBigSig cls
sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
; sc_vars <- zipWithM inst_one sc_theta1 [0..]
; mkCanonicals flavor sc_vars }
where
inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
data LookupInstResult
= NoInstance
| GenInst [WantedEvVar] EvTerm
matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
matchClassInst clas tys loc
= do { let pred = mkClassPred clas tys
; mb_result <- matchClass clas tys
; case mb_result of
MatchInstNo -> return NoInstance
MatchInstMany -> return NoInstance
MatchInstSingle (dfun_id, mb_inst_tys) ->
do { checkWellStagedDFun pred dfun_id loc
; tys <- instDFunTypes mb_inst_tys
; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
; if null theta then
return (GenInst [] (EvDFunApp dfun_id tys []))
else do
{ ev_vars <- instDFunConstraints theta
; let wevs = [WantedEvVar w loc | w <- ev_vars]
; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }
}
}
\end{code}