\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
solveInteract, -- 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, ipClassNameKey )
import Class
import TyCon
import Name
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 Control.Monad( when, unless )
import Pair ()
import Unique( hasKey )
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}
solveInteractGiven :: CtLoc -> [TcTyVar] -> [EvVar] -> TcS ()
-- 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 loc fsks givens
= do { implics <- solveInteract (fsk_bag `unionBags` given_bag)
; ASSERT( isEmptyBag implics )
return () } -- We do not decompose *given* polymorphic equalities
-- (forall a. t1 ~ forall a. t2)
-- What would the evidence look like?!
-- See Note [Do not decompose given polytype equalities]
-- in TcCanonical
where
given_bag = listToBag [ mkNonCanonical loc $ CtGiven { ctev_evtm = EvId ev_id
, ctev_pred = evVarPred ev_id }
| ev_id <- givens ]
fsk_bag = listToBag [ mkNonCanonical loc $ CtGiven { ctev_evtm = EvCoercion (mkTcReflCo tv_ty)
, ctev_pred = pred }
| tv <- fsks
, let FlatSkol fam_ty = tcTyVarDetails tv
tv_ty = mkTyVarTy tv
pred = mkTcEqPred fam_ty tv_ty
]
-- The main solver loop implements Note [Basic Simplifier Plan]
---------------------------------------------------------------
solveInteract :: Cts -> TcS (Bag Implication)
-- Returns the final InertSet in TcS
-- Has no effect on work-list or residual-iplications
solveInteract cts
= {-# SCC "solveInteract" #-}
withWorkList cts $
do { dyn_flags <- getDynFlags
; solve_loop (ctxtStkDepth dyn_flags) }
where
solve_loop max_depth
= {-# SCC "solve_loop" #-}
do { sel <- selectNextWorkItem max_depth
; case sel of
NoWorkRemaining -- Done, successfuly (modulo frozen)
-> return ()
MaxDepthExceeded ct -- Failure, depth exceeded
-> wrapErrTcS $ solverDepthErrorTcS ct
NextWorkItem ct -- More work, loop around!
-> do { runSolverPipeline thePipeline ct; solve_loop max_depth } }
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)
| ctLocDepth (cc_loc 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]
; bumpStepCountTcS -- One step for each constraint processed
; 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 { traceFireTcS ct (ptext (sLit "Kept as inert:") <+> ppr ct)
; traceTcS "End solver pipeline (not discharged) }" $
vcat [ ptext (sLit "final_item = ") <+> ppr ct
, pprTvBndrs (varSetElems $ tyVarsOfCt ct)
, ptext (sLit "inerts = ") <+> ppr final_is]
; insertInertItemTcS 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 = [ ("canonicalization", TcCanonical.canonicalize)
, ("spontaneous solve", spontaneousSolveStage)
, ("interact with inerts", interactWithInertsStage)
, ("top-level reactions", topReactionsStage) ]
\end{code}
*********************************************************************************
* *
The spontaneous-solve Stage
* *
*********************************************************************************
\begin{code}
spontaneousSolveStage :: SimplifierStage
-- CTyEqCans are always consumed, returning Stop
spontaneousSolveStage workItem
= do { mb_solved <- trySpontaneousSolve workItem
; case mb_solved of
SPCantSolve
| CTyEqCan { cc_tyvar = tv, cc_ev = fl } <- workItem
-- Unsolved equality
-> do { n_kicked <- kickOutRewritable (ctEvFlavour fl) tv
; traceFireTcS workItem $
ptext (sLit "Kept as inert") <+> ppr_kicked n_kicked <> colon
<+> ppr workItem
; insertInertItemTcS workItem
; return Stop }
| otherwise
-> continueWith workItem
SPSolved new_tv
-- Post: tv ~ xi is now in TyBinds, no need to put in inerts as well
-- see Note [Spontaneously solved in TyBinds]
-> do { n_kicked <- kickOutRewritable Given new_tv
; traceFireTcS workItem $
ptext (sLit "Spontaneously solved") <+> ppr_kicked n_kicked <> colon
<+> ppr workItem
; return Stop } }
ppr_kicked :: Int -> SDoc
ppr_kicked 0 = empty
ppr_kicked n = parens (int n <+> ptext (sLit "kicked out"))
\end{code}
Note [Spontaneously solved in TyBinds]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we encounter a constraint ([W] alpha ~ tau) which can be spontaneously solved,
we record the equality on the TyBinds of the TcSMonad. In the past, we used to also
add a /given/ version of the constraint ([G] alpha ~ tau) to the inert
canonicals -- and potentially kick out other equalities that mention alpha.
Then, the flattener only had to look in the inert equalities during flattening of a
type (TcCanonical.flattenTyVar).
However it is a bit silly to record these equalities /both/ in the inerts AND the
TyBinds, so we have now eliminated spontaneously solved equalities from the inerts,
and only record them in the TyBinds of the TcS monad. The flattener is now consulting
these binds /and/ the inerts for potentially unsolved or other given equalities.
\begin{code}
kickOutRewritable :: CtFlavour -- Flavour of the equality that is
-- being added to the inert set
-> TcTyVar -- The new equality is tv ~ ty
-> TcS Int
kickOutRewritable new_flav new_tv
= do { wl <- modifyInertTcS kick_out
; traceTcS "kickOutRewritable" $
vcat [ text "tv = " <+> ppr new_tv
, ptext (sLit "Kicked out =") <+> ppr wl]
; updWorkListTcS (appendWorkList wl)
; return (workListSize wl) }
where
kick_out :: InertSet -> (WorkList, InertSet)
kick_out (is@(IS { inert_cans = IC { inert_eqs = tv_eqs
, inert_dicts = dictmap
, inert_funeqs = funeqmap
, inert_irreds = irreds
, inert_insols = insols } }))
= (kicked_out, is { inert_cans = inert_cans_in })
-- NB: Notice that don't rewrite
-- inert_solved_dicts, and inert_solved_funeqs
-- optimistically. But when we lookup we have to take the
-- subsitution into account
where
inert_cans_in = IC { inert_eqs = tv_eqs_in
, inert_dicts = dicts_in
, inert_funeqs = feqs_in
, inert_irreds = irs_in
, inert_insols = insols_in }
kicked_out = WorkList { wl_eqs = varEnvElts tv_eqs_out
, wl_funeqs = foldrBag insertDeque emptyDeque feqs_out
, wl_rest = bagToList (dicts_out `andCts` irs_out
`andCts` insols_out) }
(tv_eqs_out, tv_eqs_in) = partitionVarEnv kick_out_eq tv_eqs
(feqs_out, feqs_in) = partCtFamHeadMap kick_out_ct funeqmap
(dicts_out, dicts_in) = partitionCCanMap kick_out_ct dictmap
(irs_out, irs_in) = partitionBag kick_out_ct irreds
(insols_out, insols_in) = partitionBag kick_out_ct insols
-- Kick out even insolubles; see Note [Kick out insolubles]
kick_out_ct inert_ct = new_flav `canRewrite` (ctFlavour inert_ct) &&
(new_tv `elemVarSet` tyVarsOfCt inert_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!
kick_out_eq (CTyEqCan { cc_tyvar = tv, cc_rhs = rhs, cc_ev = ev })
= (new_flav `canRewrite` inert_flav) -- See Note [Delicate equality kick-out]
&& (new_tv `elemVarSet` kind_vars || -- (1)
(not (inert_flav `canRewrite` new_flav) && -- (2)
new_tv `elemVarSet` (extendVarSet (tyVarsOfType rhs) tv)))
where
inert_flav = ctEvFlavour ev
kind_vars = tyVarsOfType (tyVarKind tv) `unionVarSet`
tyVarsOfType (typeKind rhs)
kick_out_eq other_ct = pprPanic "kick_out_eq" (ppr other_ct)
\end{code}
Note [Kick out insolubles]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we have an insoluble alpha ~ [alpha], which is insoluble
because an occurs check. And then we unify alpha := [Int].
Then we really want to rewrite the insouluble to [Int] ~ [[Int]].
Now it can be decomposed. Otherwise we end up with a "Can't match
[Int] ~ [[Int]]" which is true, but a bit confusing because the
outer type constructors match.
Note [Delicate equality kick-out]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When adding an equality (a ~ xi), we kick out an inert type-variable
equality (b ~ phi) in two cases
(1) If the new tyvar can rewrite the kind LHS or RHS of the inert
equality. Example:
Work item: [W] k ~ *
Inert: [W] (a:k) ~ ty
[W] (b:*) ~ c :: k
We must kick out those blocked inerts so that we rewrite them
and can subsequently unify.
(2) If the new tyvar can
Work item: [G] a ~ b
Inert: [W] b ~ [a]
Now at this point the work item cannot be further rewritten by the
inert (due to the weaker inert flavor). But we can't add the work item
as-is because the inert set would then have a cyclic substitution,
when rewriting a wanted type mentioning 'a'. So we must kick the inert out.
We have to do this only if the inert *cannot* rewrite the work item;
it it can, then the work item will have been fully rewritten by the
inert during canonicalisation. So for example:
Work item: [W] a ~ Int
Inert: [W] b ~ [a]
No need to kick out the inert, beause the inert substitution is not
necessarily idemopotent. See Note [Non-idempotent inert substitution].
See also point (8) of Note [Detailed InertCans Invariants]
\begin{code}
data SPSolveResult = SPCantSolve
| SPSolved TcTyVar
-- We solved this /unification/ variable to some type using reflexivity
-- 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_loc = d })
| isGiven gw
= return SPCantSolve
| Just tv2 <- tcGetTyVar_maybe xi
= do { tch1 <- isTouchableMetaTyVarTcS tv1
; tch2 <- isTouchableMetaTyVarTcS 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 <- isTouchableMetaTyVarTcS tv1
; if tch1 then trySpontaneousEqOneWay d gw tv1 xi
else do { untch <- getUntouchables
; traceTcS "Untouchable LHS, can't spontaneously solve workitem" $
vcat [text "Untouchables =" <+> ppr untch
, text "Workitem =" <+> ppr workItem ]
; return SPCantSolve }
}
-- No need for
-- trySpontaneousSolve (CFunEqCan ...) = ...
-- See Note [No touchables as FunEq RHS] in TcSMonad
trySpontaneousSolve _ = return SPCantSolve
----------------
trySpontaneousEqOneWay :: CtLoc -> CtEvidence
-> TcTyVar -> Xi -> TcS SPSolveResult
-- tv is a MetaTyVar, not untouchable
trySpontaneousEqOneWay d gw tv xi
| not (isSigTyVar tv) || isTyVarTy xi
, typeKind xi `tcIsSubKind` tyVarKind tv
= solveWithIdentity d gw tv xi
| otherwise -- Still can't solve, sig tyvar and non-variable rhs
= return SPCantSolve
----------------
trySpontaneousEqTwoWay :: CtLoc -> 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
| k1 `tcIsSubKind` k2 && nicer_to_update_tv2
= solveWithIdentity d gw tv2 (mkTyVarTy tv1)
| k2 `tcIsSubKind` k1
= solveWithIdentity d gw tv1 (mkTyVarTy tv2)
| otherwise
= return SPCantSolve
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 :: CtLoc -> 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 "Unifies:" <+> ppr tv <+> ptext (sLit ":=") <+> ppr xi,
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')
; when (isWanted wd) $
setEvBind (ctev_evar wd) refl_evtm
; return (SPSolved tv) }
\end{code}
*********************************************************************************
* *
The interact-with-inert Stage
* *
*********************************************************************************
Note [
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 } -- Work item discharged by interaction; stop
| IRReplace { ir_fire :: String } -- Inert item replaced by work item; stop
| IRInertConsumed { ir_fire :: String } -- Inert item consumed, keep going with work item
| IRKeepGoing { ir_fire :: String } -- Inert item remains, keep going with work item
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
= do { insertInertItemTcS 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 { traceFireTcS wi (mk_msg rule (text "WorkItemConsumed"))
; insertInertItemTcS atomic_inert
; return Stop }
IRReplace { ir_fire = rule }
-> do { traceFireTcS atomic_inert
(mk_msg rule (text "InertReplace"))
; insertInertItemTcS wi
; return Stop }
IRInertConsumed { ir_fire = rule }
-> do { traceFireTcS atomic_inert
(mk_msg rule (text "InertItemConsumed"))
; return (ContinueWith wi) }
IRKeepGoing {}
-> do { insertInertItemTcS 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, cc_loc = loc1 })
workItem@(CDictCan { cc_ev = fl2, cc_class = cls2, cc_tyargs = tys2, cc_loc = loc2 })
| cls1 == cls2
= do { let pty1 = mkClassPred cls1 tys1
pty2 = mkClassPred cls2 tys2
inert_pred_loc = (pty1, pprArisingAt loc1)
work_item_pred_loc = (pty2, pprArisingAt loc2)
; let fd_eqns = improveFromAnother inert_pred_loc work_item_pred_loc
; fd_work <- rewriteWithFunDeps fd_eqns loc2
-- We don't really rewrite tys2, see below _rewritten_tys2, so that's ok
-- NB: We do create FDs for given to report insoluble equations that arise
-- from pairs of Givens, and also because of floating when we approximate
-- implications. The relevant test is: typecheck/should_fail/FDsFromGivens.hs
-- Also see Note [When improvement happens]
; traceTcS "doInteractWithInert:dict"
(vcat [ text "inertItem =" <+> ppr inertItem
, text "workItem =" <+> ppr workItem
, text "fundeps =" <+> ppr fd_work ])
; case fd_work of
-- No Functional Dependencies
[] | eqTypes tys1 tys2 -> solveOneFromTheOther "Cls/Cls" fl1 workItem
| otherwise -> return (IRKeepGoing "NOP")
-- Actual Functional Dependencies
_ | cls1 `hasKey` ipClassNameKey
, isGiven fl1, isGiven fl2 -- See Note [Shadowing of Implicit Parameters]
-> return (IRReplace ("Replace IP"))
-- 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.
| otherwise
-> do { updWorkListTcS (extendWorkListEqs fd_work)
; return (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 })
workItem@(CIrredEvCan { cc_ev = wfl })
| ctEvPred ifl `eqType` ctEvPred wfl
= solveOneFromTheOther "Irred/Irred" ifl workItem
doInteractWithInert ii@(CFunEqCan { cc_ev = ev1, cc_fun = tc1
, cc_tyargs = args1, cc_rhs = xi1, cc_loc = d1 })
wi@(CFunEqCan { cc_ev = ev2, cc_fun = tc2
, cc_tyargs = args2, cc_rhs = xi2, cc_loc = d2 })
| i_solves_w && (not (w_solves_i && isMetaTyVarTy xi1))
-- See Note [Carefully solve the right CFunEqCan]
= ASSERT( lhss_match ) -- extractRelevantInerts ensures this
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 ev2 [mkTcEqPred xi2 xi1] xev
-- No caching! See Note [Cache-caused loops]
-- Why not (mkTcEqPred xi1 xi2)? See Note [Efficient orientation]
; emitWorkNC d2 ctevs
; return (IRWorkItemConsumed "FunEq/FunEq") }
| fl2 `canSolve` fl1
= ASSERT( lhss_match ) -- extractRelevantInerts ensures this
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 ev1 [mkTcEqPred xi2 xi1] xev
-- Why not (mkTcEqPred xi1 xi2)? See Note [Efficient orientation]
; emitWorkNC d1 ctevs
; return (IRInertConsumed "FunEq/FunEq") }
where
lhss_match = tc1 == tc2 && eqTypes args1 args2
co1 = evTermCoercion $ ctEvTerm ev1
co2 = evTermCoercion $ ctEvTerm ev2
mk_sym_co x = mkTcSymCo (evTermCoercion x)
fl1 = ctEvFlavour ev1
fl2 = ctEvFlavour ev2
i_solves_w = fl1 `canSolve` fl2
w_solves_i = fl2 `canSolve` fl1
doInteractWithInert _ _ = return (IRKeepGoing "NOP")
\end{code}
Note [Efficient Orientation]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose we are interacting two FunEqCans with the same LHS:
(inert) ci :: (F ty ~ xi_i)
(work) cw :: (F ty ~ xi_w)
We prefer to keep the inert (else we pass the work item on down
the pipeline, which is a bit silly). If we keep the inert, we
will (a) discharge 'cw'
(b) produce a new equality work-item (xi_w ~ xi_i)
Notice the orientation (xi_w ~ xi_i) NOT (xi_i ~ xi_w):
new_work :: xi_w ~ xi_i
cw := ci ; sym new_work
Why? Consider the simplest case when xi1 is a type variable. If
we generate xi1~xi2, porcessing that constraint will kick out 'ci'.
If we generate xi2~xi1, there is less chance of that happening.
Of course it can and should still happen if xi1=a, xi1=Int, say.
But we want to avoid it happening needlessly.
Similarly, if we *can't* keep the inert item (because inert is Wanted,
and work is Given, say), we prefer to orient the new equality (xi_i ~
xi_w).
Note [Carefully solve the right CFunEqCan]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the constraints
c1 :: F Int ~ a -- Arising from an application line 5
c2 :: F Int ~ Bool -- Arising from an application line 10
Suppose that 'a' is a unification variable, arising only from
flattening. So there is no error on line 5; it's just a flattening
variable. But there is (or might be) an error on line 10.
Two ways to combine them, leaving either (Plan A)
c1 :: F Int ~ a -- Arising from an application line 5
c3 :: a ~ Bool -- Arising from an application line 10
or (Plan B)
c2 :: F Int ~ Bool -- Arising from an application line 10
c4 :: a ~ Bool -- Arising from an application line 5
Plan A will unify c3, leaving c1 :: F Int ~ Bool as an error
on the *totally innocent* line 5. An example is test SimpleFail16
where the expected/actual message comes out backwards if we use
the wrong plan.
The second is the right thing to do. Hence the isMetaTyVarTy
test when solving pairwise CFunEqCan.
Note [Shadowing of Implicit Parameters]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the following example:
f :: (?x :: Char) => Char
f = let ?x = 'a' in ?x
The "let ?x = ..." generates an implication constraint of the form:
?x :: Char => ?x :: Char
Furthermore, the signature for `f` also generates an implication
constraint, so we end up with the following nested implication:
?x :: Char => (?x :: Char => ?x :: Char)
Note that the wanted (?x :: Char) constraint may be solved in
two incompatible ways: either by using the parameter from the
signature, or by using the local definition. Our intention is
that the local definition should "shadow" the parameter of the
signature, and we implement this as follows: when we add a new
given implicit parameter to the inert set, it replaces any existing
givens for the same implicit parameter.
This works for the normal cases but it has an odd side effect
in some pathological programs like this:
-- This is accepted, the second parameter shadows
f1 :: (?x :: Int, ?x :: Char) => Char
f1 = ?x
-- This is rejected, the second parameter shadows
f2 :: (?x :: Int, ?x :: Char) => Int
f2 = ?x
Both of these are actually wrong: when we try to use either one,
we'll get two incompatible wnated constraints (?x :: Int, ?x :: Char),
which would lead to an error.
I can think of two ways to fix this:
1. Simply disallow multiple constratits for the same implicit
parameter---this is never useful, and it can be detected completely
syntactically.
2. Move the shadowing machinery to the location where we nest
implications, and add some code here that will produce an
error if we get multiple givens for the same implicit parameter.
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
= return (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
= return (IRInertConsumed ("Solved[DI] " ++ info))
| CtWanted { ctev_evar = ev_id } <- wfl
= do { setEvBind ev_id (ctEvTerm ifl); return (IRWorkItemConsumed ("Solved(w) " ++ info)) }
| CtWanted { ctev_evar = ev_id } <- ifl
= do { setEvBind ev_id (ctEvTerm wfl); return (IRInertConsumed ("Solved(g) " ++ info)) }
| otherwise -- If both are Given, we already have evidence; no need to duplicate
-- But the work item *overrides* the inert item (hence IRReplace)
-- See Note [Shadowing of Implicit Parameters]
= return (IRReplace ("Replace(gg) " ++ info))
where
wfl = cc_ev workItem
\end{code}
Note [Shadowing of Implicit Parameters]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the following example:
f :: (?x :: Char) => Char
f = let ?x = 'a' in ?x
The "let ?x = ..." generates an implication constraint of the form:
?x :: Char => ?x :: Char
Furthermore, the signature for `f` also generates an implication
constraint, so we end up with the following nested implication:
?x :: Char => (?x :: Char => ?x :: Char)
Note that the wanted (?x :: Char) constraint may be solved in
two incompatible ways: either by using the parameter from the
signature, or by using the local definition. Our intention is
that the local definition should "shadow" the parameter of the
signature, and we implement this as follows: when we nest implications,
we remove any implicit parameters in the outer implication, that
have the same name as givens of the inner implication.
Here is another variation of the example:
f :: (?x :: Int) => Char
f = let ?x = 'x' in ?x
This program should also be accepted: the two constraints `?x :: Int`
and `?x :: Char` never exist in the same context, so they don't get to
interact to cause failure.
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
topReactionsStage, 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,
because 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] -> CtLoc -> TcS [Ct]
-- NB: The returned constraints are all Derived
-- Post: returns no trivial equalities (identities) and all EvVars returned are fresh
rewriteWithFunDeps eqn_pred_locs loc
= do { fd_cts <- mapM (instFunDepEqn loc) eqn_pred_locs
; return (concat fd_cts) }
instFunDepEqn :: CtLoc -> Equation -> TcS [Ct]
-- Post: Returns the position index as well as the corresponding FunDep equality
instFunDepEqn loc (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
der_loc = pushErrCtxt FunDepOrigin (False, mkEqnMsg d1 d2) loc
do_one subst ievs (FDEq { fd_ty_left = ty1, fd_ty_right = ty2 })
| eqType sty1 sty2
= return ievs -- Return no trivial equalities
| otherwise
= do { mb_eqv <- newDerived (mkTcEqPred sty1 sty2)
; case mb_eqv of
Just ev -> return (mkNonCanonical der_loc ev : 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!
where
sty1 = Type.substTy subst ty1
sty2 = Type.substTy subst ty2
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) }
\end{code}
*********************************************************************************
* *
The top-reaction Stage
* *
*********************************************************************************
\begin{code}
topReactionsStage :: WorkItem -> TcS StopOrContinue
topReactionsStage wi
= do { inerts <- getTcSInerts
; tir <- doTopReact inerts wi
; case tir of
NoTopInt -> return (ContinueWith wi)
SomeTopInt rule what_next
-> do { traceFireTcS 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. Note:
--
-- (a) The place to add superclasses in not here in doTopReact stage.
-- Instead superclasses are added in the worklist as part of the
-- canonicalization process. See Note [Adding superclasses].
--
-- (b) See Note [Given constraint that matches an instance declaration]
-- for some design decisions for given dictionaries.
doTopReact inerts workItem
= do { traceTcS "doTopReact" (ppr workItem)
; case workItem of
CDictCan { cc_ev = fl, cc_class = cls, cc_tyargs = xis
, cc_loc = d }
-> doTopReactDict inerts fl cls xis d
CFunEqCan { cc_ev = fl, cc_fun = tc, cc_tyargs = args
, cc_rhs = xi, cc_loc = d }
-> doTopReactFunEq workItem fl tc args xi d
_ -> -- Any other work item does not react with any top-level equations
return NoTopInt }
--------------------
doTopReactDict :: InertSet -> CtEvidence -> Class -> [Xi]
-> CtLoc -> TcS TopInteractResult
doTopReactDict inerts fl cls xis loc
| not (isWanted fl)
= try_fundeps_and_return
| Just ev <- lookupSolvedDict inerts pred -- Cached
= do { setEvBind dict_id (ctEvTerm ev);
; return $ SomeTopInt { tir_rule = "Dict/Top (cached)"
, tir_new_item = Stop } }
| otherwise -- Not cached
= do { lkup_inst_res <- matchClassInst inerts cls xis loc
; case lkup_inst_res of
GenInst wtvs ev_term -> do { addSolvedDict fl
; solve_from_instance wtvs ev_term }
NoInstance -> try_fundeps_and_return }
where
arising_sdoc = pprArisingAt loc
dict_id = ctEvId fl
pred = mkClassPred cls xis
solve_from_instance :: [CtEvidence] -> EvTerm -> TcS TopInteractResult
-- Precondition: evidence term matches the predicate workItem
solve_from_instance 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_loc = bumpCtLocDepth loc }
; updWorkListTcS (extendWorkListCts (map mk_new_wanted evs))
; return $
SomeTopInt { tir_rule = "Dict/Top (solved, more work)"
, tir_new_item = Stop } }
-- We didn't solve it; so try functional dependencies with
-- the instance environment, and return
-- NB: even if there *are* some functional dependencies against the
-- instance environment, there might be a unique match, and if
-- so we make sure we get on and solve it first. See Note [Weird fundeps]
try_fundeps_and_return
= do { instEnvs <- getInstEnvs
; let fd_eqns = improveFromInstEnv instEnvs (pred, arising_sdoc)
; fd_work <- rewriteWithFunDeps fd_eqns loc
; unless (null fd_work) (updWorkListTcS (extendWorkListEqs fd_work))
; return NoTopInt }
--------------------
doTopReactFunEq :: Ct -> CtEvidence -> TyCon -> [Xi] -> Xi
-> CtLoc -> TcS TopInteractResult
doTopReactFunEq _ct fl fun_tc args xi loc
= ASSERT (isSynFamilyTyCon fun_tc) -- No associated data families have
-- reached this far
-- Look in the cache of solved funeqs
do { fun_eq_cache <- getTcSInerts >>= (return . inert_solved_funeqs)
; case lookupFamHead fun_eq_cache fam_ty of {
Just (ctev, rhs_ty)
| ctEvFlavour ctev `canRewrite` ctEvFlavour fl
-> ASSERT( not (isDerived ctev) )
succeed_with "Fun/Cache" (evTermCoercion (ctEvTerm ctev)) rhs_ty ;
_other ->
-- Look up in top-level instances
do { match_res <- matchFam fun_tc args -- See Note [MATCHING-SYNONYMS]
; case match_res of {
Nothing -> return NoTopInt ;
Just (FamInstMatch { fim_instance = famInst
, fim_index = index
, fim_tys = rep_tys }) ->
-- Found a top-level instance
do { -- Add it to the solved goals
unless (isDerived fl) (addSolvedFunEq fam_ty fl xi)
; let coe_ax = famInstAxiom famInst
; succeed_with "Fun/Top" (mkTcAxInstCo coe_ax index rep_tys)
(mkAxInstRHS coe_ax index rep_tys) } } } } }
where
fam_ty = mkTyConApp fun_tc args
succeed_with :: String -> TcCoercion -> TcType -> TcS TopInteractResult
succeed_with str co rhs_ty -- co :: fun_tc args ~ rhs_ty
= do { ctevs <- xCtFlavor fl [mkTcEqPred rhs_ty xi] xev
; traceTcS ("doTopReactFunEq " ++ str) (ppr ctevs)
; case ctevs of
[ctev] -> updWorkListTcS $ extendWorkListEq $
CNonCanonical { cc_ev = ctev
, cc_loc = bumpCtLocDepth loc }
ctevs -> -- No subgoal (because it's cached)
ASSERT( null ctevs) return ()
; return $ SomeTopInt { tir_rule = str
, tir_new_item = Stop } }
where
xdecomp x = [EvCoercion (mkTcSymCo co `mkTcTransCo` evTermCoercion x)]
xcomp [x] = EvCoercion (co `mkTcTransCo` evTermCoercion x)
xcomp _ = panic "No more goals!"
xev = XEvTerm xcomp xdecomp
\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 Derived 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 :d alpha ~ Bool
where 'cv' is currently unused. However, this new item can perhaps be
spontaneously solved to become given and react 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, but that requires those equalities to carry
evidence and derived do not carry evidence.
If that were the case 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
Note that we *do* fire the improvement if one is Given and one is Derived (e.g. a
superclass of a Wanted goal) or if both are Given.
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)
Test typecheck/should_fail/FDsFromGivens also shows why it's a good idea to
emit Derived FDs for givens as well.
Note [Weird fundeps]
~~~~~~~~~~~~~~~~~~~~
Consider class Het a b | a -> b where
het :: m (f c) -> a -> m b
class GHet (a :: * -> *) (b :: * -> *) | a -> b
instance GHet (K a) (K [a])
instance Het a b => GHet (K a) (K b)
The two instances don't actually conflict on their fundeps,
although it's pretty strange. So they are both accepted. Now
try [W] GHet (K Int) (K Bool)
This triggers fudeps from both instance decls; but it also
matches a *unique* instance decl, and we should go ahead and
pick that one right now. Otherwise, if we don't, it ends up
unsolved in the inert set and is reported as an error.
Trac #7875 is a case in point.
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] -> CtLoc -> TcS LookupInstResult
matchClassInst _ clas [ k, ty ] _
| className clas == singIClassName
, Just n <- isNumLitTy ty = makeDict (EvNum n)
| className clas == singIClassName
, Just s <- isStrLitTy ty = makeDict (EvStr s)
where
{- This adds a coercion that will convert the literal into a dictionary
of the appropriate type. See Note [SingI and EvLit] in TcEvidence.
The coercion happens in 3 steps:
evLit -> Sing_k_n -- literal to representation of data family
Sing_k_n -> Sing k n -- representation of data family to data family
Sing k n -> SingI k n -- data family to class dictionary.
-}
makeDict evLit =
case unwrapNewTyCon_maybe (classTyCon clas) of
Just (_,dictRep, axDict)
| Just tcSing <- tyConAppTyCon_maybe dictRep ->
do mbInst <- matchFam tcSing [k,ty]
case mbInst of
Just FamInstMatch
{ fim_instance = FamInst { fi_axiom = axDataFam
, fi_flavor = DataFamilyInst tcon
}
, fim_index = ix, fim_tys = tys
} | Just (_,_,axSing) <- unwrapNewTyCon_maybe tcon ->
do let co1 = mkTcSymCo $ mkTcUnbranchedAxInstCo axSing tys
co2 = mkTcSymCo $ mkTcAxInstCo axDataFam ix tys
co3 = mkTcSymCo $ mkTcUnbranchedAxInstCo axDict [k,ty]
return $ GenInst [] $ EvCast (EvLit evLit) $
mkTcTransCo co1 $ mkTcTransCo co2 co3
_ -> unexpected
_ -> unexpected
unexpected = panicTcS (text "Unexpected evidence for SingI")
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 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 :: Untouchables -> 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 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.