TcInteract.lhs 83.4 KB
 simonpj@microsoft.com committed Sep 13, 2010 1 2 3 \begin{code} module TcInteract ( solveInteract, AtomicInert,  4  InertSet, emptyInert, updInertSet, extractUnsolved, solveOne  simonpj@microsoft.com committed Sep 13, 2010 5 6 7 8  ) where #include "HsVersions.h"  dimitris@microsoft.com committed Oct 04, 2010 9   simonpj@microsoft.com committed Sep 13, 2010 10 11 12 13 import BasicTypes import TcCanonical import VarSet import Type  dimitris@microsoft.com committed Oct 04, 2010 14 import TypeRep  simonpj@microsoft.com committed Sep 13, 2010 15 16  import Id  simonpj@microsoft.com committed Oct 07, 2010 17 import VarEnv  simonpj@microsoft.com committed Sep 13, 2010 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 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  simonpj@microsoft.com committed Oct 07, 2010 38 import Bag  dimitris@microsoft.com committed Oct 04, 2010 39 40 41 import qualified Data.Map as Map import Maybes  simonpj@microsoft.com committed Sep 13, 2010 42 43 44 45 46 import Control.Monad( zipWithM, unless ) import FastString ( sLit ) import DynFlags \end{code}  dimitris@microsoft.com committed Oct 06, 2010 47 Note [InertSet invariants]  simonpj@microsoft.com committed Sep 13, 2010 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ An InertSet is a bag of canonical constraints, with the following invariants: 1 No two constraints react with each other. A tricky case is when there exists a given (solved) dictionary constraint and a wanted identical constraint in the inert set, but do not react because reaction would create loopy dictionary evidence for the wanted. See note [Recursive dictionaries] 2 Given equalities form an idempotent substitution [none of the given LHS's occur in any of the given RHS's or reactant parts] 3 Wanted equalities also form an idempotent substitution 4 The entire set of equalities is acyclic. 5 Wanted dictionaries are inert with the top-level axiom set 6 Equalities of the form tv1 ~ tv2 always have a touchable variable on the left (if possible). 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints will be marked as solved right before being pushed into the inert set. See note [Touchables and givens]. Note that 6 and 7 are /not/ enforced by canonicalization but rather by insertion in the inert list, ie by TcInteract. During the process of solving, the inert set will contain some previously given constraints, some wanted constraints, and some given constraints which have arisen from solving wanted constraints. For now we do not distinguish between given and solved constraints. Note that we must switch wanted inert items to given when going under an implication constraint (when in top-level inference mode).  dimitris@microsoft.com committed Oct 06, 2010 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 Note [InertSet FlattenSkolemEqClass] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The inert_fsks field of the inert set contains an "inverse map" of all the flatten skolem equalities in the inert set. For instance, if inert_cts looks like this: fsk1 ~ fsk2 fsk3 ~ fsk2 fsk4 ~ fsk5 Then, the inert_fsks fields holds the following map: fsk2 |-> { fsk1, fsk3 } fsk5 |-> { fsk4 } Along with the necessary coercions to convert fsk1 and fsk3 back to fsk2 and fsk4 back to fsk5. Hence, the invariants of the inert_fsks field are: (a) All TcTyVars in the domain and range of inert_fsks are flatten skolems (b) All TcTyVars in the domain of inert_fsk occur naked as rhs in some equalities of inert_cts (c) For every mapping fsk1 |-> { (fsk2,co), ... } it must be: co : fsk2 ~ fsk1 The role of the inert_fsks is to make it easy to maintain the equivalence class of each flatten skolem, which is much needed to correctly do spontaneous solving. See Note [Loopy Spontaneous Solving]  simonpj@microsoft.com committed Sep 13, 2010 109 110 111 \begin{code} -- See Note [InertSet invariants]  dimitris@microsoft.com committed Oct 04, 2010 112 data InertSet  113 114  = IS { inert_eqs :: Bag.Bag CanonicalCt -- Equalities only (CTyEqCan,CFunEqCan) , inert_cts :: Bag.Bag CanonicalCt -- Other constraints  dimitris@microsoft.com committed Oct 04, 2010 115  , inert_fsks :: Map.Map TcTyVar [(TcTyVar,Coercion)] }  dimitris@microsoft.com committed Oct 06, 2010 116  -- See Note [InertSet FlattenSkolemEqClass]  dimitris@microsoft.com committed Oct 04, 2010 117   simonpj@microsoft.com committed Sep 13, 2010 118 instance Outputable InertSet where  119 120  ppr is = vcat [ vcat (map ppr (Bag.bagToList $inert_eqs is)) , vcat (map ppr (Bag.bagToList$ inert_cts is))  dimitris@microsoft.com committed Oct 04, 2010 121 122 123 124 125  , vcat (map (\(v,rest) -> ppr v <+> text "|->" <+> hsep (map (ppr.fst) rest)) (Map.toList $inert_fsks is) ) ]  simonpj@microsoft.com committed Sep 13, 2010 126 emptyInert :: InertSet  127 128 emptyInert = IS { inert_eqs = Bag.emptyBag , inert_cts = Bag.emptyBag, inert_fsks = Map.empty }  dimitris@microsoft.com committed Oct 04, 2010 129 130 131  updInertSet :: InertSet -> AtomicInert -> InertSet -- Introduces an element in the inert set for the first time  132 updInertSet (IS { inert_eqs = eqs, inert_cts = cts, inert_fsks = fsks })  dimitris@microsoft.com committed Oct 04, 2010 133 134 135 136 137 138  item@(CTyEqCan { cc_id = cv , cc_tyvar = tv1 , cc_rhs = xi }) | Just tv2 <- tcGetTyVar_maybe xi, FlatSkol {} <- tcTyVarDetails tv1, FlatSkol {} <- tcTyVarDetails tv2  139  = let eqs' = eqs Bag.snocBag item  dimitris@microsoft.com committed Oct 04, 2010 140  fsks' = Map.insertWith (++) tv2 [(tv1, mkCoVarCoercion cv)] fsks  dimitris@microsoft.com committed Oct 06, 2010 141  -- See Note [InertSet FlattenSkolemEqClass]  142 143  in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks' } updInertSet (IS { inert_eqs = eqs, inert_cts = cts  dimitris@microsoft.com committed Oct 04, 2010 144  , inert_fsks = fsks }) item  145 146 147 148  | isEqCCan item = let eqs' = eqs Bag.snocBag item in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks } | otherwise  dimitris@microsoft.com committed Oct 04, 2010 149  = let cts' = cts Bag.snocBag item  150  in IS { inert_eqs = eqs, inert_cts = cts', inert_fsks = fsks }  dimitris@microsoft.com committed Oct 04, 2010 151   simonpj@microsoft.com committed Sep 13, 2010 152 foldlInertSetM :: (Monad m) => (a -> AtomicInert -> m a) -> a -> InertSet -> m a  153 154 155 156 -- Prioritize over the equalities see Note [Prioritizing Equalities] foldlInertSetM k z (IS { inert_eqs = eqs, inert_cts = cts }) = do { z' <- Bag.foldlBagM k z eqs ; Bag.foldlBagM k z' cts }  simonpj@microsoft.com committed Sep 13, 2010 157 158  extractUnsolved :: InertSet -> (InertSet, CanonicalCts)  159 160 161 162 163 164 165 166 extractUnsolved is@(IS {inert_eqs = eqs, inert_cts = cts}) = let is_init = is { inert_eqs = emptyCCan , inert_cts = solved_cts, inert_fsks = Map.empty } is_final = Bag.foldlBag updInertSet is_init solved_eqs -- Add equalities carefully in (is_final, unsolved) where (unsolved_cts, solved_cts) = Bag.partitionBag isWantedCt cts (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs unsolved = unsolved_cts unionBags unsolved_eqs  simonpj@microsoft.com committed Sep 13, 2010 167   dimitris@microsoft.com committed Oct 04, 2010 168 169  getFskEqClass :: InertSet -> TcTyVar -> [(TcTyVar,Coercion)]  dimitris@microsoft.com committed Oct 06, 2010 170 -- Precondition: tv is a FlatSkol. See Note [InertSet FlattenSkolemEqClass]  dimitris@microsoft.com committed Oct 04, 2010 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 getFskEqClass (IS { inert_cts = cts, inert_fsks = fsks }) tv = case lkpTyEqCanByLhs of Nothing -> fromMaybe [] (Map.lookup tv fsks) Just ceq -> case tcGetTyVar_maybe (cc_rhs ceq) of Just tv_rhs | FlatSkol {} <- tcTyVarDetails tv_rhs -> let ceq_co = mkSymCoercion$ mkCoVarCoercion (cc_id ceq) mk_co (v,c) = (v, mkTransCoercion c ceq_co) in (tv_rhs, ceq_co): map mk_co (fromMaybe [] $Map.lookup tv fsks) _ -> [] where lkpTyEqCanByLhs = Bag.foldlBag lkp Nothing cts lkp :: Maybe CanonicalCt -> CanonicalCt -> Maybe CanonicalCt lkp Nothing ct@(CTyEqCan {cc_tyvar = tv'}) | tv' == tv = Just ct lkp other _ct = other  simonpj@microsoft.com committed Sep 13, 2010 187 188 isWantedCt :: CanonicalCt -> Bool isWantedCt ct = isWanted (cc_flavor ct)  dimitris@microsoft.com committed Oct 04, 2010 189 190 191 192 193 194 195 196 197 198 199  {- TODO: Later ... data Inert = IS { class_inerts :: FiniteMap Class Atomics ip_inerts :: FiniteMap Class Atomics tyfun_inerts :: FiniteMap TyCon Atomics tyvar_inerts :: FiniteMap TyVar Atomics } Later should we also separate out givens and wanteds? -}  simonpj@microsoft.com committed Sep 13, 2010 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 \end{code} Note [Touchables and givens] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Touchable variables will never show up in givens which are inputs to the solver. However, touchables may show up in givens generated by the flattener. For example, axioms: G Int ~ Char F Char ~ Int wanted: F (G alpha) ~w Int canonicalises to G alpha ~g b F b ~w Int which can be put in the inert set. Suppose we also have a wanted alpha ~w Int We cannot rewrite the given G alpha ~g b using the wanted alpha ~w Int. Instead, after reacting alpha ~w Int with the whole inert set, we observe that we can solve it by unifying alpha with Int, so we mark it as solved and put it back in the *work list*. [We also immediately unify alpha := Int, without telling anyone, see trySpontaneousSolve function, to avoid doing this in the end.] Later, because it is solved (given, in effect), we can use it to rewrite G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually, we will dispatch the remaining wanted constraints using the top-level axioms. Finally, note that after reacting a wanted equality with the entire inert set we may end up with something like b ~w alpha which we should flip around to generate the solved constraint alpha ~s b. %********************************************************************* %* * * Main Interaction Solver * * * ********************************************************************** Note [Basic plan] ~~~~~~~~~~~~~~~~~ 1. Canonicalise (unary) 2. Pairwise interaction (binary) * Take one from work list * Try all pair-wise interactions with each constraint in inert 3. Try to solve spontaneously for equalities involving touchables 4. Top-level interaction (binary wrt top-level) Superclass decomposition belongs in (4), see note [Superclasses] \begin{code} type AtomicInert = CanonicalCt -- constraint pulled from InertSet type WorkItem = CanonicalCt -- constraint pulled from WorkList  263 264 265 266 267 268 -- A mixture of Given, Wanted, and Derived constraints. -- We split between equalities and the rest to process equalities first. data WorkList = WL { wl_eqs :: CanonicalCts -- Equalities (CTyEqCan, CFunEqCan) , wl_other :: CanonicalCts -- Other } type SWorkList = WorkList -- A worklist of solved  simonpj@microsoft.com committed Sep 13, 2010 269 270  unionWorkLists :: WorkList -> WorkList -> WorkList  271 272 273 unionWorkLists wl1 wl2 = WL { wl_eqs = andCCan (wl_eqs wl1) (wl_eqs wl2) , wl_other = andCCan (wl_other wl1) (wl_other wl2) }  simonpj@microsoft.com committed Sep 13, 2010 274 275  foldlWorkListM :: (Monad m) => (a -> WorkItem -> m a) -> a -> WorkList -> m a  276 277 278 279 -- This fold prioritizes equalities foldlWorkListM f r wl = do { r' <- Bag.foldlBagM f r (wl_eqs wl) ; Bag.foldlBagM f r' (wl_other wl) }  simonpj@microsoft.com committed Sep 13, 2010 280 281  isEmptyWorkList :: WorkList -> Bool  282 isEmptyWorkList wl = isEmptyCCan (wl_eqs wl) && isEmptyCCan (wl_other wl)  simonpj@microsoft.com committed Sep 13, 2010 283 284  emptyWorkList :: WorkList  285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 emptyWorkList = WL { wl_eqs = emptyCCan, wl_other = emptyCCan } mkEqWorkList :: CanonicalCts -> WorkList -- Precondition: *ALL* equalities mkEqWorkList eqs = WL { wl_eqs = eqs, wl_other = emptyCCan } mkNonEqWorkList :: CanonicalCts -> WorkList -- Precondition: *NO* equalities mkNonEqWorkList cts = WL { wl_eqs = emptyCCan, wl_other = cts } workListFromCCans :: CanonicalCts -> WorkList -- Generic, no precondition workListFromCCans cts = WL eqs others where (eqs, others) = Bag.partitionBag isEqCCan cts -- Convenience singleEqWL :: CanonicalCt -> WorkList singleNonEqWL :: CanonicalCt -> WorkList singleEqWL = mkEqWorkList . singleCCan singleNonEqWL = mkNonEqWorkList . singleCCan  simonpj@microsoft.com committed Sep 13, 2010 305   dimitris@microsoft.com committed Oct 04, 2010 306   simonpj@microsoft.com committed Sep 13, 2010 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 data StopOrContinue = Stop -- Work item is consumed | ContinueWith WorkItem -- Not consumed instance Outputable StopOrContinue where ppr Stop = ptext (sLit "Stop") ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w -- Results after interacting a WorkItem as far as possible with an InertSet data StageResult = SR { sr_inerts :: InertSet -- The new InertSet to use (REPLACES the old InertSet) , sr_new_work :: WorkList -- Any new work items generated (should be ADDED to the old WorkList) -- Invariant: -- sr_stop = Just workitem => workitem is *not* in sr_inerts and -- workitem is inert wrt to sr_inerts , sr_stop :: StopOrContinue } instance Outputable StageResult where ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop }) = ptext (sLit "SR") <+> braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma , ptext (sLit "new work =") <+> ppr work <> comma , ptext (sLit "stop =") <+> ppr stop])  334 335 336 instance Outputable WorkList where ppr (WL eqcts othercts) = vcat [ppr eqcts, ppr othercts]  simonpj@microsoft.com committed Sep 13, 2010 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 type SimplifierStage = WorkItem -> InertSet -> TcS StageResult -- Combine a sequence of simplifier 'stages' to create a pipeline runSolverPipeline :: [(String, SimplifierStage)] -> InertSet -> WorkItem -> TcS (InertSet, WorkList) -- Precondition: non-empty list of stages runSolverPipeline pipeline inerts workItem = do { traceTcS "Start solver pipeline"$ vcat [ ptext (sLit "work item =") <+> ppr workItem , ptext (sLit "inerts =") <+> ppr inerts] ; let itr_in = SR { sr_inerts = inerts , sr_new_work = emptyWorkList , sr_stop = ContinueWith workItem } ; itr_out <- run_pipeline pipeline itr_in ; let new_inert = case sr_stop itr_out of Stop -> sr_inerts itr_out  dimitris@microsoft.com committed Oct 04, 2010 356  ContinueWith item -> sr_inerts itr_out updInertSet item  simonpj@microsoft.com committed Sep 13, 2010 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402  ; 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 = sr_new_work itr unionWorkLists accum_work } ; run_pipeline stages itr' } \end{code} Example 1: Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given) Reagent: a ~ [b] (given) React with (c~d) ==> IR (ContinueWith (a~[b])) True [] React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t] React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True [] Example 2: Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty} Reagent: a ~w [b] React with (c ~w d) ==> IR (ContinueWith (a~[b])) True [] React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!) etc. Example 3: Inert: {a ~ Int, F Int ~ b} (given) Reagent: F a ~ b (wanted) React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True [] React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing \begin{code} -- Main interaction solver: we fully solve the worklist 'in one go', -- returning an extended inert set. -- -- See Note [Touchables and givens].  403 solveInteract :: InertSet -> CanonicalCts -> TcS InertSet  simonpj@microsoft.com committed Sep 13, 2010 404 405 solveInteract inert ws = do { dyn_flags <- getDynFlags  406 407  ; let worklist = workListFromCCans ws ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert worklist  simonpj@microsoft.com committed Sep 13, 2010 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467  } 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" $vcat [ text "Current depth =" <+> ppr n , text "Max depth =" <+> ppr max_depth ] ; foldlWorkListM (solveOneWithDepth ctxt) inert ws } ------------------ -- Fully interact the given work item with an inert set, and return a -- new inert set which has assimilated the new information. solveOneWithDepth :: (Int, Int, [WorkItem]) -> InertSet -> WorkItem -> TcS InertSet solveOneWithDepth (max_depth, n, stack) inert work = do { traceTcS0 (indent ++ "Solving {") (ppr work) ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work) -- Recursively solve the new work generated -- from workItem, with a greater depth ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack) new_inert new_work ; traceTcS0 (indent ++ "Done }") (ppr work) ; return res_inert } where indent = replicate (2*n) ' ' thePipeline :: [(String,SimplifierStage)] thePipeline = [ ("interact with inerts", interactWithInertsStage) , ("spontaneous solve", spontaneousSolveStage) , ("top-level reactions", topReactionsStage) ] \end{code} ********************************************************************************* * * The spontaneous-solve Stage * * ********************************************************************************* \begin{code} spontaneousSolveStage :: SimplifierStage spontaneousSolveStage workItem inerts  468  = do { mSolve <- trySpontaneousSolve workItem inerts  simonpj@microsoft.com committed Sep 13, 2010 469 470  ; case mSolve of Nothing -> -- no spontaneous solution for him, keep going  471 472  return$ SR { sr_new_work = emptyWorkList , sr_inerts = inerts  simonpj@microsoft.com committed Sep 13, 2010 473 474  , sr_stop = ContinueWith workItem }  475  Just workList' -> -- He has been solved; workList' are all givens  dimitris@microsoft.com committed Oct 04, 2010 476 477  return $SR { sr_new_work = workList' , sr_inerts = inerts  478  , sr_stop = Stop }  dimitris@microsoft.com committed Oct 04, 2010 479  }  dimitris@microsoft.com committed Oct 06, 2010 480 481 482 483 484 485 486 487 488  {-- This is all old code, but does not quite work now. The problem is that due to Note [Loopy Spontaneous Solving] we may have unflattened a type, to be able to perform a sneaky unification. This unflattening means that we may have to recanonicalize a given (solved) equality, this is why the result of trySpontaneousSolve is now a list of constraints (instead of an atomic solved constraint). We would have to react all of them once again with the worklist but that is very tiresome. Instead we throw them back in the worklist.  simonpj@microsoft.com committed Sep 13, 2010 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513  | isWantedCt workItem -- Original was wanted we have now made him given so -- we have to ineract him with the inerts again because -- of the change in his status. This may produce some work. -> do { traceTcS "recursive interact with inerts {"$ vcat [ text "work = " <+> ppr workItem' , text "inerts = " <+> ppr inerts ] ; itr_again <- interactWithInertsStage workItem' inerts ; case sr_stop itr_again of Stop -> pprPanic "BUG: Impossible to happen" $vcat [ text "Original workitem:" <+> ppr workItem , text "Spontaneously solved:" <+> ppr workItem' , text "Solved was consumed, when reacting with inerts:" , nest 2 (ppr inerts) ] ContinueWith workItem'' -- Now *this* guy is inert wrt to inerts -> do { traceTcS "end recursive interact }"$ ppr workItem'' ; return $SR { sr_new_work = sr_new_work itr_again , sr_inerts = sr_inerts itr_again extendInertSet workItem'' , sr_stop = Stop } } } | otherwise -> return$ SR { sr_new_work = emptyWorkList , sr_inerts = inerts extendInertSet workItem' , sr_stop = Stop } }  dimitris@microsoft.com committed Oct 04, 2010 514 --}  simonpj@microsoft.com committed Sep 13, 2010 515 516 517 518 519 520  -- @trySpontaneousSolve wi@ solves equalities where one side is a -- touchable unification variable. Returns: -- * Nothing if we were not able to solve it -- * Just wi' if we solved it, wi' (now a "given") should be put in the work list. -- See Note [Touchables and givens]  521 -- NB: just passing the inerts through for the skolem equivalence classes  dimitris@microsoft.com committed Oct 04, 2010 522 523 trySpontaneousSolve :: WorkItem -> InertSet -> TcS (Maybe SWorkList) trySpontaneousSolve (CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi }) inerts  simonpj@microsoft.com committed Oct 07, 2010 524 525  | isGiven gw = return Nothing  simonpj@microsoft.com committed Sep 13, 2010 526 527 528 529  | Just tv2 <- tcGetTyVar_maybe xi = do { tch1 <- isTouchableMetaTyVar tv1 ; tch2 <- isTouchableMetaTyVar tv2 ; case (tch1, tch2) of  dimitris@microsoft.com committed Oct 04, 2010 530 531  (True, True) -> trySpontaneousEqTwoWay inerts cv gw tv1 tv2 (True, False) -> trySpontaneousEqOneWay inerts cv gw tv1 xi  532  (False, True) -> trySpontaneousEqOneWay inerts cv gw tv2 (mkTyVarTy tv1)  simonpj@microsoft.com committed Sep 13, 2010 533 534 535  _ -> return Nothing } | otherwise = do { tch1 <- isTouchableMetaTyVar tv1  dimitris@microsoft.com committed Oct 04, 2010 536  ; if tch1 then trySpontaneousEqOneWay inerts cv gw tv1 xi  simonpj@microsoft.com committed Sep 13, 2010 537 538 539 540 541  else return Nothing } -- No need for -- trySpontaneousSolve (CFunEqCan ...) = ... -- See Note [No touchables as FunEq RHS] in TcSMonad  dimitris@microsoft.com committed Oct 04, 2010 542 trySpontaneousSolve _ _ = return Nothing  simonpj@microsoft.com committed Sep 13, 2010 543 544  ----------------  dimitris@microsoft.com committed Oct 04, 2010 545 546 trySpontaneousEqOneWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS (Maybe SWorkList)  simonpj@microsoft.com committed Sep 13, 2010 547 -- tv is a MetaTyVar, not untouchable  dimitris@microsoft.com committed Oct 04, 2010 548 trySpontaneousEqOneWay inerts cv gw tv xi  549 550  | not (isSigTyVar tv) || isTyVarTy xi, typeKind xi isSubKind tyVarKind tv  dimitris@microsoft.com committed Oct 04, 2010 551  = solveWithIdentity inerts cv gw tv xi  simonpj@microsoft.com committed Sep 13, 2010 552 553 554 555  | otherwise = return Nothing ----------------  dimitris@microsoft.com committed Oct 04, 2010 556 557 trySpontaneousEqTwoWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS (Maybe SWorkList)  simonpj@microsoft.com committed Sep 13, 2010 558 559 -- Both tyvars are *touchable* MetaTyvars -- By the CTyEqCan invariant, k2 isSubKind k1  dimitris@microsoft.com committed Oct 04, 2010 560 trySpontaneousEqTwoWay inerts cv gw tv1 tv2  561  | k1 isSubKind k2  dimitris@microsoft.com committed Oct 04, 2010 562  , nicer_to_update_tv2 = solveWithIdentity inerts cv gw tv2 (mkTyVarTy tv1)  563 564 565  | k2 isSubKind k1 = solveWithIdentity inerts cv gw tv1 (mkTyVarTy tv2) | otherwise = return Nothing  simonpj@microsoft.com committed Sep 13, 2010 566 567 568 569 570 571  where k1 = tyVarKind tv1 k2 = tyVarKind tv2 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2) \end{code}  572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599  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 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'  simonpj@microsoft.com committed Sep 13, 2010 600 601 602 603 604 605 606 607 608 609 610 611 612 Note [Loopy spontaneous solving] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider the original wanted: wanted : Maybe (E alpha) ~ alpha where E is a type family, such that E (T x) = x. After canonicalization, as a result of flattening, we will get: given : E alpha ~ fsk wanted : alpha ~ Maybe fsk where (fsk := E alpha, on the side). Now, if we spontaneously *solve* (alpha := Maybe fsk) we are in trouble! Instead, we should refrain from solving it and keep it as wanted. In inference mode we'll end up quantifying over (alpha ~ Maybe (E alpha)) Hence, 'solveWithIdentity' performs a small occurs check before  dimitris@microsoft.com committed Oct 06, 2010 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 actually solving. But this occurs check *must look through* flatten skolems. However, it may be the case that the flatten skolem in hand is equal to some other flatten skolem whith *does not* mention our unification variable. Here's a typical example: Original wanteds: g: F alpha ~ F beta w: alpha ~ F alpha After canonicalization: g: F beta ~ f1 g: F alpha ~ f1 w: alpha ~ f2 g: F alpha ~ f2 After some reactions: g: f1 ~ f2 g: F beta ~ f1 w: alpha ~ f2 g: F alpha ~ f2 At this point, we will try to spontaneously solve (alpha ~ f2) which remains as yet unsolved. We will look inside f2, which immediately mentions (F alpha), so it's not good to unify! However by looking at the equivalence class of the flatten skolems, we can see that it is fine to unify (alpha ~ f1) which solves our goals! A similar problem happens because of other spontaneous solving. Suppose we have the following wanteds, arriving in this exact order: (first) w: beta ~ alpha (second) w: alpha ~ fsk (third) g: F beta ~ fsk Then, we first spontaneously solve the first constraint, making (beta := alpha), and having (beta ~ alpha) as given. *Then* we encounter the second wanted (alpha ~ fsk). "fsk" does not obviously mention alpha, so naively we can also spontaneously solve (alpha := fsk). But that is wrong since fsk mentions beta, which has already secretly been unified to alpha! To avoid this problem, the same occurs check must unveil rewritings that can happen because of spontaneously having solved other constraints.  simonpj@microsoft.com committed Sep 13, 2010 649 650 651 652 653 654 655  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!  simonpj@microsoft.com committed Oct 07, 2010 656  given : a ~ alpha [having unified alpha := a]  simonpj@microsoft.com committed Sep 13, 2010 657 658 659 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]  simonpj@microsoft.com committed Oct 07, 2010 660 661 662 We avoid this problem by orienting the given so that the unification variable is on the left. [Note that alternatively we could attempt to enforce this at canonicalization]  simonpj@microsoft.com committed Sep 13, 2010 663   simonpj@microsoft.com committed Oct 07, 2010 664 665 666 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.  simonpj@microsoft.com committed Sep 13, 2010 667 668 669  \begin{code} ----------------  dimitris@microsoft.com committed Oct 04, 2010 670 671 672 solveWithIdentity :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS (Maybe SWorkList)  simonpj@microsoft.com committed Sep 13, 2010 673 674 -- Solve with the identity coercion -- Precondition: kind(xi) is a sub-kind of kind(tv)  simonpj@microsoft.com committed Oct 07, 2010 675 676 677 -- Precondition: CtFlavor is Wanted or Derived -- See [New Wanted Superclass Work] to see why solveWithIdentity -- must work for Derived as well as Wanted  dimitris@microsoft.com committed Oct 04, 2010 678 solveWithIdentity inerts cv gw tv xi  simonpj@microsoft.com committed Oct 07, 2010 679  = do { tybnds <- getTcSTyBindsMap  simonpj@microsoft.com committed Oct 07, 2010 680 681 682 683 684 685  ; case occurCheck tybnds inerts tv xi of Nothing -> return Nothing Just (xi_unflat,coi) -> solve_with xi_unflat coi } where solve_with xi_unflat coi -- coi : xi_unflat ~ xi = do { traceTcS "Sneaky unification:" $ dimitris@microsoft.com committed Oct 04, 2010 686 687 688 689  vcat [text "Coercion variable: " <+> ppr gw, text "Coercion: " <+> pprEq (mkTyVarTy tv) xi, text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)), text "Right Kind is : " <+> ppr (typeKind xi)  simonpj@microsoft.com committed Oct 07, 2010 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708  ] ; setWantedTyBind tv xi_unflat -- Set tv := xi_unflat ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat ; let flav = mkGivenFlavor gw UnkSkol ; (cts, co) <- case coi of ACo co -> do { can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi_unflat ; return (can_eqs, co) } IdCo co -> return$ (singleCCan (CTyEqCan { cc_id = cv_given , cc_flavor = mkGivenFlavor gw UnkSkol , cc_tyvar = tv, cc_rhs = xi } -- xi, *not* xi_unflat because -- xi_unflat may require flattening! ), co) ; case gw of Wanted {} -> setWantedCoBind cv co Derived {} -> setDerivedCoBind cv co _ -> pprPanic "Can't spontaneously solve *given*" empty -- See Note [Avoid double unifications]  709  ; return $Just (mkEqWorkList cts) }  simonpj@microsoft.com committed Oct 07, 2010 710   simonpj@microsoft.com committed Oct 07, 2010 711 occurCheck :: VarEnv (TcTyVar, TcType) -> InertSet  simonpj@microsoft.com committed Oct 07, 2010 712 713 714 715 716 717 718 719 720 721  -> TcTyVar -> TcType -> Maybe (TcType,CoercionI) -- Traverse @ty@ to make sure that @tv@ does not appear under some flatten skolem. -- If it appears under some flatten skolem look in that flatten skolem equivalence class -- (see Note [InertSet FlattenSkolemEqClass], [Loopy Spontaneous Solving]) to see if you -- can find a different flatten skolem to use, that is, one that does not mention @tv@. -- -- Postcondition: Just (ty', coi) = occurCheck binds inerts tv ty -- coi :: ty' ~ ty -- NB: The returned type ty' may not be flat!  simonpj@microsoft.com committed Oct 07, 2010 722 723 occurCheck ty_binds inerts the_tv the_ty = ok emptyVarSet the_ty  simonpj@microsoft.com committed Oct 07, 2010 724  where  simonpj@microsoft.com committed Oct 07, 2010 725 726  -- If (fsk elem bad) then tv occurs in any rendering -- of the type under the expansion of fsk  simonpj@microsoft.com committed Oct 07, 2010 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747  ok bad this_ty@(TyConApp tc tys) | Just tys_cois <- allMaybes (map (ok bad) tys) , (tys',cois') <- unzip tys_cois = Just (TyConApp tc tys', mkTyConAppCoI tc cois') | isSynTyCon tc, Just ty_expanded <- tcView this_ty = ok bad ty_expanded -- See Note [Type synonyms and the occur check] in TcUnify ok bad (PredTy sty) | Just (sty',coi) <- ok_pred bad sty = Just (PredTy sty', coi) ok bad (FunTy arg res) | Just (arg', coiarg) <- ok bad arg, Just (res', coires) <- ok bad res = Just (FunTy arg' res', mkFunTyCoI coiarg coires) ok bad (AppTy fun arg) | Just (fun', coifun) <- ok bad fun, Just (arg', coiarg) <- ok bad arg = Just (AppTy fun' arg', mkAppTyCoI coifun coiarg) ok bad (ForAllTy tv1 ty1) -- WARNING: What if it is a (t1 ~ t2) => t3? It's not handled properly at the moment. | Just (ty1', coi) <- ok bad ty1 = Just (ForAllTy tv1 ty1', mkForAllTyCoI tv1 coi) -- Variable cases  simonpj@microsoft.com committed Oct 07, 2010 748 749 750 751 752 753  ok bad this_ty@(TyVarTy tv) | tv == the_tv = Nothing -- Occurs check error | not (isTcTyVar tv) = Just (this_ty, IdCo this_ty) -- Bound var | FlatSkol zty <- tcTyVarDetails tv = ok_fsk bad tv zty | Just (_,ty) <- lookupVarEnv ty_binds tv = ok bad ty | otherwise = Just (this_ty, IdCo this_ty)  simonpj@microsoft.com committed Oct 07, 2010 754 755 756 757 758  -- Check if there exists a ty bind already, as a result of sneaky unification. -- Fall through ok _bad _ty = Nothing  simonpj@microsoft.com committed Oct 07, 2010 759  -----------  simonpj@microsoft.com committed Oct 07, 2010 760 761 762 763 764 765 766 767 768 769 770 771  ok_pred bad (ClassP cn tys) | Just tys_cois <- allMaybes$ map (ok bad) tys = let (tys', cois') = unzip tys_cois in Just (ClassP cn tys', mkClassPPredCoI cn cois') ok_pred bad (IParam nm ty) | Just (ty',co') <- ok bad ty = Just (IParam nm ty', mkIParamPredCoI nm co') ok_pred bad (EqPred ty1 ty2) | Just (ty1',coi1) <- ok bad ty1, Just (ty2',coi2) <- ok bad ty2 = Just (EqPred ty1' ty2', mkEqPredCoI coi1 coi2) ok_pred _ _ = Nothing  simonpj@microsoft.com committed Oct 07, 2010 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790  ----------- ok_fsk bad fsk zty | fsk elemVarSet bad -- We are already trying to find a rendering of fsk, -- and to do that it seems we need a rendering, so fail = Nothing | otherwise = firstJusts (ok new_bad zty : map (go_under_fsk new_bad) fsk_equivs) where fsk_equivs = getFskEqClass inerts fsk new_bad = bad extendVarSetList (fsk : map fst fsk_equivs) ----------- go_under_fsk bad_tvs (fsk,co) | FlatSkol zty <- tcTyVarDetails fsk = case ok bad_tvs zty of Nothing -> Nothing Just (ty,coi') -> Just (ty, mkTransCoI coi' (ACo co)) | otherwise = pprPanic "go_down_equiv" (ppr fsk)  simonpj@microsoft.com committed Sep 13, 2010 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 \end{code} ********************************************************************************* * * The interact-with-inert Stage * * ********************************************************************************* \begin{code} -- Interaction result of WorkItem <~> AtomicInert data InteractResult = IR { ir_stop :: StopOrContinue -- Stop -- => Reagent (work item) consumed. -- ContinueWith new_reagent -- => Reagent transformed but keep gathering interactions. -- The transformed item remains inert with respect -- to any previously encountered inerts. , ir_inert_action :: InertAction -- Whether the inert item should remain in the InertSet. , ir_new_work :: WorkList -- new work items to add to the WorkList } -- What to do with the inert reactant. data InertAction = KeepInert | DropInert deriving Eq mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult mkIRContinue wi keep newWork = return $IR (ContinueWith wi) keep newWork mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult mkIRStop keep newWork = return$ IR Stop keep newWork dischargeWorkItem :: Monad m => m InteractResult  829 dischargeWorkItem = mkIRStop KeepInert emptyWorkList  simonpj@microsoft.com committed Sep 13, 2010 830 831  noInteraction :: Monad m => WorkItem -> m InteractResult  832 noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList  simonpj@microsoft.com committed Sep 13, 2010 833   dimitris@microsoft.com committed Sep 23, 2010 834 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert  simonpj@microsoft.com committed Sep 13, 2010 835 836 837 838 839 840 841 842 843 844 845 846 847 848  --------------------------------------------------- -- Interact a single WorkItem with an InertSet as far as possible, i.e. until we get a Stop -- result from an individual interaction (i.e. when the WorkItem is consumed), or until we've -- interacted the WorkItem with the entire InertSet. -- -- Postcondition: the new InertSet in the resulting StageResult is subset -- of the input InertSet. interactWithInertsStage :: SimplifierStage interactWithInertsStage workItem inert = foldlInertSetM interactNext initITR inert where initITR = SR { sr_inerts = emptyInert  849  , sr_new_work = emptyWorkList  simonpj@microsoft.com committed Sep 13, 2010 850 851  , sr_stop = ContinueWith workItem }  dimitris@microsoft.com committed Oct 04, 2010 852   simonpj@microsoft.com committed Sep 13, 2010 853 854 855 856 857 858  interactNext :: StageResult -> AtomicInert -> TcS StageResult interactNext it inert | ContinueWith workItem <- sr_stop it = do { ir <- interactWithInert inert workItem ; let inerts = sr_inerts it ; return $SR { sr_inerts = if ir_inert_action ir == KeepInert  dimitris@microsoft.com committed Oct 04, 2010 859  then inerts updInertSet inert  simonpj@microsoft.com committed Sep 13, 2010 860 861 862 863 864 865 866  else inerts , sr_new_work = sr_new_work it unionWorkLists ir_new_work ir , sr_stop = ir_stop ir } } | otherwise = return$ itrAddInert inert it itrAddInert :: AtomicInert -> StageResult -> StageResult  dimitris@microsoft.com committed Oct 04, 2010 867  itrAddInert inert itr = itr { sr_inerts = (sr_inerts itr) updInertSet inert }  simonpj@microsoft.com committed Sep 13, 2010 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915  -- Do a single interaction of two constraints. interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult interactWithInert inert workitem = do { ctxt <- getTcSContext ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem inert_ev = cc_id inert work_ev = cc_id workitem -- Never interact a wanted and a derived where the derived's evidence -- mentions the wanted evidence in an unguarded way. -- See Note [Superclasses and recursive dictionaries] -- and Note [New Wanted Superclass Work] -- We don't have to do this for givens, as we fully know the evidence for them. ; rec_ev_ok <- case (cc_flavor inert, cc_flavor workitem) of (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 inert workitem else noInteraction workitem } allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool -- Allowed interactions allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only allowedInteraction _ _ _ = True -------------------------------------------- doInteractWithInert :: CanonicalCt -> CanonicalCt -> TcS InteractResult -- Identical class constraints. doInteractWithInert (CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 }) workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 }) | cls1 == cls2 && (and $zipWith tcEqType tys1 tys2) = solveOneFromTheOther (d1,fl1) workItem | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2)) = -- See Note [When improvement happens] do { let work_item_pred_loc = (ClassP cls2 tys2, ppr d2) inert_pred_loc = (ClassP cls1 tys1, ppr d1) loc = combineCtLoc fl1 fl2 eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc  916   simonpj@microsoft.com committed Sep 13, 2010 917  ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs  918 919  ; fd_cts <- canWanteds wevvars ; let fd_work = mkEqWorkList fd_cts  simonpj@microsoft.com committed Sep 13, 2010 920  -- See Note [Generating extra equalities]  921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937  ; if isEmptyCCan fd_cts || not (isWanted fl2) then -- || or impr. had previously kicked in -- No improvement kicked in, keep going mkIRContinue workItem KeepInert fd_work else -- Improvement kicked in, throw him back into the worklist so that he -- gets rewritten. The reason is that we do not want to let him fall off -- at the end and then add its potential un-improved superclasses. This -- optimisation crucially relies on prioritizing the equalities in the -- worklist. -- The termination of this relies on wanteds being able to rewrite wanteds. -- Since the class may be at the bottom of an equality worklist, which may -- consist of insoluble wanteds, if these wanteds *never* become solved or given -- (because they mention untouchables), the workitem will *never* be rewritten -- so next time we meet him we will be once again producing FunDep equalities -- for ever and ever! mkIRStop KeepInert$ fd_work unionWorkLists singleNonEqWL workItem  simonpj@microsoft.com committed Sep 13, 2010 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961  -- See Note [FunDep Reactions] } -- Class constraint and given equality: use the equality to rewrite -- the class constraint. doInteractWithInert (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 -- substitute for tv in xis. Note that the resulting class -- constraint is still canonical, since substituting xi-types in -- xi-types generates xi-types. However, it may no longer be -- inert with respect to the inert set items we've already seen. -- For example, consider the inert set -- -- D Int (g) -- a ~g Int -- -- and the work item D a (w). D a does not interact with D Int. -- Next, it does interact with a ~g Int, getting rewritten to D -- Int (w). But now we must go back through the rest of the inert -- set again, to find that it can now be discharged by the given D -- Int instance. = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)  962  ; mkIRStop KeepInert $singleNonEqWL rewritten_dict }  simonpj@microsoft.com committed Sep 13, 2010 963 964 965 966 967 968  doInteractWithInert (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 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)  969  ; mkIRContinue workItem DropInert (singleNonEqWL rewritten_dict) }  simonpj@microsoft.com committed Sep 13, 2010 970 971 972 973 974 975 976 977  -- Class constraint and given equality: use the equality to rewrite -- the class constraint. doInteractWithInert (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)  978  ; mkIRStop KeepInert (singleNonEqWL rewritten_ip) }  simonpj@microsoft.com committed Sep 13, 2010 979 980 981 982 983 984  doInteractWithInert (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)  985  ; mkIRContinue workItem DropInert (singleNonEqWL rewritten_ip) }  simonpj@microsoft.com committed Sep 13, 2010 986 987 988 989 990 991 992 993  -- Two implicit parameter constraints. If the names are the same, -- but their types are not, we generate a wanted type equality -- that equates the type (this is "improvement"). -- However, we don't actually need the coercion evidence, -- so we just generate a fresh coercion variable that isn't used anywhere. doInteractWithInert (CIPCan { cc_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 })  simonpj@microsoft.com committed Sep 17, 2010 994 995 996 997  | nm1 == nm2 && isGiven wfl && isGiven ifl = -- See Note [Overriding implicit parameters] -- Dump the inert item, override totally with the new one -- Do not require type equality  998  mkIRContinue workItem DropInert emptyWorkList  simonpj@microsoft.com committed Sep 17, 2010 999   simonpj@microsoft.com committed Sep 13, 2010 1000 1001 1002  | nm1 == nm2 && ty1 tcEqType ty2 = solveOneFromTheOther (id1,ifl) workItem  simonpj@microsoft.com committed Sep 17, 2010 1003  | nm1 == nm2  simonpj@microsoft.com committed Sep 13, 2010 1004 1005 1006  = -- See Note [When improvement happens] do { co_var <- newWantedCoVar ty1 ty2 ; let flav = Wanted (combineCtLoc ifl wfl)  1007 1008  ; cans <- mkCanonical flav co_var ; mkIRContinue workItem KeepInert (mkEqWorkList cans) }  simonpj@microsoft.com committed Sep 13, 2010 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025  -- Inert: equality, work item: function equality -- Never rewrite a given with a wanted equality, and a type function -- equality can never rewrite an equality. Note also that if we have -- F x1 ~ x2 and a ~ x3, and a occurs in x2, we don't rewrite it. We -- can wait until F x1 ~ x2 matches another F x1 ~ x4, and only then -- we will expose'' x2 and x4 to rewriting. -- Otherwise, we can try rewriting the type function equality with the equality. doInteractWithInert (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 args = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)  1026  ; mkIRStop KeepInert (singleEqWL rewritten_funeq) }  simonpj@microsoft.com committed Sep 13, 2010 1027 1028 1029 1030 1031 1032 1033 1034 1035  -- Inert: function equality, work item: equality doInteractWithInert (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 args = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)  1036  ; mkIRContinue workItem DropInert (singleEqWL rewritten_funeq) }  simonpj@microsoft.com committed Sep 13, 2010 1037 1038 1039 1040 1041  doInteractWithInert (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 })  1042  | fl1 canSolve fl2 && lhss_match  dimitris@microsoft.com committed Sep 23, 2010 1043  = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)  1044  ; mkIRStop KeepInert (mkEqWorkList cans) }  1045  | fl2 canSolve fl1 && lhss_match  dimitris@microsoft.com committed Sep 23, 2010 1046  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)  1047  ; mkIRContinue workItem DropInert (mkEqWorkList cans) }  simonpj@microsoft.com committed Sep 13, 2010 1048 1049 1050  where lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)  dimitris@microsoft.com committed Oct 04, 2010 1051 1052 doInteractWithInert inert@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })  simonpj@microsoft.com committed Sep 13, 2010 1053 1054  workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 }) -- Check for matching LHS  1055  | fl1 canSolve fl2 && tv1 == tv2  dimitris@microsoft.com committed Sep 23, 2010 1056  = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)  1057  ; mkIRStop KeepInert (mkEqWorkList cans) }  simonpj@microsoft.com committed Sep 13, 2010 1058   1059  | fl2 canSolve fl1 && tv1 == tv2  dimitris@microsoft.com committed Sep 23, 2010 1060  = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)  1061  ; mkIRContinue workItem DropInert (mkEqWorkList cans) }  simonpj@microsoft.com committed Sep 13, 2010 1062 1063 1064 1065  -- Check for rewriting RHS | fl1 canRewrite fl2 && tv1 elemVarSet tyVarsOfType xi2 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)  1066  ; mkIRStop KeepInert (mkEqWorkList rewritten_eq) }  simonpj@microsoft.com committed Sep 13, 2010 1067 1068  | fl2 canRewrite fl1 && tv2 elemVarSet tyVarsOfType xi1 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)  1069  ; mkIRContinue workItem DropInert (mkEqWorkList rewritten_eq) }  dimitris@microsoft.com committed Oct 06, 2010 1070 1071 1072 1073 1074 1075  -- Finally, if workitem is a Flatten Equivalence Class constraint and the -- inert is a wanted constraint, even when the workitem cannot rewrite the -- inert, drop the inert out because you may have to reconsider solving the -- inert *using* the equivalence class you created. See note [Loopy Spontaneous Solving] -- and [InertSet FlattenSkolemEqClass]  dimitris@microsoft.com committed Oct 04, 2010 1076 1077 1078 1079 1080  | not$ isGiven fl1, -- The inert is wanted or derived isMetaTyVar tv1, -- and has a unification variable lhs FlatSkol {} <- tcTyVarDetails tv2, -- And workitem is a flatten skolem equality Just tv2' <- tcGetTyVar_maybe xi2, FlatSkol {} <- tcTyVarDetails tv2'  1081  = mkIRContinue workItem DropInert (singleEqWL inert)  simonpj@microsoft.com committed Sep 13, 2010 1082 1083   dimitris@microsoft.com committed Oct 06, 2010 1084 -- Fall-through case for all other situations  simonpj@microsoft.com committed Sep 13, 2010 1085 1086 doInteractWithInert _ workItem = noInteraction workItem  simonpj@microsoft.com committed Oct 08, 2010 1087 -------------------------  simonpj@microsoft.com committed Sep 13, 2010 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 -- Equational Rewriting rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt rewriteDict (cv,tv,xi) (dv,gw,cl,xis) = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi] args = substTysWith [tv] [xi] xis con = classTyCon cl dict_co = mkTyConCoercion con cos ; dv' <- newDictVar cl args ; case gw of Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co)) _given_or_derived -> setDictBind dv' (EvCast dv dict_co) ; return (CDictCan { cc_id = dv' , cc_flavor = gw , cc_class = cl , cc_tyargs = args }) } rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt rewriteIP (cv,tv,xi) (ipid,gw,nm,ty) = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi] ty' = substTyWith [tv] [xi] ty ; ipid' <- newIPVar nm ty' ; case gw of Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co)) _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co) ; return (CIPCan { cc_id = ipid' , cc_flavor = gw , cc_ip_nm = nm , cc_ip_ty = ty' }) } rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args args' = substTysWith [tv] [xi1] args fun_co = mkTyConCoercion tc arg_cos ; cv2' <- case gw of Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2 ; setWantedCoBind cv2 $mkTransCoercion fun_co (mkCoVarCoercion cv2') ; return cv2' } _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2$ mkTransCoercion (mkSymCoercion fun_co) (mkCoVarCoercion cv2) ; return (CFunEqCan { cc_id = cv2' , cc_flavor = gw , cc_tyargs = args' , cc_fun = tc , cc_rhs = xi2 }) } rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS CanonicalCts -- Use the first equality to rewrite the second, flavors already checked. -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2 -- rewrites c2 to give -- c2' : tv2 ~ xi2[xi1/tv1] -- We must do an occurs check to sure the new constraint is canonical -- So we might return an empty bag rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2) | Just tv2' <- tcGetTyVar_maybe xi2' , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2 = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2')) ; return emptyCCan } | otherwise = do { cv2' <- case gw of Wanted {} -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2' ; setWantedCoBind cv2 $mkCoVarCoercion cv2' mkTransCoercion mkSymCoercion co2' ; return cv2' } _giv_or_der -> newGivOrDerCoVar (mkTyVarTy tv2) xi2'$ mkCoVarCoercion cv2 mkTransCoercion co2' ; xi2'' <- canOccursCheck gw tv2 xi2' -- we know xi2' is *not* tv2 ; return (singleCCan $CTyEqCan { cc_id = cv2' , cc_flavor = gw , cc_tyvar = tv2  1164  , cc_rhs = xi2'' })  simonpj@microsoft.com committed Sep 13, 2010 1165 1166 1167 1168 1169  } where xi2' = substTyWith [tv1] [xi1] xi2 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]  dimitris@microsoft.com committed Sep 23, 2010 1170 1171  rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS CanonicalCts  simonpj@microsoft.com committed Sep 13, 2010 1172 1173 1174 -- Used to ineratct two equalities of the following form: -- First Equality: co1: (XXX ~ xi1) -- Second Equality: cv2: (XXX ~ xi2)  1175 -- Where the cv1 canSolve cv2 equality  dimitris@microsoft.com committed Sep 23, 2010 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1). This -- depends on whether the left or the right equality comes from the inert set. -- We must: -- prefer to create (xi2 ~ xi1) if the first comes from the inert -- prefer to create (xi1 ~ xi2) if the second comes from the inert rewriteEqLHS which (co1,xi1) (cv2,gw,xi2) = do { cv2' <- case (isWanted gw, which) of (True,LeftComesFromInert) -> do { cv2' <- newWantedCoVar xi2 xi1 ; setWantedCoBind cv2$ co1 mkTransCoercion mkSymCoercion (mkCoVarCoercion cv2') ; return cv2' } (True,RightComesFromInert) -> do { cv2' <- newWantedCoVar xi1 xi2 ; setWantedCoBind cv2 $co1 mkTransCoercion mkCoVarCoercion cv2' ; return cv2' } (False,LeftComesFromInert) -> newGivOrDerCoVar xi2 xi1$ mkSymCoercion (mkCoVarCoercion cv2) mkTransCoercion co1 (False,RightComesFromInert) -> newGivOrDerCoVar xi1 xi2 $mkSymCoercion co1 mkTransCoercion mkCoVarCoercion cv2  1199 1200 1201  ; mkCanonical gw cv2' }  simonpj@microsoft.com committed Sep 13, 2010 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult -- First argument inert, second argument workitem. They both represent -- wanted/given/derived evidence for the *same* predicate so we try here to -- discharge one directly from the other. -- -- Precondition: value evidence only (implicit parameters, classes) -- not coercion solveOneFromTheOther (iid,ifl) workItem -- Both derived needs a special case. You might think that we do not need -- two evidence terms for the same claim. But, since the evidence is partial, -- either evidence may do in some cases; see TcSMonad.isGoodRecEv. -- See also Example 3 in Note [Superclasses and recursive dictionaries] | isDerived ifl && isDerived wfl = noInteraction workItem  1217  | ifl canSolve wfl  simonpj@microsoft.com committed Sep 17, 2010 1218 1219 1220 1221 1222  = do { unless (isGiven wfl)$ setEvBind wid (EvId iid) -- Overwrite the binding, if one exists -- For Givens, which are lambda-bound, nothing to overwrite, ; dischargeWorkItem }  1223  | otherwise -- wfl canSolve ifl  simonpj@microsoft.com committed Sep 13, 2010 1224  = do { unless (isGiven ifl) $setEvBind iid (EvId wid)  1225  ; mkIRContinue workItem DropInert emptyWorkList }  simonpj@microsoft.com committed Sep 13, 2010 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648  where wfl = cc_flavor workItem wid = cc_id workItem \end{code} Note [Superclasses and recursive dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Overlaps with Note [SUPERCLASS-LOOP 1] Note [SUPERCLASS-LOOP 2] Note [Recursive instances and superclases] ToDo: check overlap and delete redundant stuff Right before adding a given into the inert set, we must produce some more work, that will bring the superclasses of the given into scope. The superclass constraints go into our worklist. When we simplify a wanted constraint, if we first see a matching instance, we may produce new wanted work. To (1) avoid doing this work twice in the future and (2) to handle recursive dictionaries we may cache'' this item as solved (in effect, given) into our inert set and with that add its superclass constraints (as given) in our worklist. But now we have added partially solved constraints to the worklist which may interact with other wanteds. Consider the example: Example 1: class Eq b => Foo a b --- 0-th selector instance Eq a => Foo [a] a --- fooDFun and wanted (Foo [t] t). We are first going to see that the instance matches and create an inert set that includes the solved (Foo [t] t) and its superclasses. d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3 d2 :_g Eq t d2 := EvSuperClass d1 0 Our work list is going to contain a new *wanted* goal d3 :_w Eq t It is wrong to react the wanted (Eq t) with the given (Eq t) because that would construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert. OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries, at all? Consider Example 2: data D r = ZeroD | SuccD (r (D r)); instance (Eq (r (D r))) => Eq (D r) where ZeroD == ZeroD = True (SuccD a) == (SuccD b) = a == b _ == _ = False; equalDC :: D [] -> D [] -> Bool; equalDC = (==); We need to prove (Eq (D [])). Here's how we go: d1 :_w Eq (D []) by instance decl, holds if d2 :_w Eq [D []] where d1 = dfEqD d2 *BUT* we have an inert set which gives us (no superclasses): d1 :_g Eq (D []) By the instance declaration of Eq we can show the 'd2' goal if d3 :_w Eq (D []) where d2 = dfEqList d3 d1 = dfEqD d2 Now, however this wanted can interact with our inert d1 to set: d3 := d1 and solve the goal. Why was this interaction OK? Because, if we chase the evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we are really setting d3 := dfEqD2 (dfEqList d3) which is FINE because the use of d3 is protected by the instance function applications. So, our strategy is to try to put solved wanted dictionaries into the inert set along with their superclasses (when this is meaningful, i.e. when new wanted goals are generated) but solve a wanted dictionary from a given only in the case where the evidence variable of the wanted is mentioned in the evidence of the given (recursively through the evidence binds) in a protected way: more instance function applications than superclass selectors. Here are some more examples from GHC's previous type checker Example 3: This code arises in the context of "Scrap Your Boilerplate with Class" class Sat a class Data ctx a instance Sat (ctx Char) => Data ctx Char -- dfunData1 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2 class Data Maybe a => Foo a instance Foo t => Sat (Maybe t) -- dfunSat instance Data Maybe a => Foo a -- dfunFoo1 instance Foo a => Foo [a] -- dfunFoo2 instance Foo [Char] -- dfunFoo3 Consider generating the superclasses of the instance declaration instance Foo a => Foo [a] So our problem is this d0 :_g Foo t d1 :_w Data Maybe [t] We may add the given in the inert set, along with its superclasses [assuming we don't fail because there is a matching instance, see tryTopReact, given case ] Inert: d0 :_g Foo t WorkList d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0 d1 :_w Data Maybe [t] Then d2 can readily enter the inert, and we also do solving of the wanted Inert: d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 WorkList d2 :_w Sat (Maybe [t]) d3 :_w Data Maybe t d01 :_g Data Maybe t Now, we may simplify d2 more: Inert: d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d1 :_g Data Maybe [t] d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 WorkList: d3 :_w Data Maybe t d4 :_w Foo [t] d01 :_g Data Maybe t Now, we can just solve d3. Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 WorkList d4 :_w Foo [t] d01 :_g Data Maybe t And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist: Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 d4 :_g Foo [t] d4 := dfunFoo2 d5 WorkList: d5 :_w Foo t d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0 d01 :_g Data Maybe t Now, d5 can be solved! (and its superclass enter scope) Inert d0 :_g Foo t d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4 d4 :_g Foo [t] d4 := dfunFoo2 d5 d5 :_g Foo t d5 := dfunFoo1 d7 WorkList: d7 :_w Data Maybe t d6 :_g Data Maybe [t] d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0 d01 :_g Data Maybe t Now, two problems: [1] Suppose we pick d8 and we react him with d01. Which of the two givens should we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence that must not be used (look at case interactInert where both inert and workitem are givens). So we have several options: - Drop the workitem always (this will drop d8) This feels very unsafe -- what if the work item was the "good" one that should be used later to solve another wanted? - Don't drop anyone: the inert set may contain multiple givens! [This is currently implemented] The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2: [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted d7. Now the [isRecDictEv] function in the ineration solver [case inert-given workitem-wanted] will prevent us from interacting d7 := d8 precisely because chasing the evidence of d8 leads us to an unguarded use of d7. So, no interaction happens there. Then we meet d01 and there is no recursion problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01! Note [SUPERCLASS-LOOP 1] ~~~~~~~~~~~~~~~~~~~~~~~~ We have to be very, very careful when generating superclasses, lest we accidentally build a loop. Here's an example: class S a class S a => C a where { opc :: a -> a } class S b => D b where { opd :: b -> b } instance C Int where opc = opd instance D Int where opd = opc From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int} Simplifying, we may well get:$dfCInt = :C ds1 (opd dd) dd = $dfDInt ds1 =$p1 dd Notice that we spot that we can extract ds1 from dd. Alas! Alack! We can do the same for (instance D Int): $dfDInt = :D ds2 (opc dc) dc =$dfCInt ds2 = $p1 dc And now we've defined the superclass in terms of itself. Two more nasty cases are in tcrun021 tcrun033 Solution: - Satisfy the superclass context *all by itself* (tcSimplifySuperClasses) - And do so completely; i.e. no left-over constraints to mix with the constraints arising from method declarations Note [SUPERCLASS-LOOP 2] ~~~~~~~~~~~~~~~~~~~~~~~~ We need to be careful when adding "the constaint we are trying to prove". Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where class Ord a => C a where instance Ord [a] => C [a] where ... Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the superclasses of C [a] to avails. But we must not overwrite the binding for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just build a loop! Here's another variant, immortalised in tcrun020 class Monad m => C1 m class C1 m => C2 m x instance C2 Maybe Bool For the instance decl we need to build (C1 Maybe), and it's no good if we run around and add (C2 Maybe Bool) and its superclasses to the avails before we search for C1 Maybe. Here's another example class Eq b => Foo a b instance Eq a => Foo [a] a If we are reducing (Foo [t] t) we'll first deduce that it holds (via the instance decl). We must not then overwrite the Eq t constraint with a superclass selection! At first I had a gross hack, whereby I simply did not add superclass constraints in addWanted, though I did for addGiven and addIrred. This was sub-optimal, becuase it lost legitimate superclass sharing, and it still didn't do the job: I found a very obscure program (now tcrun021) in which improvement meant the simplifier got two bites a the cherry... so something seemed to be an Stop first time, but reducible next time. Now we implement the Right Solution, which is to check for loops directly when adding superclasses. It's a bit like the occurs check in unification. Note [Recursive instances and superclases] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider this code, which arises in the context of "Scrap Your Boilerplate with Class". class Sat a class Data ctx a instance Sat (ctx Char) => Data ctx Char instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] class Data Maybe a => Foo a instance Foo t => Sat (Maybe t) instance Data Maybe a => Foo a instance Foo a => Foo [a] instance Foo [Char] In the instance for Foo [a], when generating evidence for the superclasses (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]). Using the instance for Data, we therefore need (Sat (Maybe [a], Data Maybe a) But we are given (Foo a), and hence its superclass (Data Maybe a). So that leaves (Sat (Maybe [a])). Using the instance for Sat means we need (Foo [a]). And that is the very dictionary we are bulding an instance for! So we must put that in the "givens". So in this case we have Given: Foo a, Foo [a] Wanted: Data Maybe [a] BUT we must *not not not* put the *superclasses* of (Foo [a]) in the givens, which is what 'addGiven' would normally do. Why? Because (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted by selecting a superclass from Foo [a], which simply makes a loop. On the other hand we *must* put the superclasses of (Foo a) in the givens, as you can see from the derivation described above. Conclusion: in the very special case of tcSimplifySuperClasses we have one 'given' (namely the "this" dictionary) whose superclasses must not be added to 'givens' by addGiven. There is a complication though. Suppose there are equalities instance (Eq a, a~b) => Num (a,b) Then we normalise the 'givens' wrt the equalities, so the original given "this" dictionary is cast to one of a different type. So it's a bit trickier than before to identify the "special" dictionary whose superclasses must not be added. See test indexed-types/should_run/EqInInstance We need a persistent property of the dictionary to record this special-ness. Current I'm using the InstLocOrigin (a bit of a hack, but cool), which is maintained by dictionary normalisation. Specifically, the InstLocOrigin is NoScOrigin then the no-superclass thing kicks in. WATCH OUT if you fiddle with InstLocOrigin! Note [MATCHING-SYNONYMS] ~~~~~~~~~~~~~~~~~~~~~~~~ When trying to match a dictionary (D tau) to a top-level instance, or a type family equation (F taus_1 ~ tau_2) to a top-level family instance, we do *not* need to expand type synonyms because the matcher will do that for us. Note [RHS-FAMILY-SYNONYMS] ~~~~~~~~~~~~~~~~~~~~~~~~~~ The RHS of a family instance is represented as yet another constructor which is like a type synonym for the real RHS the programmer declared. Eg: type instance F (a,a) = [a] Becomes: :R32 a = [a] -- internal type synonym introduced F (a,a) ~ :R32 a -- instance When we react a family instance with a type family equation in the work list we keep the synonym-using RHS without expansion. ********************************************************************************* * * The top-reaction Stage * * ********************************************************************************* \begin{code} -- If a work item has any form of interaction with top-level we get this data TopInteractResult = NoTopInt -- No top-level interaction | SomeTopInt { tir_new_work :: WorkList -- Sub-goals or new work (could be given, -- for superclasses) , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now: } -- NB: in given'' (solved) form if the -- original was wanted or given and instance match -- was found, but may also be in wanted form if we -- only reacted with functional dependencies -- arising from top-level instances. 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 $SR { sr_inerts = inerts , sr_new_work = tir_new_work , sr_stop = tir_new_inert } } tryTopReact :: WorkItem -> TcS TopInteractResult tryTopReact workitem = do { -- A flag controls the amount of interaction allowed -- See Note [Simplifying RULE lhs constraints] ctxt <- getTcSContext ; if allowedTopReaction (simplEqsOnly ctxt) workitem then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem) ; doTopReact workitem } else return NoTopInt } allowedTopReaction :: Bool -> WorkItem -> Bool allowedTopReaction eqs_only (CDictCan {}) = not eqs_only allowedTopReaction _ _ = True doTopReact :: WorkItem -> TcS TopInteractResult -- The work item does not react with the inert set, -- so try interaction with top-level instances doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc , cc_class = cls, cc_tyargs = xis }) = do { -- See Note [MATCHING-SYNONYMS] ; lkp_inst_res <- matchClassInst cls xis loc ; case lkp_inst_res of NoInstance -> do { traceTcS "doTopReact/ no class instance for" (ppr dv) ; funDepReact } GenInst wtvs ev_term -> -- Solved -- No need to do fundeps stuff here; the instance -- matches already so we won't get any more info -- from functional dependencies do { traceTcS "doTopReact/ found class instance for" (ppr dv) ; setDictBind dv ev_term ; workList <- canWanteds wtvs ; if null wtvs -- Solved in one step and no new wanted work produced. -- i.e we directly matched a top-level instance -- No point in caching this in 'inert', nor in adding superclasses  1649  then return$ SomeTopInt { tir_new_work = emptyWorkList  simonpj@microsoft.com committed Sep 13, 2010 1650 1651 1652 1653 1654 1655  , tir_new_inert = Stop } -- Solved and new wanted work produced, you may cache the -- (tentatively solved) dictionary as Derived and its superclasses else do { let solved = makeSolved workItem ; sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis  1656  ; let inst_work = workListFromCCans workList  simonpj@microsoft.com committed Sep 13, 2010 1657  ; return $SomeTopInt  1658  { tir_new_work = inst_work unionWorkLists sc_work  simonpj@microsoft.com committed Sep 13, 2010 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671  , tir_new_inert = ContinueWith solved } } } } where -- Try for a fundep reaction beween the wanted item -- and a top-level instance declaration funDepReact = do { instEnvs <- getInstEnvs ; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs) (ClassP cls xis, ppr dv) ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs -- NB: fundeps generate some wanted equalities, but -- we don't use their evidence for anything  1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685  ; fd_cts <- canWanteds wevvars ; let fd_work = mkEqWorkList fd_cts ; if isEmptyCCan fd_cts then do { sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis ; return$ SomeTopInt { tir_new_work = fd_work unionWorkLists sc_work , tir_new_inert = ContinueWith workItem } } else -- More fundep work produced, don't do any superlcass stuff, just -- thow him back in the worklist prioritizing the solution of fd equalities return $SomeTopInt { tir_new_work = fd_work unionWorkLists singleNonEqWL workItem , tir_new_inert = Stop }  simonpj@microsoft.com committed Sep 13, 2010 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724  -- NB: workItem is inert, but it isn't solved -- keep it as inert, although it's not solved because we -- have now reacted all its top-level fundep-induced equalities! -- See Note [FunDep Reactions] } -- Otherwise, we have a given or derived doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl , cc_class = cls, cc_tyargs = xis }) = do { sc_work <- newSCWorkFromFlavored dv fl cls xis ; return$ SomeTopInt sc_work (ContinueWith workItem) } -- See Note [Given constraint that matches an instance declaration] -- Type functions doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl , cc_fun = tc, cc_tyargs = args, cc_rhs = xi }) = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS] ; case match_res of 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) -- Eagerly expand away the type synonym on the -- RHS of a type function, so that it never -- appears in an error message -- See Note [Type synonym families] in TyCon 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  1725 1726  ; can_cts <- mkCanonical fl cv' ; let workList = mkEqWorkList can_cts  simonpj@microsoft.com committed Sep 13, 2010 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764  ; return $SomeTopInt workList Stop } _ -> panicTcS$ text "TcSMonad.matchFam returned multiple instances!" } -- Any other work item does not react with any top-level equations doTopReact _workItem = return NoTopInt \end{code} Note [FunDep and implicit parameter reactions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Currently, our story of interacting two dictionaries (or a dictionary and top-level instances) for functional dependencies, and implicit paramters, is that we simply produce new wanted equalities. So for example class D a b | a -> b where ... Inert: d1 :g D Int Bool WorkItem: d2 :w D Int alpha We generate the extra work item cv :w alpha ~ Bool where 'cv' is currently unused. However, this new item reacts with d2, discharging it in favour of a new constraint d2' thus: d2' :w D Int Bool d2 := d2' |> D Int cv Now d2' can be discharged from d1 We could be more aggressive and try to *immediately* solve the dictionary using those extra equalities. With the same inert set and work item we might dischard d2 directly: cv :w alpha ~ Bool d2 := d1 |> D Int cv But in general it's a bit painful to figure out the necessary coercion,  1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 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.  simonpj@microsoft.com committed Sep 13, 2010 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886  It's exactly the same with implicit parameters, except that the "aggressive" approach would be much easier to implement. Note [When improvement happens] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We fire an improvement rule when * Two constraints match (modulo the fundep) e.g. C t1 t2, C t1 t3 where C a b | a->b The two match because the first arg is identical * At least one is not Given. If they are both given, we don't fire the reaction because we have no way of constructing evidence for a new equality nor does it seem right to create a new wanted goal (because the goal will most likely contain untouchables, which can't be solved anyway)! Note that we *do* fire the improvement if one is Given and one is Derived. The latter can be a superclass of a wanted goal. Example (tcfail138) class L a b | a -> b class (G a, L a b) => C a b instance C a b' => G (Maybe a) instance C a b => C (Maybe a) a instance L (Maybe a) a When solving the superclasses of the (C (Maybe a) a) instance, we get Given: C a b ... and hance by superclasses, (G a, L a b) Wanted: G (Maybe a) Use the instance decl to get Wanted: C a b' The (C a b') is inert, so we generate its Derived superclasses (L a b'), and now we need improvement between that derived superclass an the Given (L a b) Note [Overriding implicit parameters] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider f :: (?x::a) -> Bool -> a g v = let ?x::Int = 3 in (f v, let ?x::Bool = True in f v) This should probably be well typed, with g :: Bool -> (Int, Bool) So the inner binding for ?x::Bool *overrides* the outer one. Hence a work-item Given overrides an inert-item Given. Note [Given constraint that matches an instance declaration] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ What should we do when we discover that one (or more) top-level instances match a given (or solved) class constraint? We have two possibilities: 1. Reject the program. The reason is that there may not be a unique best strategy for the solver. Example, from the OutsideIn(X) paper: instance P x => Q [x] instance (x ~ y) => R [x] y wob :: forall a b. (Q [b], R b a) => a -> Int g :: forall a. Q [a] => [a] -> Int g x = wob x will generate the impliation constraint: Q [a] => (Q [beta], R beta [a]) If we react (Q [beta]) with its top-level axiom, we end up with a (P beta), which we have no way of discharging. On the other hand, if we react R beta [a] with the top-level we get (beta ~ a), which is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is now solvable by the given Q [a]. However, this option is restrictive, for instance [Example 3] from Note [Recursive 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 sub-problem d) To allow FD-like improvement for type families. Assume that we have a class <