TcCanonical.lhs 40.4 KB
 simonpj@microsoft.com committed Sep 13, 2010 1 2 \begin{code} module TcCanonical(  simonpj@microsoft.com committed Jan 12, 2011 3 4  mkCanonical, mkCanonicals, mkCanonicalFEV, canWanteds, canGivens, canOccursCheck, canEq  simonpj@microsoft.com committed Sep 13, 2010 5 6 7 8  ) where #include "HsVersions.h"  simonpj@microsoft.com committed Jan 12, 2011 9 import BasicTypes  simonpj@microsoft.com committed Sep 13, 2010 10 11 12 13 14 15 16 17 18 19 20 21 import Type import TcRnTypes import TcType import TcErrors import Coercion import Class import TyCon import TypeRep import Name import Var import Outputable  simonpj@microsoft.com committed Jan 12, 2011 22 import Control.Monad ( unless, when, zipWithM, zipWithM_ )  simonpj@microsoft.com committed Sep 13, 2010 23 24 25 26 27 28 import MonadUtils import Control.Applicative ( (<|>) ) import VarSet import Bag  simonpj@microsoft.com committed Jan 12, 2011 29 30 import HsBinds import TcSMonad  simonpj@microsoft.com committed Sep 13, 2010 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 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 84 85 86 87 88 89 90 91 92 \end{code} Note [Canonicalisation] ~~~~~~~~~~~~~~~~~~~~~~~ * Converts (Constraint f) _which_does_not_contain_proper_implications_ to CanonicalCts * Unary: treats individual constraints one at a time * Does not do any zonking * Lives in TcS monad so that it can create new skolem variables %************************************************************************ %* * %* Flattening (eliminating all function symbols) * %* * %************************************************************************ Note [Flattening] ~~~~~~~~~~~~~~~~~~~~ flatten ty ==> (xi, cc) where xi has no type functions cc = Auxiliary given (equality) constraints constraining the fresh type variables in xi. Evidence for these is always the identity coercion, because internally the fresh flattening skolem variables are actually identified with the types they have been generated to stand in for. Note that it is flatten's job to flatten *every type function it sees*. flatten is only called on *arguments* to type functions, by canEqGiven. Recall that in comments we use alpha[flat = ty] to represent a flattening skolem variable alpha which has been generated to stand in for ty. ----- Example of flattening a constraint: ------ flatten (List (F (G Int))) ==> (xi, cc) where xi = List alpha cc = { G Int ~ beta[flat = G Int], F beta ~ alpha[flat = F beta] } Here * alpha and beta are 'flattening skolem variables'. * All the constraints in cc are 'given', and all their coercion terms are the identity. NB: Flattening Skolems only occur in canonical constraints, which are never zonked, so we don't need to worry about zonking doing accidental unflattening. Note that we prefer to leave type synonyms unexpanded when possible, so when the flattener encounters one, it first asks whether its transitive expansion contains any type function applications. If so, it expands the synonym and proceeds; if not, it simply returns the unexpanded synonym. TODO: caching the information about whether transitive synonym expansions contain any type function applications would speed things up a bit; right now we waste a lot of energy traversing the same types multiple times. \begin{code} -- Flatten a bunch of types all at once.  simonpj@microsoft.com committed Nov 12, 2010 93 94 flattenMany :: CtFlavor -> [Type] -> TcS ([Xi], [Coercion], CanonicalCts) -- Coercions :: Xi ~ Type  simonpj@microsoft.com committed Sep 13, 2010 95 flattenMany ctxt tys  simonpj@microsoft.com committed Nov 12, 2010 96 97  = do { (xis, cos, cts_s) <- mapAndUnzip3M (flatten ctxt) tys ; return (xis, cos, andCCans cts_s) }  simonpj@microsoft.com committed Sep 13, 2010 98 99 100  -- Flatten a type to get rid of type function applications, returning -- the new type-function-free type, and a collection of new equality  simonpj@microsoft.com committed Nov 12, 2010 101 102 103 -- constraints. See Note [Flattening] for more detail. flatten :: CtFlavor -> TcType -> TcS (Xi, Coercion, CanonicalCts) -- Postcondition: Coercion :: Xi ~ TcType  simonpj@microsoft.com committed Sep 13, 2010 104 105 flatten ctxt ty | Just ty' <- tcView ty  simonpj@microsoft.com committed Nov 12, 2010 106  = do { (xi, co, ccs) <- flatten ctxt ty'  simonpj@microsoft.com committed Sep 13, 2010 107  -- Preserve type synonyms if possible  simonpj@microsoft.com committed Nov 12, 2010 108  -- We can tell if ty' is function-free by  simonpj@microsoft.com committed Sep 13, 2010 109 110  -- whether there are any floated constraints ; if isEmptyCCan ccs then  simonpj@microsoft.com committed Nov 12, 2010 111  return (ty, ty, emptyCCan)  simonpj@microsoft.com committed Sep 13, 2010 112  else  simonpj@microsoft.com committed Nov 12, 2010 113  return (xi, co, ccs) }  simonpj@microsoft.com committed Sep 13, 2010 114 115  flatten _ v@(TyVarTy _)  simonpj@microsoft.com committed Nov 12, 2010 116  = return (v, v, emptyCCan)  simonpj@microsoft.com committed Sep 13, 2010 117 118  flatten ctxt (AppTy ty1 ty2)  simonpj@microsoft.com committed Nov 12, 2010 119 120 121  = do { (xi1,co1,c1) <- flatten ctxt ty1 ; (xi2,co2,c2) <- flatten ctxt ty2 ; return (mkAppTy xi1 xi2, mkAppCoercion co1 co2, c1 andCCan c2) }  simonpj@microsoft.com committed Sep 13, 2010 122 123  flatten ctxt (FunTy ty1 ty2)  simonpj@microsoft.com committed Nov 12, 2010 124 125 126  = do { (xi1,co1,c1) <- flatten ctxt ty1 ; (xi2,co2,c2) <- flatten ctxt ty2 ; return (mkFunTy xi1 xi2, mkFunCoercion co1 co2, c1 andCCan c2) }  simonpj@microsoft.com committed Sep 13, 2010 127 128 129 130 131  flatten fl (TyConApp tc tys) -- For a normal type constructor or data family application, we just -- recursively flatten the arguments. | not (isSynFamilyTyCon tc)  simonpj@microsoft.com committed Nov 12, 2010 132 133  = do { (xis,cos,ccs) <- flattenMany fl tys ; return (mkTyConApp tc xis, mkTyConCoercion tc cos, ccs) }  simonpj@microsoft.com committed Sep 13, 2010 134 135 136 137  -- Otherwise, it's a type function application, and we have to -- flatten it away as well, and generate a new given equality constraint -- between the application and a newly generated flattening skolem variable.  simonpj@microsoft.com committed Nov 12, 2010 138 139 140 141 142  | otherwise = ASSERT( tyConArity tc <= length tys ) -- Type functions are saturated do { (xis, cos, ccs) <- flattenMany fl tys ; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis (cos_args, cos_rest) = splitAt (tyConArity tc) cos  simonpj@microsoft.com committed Sep 13, 2010 143 144 145 146 147 148  -- The type function might be *over* saturated -- in which case the remaining arguments should -- be dealt with by AppTys fam_ty = mkTyConApp tc xi_args fam_co = fam_ty -- identity  simonpj@microsoft.com committed Nov 12, 2010 149 150 151  ; (ret_co, rhs_var, ct) <- if isGiven fl then do { rhs_var <- newFlattenSkolemTy fam_ty  simonpj@microsoft.com committed Jan 12, 2011 152  ; cv <- newGivenCoVar fam_ty rhs_var fam_co  simonpj@microsoft.com committed Nov 12, 2010 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173  ; let ct = CFunEqCan { cc_id = cv , cc_flavor = fl -- Given , cc_fun = tc , cc_tyargs = xi_args , cc_rhs = rhs_var } ; return $(mkCoVarCoercion cv, rhs_var, ct) } else -- Derived or Wanted: make a new *unification* flatten variable do { rhs_var <- newFlexiTcSTy (typeKind fam_ty) ; cv <- newWantedCoVar fam_ty rhs_var ; let ct = CFunEqCan { cc_id = cv , cc_flavor = mkWantedFlavor fl -- Always Wanted, not Derived , cc_fun = tc , cc_tyargs = xi_args , cc_rhs = rhs_var } ; return$ (mkCoVarCoercion cv, rhs_var, ct) } ; return ( foldl AppTy rhs_var xi_rest , foldl AppTy (mkSymCoercion ret_co mkTransCoercion mkTyConCoercion tc cos_args) cos_rest , ccs extendCCans ct) }  simonpj@microsoft.com committed Sep 13, 2010 174 175 176  flatten ctxt (PredTy pred)  simonpj@microsoft.com committed Nov 12, 2010 177 178  = do { (pred', co, ccs) <- flattenPred ctxt pred ; return (PredTy pred', co, ccs) }  simonpj@microsoft.com committed Sep 13, 2010 179 180 181 182  flatten ctxt ty@(ForAllTy {}) -- We allow for-alls when, but only when, no type function -- applications inside the forall involve the bound type variables  simonpj@microsoft.com committed Nov 12, 2010 183 184 -- TODO: What if it is a (t1 ~ t2) => t3 -- Must revisit when the New Coercion API is here!  simonpj@microsoft.com committed Sep 13, 2010 185  = do { let (tvs, rho) = splitForAllTys ty  simonpj@microsoft.com committed Nov 12, 2010 186  ; (rho', co, ccs) <- flatten ctxt rho  simonpj@microsoft.com committed Sep 13, 2010 187 188 189 190 191  ; let bad_eqs = filterBag is_bad ccs is_bad c = tyVarsOfCanonical c intersectsVarSet tv_set tv_set = mkVarSet tvs ; unless (isEmptyBag bad_eqs) (flattenForAllErrorTcS ctxt ty bad_eqs)  simonpj@microsoft.com committed Nov 12, 2010 192  ; return (mkForAllTys tvs rho', mkForAllTys tvs co, ccs) }  simonpj@microsoft.com committed Sep 13, 2010 193 194  ---------------  simonpj@microsoft.com committed Nov 12, 2010 195 flattenPred :: CtFlavor -> TcPredType -> TcS (TcPredType, Coercion, CanonicalCts)  simonpj@microsoft.com committed Sep 13, 2010 196 flattenPred ctxt (ClassP cls tys)  simonpj@microsoft.com committed Nov 12, 2010 197 198  = do { (tys', cos, ccs) <- flattenMany ctxt tys ; return (ClassP cls tys', mkClassPPredCo cls cos, ccs) }  simonpj@microsoft.com committed Sep 13, 2010 199 flattenPred ctxt (IParam nm ty)  simonpj@microsoft.com committed Nov 12, 2010 200 201 202  = do { (ty', co, ccs) <- flatten ctxt ty ; return (IParam nm ty', mkIParamPredCo nm co, ccs) } -- TODO: Handling of coercions between EqPreds must be revisited once the New Coercion API is ready!  simonpj@microsoft.com committed Sep 13, 2010 203 flattenPred ctxt (EqPred ty1 ty2)  simonpj@microsoft.com committed Nov 12, 2010 204 205 206 207  = do { (ty1', co1, ccs1) <- flatten ctxt ty1 ; (ty2', co2, ccs2) <- flatten ctxt ty2 ; return (EqPred ty1' ty2', mkEqPredCo co1 co2, ccs1 andCCan ccs2) }  simonpj@microsoft.com committed Sep 13, 2010 208 209 210 211 212 213 214 215 216 217 \end{code} %************************************************************************ %* * %* Canonicalising given constraints * %* * %************************************************************************ \begin{code} canWanteds :: [WantedEvVar] -> TcS CanonicalCts  simonpj@microsoft.com committed Jan 12, 2011 218 canWanteds = fmap andCCans . mapM (\(EvVarX ev loc) -> mkCanonical (Wanted loc) ev)  simonpj@microsoft.com committed Sep 13, 2010 219 220 221 222 223 224 225 226  canGivens :: GivenLoc -> [EvVar] -> TcS CanonicalCts canGivens loc givens = do { ccs <- mapM (mkCanonical (Given loc)) givens ; return (andCCans ccs) } mkCanonicals :: CtFlavor -> [EvVar] -> TcS CanonicalCts mkCanonicals fl vs = fmap andCCans (mapM (mkCanonical fl) vs)  simonpj@microsoft.com committed Jan 12, 2011 227 228 229 230 mkCanonicalFEV :: FlavoredEvVar -> TcS CanonicalCts mkCanonicalFEV (EvVarX ev fl) = mkCanonical fl ev mkCanonical :: CtFlavor -> EvVar -> TcS CanonicalCts  simonpj@microsoft.com committed Sep 13, 2010 231 232 233 234 235 236 237 238 mkCanonical fl ev = case evVarPred ev of ClassP clas tys -> canClass fl ev clas tys IParam ip ty -> canIP fl ev ip ty EqPred ty1 ty2 -> canEq fl ev ty1 ty2 canClass :: CtFlavor -> EvVar -> Class -> [TcType] -> TcS CanonicalCts canClass fl v cn tys  simonpj@microsoft.com committed Nov 12, 2010 239 240 241 242 243 244 245 246  = do { (xis,cos,ccs) <- flattenMany fl tys -- cos :: xis ~ tys ; let no_flattening_happened = isEmptyCCan ccs dict_co = mkTyConCoercion (classTyCon cn) cos ; v_new <- if no_flattening_happened then return v else if isGiven fl then return v -- The cos are all identities if fl=Given, -- hence nothing to do else do { v' <- newDictVar cn xis -- D xis  simonpj@microsoft.com committed Jan 12, 2011 247 248 249  ; when (isWanted fl) $setDictBind v (EvCast v' dict_co) ; when (isGiven fl)$ setDictBind v' (EvCast v (mkSymCoercion dict_co)) -- NB: No more setting evidence for derived now  simonpj@microsoft.com committed Nov 12, 2010 250 251  ; return v' }  252 253 254 255 256  -- Add the superclasses of this one here, See Note [Adding superclasses]. -- But only if we are not simplifying the LHS of a rule. ; sctx <- getTcSContext ; sc_cts <- if simplEqsOnly sctx then return emptyCCan else newSCWorkFromFlavored v_new fl cn xis  simonpj@microsoft.com committed Nov 18, 2010 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275  ; return (sc_cts andCCan ccs extendCCans CDictCan { cc_id = v_new , cc_flavor = fl , cc_class = cn , cc_tyargs = xis }) } \end{code} Note [Adding superclasses] ~~~~~~~~~~~~~~~~~~~~~~~~~~ Since dictionaries are canonicalized only once in their lifetime, the place to add their superclasses is canonicalisation (The alternative would be to do it during constraint solving, but we'd have to be extremely careful to not repeatedly introduced the same superclass in our worklist). Here is what we do: For Givens: We add all their superclasses as Givens. For Wanteds:  simonpj@microsoft.com committed Jan 12, 2011 276 277  Generally speaking we want to be able to add superclasses of wanteds for two reasons:  simonpj@microsoft.com committed Nov 18, 2010 278   simonpj@microsoft.com committed Jan 12, 2011 279 280 281 282 283 284 285 286 287  (1) Oportunities for improvement. Example: class (a ~ b) => C a b Wanted constraint is: C alpha beta We'd like to simply have C alpha alpha. Similar situations arise in relation to functional dependencies. (2) To have minimal constraints to quantify over: For instance, if our wanted constraint is (Eq a, Ord a) we'd only like to quantify over Ord a.  simonpj@microsoft.com committed Nov 18, 2010 288   simonpj@microsoft.com committed Jan 12, 2011 289 290 291 292 293 294 295 296 297 298 299 300  To deal with (1) above we only add the superclasses of wanteds which may lead to improvement, that is: equality superclasses or superclasses with functional dependencies. We deal with (2) completely independently in TcSimplify. See Note [Minimize by SuperClasses] in TcSimplify. Moreover, in all cases the extra improvement constraints are Derived. Derived constraints have an identity (for now), but we don't do anything with their evidence. For instance they are never used to rewrite other constraints.  simonpj@microsoft.com committed Nov 18, 2010 301   simonpj@microsoft.com committed Jan 12, 2011 302  See also [New Wanted Superclass Work] in TcInteract.  simonpj@microsoft.com committed Nov 18, 2010 303   simonpj@microsoft.com committed Jan 12, 2011 304 305 306  For Deriveds: We do nothing.  simonpj@microsoft.com committed Nov 18, 2010 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327  Here's an example that demonstrates why we chose to NOT add superclasses during simplification: [Comes from ticket #4497] class Num (RealOf t) => Normed t type family RealOf x Assume the generated wanted constraint is: RealOf e ~ e, Normed e If we were to be adding the superclasses during simplification we'd get: Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf ==> e ~ uf, Num uf, Normed e, RealOf e ~ e ==> [Spontaneous solve] Num uf, Normed uf, RealOf uf ~ uf While looks exactly like our original constraint. If we add the superclass again we'd loop. By adding superclasses definitely only once, during canonicalisation, this situation can't happen. \begin{code}  simonpj@microsoft.com committed Jan 12, 2011 328   simonpj@microsoft.com committed Nov 18, 2010 329 330 331 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS CanonicalCts -- Returns superclasses, see Note [Adding superclasses] newSCWorkFromFlavored ev orig_flavor cls xis  simonpj@microsoft.com committed Jan 12, 2011 332 333 334 335 336 337 338 339 340  | isDerived orig_flavor = return emptyCCan -- Deriveds don't yield more superclasses because we will -- add them transitively in the case of wanteds. | isGiven orig_flavor = do { let sc_theta = immSuperClasses cls xis flavor = orig_flavor ; sc_vars <- mapM newEvVar sc_theta ; _ <- zipWithM_ setEvBind sc_vars [EvSuperClass ev n | n <- [0..]]  simonpj@microsoft.com committed Nov 18, 2010 341  ; mkCanonicals flavor sc_vars }  simonpj@microsoft.com committed Jan 12, 2011 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363  | isEmptyVarSet (tyVarsOfTypes xis) = return emptyCCan -- Wanteds with no variables yield no deriveds. -- See Note [Improvement from Ground Wanteds] | otherwise -- Wanted case, just add those SC that can lead to improvement. = do { let sc_rec_theta = transSuperClasses cls xis impr_theta = filter is_improvement_pty sc_rec_theta Wanted wloc = orig_flavor ; der_ids <- mapM newDerivedId impr_theta ; mkCanonicals (Derived wloc) der_ids } is_improvement_pty :: PredType -> Bool -- Either it's an equality, or has some functional dependency is_improvement_pty (EqPred {}) = True is_improvement_pty (ClassP cls _ty) = not $null fundeps where (_,fundeps,_,_,_,_) = classExtraBigSig cls is_improvement_pty _ = False  simonpj@microsoft.com committed Nov 12, 2010 364 365 366 367  canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts -- See Note [Canonical implicit parameter constraints] to see why we don't -- immediately canonicalize (flatten) IP constraints.  simonpj@microsoft.com committed Sep 13, 2010 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 canIP fl v nm ty = return$ singleCCan $CIPCan { cc_id = v , cc_flavor = fl , cc_ip_nm = nm , cc_ip_ty = ty } ----------------- canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts canEq fl cv ty1 ty2 | tcEqType ty1 ty2 -- Dealing with equality here avoids -- later spurious occurs checks for a~a = do { when (isWanted fl) (setWantedCoBind cv ty1) ; return emptyCCan } -- If one side is a variable, orient and flatten, -- WITHOUT expanding type synonyms, so that we tend to  384 385 386 387 388 389 390 391 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@ canEq fl cv ty1@(TyVarTy {}) ty2 = do { untch <- getUntouchables ; canEqLeaf untch fl cv (classify ty1) (classify ty2) } canEq fl cv ty1 ty2@(TyVarTy {}) = do { untch <- getUntouchables ; canEqLeaf untch fl cv (classify ty1) (classify ty2) } -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!  simonpj@microsoft.com committed Sep 13, 2010 392 393 394  canEq fl cv (TyConApp fn tys) ty2 | isSynFamilyTyCon fn, length tys == tyConArity fn  395 396  = do { untch <- getUntouchables ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }  simonpj@microsoft.com committed Sep 13, 2010 397 398 canEq fl cv ty1 (TyConApp fn tys) | isSynFamilyTyCon fn, length tys == tyConArity fn  399 400  = do { untch <- getUntouchables ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }  simonpj@microsoft.com committed Sep 13, 2010 401   dimitris@microsoft.com committed Oct 06, 2010 402 403 404 canEq fl cv s1 s2 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1, Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2  simonpj@microsoft.com committed Jan 12, 2011 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427  = do { (v1,v2,v3) <- if isWanted fl then -- Wanted do { v1 <- newWantedCoVar t1a t2a ; v2 <- newWantedCoVar t1b t2b ; v3 <- newWantedCoVar t1c t2c ; let res_co = mkCoPredCo (mkCoVarCoercion v1) (mkCoVarCoercion v2) (mkCoVarCoercion v3) ; setWantedCoBind cv res_co ; return (v1,v2,v3) } else if isGiven fl then -- Given let co_orig = mkCoVarCoercion cv coa = mkCsel1Coercion co_orig cob = mkCsel2Coercion co_orig coc = mkCselRCoercion co_orig in do { v1 <- newGivenCoVar t1a t2a coa ; v2 <- newGivenCoVar t1b t2b cob ; v3 <- newGivenCoVar t1c t2c coc ; return (v1,v2,v3) } else -- Derived do { v1 <- newDerivedId (EqPred t1a t2a) ; v2 <- newDerivedId (EqPred t1b t2b) ; v3 <- newDerivedId (EqPred t1c t2c) ; return (v1,v2,v3) }  dimitris@microsoft.com committed Oct 06, 2010 428 429 430 431 432 433  ; cc1 <- canEq fl v1 t1a t2a ; cc2 <- canEq fl v2 t1b t2b ; cc3 <- canEq fl v3 t1c t2c ; return (cc1 andCCan cc2 andCCan cc3) }  simonpj@microsoft.com committed Sep 13, 2010 434 435 436 437 438 439 440 441 442 -- Split up an equality between function types into two equalities. canEq fl cv (FunTy s1 t1) (FunTy s2 t2) = do { (argv, resv) <- if isWanted fl then do { argv <- newWantedCoVar s1 s2 ; resv <- newWantedCoVar t1 t2 ; setWantedCoBind cv$ mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv) ; return (argv,resv) }  simonpj@microsoft.com committed Jan 12, 2011 443 444 445 446 447 448 449 450 451 452 453 454  else if isGiven fl then let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv) in do { argv <- newGivenCoVar s1 s2 arg ; resv <- newGivenCoVar t1 t2 res ; return (argv,resv) } else -- Derived do { argv <- newDerivedId (EqPred s1 s2) ; resv <- newDerivedId (EqPred t1 t2) ; return (argv,resv) }  simonpj@microsoft.com committed Sep 13, 2010 455 456 457 458  ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations ; cc2 <- canEq fl resv t1 t2 ; return (cc1 andCCan cc2) }  simonpj@microsoft.com committed Nov 12, 2010 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2)) | n1 == n2 = if isWanted fl then do { v <- newWantedCoVar t1 t2 ; setWantedCoBind cv $mkIParamPredCo n1 (mkCoVarCoercion cv) ; canEq fl v t1 t2 } else return emptyCCan -- DV: How to decompose given IP coercions? canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2)) | c1 == c2 = if isWanted fl then do { vs <- zipWithM newWantedCoVar tys1 tys2 ; setWantedCoBind cv$ mkClassPPredCo c1 (map mkCoVarCoercion vs) ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2 } else return emptyCCan -- How to decompose given dictionary (and implicit parameter) coercions? -- You may think that the following is right: -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv) -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos -- But this assumes that the coercion is a type constructor-based -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose -- to not decompose these coercions. We have to get back to this -- when we clean up the Coercion API. canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)  simonpj@microsoft.com committed Sep 13, 2010 485 486 487 488  | isAlgTyCon tc1 && isAlgTyCon tc2 , tc1 == tc2 , length tys1 == length tys2 = -- Generate equalities for each of the corresponding arguments  simonpj@microsoft.com committed Jan 12, 2011 489 490  do { argsv <- if isWanted fl then  simonpj@microsoft.com committed Sep 13, 2010 491  do { argsv <- zipWithM newWantedCoVar tys1 tys2  simonpj@microsoft.com committed Jan 12, 2011 492 493 494 495 496  ; setWantedCoBind cv$ mkTyConCoercion tc1 (map mkCoVarCoercion argsv) ; return argsv } else if isGiven fl then  simonpj@microsoft.com committed Sep 13, 2010 497  let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)  simonpj@microsoft.com committed Jan 12, 2011 498 499 500 501 502  in zipWith3M newGivenCoVar tys1 tys2 cos else -- Derived zipWithM (\t1 t2 -> newDerivedId (EqPred t1 t2)) tys1 tys2  simonpj@microsoft.com committed Sep 13, 2010 503 504 505 506 507 508 509 510 511 512 513 514 515 516  ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 } -- See Note [Equality between type applications] -- Note [Care with type applications] in TcUnify canEq fl cv ty1 ty2 | Just (s1,t1) <- tcSplitAppTy_maybe ty1 , Just (s2,t2) <- tcSplitAppTy_maybe ty2 = do { (cv1,cv2) <- if isWanted fl then do { cv1 <- newWantedCoVar s1 s2 ; cv2 <- newWantedCoVar t1 t2 ; setWantedCoBind cv$ mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2) ; return (cv1,cv2) }  simonpj@microsoft.com committed Jan 12, 2011 517 518 519 520 521 522 523 524 525 526 527 528  else if isGiven fl then let co1 = mkLeftCoercion $mkCoVarCoercion cv co2 = mkRightCoercion$ mkCoVarCoercion cv in do { cv1 <- newGivenCoVar s1 s2 co1 ; cv2 <- newGivenCoVar t1 t2 co2 ; return (cv1,cv2) } else -- Derived do { cv1 <- newDerivedId (EqPred s1 s2) ; cv2 <- newDerivedId (EqPred t1 t2) ; return (cv1,cv2) }  simonpj@microsoft.com committed Sep 13, 2010 529 530 531 532  ; cc1 <- canEq fl cv1 s1 s2 ; cc2 <- canEq fl cv2 t1 t2 ; return (cc1 andCCan cc2) }  simonpj@microsoft.com committed Jan 12, 2011 533 canEq fl cv s1@(ForAllTy {}) s2@(ForAllTy {})  dimitris@microsoft.com committed Oct 06, 2010 534 535  | tcIsForAllTy s1, tcIsForAllTy s2, Wanted {} <- fl  simonpj@microsoft.com committed Jan 12, 2011 536  = canEqFailure fl cv  simonpj@microsoft.com committed Nov 12, 2010 537  | otherwise  simonpj@microsoft.com committed Sep 13, 2010 538 539 540 541 542 543  = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2) ; return emptyCCan } -- Finally expand any type synonym applications. canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'  simonpj@microsoft.com committed Jan 12, 2011 544 canEq fl cv _ _ = canEqFailure fl cv  dimitris@microsoft.com committed Oct 06, 2010 545   simonpj@microsoft.com committed Jan 12, 2011 546 547 canEqFailure :: CtFlavor -> EvVar -> TcS CanonicalCts canEqFailure fl cv = return (singleCCan (mkFrozenError fl cv))  simonpj@microsoft.com committed Sep 13, 2010 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 \end{code} Note [Equality between type applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we see an equality of the form s1 t1 ~ s2 t2 we can always split it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type functions (type functions use the TyConApp constructor, which never shows up as the LHS of an AppTy). Other than type functions, types in Haskell are always (1) generative: a b ~ c d implies a ~ c, since different type constructors always generate distinct types (2) injective: a b ~ a d implies b ~ d; we never generate the same type from different type arguments. Note [Canonical ordering for equality constraints] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Implemented as (<+=) below: - Type function applications always come before anything else. - Variables always come before non-variables (other than type function applications). Note that we don't need to unfold type synonyms on the RHS to check the ordering; that is, in the rules above it's OK to consider only whether something is *syntactically* a type function application or not. To illustrate why this is OK, suppose we have an equality of the form 'tv ~ S a b c', where S is a type synonym which expands to a top-level application of the type function F, something like type S a b c = F d e Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's expansion contains type function applications the flattener will do the expansion and then generate a skolem variable for the type function application, so we end up with something like this: tv ~ x F d e ~ x where x is the skolem variable. This is one extra equation than absolutely necessary (we could have gotten away with just 'F d e ~ tv' if we had noticed that S expanded to a top-level type function application and flipped it around in the first place) but this way keeps the code simpler. Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the ordering of tv ~ tv constraints. There are several reasons why we might: (1) In order to be able to extract a substitution that doesn't mention untouchable variables after we are done solving, we might prefer to put touchable variables on the left. However, in and of itself this isn't necessary; we can always re-orient equality constraints at the end if necessary when extracting a substitution. (2) To ensure termination we might think it necessary to put variables in lexicographic order. However, this isn't actually necessary as outlined below. While building up an inert set of canonical constraints, we maintain the invariant that the equality constraints in the inert set form an acyclic rewrite system when viewed as L-R rewrite rules. Moreover, the given constraints form an idempotent substitution (i.e. none of the variables on the LHS occur in any of the RHS's, and type functions never show up in the RHS at all), the wanted constraints also form an idempotent substitution, and finally the LHS of a given constraint never shows up on the RHS of a wanted constraint. There may, however, be a wanted LHS that shows up in a given RHS, since we do not rewrite given constraints with wanted constraints. Suppose we have an inert constraint set tg_1 ~ xig_1 -- givens tg_2 ~ xig_2 ... tw_1 ~ xiw_1 -- wanteds tw_2 ~ xiw_2 ... where each t_i can be either a type variable or a type function application. Now suppose we take a new canonical equality constraint, t' ~ xi' (note among other things this means t' does not occur in xi') and try to react it with the existing inert set. We show by induction on the number of t_i which occur in t' ~ xi' that this process will terminate. There are several ways t' ~ xi' could react with an existing constraint: TODO: finish this proof. The below was for the case where the entire inert set is an idempotent subustitution... (b) We could have t' = t_j for some j. Then we obtain the new equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We now canonicalize the new equality, which may involve decomposing it into several canonical equalities, and recurse on these. However, none of the new equalities will contain t_j, so they have fewer occurrences of the t_i than the original equation. (a) We could have t_j occurring in xi' for some j, with t' /= t_j. Then we substitute xi_j for t_j in xi' and continue. However, since none of the t_i occur in xi_j, we have decreased the number of t_i that occur in xi', since we eliminated t_j and did not introduce any new ones. \begin{code} data TypeClassifier  Ian Lynagh committed Oct 20, 2010 658  = FskCls TcTyVar -- ^ Flatten skolem  simonpj@microsoft.com committed Oct 21, 2010 659  | VarCls TcTyVar -- ^ Non-flatten-skolem variable  Ian Lynagh committed Oct 20, 2010 660 661  | FunCls TyCon [Type] -- ^ Type function, exactly saturated | OtherCls TcType -- ^ Neither of the above  simonpj@microsoft.com committed Sep 13, 2010 662 663  unClassify :: TypeClassifier -> TcType  664 665 666 667 unClassify (VarCls tv) = TyVarTy tv unClassify (FskCls tv) = TyVarTy tv unClassify (FunCls fn tys) = TyConApp fn tys unClassify (OtherCls ty) = ty  simonpj@microsoft.com committed Sep 13, 2010 668 669  classify :: TcType -> TypeClassifier  670 671 672 673 674  classify (TyVarTy tv) | isTcTyVar tv, FlatSkol {} <- tcTyVarDetails tv = FskCls tv | otherwise = VarCls tv  simonpj@microsoft.com committed Sep 13, 2010 675 676 677 678 679 680 681 682 683 684 685 classify (TyConApp tc tys) | isSynFamilyTyCon tc , tyConArity tc == length tys = FunCls tc tys classify ty | Just ty' <- tcView ty = case classify ty' of OtherCls {} -> OtherCls ty var_or_fn -> var_or_fn | otherwise = OtherCls ty -- See note [Canonical ordering for equality constraints].  686 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool  simonpj@microsoft.com committed Sep 13, 2010 687 688 689 690 691 -- (t1 reOrient t2) responds True -- iff we should flip to (t2~t1) -- We try to say False if possible, to minimise evidence generation -- -- Postcondition: After re-orienting, first arg is not OTherCls  692 693 694 695 reOrient _untch (OtherCls {}) (FunCls {}) = True reOrient _untch (OtherCls {}) (FskCls {}) = True reOrient _untch (OtherCls {}) (VarCls {}) = True reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun  simonpj@microsoft.com committed Sep 13, 2010 696   simonpj@microsoft.com committed Nov 12, 2010 697 reOrient _untch (FunCls {}) (VarCls {}) = False  simonpj@microsoft.com committed Sep 13, 2010 698  -- See Note [No touchables as FunEq RHS] in TcSMonad  simonpj@microsoft.com committed Nov 12, 2010 699 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs  simonpj@microsoft.com committed Sep 13, 2010 700   simonpj@microsoft.com committed Nov 12, 2010 701 reOrient _untch (VarCls {}) (FunCls {}) = True  702   simonpj@microsoft.com committed Nov 12, 2010 703 reOrient _untch (VarCls {}) (FskCls {}) = False  704   simonpj@microsoft.com committed Nov 12, 2010 705 706 707 708 709 reOrient _untch (VarCls {}) (OtherCls {}) = False reOrient _untch (VarCls tv1) (VarCls tv2) | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True | otherwise = False -- Just for efficiency, see CTyEqCan invariants  simonpj@microsoft.com committed Sep 13, 2010 710   simonpj@microsoft.com committed Nov 12, 2010 711 712 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2 -- Just for efficiency, see CTyEqCan invariants  713   714 715 716 reOrient _untch (FskCls {}) (FskCls {}) = False reOrient _untch (FskCls {}) (FunCls {}) = True reOrient _untch (FskCls {}) (OtherCls {}) = False  simonpj@microsoft.com committed Sep 13, 2010 717 718  ------------------  719 canEqLeaf :: TcsUntouchables  720  -> CtFlavor -> CoVar  simonpj@microsoft.com committed Sep 13, 2010 721 722 723 724 725 726 727 728  -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts -- Canonicalizing "leaf" equality constraints which cannot be -- decomposed further (ie one of the types is a variable or -- saturated type function application). -- Preconditions: -- * one of the two arguments is not OtherCls -- * the two types are not equal (looking through synonyms)  729 730 canEqLeaf untch fl cv cls1 cls2 | cls1 re_orient cls2  simonpj@microsoft.com committed Sep 13, 2010 731 732 733 734  = do { cv' <- if isWanted fl then do { cv' <- newWantedCoVar s2 s1 ; setWantedCoBind cv $mkSymCoercion (mkCoVarCoercion cv') ; return cv' }  simonpj@microsoft.com committed Jan 12, 2011 735 736 737 738  else if isGiven fl then newGivenCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv)) else -- Derived newDerivedId (EqPred s2 s1)  simonpj@microsoft.com committed Sep 13, 2010 739 740 741  ; canEqLeafOriented fl cv' cls2 s1 } | otherwise  simonpj@microsoft.com committed Jan 12, 2011 742 743  = do { traceTcS "canEqLeaf" (ppr (unClassify cls1) $$ppr (unClassify cls2)) ; canEqLeafOriented fl cv cls1 s2 }  simonpj@microsoft.com committed Sep 13, 2010 744  where  745  re_orient = reOrient untch  simonpj@microsoft.com committed Sep 13, 2010 746 747 748 749 750 751 752  s1 = unClassify cls1 s2 = unClassify cls2 ------------------ canEqLeafOriented :: CtFlavor -> CoVar -> TypeClassifier -> TcType -> TcS CanonicalCts -- First argument is not OtherCls  simonpj@microsoft.com committed Nov 12, 2010 753 754 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1 | let k1 = kindAppResult (tyConKind fn) tys1,  755  let k2 = typeKind s2,  simonpj@microsoft.com committed Jan 12, 2011 756 757  not (k1 compatKind k2) -- Establish the kind invariant for CFunEqCan = canEqFailure fl cv  simonpj@microsoft.com committed Nov 12, 2010 758 759  -- Eagerly fails, see Note [Kind errors] in TcInteract  simonpj@microsoft.com committed Sep 13, 2010 760 761  | otherwise = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )  simonpj@microsoft.com committed Nov 12, 2010 762 763 764 765 766 767 768 769  do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments -- cos1 :: xis1 ~ tys1 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS -- co2 :: xi2 ~ s2 ; let ccs = ccs1 andCCan ccs2 no_flattening_happened = isEmptyCCan ccs ; cv_new <- if no_flattening_happened then return cv else if isGiven fl then return cv  simonpj@microsoft.com committed Jan 12, 2011 770 771  else if isWanted fl then do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2  simonpj@microsoft.com committed Nov 12, 2010 772  -- cv' : F xis ~ xi2  simonpj@microsoft.com committed Jan 12, 2011 773  ; let -- fun_co :: F xis1 ~ F tys1  simonpj@microsoft.com committed Nov 12, 2010 774 775 776 777 778  fun_co = mkTyConCoercion fn cos1 -- want_co :: F tys1 ~ s2 want_co = mkSymCoercion fun_co mkTransCoercion mkCoVarCoercion cv' mkTransCoercion co2  simonpj@microsoft.com committed Jan 12, 2011 779 780 781 782  ; setWantedCoBind cv want_co ; return cv' } else -- Derived newDerivedId (EqPred (unClassify (FunCls fn xis1)) xi2)  simonpj@microsoft.com committed Nov 12, 2010 783 784 785  ; let final_cc = CFunEqCan { cc_id = cv_new , cc_flavor = fl  simonpj@microsoft.com committed Sep 13, 2010 786 787 788  , cc_fun = fn , cc_tyargs = xis1 , cc_rhs = xi2 }  simonpj@microsoft.com committed Nov 12, 2010 789  ; return ccs extendCCans final_cc }  simonpj@microsoft.com committed Sep 13, 2010 790   791 792 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft canEqLeafOriented fl cv (FskCls tv) s2  simonpj@microsoft.com committed Nov 12, 2010 793  = canEqLeafTyVarLeft fl cv tv s2  simonpj@microsoft.com committed Sep 13, 2010 794 canEqLeafOriented fl cv (VarCls tv) s2  simonpj@microsoft.com committed Nov 12, 2010 795  = canEqLeafTyVarLeft fl cv tv s2  796 797 798 canEqLeafOriented _ cv (OtherCls ty1) ty2 = pprPanic "canEqLeaf" (ppr cv$$ ppr ty1$$ppr ty2)  simonpj@microsoft.com committed Nov 12, 2010 799 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts  800 -- Establish invariants of CTyEqCans  simonpj@microsoft.com committed Nov 12, 2010 801 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2  simonpj@microsoft.com committed Jan 12, 2011 802 803  | not (k1 compatKind k2) -- Establish the kind invariant for CTyEqCan = canEqFailure fl cv  simonpj@microsoft.com committed Nov 12, 2010 804  -- Eagerly fails, see Note [Kind errors] in TcInteract  simonpj@microsoft.com committed Sep 13, 2010 805  | otherwise  simonpj@microsoft.com committed Nov 12, 2010 806 807 808 809 810  = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly -- unfolded version of the RHS, if we had to -- unfold any type synonyms to get rid of tv. ; case mxi2' of {  simonpj@microsoft.com committed Jan 12, 2011 811  Nothing -> canEqFailure fl cv ;  simonpj@microsoft.com committed Nov 12, 2010 812 813 814 815  Just xi2' -> do { let no_flattening_happened = isEmptyCCan ccs2 ; cv_new <- if no_flattening_happened then return cv else if isGiven fl then return cv  simonpj@microsoft.com committed Jan 12, 2011 816 817 818 819 820 821  else if isWanted fl then do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2 ; setWantedCoBind cv (mkCoVarCoercion cv' mkTransCoercion co) ; return cv' } else -- Derived newDerivedId (EqPred (mkTyVarTy tv) xi2')  simonpj@microsoft.com committed Nov 12, 2010 822 823 824 825 826  ; return$ ccs2 extendCCans CTyEqCan { cc_id = cv_new , cc_flavor = fl , cc_tyvar = tv , cc_rhs = xi2' } } } }  simonpj@microsoft.com committed Sep 13, 2010 827 828 829 830 831 832 833 834 835 836 837 838 839  where k1 = tyVarKind tv k2 = typeKind s2 -- See Note [Type synonyms and canonicalization]. -- Check whether the given variable occurs in the given type. We may -- have needed to do some type synonym unfolding in order to get rid -- of the variable, so we also return the unfolded version of the -- type, which is guaranteed to be syntactically free of the given -- type variable. If the type is already syntactically free of the -- variable, then the same type is returned. -- -- Precondition: the two types are not equal (looking though synonyms)  simonpj@microsoft.com committed Nov 12, 2010 840 841 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi) canOccursCheck _gw tv xi = return (expandAway tv xi)  simonpj@microsoft.com committed Sep 13, 2010 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 \end{code} @expandAway tv xi@ expands synonyms in xi just enough to get rid of occurrences of tv, if that is possible; otherwise, it returns Nothing. For example, suppose we have type F a b = [a] Then expandAway b (F Int b) = Just [Int] but expandAway a (F a Int) = Nothing We don't promise to do the absolute minimum amount of expanding necessary, but we try not to do expansions we don't need to. We prefer doing inner expansions first. For example, type F a b = (a, Int, a, [a]) type G b = Char We have expandAway b (F (G b)) = F Char even though we could also expand F to get rid of b. \begin{code} expandAway :: TcTyVar -> Xi -> Maybe Xi expandAway tv t@(TyVarTy tv') | tv == tv' = Nothing | otherwise = Just t expandAway tv xi | not (tv elemVarSet tyVarsOfType xi) = Just xi expandAway tv (AppTy ty1 ty2)  simonpj@microsoft.com committed Nov 12, 2010 870 871 872 873  = do { ty1' <- expandAway tv ty1 ; ty2' <- expandAway tv ty2 ; return (mkAppTy ty1' ty2') } -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2  simonpj@microsoft.com committed Sep 13, 2010 874 expandAway tv (FunTy ty1 ty2)  simonpj@microsoft.com committed Nov 12, 2010 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890  = do { ty1' <- expandAway tv ty1 ; ty2' <- expandAway tv ty2 ; return (mkFunTy ty1' ty2') } -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2 expandAway tv ty@(ForAllTy {}) = let (tvs,rho) = splitForAllTys ty tvs_knds = map tyVarKind tvs in if tv elemVarSet tyVarsOfTypes tvs_knds then -- Can't expand away the kinds unless we create -- fresh variables which we don't want to do at this point. Nothing else do { rho' <- expandAway tv rho ; return (mkForAllTys tvs rho') } expandAway tv (PredTy pred) = do { pred' <- expandAwayPred tv pred ; return (PredTy pred') }  simonpj@microsoft.com committed Sep 13, 2010 891 892 893 894 895 -- For a type constructor application, first try expanding away the -- offending variable from the arguments. If that doesn't work, next -- see if the type constructor is a type synonym, and if so, expand -- it and try again. expandAway tv ty@(TyConApp tc tys)  simonpj@microsoft.com committed Nov 12, 2010 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910  = (mkTyConApp tc <\$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv) expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType expandAwayPred tv (ClassP cls tys) = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') } expandAwayPred tv (EqPred ty1 ty2) = do { ty1' <- expandAway tv ty1 ; ty2' <- expandAway tv ty2 ; return (EqPred ty1' ty2') } expandAwayPred tv (IParam nm ty) = do { ty' <- expandAway tv ty ; return (IParam nm ty') }  simonpj@microsoft.com committed Sep 13, 2010 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 \end{code} Note [Type synonyms and canonicalization] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We treat type synonym applications as xi types, that is, they do not count as type function applications. However, we do need to be a bit careful with type synonyms: like type functions they may not be generative or injective. However, unlike type functions, they are parametric, so there is no problem in expanding them whenever we see them, since we do not need to know anything about their arguments in order to expand them; this is what justifies not having to treat them as specially as type function applications. The thing that causes some subtleties is that we prefer to leave type synonym applications *unexpanded* whenever possible, in order to generate better error messages. If we encounter an equality constraint with type synonym applications on both sides, or a type synonym application on one side and some sort of type application on the other, we simply must expand out the type synonyms in order to continue decomposing the equality constraint into primitive equality constraints. For example, suppose we have type F a = [Int] and we encounter the equality F a ~ [b] In order to continue we must expand F a into [Int], giving us the equality [Int] ~ [b] which we can then decompose into the more primitive equality constraint Int ~ b. However, if we encounter an equality constraint with a type synonym application on one side and a variable on the other side, we should NOT (necessarily) expand the type synonym, since for the purpose of good error messages we want to leave type synonyms unexpanded as much as possible. However, there is a subtle point with type synonyms and the occurs check that takes place for equality constraints of the form tv ~ xi. As an example, suppose we have type F a = Int and we come across the equality constraint a ~ F a This should not actually fail the occurs check, since expanding out the type synonym results in the legitimate equality constraint a ~ Int. We must actually do this expansion, because unifying a with F a will lead the type checker into infinite loops later. Put another way, canonical equality constraints should never *syntactically* contain the LHS variable in the RHS type. However, we don't always need to expand type synonyms when doing an occurs check; for example, the constraint a ~ F b is obviously fine no matter what F expands to. And in this case we would rather unify a with F b (rather than F b's expansion) in order to get better error messages later. So, when doing an occurs check with a type synonym application on the RHS, we use some heuristics to find an expansion of the RHS which does not contain the variable from the LHS. In particular, given a ~ F t1 ... tn we first try expanding each of the ti to types which no longer contain a. If this turns out to be impossible, we next try expanding F itself, and so on.