2 % (c) The GRASP/AQUA Project, Glasgow University, 1993-1996
4 \section[SaAbsInt]{Abstract interpreter for strictness analysis}
7 #include "HsVersions.h"
21 import CoreUnfold ( UnfoldingDetails(..), FormSummary )
22 import CoreUtils ( unTagBinders )
23 import Id ( idType, getIdStrictness, getIdUnfolding,
24 dataConTyCon, dataConArgTys
26 import IdInfo ( StrictnessInfo(..), Demand(..),
27 wwPrim, wwStrict, wwEnum, wwUnpack
29 import MagicUFs ( MagicUnfoldingFun )
30 import Maybes ( maybeToBool )
31 import Outputable ( Outputable(..){-instance * []-} )
32 import PprStyle ( PprStyle(..) )
33 import Pretty ( ppStr )
34 import PrimOp ( PrimOp(..) )
36 import TyCon ( maybeTyConSingleCon, isEnumerationTyCon,
39 import Type ( maybeAppDataTyConExpandingDicts, isPrimType )
40 import TysWiredIn ( intTyCon, integerTyCon, doubleTyCon,
41 floatTyCon, wordTyCon, addrTyCon
43 import Util ( isIn, isn'tIn, nOfThem, zipWithEqual,
44 pprTrace, panic, pprPanic, assertPanic
47 returnsRealWorld x = False -- ToDo: panic "SaAbsInt.returnsRealWorld (ToDo)"
50 %************************************************************************
52 \subsection[AbsVal-ops]{Operations on @AbsVals@}
54 %************************************************************************
56 Least upper bound, greatest lower bound.
59 lub, glb :: AbsVal -> AbsVal -> AbsVal
61 lub val1 val2 | isBot val1 = val2 -- The isBot test includes the case where
62 lub val1 val2 | isBot val2 = val1 -- one of the val's is a function which
63 -- always returns bottom, such as \y.x,
64 -- when x is bound to bottom.
66 lub (AbsProd xs) (AbsProd ys) = AbsProd (zipWithEqual "lub" lub xs ys)
68 lub _ _ = AbsTop -- Crude, but conservative
69 -- The crudity only shows up if there
70 -- are functions involved
72 -- Slightly funny glb; for absence analysis only;
73 -- AbsBot is the safe answer.
75 -- Using anyBot rather than just testing for AbsBot is important.
80 -- g = \x y z -> case x of
84 -- Now, the abstract value of the branches of the case will be an
85 -- AbsFun, but when testing for z's absence we want to spot that it's
86 -- an AbsFun which can't possibly return AbsBot. So when glb'ing we
87 -- mustn't be too keen to bale out and return AbsBot; the anyBot test
88 -- spots that (f x) can't possibly return AbsBot.
90 -- We have also tripped over the following interesting case:
95 -- Now, suppose f is bound to AbsTop. Does this expression mention z?
96 -- Obviously not. But the case will take the glb of AbsTop (for f) and
97 -- an AbsFun (for \y->1). We should not bale out and give AbsBot, because
98 -- that would say that it *does* mention z (or anything else for that matter).
99 -- Nor can we always return AbsTop, because the AbsFun might be something
100 -- like (\y->z), which obviously does mention z. The point is that we're
101 -- glbing two functions, and AbsTop is not actually the top of the function
102 -- lattice. It is more like (\xyz -> x|y|z); that is, AbsTop returns
103 -- poison iff any of its arguments do.
105 -- Deal with functions specially, because AbsTop isn't the
106 -- top of their domain.
109 | is_fun v1 || is_fun v2
110 = if not (anyBot v1) && not (anyBot v2)
116 is_fun (AbsFun _ _ _) = True
117 is_fun (AbsApproxFun _) = True -- Not used, but the glb works ok
120 -- The non-functional cases are quite straightforward
122 glb (AbsProd xs) (AbsProd ys) = AbsProd (zipWithEqual "glb" glb xs ys)
127 glb _ _ = AbsBot -- Be pessimistic
133 -> AbsVal -- Value of scrutinee
134 -> [AbsVal] -- Value of branches (at least one)
137 -- For strictness analysis, see if the scrutinee is bottom; if so
138 -- return bottom; otherwise, the lub of the branches.
140 combineCaseValues StrAnal AbsBot branches = AbsBot
141 combineCaseValues StrAnal other_scrutinee branches
142 -- Scrutinee can only be AbsBot, AbsProd or AbsTop
143 = ASSERT(ok_scrutinee)
147 = case other_scrutinee of {
148 AbsTop -> True; -- i.e., cool
149 AbsProd _ -> True; -- ditto
150 _ -> False -- party over
153 -- For absence analysis, check if the scrutinee is all poison (isBot)
154 -- If so, return poison (AbsBot); otherwise, any nested poison will come
155 -- out from looking at the branches, so just glb together the branches
156 -- to get the worst one.
158 combineCaseValues AbsAnal AbsBot branches = AbsBot
159 combineCaseValues AbsAnal other_scrutinee branches
160 -- Scrutinee can only be AbsBot, AbsProd or AbsTop
161 = ASSERT(ok_scrutinee)
163 result = foldr1 glb branches
165 tracer = if at_least_one_AbsFun && at_least_one_AbsTop
167 pprTrace "combineCase:" (ppr PprDebug branches)
176 = case other_scrutinee of {
177 AbsTop -> True; -- i.e., cool
178 AbsProd _ -> True; -- ditto
179 _ -> False -- party over
182 at_least_one_AbsFun = foldr ((||) . is_AbsFun) False branches
183 at_least_one_AbsTop = foldr ((||) . is_AbsTop) False branches
184 no_AbsBots = foldr ((&&) . is_not_AbsBot) True branches
186 is_AbsFun x = case x of { AbsFun _ _ _ -> True; _ -> False }
187 is_AbsTop x = case x of { AbsTop -> True; _ -> False }
188 is_not_AbsBot x = case x of { AbsBot -> False; _ -> True }
191 @isBot@ returns True if its argument is (a representation of) bottom. The
192 ``representation'' part is because we need to detect the bottom {\em function}
193 too. To detect the bottom function, bind its args to top, and see if it
196 Used only in strictness analysis:
198 isBot :: AbsVal -> Bool
201 isBot (AbsFun args body env) = isBot (absEval StrAnal body env)
202 -- Don't bother to extend the envt because
203 -- unbound variables default to AbsTop anyway
207 Used only in absence analysis:
209 anyBot :: AbsVal -> Bool
211 anyBot AbsBot = True -- poisoned!
212 anyBot AbsTop = False
213 anyBot (AbsProd vals) = any anyBot vals
214 anyBot (AbsFun args body env) = anyBot (absEval AbsAnal body env)
215 anyBot (AbsApproxFun demands) = False
217 -- AbsApproxFun can only arise in absence analysis from the Demand
218 -- info of an imported value; whatever it is we're looking for is
219 -- certainly not present over in the imported value.
222 @widen@ takes an @AbsVal@, $val$, and returns and @AbsVal@ which is
223 approximated by $val$. Furthermore, the result has no @AbsFun@s in
224 it, so it can be compared for equality by @sameVal@.
227 widen :: AnalysisKind -> AbsVal -> AbsVal
229 widen StrAnal (AbsFun args body env)
230 | isBot (absEval StrAnal body env) = AbsBot
232 = ASSERT (not (null args))
233 AbsApproxFun (map (findDemandStrOnly env body) args)
235 -- It's worth checking for a function which is unconditionally
238 -- f x y = let g y = case x of ...
239 -- in (g ..) + (g ..)
241 -- Here, when we are considering strictness of f in x, we'll
242 -- evaluate the body of f with x bound to bottom. The current
243 -- strategy is to bind g to its *widened* value; without the isBot
244 -- (...) test above, we'd bind g to an AbsApproxFun, and deliver
245 -- Top, not Bot as the value of f's rhs. The test spots the
246 -- unconditional bottom-ness of g when x is bottom. (Another
247 -- alternative here would be to bind g to its exact abstract
248 -- value, but that entails lots of potential re-computation, at
249 -- every application of g.)
251 widen StrAnal (AbsProd vals) = AbsProd (map (widen StrAnal) vals)
252 widen StrAnal other_val = other_val
255 widen AbsAnal (AbsFun args body env)
256 | anyBot (absEval AbsAnal body env) = AbsBot
257 -- In the absence-analysis case it's *essential* to check
258 -- that the function has no poison in its body. If it does,
259 -- anywhere, then the whole function is poisonous.
262 = ASSERT (not (null args))
263 AbsApproxFun (map (findDemandAbsOnly env body) args)
265 widen AbsAnal (AbsProd vals) = AbsProd (map (widen AbsAnal) vals)
267 -- It's desirable to do a good job of widening for product
271 -- in ...(case p of (x,y) -> x)...
273 -- Now, is y absent in this expression? Currently the
274 -- analyser widens p before looking at p's scope, to avoid
275 -- lots of recomputation in the case where p is a function.
276 -- So if widening doesn't have a case for products, we'll
277 -- widen p to AbsBot (since when searching for absence in y we
278 -- bind y to poison ie AbsBot), and now we are lost.
280 widen AbsAnal other_val = other_val
282 -- WAS: if anyBot val then AbsBot else AbsTop
283 -- Nowadays widen is doing a better job on functions for absence analysis.
286 @crudeAbsWiden@ is used just for absence analysis, and always
287 returns AbsTop or AbsBot, so it widens to a two-point domain
290 crudeAbsWiden :: AbsVal -> AbsVal
291 crudeAbsWiden val = if anyBot val then AbsBot else AbsTop
294 @sameVal@ compares two abstract values for equality. It can't deal with
295 @AbsFun@, but that should have been removed earlier in the day by @widen@.
298 sameVal :: AbsVal -> AbsVal -> Bool -- Can't handle AbsFun!
301 sameVal (AbsFun _ _ _) _ = panic "sameVal: AbsFun: arg1"
302 sameVal _ (AbsFun _ _ _) = panic "sameVal: AbsFun: arg2"
305 sameVal AbsBot AbsBot = True
306 sameVal AbsBot other = False -- widen has reduced AbsFun bots to AbsBot
308 sameVal AbsTop AbsTop = True
309 sameVal AbsTop other = False -- Right?
311 sameVal (AbsProd vals1) (AbsProd vals2) = and (zipWithEqual "sameVal" sameVal vals1 vals2)
312 sameVal (AbsProd _) AbsTop = False
313 sameVal (AbsProd _) AbsBot = False
315 sameVal (AbsApproxFun str1) (AbsApproxFun str2) = str1 == str2
316 sameVal (AbsApproxFun _) AbsTop = False
317 sameVal (AbsApproxFun _) AbsBot = False
319 sameVal val1 val2 = panic "sameVal: type mismatch or AbsFun encountered"
323 @evalStrictness@ compares a @Demand@ with an abstract value, returning
324 @True@ iff the abstract value is {\em less defined} than the demand.
325 (@True@ is the exciting answer; @False@ is always safe.)
328 evalStrictness :: Demand
330 -> Bool -- True iff the value is sure
331 -- to be less defined than the Demand
333 evalStrictness (WwLazy _) _ = False
334 evalStrictness WwStrict val = isBot val
335 evalStrictness WwEnum val = isBot val
337 evalStrictness (WwUnpack demand_info) val
341 AbsProd vals -> or (zipWithEqual "evalStrictness" evalStrictness demand_info vals)
342 _ -> trace "evalStrictness?" False
344 evalStrictness WwPrim val
348 other -> -- A primitive value should be defined, never bottom;
349 -- hence this paranoia check
350 pprPanic "evalStrictness: WwPrim:" (ppr PprDebug other)
353 For absence analysis, we're interested in whether "poison" in the
354 argument (ie a bottom therein) can propagate to the result of the
355 function call; that is, whether the specified demand can {\em
356 possibly} hit poison.
359 evalAbsence (WwLazy True) _ = False -- Can't possibly hit poison
360 -- with Absent demand
362 evalAbsence (WwUnpack demand_info) val
364 AbsTop -> False -- No poison in here
365 AbsBot -> True -- Pure poison
366 AbsProd vals -> or (zipWithEqual "evalAbsence" evalAbsence demand_info vals)
367 _ -> panic "evalAbsence: other"
369 evalAbsence other val = anyBot val
370 -- The demand is conservative; even "Lazy" *might* evaluate the
371 -- argument arbitrarily so we have to look everywhere for poison
374 %************************************************************************
376 \subsection[absEval]{Evaluate an expression in the abstract domain}
378 %************************************************************************
381 -- The isBottomingId stuf is now dealt with via the Id's strictness info
382 -- absId anal var env | isBottomingId var
384 -- StrAnal -> AbsBot -- See discussion below
385 -- AbsAnal -> AbsTop -- Just want to see if there's any poison in
391 case (lookupAbsValEnv env var, getIdStrictness var, getIdUnfolding var) of
393 (Just abs_val, _, _) ->
394 abs_val -- Bound in the environment
396 (Nothing, NoStrictnessInfo, GenForm _ unfolding _) ->
397 -- We have an unfolding for the expr
398 -- Assume the unfolding has no free variables since it
399 -- came from inside the Id
400 absEval anal (unTagBinders unfolding) env
401 -- Notice here that we only look in the unfolding if we don't
402 -- have strictness info (an unusual situation).
403 -- We could have chosen to look in the unfolding if it exists,
404 -- and only try the strictness info if it doesn't, and that would
405 -- give more accurate results, at the cost of re-abstract-interpreting
406 -- the unfolding every time.
407 -- We found only one place where the look-at-unfolding-first
408 -- method gave better results, which is in the definition of
409 -- showInt in the Prelude. In its defintion, fromIntegral is
410 -- not inlined (it's big) but ab-interp-ing its unfolding gave
411 -- a better result than looking at its strictness only.
412 -- showInt :: Integral a => a -> [Char] -> [Char]
413 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
414 -- "U(U(U(U(SA)AAAAAAAAL)AA)AAAAASAAASA)" {...} _N_ _N_ #-}
416 -- showInt :: Integral a => a -> [Char] -> [Char]
417 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
418 -- "U(U(U(U(SL)LLLLLLLLL)LL)LLLLLSLLLLL)" _N_ _N_ #-}
421 (Nothing, strictness_info, _) ->
422 -- Includes MagicForm, IWantToBeINLINEd, NoUnfoldingDetails
423 -- Try the strictness info
424 absValFromStrictness anal strictness_info
426 -- pprTrace "absId:" (ppBesides [ppr PprDebug var, ppStr "=:", pp_anal anal, ppStr ":=",ppr PprDebug result]) $
429 pp_anal StrAnal = ppStr "STR"
430 pp_anal AbsAnal = ppStr "ABS"
432 absEvalAtom anal (VarArg v) env = absId anal v env
433 absEvalAtom anal (LitArg _) env = AbsTop
437 absEval :: AnalysisKind -> CoreExpr -> AbsValEnv -> AbsVal
439 absEval anal (Var var) env = absId anal var env
441 absEval anal (Lit _) env = AbsTop
442 -- What if an unboxed literal? That's OK: it terminates, so its
443 -- abstract value is AbsTop.
445 -- For absence analysis, a literal certainly isn't the "poison" variable
448 Discussion about \tr{error} (following/quoting Lennart): Any expression
449 \tr{error e} is regarded as bottom (with HBC, with the
450 \tr{-ffail-strict} flag, on with \tr{-O}).
452 Regarding it as bottom gives much better strictness properties for
456 f (x:xs) y = f xs (x+y)
458 f [] _ = error "no match"
460 f (x:xs) y = f xs (x+y)
462 is strict in \tr{y}, which you really want. But, it may lead to
463 transformations that turn a call to \tr{error} into non-termination.
464 (The odds of this happening aren't good.)
467 Things are a little different for absence analysis, because we want
468 to make sure that any poison (?????)
471 absEval StrAnal (Prim SeqOp [TyArg _, e]) env
473 if isBot (absEvalAtom StrAnal e env) then AbsBot else AbsTop
474 -- This is a special case to ensure that seq# is strict in its argument.
475 -- The comments below (for most normal PrimOps) do not apply.
477 absEval StrAnal (Prim op es) env = AbsTop
478 -- The arguments are all of unboxed type, so they will already
479 -- have been eval'd. If the boxed version was bottom, we'll
480 -- already have returned bottom.
482 -- Actually, I believe we are saying that either (1) the
483 -- primOp uses unboxed args and they've been eval'ed, so
484 -- there's no need to force strictness here, _or_ the primOp
485 -- uses boxed args and we don't know whether or not it's
486 -- strict, so we assume laziness. (JSM)
488 absEval AbsAnal (Prim op as) env
489 = if any anyBot [absEvalAtom AbsAnal a env | a <- as, isValArg a]
492 -- For absence analysis, we want to see if the poison shows up...
494 absEval anal (Con con as) env
496 = AbsProd [absEvalAtom anal a env | a <- as, isValArg a]
498 | otherwise -- Not single-constructor
500 StrAnal -> -- Strictness case: it's easy: it certainly terminates
502 AbsAnal -> -- In the absence case we need to be more
503 -- careful: look to see if there's any
504 -- poison in the components
505 if any anyBot [absEvalAtom AbsAnal a env | a <- as, isValArg a]
509 has_single_con = maybeToBool (maybeTyConSingleCon (dataConTyCon con))
513 absEval anal (Lam (ValBinder binder) body) env
514 = AbsFun [binder] body env
515 absEval anal (Lam other_binder expr) env
516 = absEval anal expr env
517 absEval anal (App f a) env | isValArg a
518 = absApply anal (absEval anal f env) (absEvalAtom anal a env)
519 absEval anal (App expr _) env
520 = absEval anal expr env
523 For primitive cases, just GLB the branches, then LUB with the expr part.
526 absEval anal (Case expr (PrimAlts alts deflt)) env
528 expr_val = absEval anal expr env
529 abs_alts = [ absEval anal rhs env | (_, rhs) <- alts ]
530 -- Don't bother to extend envt, because unbound vars
531 -- default to the conservative AbsTop
533 abs_deflt = absEvalDefault anal expr_val deflt env
535 combineCaseValues anal expr_val
536 (abs_deflt ++ abs_alts)
538 absEval anal (Case expr (AlgAlts alts deflt)) env
540 expr_val = absEval anal expr env
541 abs_alts = [ absEvalAlgAlt anal expr_val alt env | alt <- alts ]
542 abs_deflt = absEvalDefault anal expr_val deflt env
546 combineCaseValues anal expr_val
547 (abs_deflt ++ abs_alts)
552 _ -> pprTrace "absCase:ABS:" (ppAbove (ppCat [ppr PprDebug expr, ppr PprDebug result, ppr PprDebug expr_val, ppr PprDebug abs_deflt, ppr PprDebug abs_alts]) (ppr PprDebug (keysFM env `zip` eltsFM env)))
558 For @Lets@ we widen the value we get. This is nothing to
559 do with fixpointing. The reason is so that we don't get an explosion
560 in the amount of computation. For example, consider:
572 If we bind @f@ and @g@ to their exact abstract value, then we'll
573 ``execute'' one call to @f@ and {\em two} calls to @g@. This can blow
574 up exponentially. Widening cuts it off by making a fixed
575 approximation to @f@ and @g@, so that the bodies of @f@ and @g@ are
576 not evaluated again at all when they are called.
578 Of course, this can lose useful joint strictness, which is sad. An
579 alternative approach would be to try with a certain amount of ``fuel''
580 and be prepared to bale out.
583 absEval anal (Let (NonRec binder e1) e2) env
585 new_env = addOneToAbsValEnv env binder (widen anal (absEval anal e1 env))
587 -- The binder of a NonRec should *not* be of unboxed type,
588 -- hence no need to strictly evaluate the Rhs.
589 absEval anal e2 new_env
591 absEval anal (Let (Rec pairs) body) env
593 (binders,rhss) = unzip pairs
594 rhs_vals = cheapFixpoint anal binders rhss env -- Returns widened values
595 new_env = growAbsValEnvList env (binders `zip` rhs_vals)
597 absEval anal body new_env
599 absEval anal (SCC cc expr) env = absEval anal expr env
600 absEval anal (Coerce c ty expr) env = absEval anal expr env
604 absEvalAlgAlt :: AnalysisKind -> AbsVal -> (Id,[Id],CoreExpr) -> AbsValEnv -> AbsVal
606 absEvalAlgAlt anal (AbsProd arg_vals) (con, args, rhs) env
607 = -- The scrutinee is a product value, so it must be of a single-constr
608 -- type; so the constructor in this alternative must be the right one
609 -- so we can go ahead and bind the constructor args to the components
610 -- of the product value.
611 ASSERT(length arg_vals == length args)
613 new_env = growAbsValEnvList env (args `zip` arg_vals)
615 absEval anal rhs new_env
617 absEvalAlgAlt anal other_scrutinee (con, args, rhs) env
618 = -- Scrutinised value is Top or Bot (it can't be a function!)
619 -- So just evaluate the rhs with all constr args bound to Top.
620 -- (If the scrutinee is Top we'll never evaluated this function
626 = case other_scrutinee of {
627 AbsTop -> True; -- i.e., OK
628 AbsBot -> True; -- ditto
629 _ -> False -- party over
633 absEvalDefault :: AnalysisKind
634 -> AbsVal -- Value of scrutinee
637 -> [AbsVal] -- Empty or singleton
639 absEvalDefault anal scrut_val NoDefault env = []
640 absEvalDefault anal scrut_val (BindDefault binder expr) env
641 = [absEval anal expr (addOneToAbsValEnv env binder scrut_val)]
644 %************************************************************************
646 \subsection[absApply]{Apply an abstract function to an abstract argument}
648 %************************************************************************
653 absApply :: AnalysisKind -> AbsVal -> AbsVal -> AbsVal
655 absApply anal AbsBot arg = AbsBot
656 -- AbsBot represents the abstract bottom *function* too
658 absApply StrAnal AbsTop arg = AbsTop
659 absApply AbsAnal AbsTop arg = if anyBot arg
662 -- To be conservative, we have to assume that a function about
663 -- which we know nothing (AbsTop) might look at some part of
667 An @AbsFun@ with only one more argument needed---bind it and eval the
668 result. A @Lam@ with two or more args: return another @AbsFun@ with
669 an augmented environment.
672 absApply anal (AbsFun [binder] body env) arg
673 = absEval anal body (addOneToAbsValEnv env binder arg)
675 absApply anal (AbsFun (binder:bs) body env) arg
676 = AbsFun bs body (addOneToAbsValEnv env binder arg)
680 absApply StrAnal (AbsApproxFun (arg1_demand:ds)) arg
681 = if evalStrictness arg1_demand arg
685 other -> AbsApproxFun ds
687 absApply AbsAnal (AbsApproxFun (arg1_demand:ds)) arg
688 = if evalAbsence arg1_demand arg
692 other -> AbsApproxFun ds
695 absApply anal (AbsApproxFun []) arg = panic ("absApply: Duff function: AbsApproxFun." ++ show anal)
696 absApply anal (AbsFun [] _ _) arg = panic ("absApply: Duff function: AbsFun." ++ show anal)
697 absApply anal (AbsProd _) arg = panic ("absApply: Duff function: AbsProd." ++ show anal)
704 %************************************************************************
706 \subsection[findStrictness]{Determine some binders' strictness}
708 %************************************************************************
710 @findStrictness@ applies the function \tr{\ ids -> expr} to
711 \tr{[bot,top,top,...]}, \tr{[top,bot,top,top,...]}, etc., (i.e., once
712 with @AbsBot@ in each argument position), and evaluates the resulting
713 abstract value; it returns a vector of @Demand@s saying whether the
714 result of doing this is guaranteed to be bottom. This tells the
715 strictness of the function in each of the arguments.
717 If an argument is of unboxed type, then we declare that function to be
718 strict in that argument.
720 We don't really have to make up all those lists of mostly-@AbsTops@;
721 unbound variables in an @AbsValEnv@ are implicitly mapped to that.
723 See notes on @addStrictnessInfoToId@.
726 findStrictness :: StrAnalFlags
727 -> [Type] -- Types of args in which strictness is wanted
728 -> AbsVal -- Abstract strictness value of function
729 -> AbsVal -- Abstract absence value of function
730 -> [Demand] -- Resulting strictness annotation
732 findStrictness strflags [] str_val abs_val = []
734 findStrictness strflags (ty:tys) str_val abs_val
736 demand = findRecDemand strflags [] str_fn abs_fn ty
737 str_fn val = absApply StrAnal str_val val
738 abs_fn val = absApply AbsAnal abs_val val
740 demands = findStrictness strflags tys
741 (absApply StrAnal str_val AbsTop)
742 (absApply AbsAnal abs_val AbsTop)
749 findDemandStrOnly str_env expr binder -- Only strictness environment available
750 = findRecDemand strflags [] str_fn abs_fn (idType binder)
752 str_fn val = absEval StrAnal expr (addOneToAbsValEnv str_env binder val)
753 abs_fn val = AbsBot -- Always says poison; so it looks as if
754 -- nothing is absent; safe
755 strflags = getStrAnalFlags str_env
757 findDemandAbsOnly abs_env expr binder -- Only absence environment available
758 = findRecDemand strflags [] str_fn abs_fn (idType binder)
760 str_fn val = AbsBot -- Always says non-termination;
761 -- that'll make findRecDemand peer into the
762 -- structure of the value.
763 abs_fn val = absEval AbsAnal expr (addOneToAbsValEnv abs_env binder val)
764 strflags = getStrAnalFlags abs_env
767 findDemand str_env abs_env expr binder
768 = findRecDemand strflags [] str_fn abs_fn (idType binder)
770 str_fn val = absEval StrAnal expr (addOneToAbsValEnv str_env binder val)
771 abs_fn val = absEval AbsAnal expr (addOneToAbsValEnv abs_env binder val)
772 strflags = getStrAnalFlags str_env
775 @findRecDemand@ is where we finally convert strictness/absence info
776 into ``Demands'' which we can pin on Ids (etc.).
778 NOTE: What do we do if something is {\em both} strict and absent?
779 Should \tr{f x y z = error "foo"} says that \tr{f}'s arguments are all
780 strict (because of bottoming effect of \tr{error}) or all absent
781 (because they're not used)?
783 Well, for practical reasons, we prefer absence over strictness. In
784 particular, it makes the ``default defaults'' for class methods (the
785 ones that say \tr{defm.foo dict = error "I don't exist"}) come out
786 nicely [saying ``the dict isn't used''], rather than saying it is
787 strict in every component of the dictionary [massive gratuitious
788 casing to take the dict apart].
790 But you could have examples where going for strictness would be better
791 than absence. Consider:
793 let x = something big
798 If \tr{x} is marked absent in \tr{f}, but not strict, and \tr{g} is
799 lazy, then the thunk for \tr{x} will be built. If \tr{f} was strict,
800 then we'd let-to-case it:
802 case something big of
808 findRecDemand :: StrAnalFlags
809 -> [TyCon] -- TyCons already seen; used to avoid
810 -- zooming into recursive types
811 -> (AbsVal -> AbsVal) -- The strictness function
812 -> (AbsVal -> AbsVal) -- The absence function
813 -> Type -- The type of the argument
816 findRecDemand strflags seen str_fn abs_fn ty
817 = if isPrimType ty then -- It's a primitive type!
820 else if not (anyBot (abs_fn AbsBot)) then -- It's absent
821 -- We prefer absence over strictness: see NOTE above.
824 else if not (all_strict ||
825 (num_strict && is_numeric_type ty) ||
826 (isBot (str_fn AbsBot))) then
827 WwLazy False -- It's not strict and we're not pretending
829 else -- It's strict (or we're pretending it is)!
831 case (maybeAppDataTyConExpandingDicts ty) of
835 Just (tycon,tycon_arg_tys,[data_con]) | tycon `not_elem` seen ->
836 -- Single constructor case, tycon not already seen higher up
838 cmpnt_tys = dataConArgTys data_con tycon_arg_tys
839 prod_len = length cmpnt_tys
842 = [ findRecDemand strflags (tycon:seen)
844 str_fn (mkMainlyTopProd prod_len i cmpnt_val)
847 abs_fn (mkMainlyTopProd prod_len i cmpnt_val)
850 | (cmpnt_ty, i) <- cmpnt_tys `zip` [1..] ]
852 if null compt_strict_infos then
853 if isEnumerationTyCon tycon then wwEnum else wwStrict
855 wwUnpack compt_strict_infos
857 not_elem = isn'tIn "findRecDemand"
860 -- Multi-constr data types, *or* an abstract data
861 -- types, *or* things we don't have a way of conveying
862 -- the info over module boundaries (class ops,
863 -- superdict sels, dfns).
864 if isEnumerationTyCon tycon then
869 (all_strict, num_strict) = strflags
872 = case (maybeAppDataTyConExpandingDicts ty) of -- NB: duplicates stuff done above
876 [intTyCon, integerTyCon,
877 doubleTyCon, floatTyCon,
878 wordTyCon, addrTyCon]
880 _{-something else-} -> False
882 is_elem = isIn "is_numeric_type"
884 -- mkMainlyTopProd: make an AbsProd that is all AbsTops ("n"-1 of
885 -- them) except for a given value in the "i"th position.
887 mkMainlyTopProd :: Int -> Int -> AbsVal -> AbsVal
889 mkMainlyTopProd n i val
891 befores = nOfThem (i-1) AbsTop
892 afters = nOfThem (n-i) AbsTop
894 AbsProd (befores ++ (val : afters))
897 %************************************************************************
899 \subsection[fixpoint]{Fixpointer for the strictness analyser}
901 %************************************************************************
903 The @fixpoint@ functions take a list of \tr{(binder, expr)} pairs, an
904 environment, and returns the abstract value of each binder.
906 The @cheapFixpoint@ function makes a conservative approximation,
907 by binding each of the variables to Top in their own right hand sides.
908 That allows us to make rapid progress, at the cost of a less-than-wonderful
912 cheapFixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
914 cheapFixpoint AbsAnal [id] [rhs] env
915 = [crudeAbsWiden (absEval AbsAnal rhs new_env)]
917 new_env = addOneToAbsValEnv env id AbsTop -- Unsafe starting point!
918 -- In the just-one-binding case, we guarantee to
919 -- find a fixed point in just one iteration,
920 -- because we are using only a two-point domain.
921 -- This improves matters in cases like:
923 -- f x y = letrec g = ...g...
926 -- Here, y isn't used at all, but if g is bound to
927 -- AbsBot we simply get AbsBot as the next
930 cheapFixpoint anal ids rhss env
931 = [widen anal (absEval anal rhs new_env) | rhs <- rhss]
932 -- We do just one iteration, starting from a safe
933 -- approximation. This won't do a good job in situations
935 -- \x -> letrec f = ...g...
939 -- Here, f will end up bound to Top after one iteration,
940 -- and hence we won't spot the strictness in x.
941 -- (A second iteration would solve this. ToDo: try the effect of
942 -- really searching for a fixed point.)
944 new_env = growAbsValEnvList env [(id,safe_val) | id <- ids]
947 = case anal of -- The safe starting point
953 mkLookupFun :: (key -> key -> Bool) -- Equality predicate
954 -> (key -> key -> Bool) -- Less-than predicate
955 -> [(key,val)] -- The assoc list
957 -> Maybe val -- The corresponding value
959 mkLookupFun eq lt alist s
960 = case [a | (s',a) <- alist, s' `eq` s] of
966 fixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
968 fixpoint anal [] _ env = []
970 fixpoint anal ids rhss env
971 = fix_loop initial_vals
974 = case anal of -- The (unsafe) starting point
975 StrAnal -> if (returnsRealWorld (idType id))
976 then AbsTop -- this is a massively horrible hack (SLPJ 95/05)
980 initial_vals = [ initial_val id | id <- ids ]
982 fix_loop :: [AbsVal] -> [AbsVal]
984 fix_loop current_widened_vals
986 new_env = growAbsValEnvList env (ids `zip` current_widened_vals)
987 new_vals = [ absEval anal rhs new_env | rhs <- rhss ]
988 new_widened_vals = map (widen anal) new_vals
990 if (and (zipWith sameVal current_widened_vals new_widened_vals)) then
993 -- NB: I was too chicken to make that a zipWithEqual,
994 -- lest I jump into a black hole. WDP 96/02
996 -- Return the widened values. We might get a slightly
997 -- better value by returning new_vals (which we used to
998 -- do, see below), but alas that means that whenever the
999 -- function is called we have to re-execute it, which is
1004 -- Return the un-widened values which may be a bit better
1005 -- than the widened ones, and are guaranteed safe, since
1006 -- they are one iteration beyond current_widened_vals,
1007 -- which itself is a fixed point.
1009 fix_loop new_widened_vals
1012 For absence analysis, we make do with a very very simple approach:
1013 look for convergence in a two-point domain.
1015 We used to use just one iteration, starting with the variables bound
1016 to @AbsBot@, which is safe.
1018 Prior to that, we used one iteration starting from @AbsTop@ (which
1019 isn't safe). Why isn't @AbsTop@ safe? Consider:
1027 Here, if p is @AbsBot@, then we'd better {\em not} end up with a ``fixed
1028 point'' of @d@ being @(AbsTop, AbsTop)@! An @AbsBot@ initial value is
1029 safe because it gives poison more often than really necessary, and
1030 thus may miss some absence, but will never claim absence when it ain't
1033 Anyway, one iteration starting with everything bound to @AbsBot@ give
1038 Here, f would always end up bound to @AbsBot@, which ain't very
1039 clever, because then it would introduce poison whenever it was
1040 applied. Much better to start with f bound to @AbsTop@, and widen it
1041 to @AbsBot@ if any poison shows up. In effect we look for convergence
1042 in the two-point @AbsTop@/@AbsBot@ domain.
1044 What we miss (compared with the cleverer strictness analysis) is
1045 spotting that in this case
1047 f = \ x y -> ...y...(f x y')...
1049 \tr{x} is actually absent, since it is only passed round the loop, never
1050 used. But who cares about missing that?
1052 NB: despite only having a two-point domain, we may still have many
1053 iterations, because there are several variables involved at once.