2 % (c) The GRASP/AQUA Project, Glasgow University, 1993-1998
4 \section[SaAbsInt]{Abstract interpreter for strictness analysis}
9 findDemand, findDemandAlts,
16 #include "HsVersions.h"
18 import CmdLineOpts ( opt_AllStrict, opt_NumbersStrict )
20 import CoreUnfold ( maybeUnfoldingTemplate )
21 import Id ( Id, idType, idStrictness, idUnfolding, isDataConId_maybe )
22 import DataCon ( dataConTyCon, splitProductType_maybe, dataConRepArgTys )
23 import IdInfo ( StrictnessInfo(..) )
24 import Demand ( Demand(..), wwPrim, wwStrict, wwUnpack, wwLazy,
25 mkStrictnessInfo, isLazy
28 import TyCon ( isProductTyCon, isRecursiveTyCon )
29 import Type ( splitTyConApp_maybe,
30 isUnLiftedType, Type )
31 import TyCon ( tyConUnique )
32 import PrelInfo ( numericTyKeys )
33 import Util ( isIn, nOfThem, zipWithEqual )
37 %************************************************************************
39 \subsection[AbsVal-ops]{Operations on @AbsVals@}
41 %************************************************************************
43 Least upper bound, greatest lower bound.
46 lub, glb :: AbsVal -> AbsVal -> AbsVal
48 lub AbsBot val2 = val2
49 lub val1 AbsBot = val1
51 lub (AbsProd xs) (AbsProd ys) = AbsProd (zipWithEqual "lub" lub xs ys)
53 lub _ _ = AbsTop -- Crude, but conservative
54 -- The crudity only shows up if there
55 -- are functions involved
57 -- Slightly funny glb; for absence analysis only;
58 -- AbsBot is the safe answer.
60 -- Using anyBot rather than just testing for AbsBot is important.
65 -- g = \x y z -> case x of
69 -- Now, the abstract value of the branches of the case will be an
70 -- AbsFun, but when testing for z's absence we want to spot that it's
71 -- an AbsFun which can't possibly return AbsBot. So when glb'ing we
72 -- mustn't be too keen to bale out and return AbsBot; the anyBot test
73 -- spots that (f x) can't possibly return AbsBot.
75 -- We have also tripped over the following interesting case:
80 -- Now, suppose f is bound to AbsTop. Does this expression mention z?
81 -- Obviously not. But the case will take the glb of AbsTop (for f) and
82 -- an AbsFun (for \y->1). We should not bale out and give AbsBot, because
83 -- that would say that it *does* mention z (or anything else for that matter).
84 -- Nor can we always return AbsTop, because the AbsFun might be something
85 -- like (\y->z), which obviously does mention z. The point is that we're
86 -- glbing two functions, and AbsTop is not actually the top of the function
87 -- lattice. It is more like (\xyz -> x|y|z); that is, AbsTop returns
88 -- poison iff any of its arguments do.
90 -- Deal with functions specially, because AbsTop isn't the
91 -- top of their domain.
94 | is_fun v1 || is_fun v2
95 = if not (anyBot v1) && not (anyBot v2)
101 is_fun (AbsFun _ _) = True
102 is_fun (AbsApproxFun _ _) = True -- Not used, but the glb works ok
105 -- The non-functional cases are quite straightforward
107 glb (AbsProd xs) (AbsProd ys) = AbsProd (zipWithEqual "glb" glb xs ys)
112 glb _ _ = AbsBot -- Be pessimistic
115 @isBot@ returns True if its argument is (a representation of) bottom. The
116 ``representation'' part is because we need to detect the bottom {\em function}
117 too. To detect the bottom function, bind its args to top, and see if it
120 Used only in strictness analysis:
122 isBot :: AbsVal -> Bool
125 isBot other = False -- Functions aren't bottom any more
128 Used only in absence analysis:
131 anyBot :: AbsVal -> Bool
133 anyBot AbsBot = True -- poisoned!
134 anyBot AbsTop = False
135 anyBot (AbsProd vals) = any anyBot vals
136 anyBot (AbsFun bndr_ty abs_fn) = anyBot (abs_fn AbsTop)
137 anyBot (AbsApproxFun _ val) = anyBot val
140 @widen@ takes an @AbsVal@, $val$, and returns and @AbsVal@ which is
141 approximated by $val$. Furthermore, the result has no @AbsFun@s in
142 it, so it can be compared for equality by @sameVal@.
145 widen :: AnalysisKind -> AbsVal -> AbsVal
147 -- Widening is complicated by the fact that funtions are lifted
148 widen StrAnal the_fn@(AbsFun bndr_ty _)
149 = case widened_body of
150 AbsApproxFun ds val -> AbsApproxFun (d : ds) val
152 d = findRecDemand str_fn abs_fn bndr_ty
153 str_fn val = isBot (foldl (absApply StrAnal) the_fn
154 (val : [AbsTop | d <- ds]))
156 other -> AbsApproxFun [d] widened_body
158 d = findRecDemand str_fn abs_fn bndr_ty
159 str_fn val = isBot (absApply StrAnal the_fn val)
161 widened_body = widen StrAnal (absApply StrAnal the_fn AbsTop)
162 abs_fn val = False -- Always says poison; so it looks as if
163 -- nothing is absent; safe
166 This stuff is now instead handled neatly by the fact that AbsApproxFun
167 contains an AbsVal inside it. SLPJ Jan 97
169 | isBot abs_body = AbsBot
170 -- It's worth checking for a function which is unconditionally
173 -- f x y = let g y = case x of ...
174 -- in (g ..) + (g ..)
176 -- Here, when we are considering strictness of f in x, we'll
177 -- evaluate the body of f with x bound to bottom. The current
178 -- strategy is to bind g to its *widened* value; without the isBot
179 -- (...) test above, we'd bind g to an AbsApproxFun, and deliver
180 -- Top, not Bot as the value of f's rhs. The test spots the
181 -- unconditional bottom-ness of g when x is bottom. (Another
182 -- alternative here would be to bind g to its exact abstract
183 -- value, but that entails lots of potential re-computation, at
184 -- every application of g.)
187 widen StrAnal (AbsProd vals) = AbsProd (map (widen StrAnal) vals)
188 widen StrAnal other_val = other_val
191 widen AbsAnal the_fn@(AbsFun bndr_ty _)
192 | anyBot widened_body = AbsBot
193 -- In the absence-analysis case it's *essential* to check
194 -- that the function has no poison in its body. If it does,
195 -- anywhere, then the whole function is poisonous.
198 = case widened_body of
199 AbsApproxFun ds val -> AbsApproxFun (d : ds) val
201 d = findRecDemand str_fn abs_fn bndr_ty
202 abs_fn val = not (anyBot (foldl (absApply AbsAnal) the_fn
203 (val : [AbsTop | d <- ds])))
205 other -> AbsApproxFun [d] widened_body
207 d = findRecDemand str_fn abs_fn bndr_ty
208 abs_fn val = not (anyBot (absApply AbsAnal the_fn val))
210 widened_body = widen AbsAnal (absApply AbsAnal the_fn AbsTop)
211 str_fn val = True -- Always says non-termination;
212 -- that'll make findRecDemand peer into the
213 -- structure of the value.
215 widen AbsAnal (AbsProd vals) = AbsProd (map (widen AbsAnal) vals)
217 -- It's desirable to do a good job of widening for product
221 -- in ...(case p of (x,y) -> x)...
223 -- Now, is y absent in this expression? Currently the
224 -- analyser widens p before looking at p's scope, to avoid
225 -- lots of recomputation in the case where p is a function.
226 -- So if widening doesn't have a case for products, we'll
227 -- widen p to AbsBot (since when searching for absence in y we
228 -- bind y to poison ie AbsBot), and now we are lost.
230 widen AbsAnal other_val = other_val
232 -- WAS: if anyBot val then AbsBot else AbsTop
233 -- Nowadays widen is doing a better job on functions for absence analysis.
236 @crudeAbsWiden@ is used just for absence analysis, and always
237 returns AbsTop or AbsBot, so it widens to a two-point domain
240 crudeAbsWiden :: AbsVal -> AbsVal
241 crudeAbsWiden val = if anyBot val then AbsBot else AbsTop
244 @sameVal@ compares two abstract values for equality. It can't deal with
245 @AbsFun@, but that should have been removed earlier in the day by @widen@.
248 sameVal :: AbsVal -> AbsVal -> Bool -- Can't handle AbsFun!
251 sameVal (AbsFun _ _) _ = panic "sameVal: AbsFun: arg1"
252 sameVal _ (AbsFun _ _) = panic "sameVal: AbsFun: arg2"
255 sameVal AbsBot AbsBot = True
256 sameVal AbsBot other = False -- widen has reduced AbsFun bots to AbsBot
258 sameVal AbsTop AbsTop = True
259 sameVal AbsTop other = False -- Right?
261 sameVal (AbsProd vals1) (AbsProd vals2) = and (zipWithEqual "sameVal" sameVal vals1 vals2)
262 sameVal (AbsProd _) AbsTop = False
263 sameVal (AbsProd _) AbsBot = False
265 sameVal (AbsApproxFun str1 v1) (AbsApproxFun str2 v2) = str1 == str2 && sameVal v1 v2
266 sameVal (AbsApproxFun _ _) AbsTop = False
267 sameVal (AbsApproxFun _ _) AbsBot = False
269 sameVal val1 val2 = panic "sameVal: type mismatch or AbsFun encountered"
273 @evalStrictness@ compares a @Demand@ with an abstract value, returning
274 @True@ iff the abstract value is {\em less defined} than the demand.
275 (@True@ is the exciting answer; @False@ is always safe.)
278 evalStrictness :: Demand
280 -> Bool -- True iff the value is sure
281 -- to be less defined than the Demand
283 evalStrictness (WwLazy _) _ = False
284 evalStrictness WwStrict val = isBot val
285 evalStrictness WwEnum val = isBot val
287 evalStrictness (WwUnpack _ demand_info) val
291 AbsProd vals -> or (zipWithEqual "evalStrictness" evalStrictness demand_info vals)
292 _ -> pprTrace "evalStrictness?" empty False
294 evalStrictness WwPrim val
297 AbsBot -> True -- Can happen: consider f (g x), where g is a
298 -- recursive function returning an Int# that diverges
300 other -> pprPanic "evalStrictness: WwPrim:" (ppr other)
303 For absence analysis, we're interested in whether "poison" in the
304 argument (ie a bottom therein) can propagate to the result of the
305 function call; that is, whether the specified demand can {\em
306 possibly} hit poison.
309 evalAbsence (WwLazy True) _ = False -- Can't possibly hit poison
310 -- with Absent demand
312 evalAbsence (WwUnpack _ demand_info) val
314 AbsTop -> False -- No poison in here
315 AbsBot -> True -- Pure poison
316 AbsProd vals -> or (zipWithEqual "evalAbsence" evalAbsence demand_info vals)
317 _ -> panic "evalAbsence: other"
319 evalAbsence other val = anyBot val
320 -- The demand is conservative; even "Lazy" *might* evaluate the
321 -- argument arbitrarily so we have to look everywhere for poison
324 %************************************************************************
326 \subsection[absEval]{Evaluate an expression in the abstract domain}
328 %************************************************************************
331 -- The isBottomingId stuf is now dealt with via the Id's strictness info
332 -- absId anal var env | isBottomingId var
334 -- StrAnal -> AbsBot -- See discussion below
335 -- AbsAnal -> AbsTop -- Just want to see if there's any poison in
339 = case (lookupAbsValEnv env var,
340 isDataConId_maybe var,
342 maybeUnfoldingTemplate (idUnfolding var)) of
344 (Just abs_val, _, _, _) ->
345 abs_val -- Bound in the environment
347 (_, Just data_con, _, _) | isProductTyCon tycon &&
348 not (isRecursiveTyCon tycon)
349 -> -- A product. We get infinite loops if we don't
350 -- check for recursive products!
351 -- The strictness info on the constructor
352 -- isn't expressive enough to contain its abstract value
353 productAbsVal (dataConRepArgTys data_con) []
355 tycon = dataConTyCon data_con
357 (_, _, NoStrictnessInfo, Just unfolding) ->
358 -- We have an unfolding for the expr
359 -- Assume the unfolding has no free variables since it
360 -- came from inside the Id
361 absEval anal unfolding env
362 -- Notice here that we only look in the unfolding if we don't
363 -- have strictness info (an unusual situation).
364 -- We could have chosen to look in the unfolding if it exists,
365 -- and only try the strictness info if it doesn't, and that would
366 -- give more accurate results, at the cost of re-abstract-interpreting
367 -- the unfolding every time.
368 -- We found only one place where the look-at-unfolding-first
369 -- method gave better results, which is in the definition of
370 -- showInt in the Prelude. In its defintion, fromIntegral is
371 -- not inlined (it's big) but ab-interp-ing its unfolding gave
372 -- a better result than looking at its strictness only.
373 -- showInt :: Integral a => a -> [Char] -> [Char]
374 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
375 -- "U(U(U(U(SA)AAAAAAAAL)AA)AAAAASAAASA)" {...} _N_ _N_ #-}
377 -- showInt :: Integral a => a -> [Char] -> [Char]
378 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
379 -- "U(U(U(U(SL)LLLLLLLLL)LL)LLLLLSLLLLL)" _N_ _N_ #-}
382 (_, _, strictness_info, _) ->
383 -- Includes NoUnfolding
384 -- Try the strictness info
385 absValFromStrictness anal strictness_info
387 productAbsVal [] rev_abs_args = AbsProd (reverse rev_abs_args)
388 productAbsVal (arg_ty : arg_tys) rev_abs_args = AbsFun arg_ty (\ abs_arg -> productAbsVal arg_tys (abs_arg : rev_abs_args))
392 absEval :: AnalysisKind -> CoreExpr -> AbsValEnv -> AbsVal
394 absEval anal (Type ty) env = AbsTop
395 absEval anal (Var var) env = absId anal var env
398 Discussion about error (following/quoting Lennart): Any expression
399 'error e' is regarded as bottom (with HBC, with the -ffail-strict
402 Regarding it as bottom gives much better strictness properties for
406 f (x:xs) y = f xs (x+y)
408 f [] _ = error "no match"
410 f (x:xs) y = f xs (x+y)
412 is strict in y, which you really want. But, it may lead to
413 transformations that turn a call to \tr{error} into non-termination.
414 (The odds of this happening aren't good.)
416 Things are a little different for absence analysis, because we want
417 to make sure that any poison (?????)
420 absEval anal (Lit _) env = AbsTop
421 -- Literals terminate (strictness) and are not poison (absence)
425 absEval anal (Lam bndr body) env
426 | isTyVar bndr = absEval anal body env -- Type lambda
427 | otherwise = AbsFun (idType bndr) abs_fn -- Value lambda
429 abs_fn arg = absEval anal body (addOneToAbsValEnv env bndr arg)
431 absEval anal (App expr (Type ty)) env
432 = absEval anal expr env -- Type appplication
433 absEval anal (App f val_arg) env
434 = absApply anal (absEval anal f env) -- Value applicationn
435 (absEval anal val_arg env)
439 absEval anal expr@(Case scrut case_bndr alts) env
441 scrut_val = absEval anal scrut env
442 alts_env = addOneToAbsValEnv env case_bndr scrut_val
444 case (scrut_val, alts) of
445 (AbsBot, _) -> AbsBot
447 (AbsProd arg_vals, [(con, bndrs, rhs)])
449 -- The scrutinee is a product value, so it must be of a single-constr
450 -- type; so the constructor in this alternative must be the right one
451 -- so we can go ahead and bind the constructor args to the components
452 -- of the product value.
453 ASSERT(length arg_vals == length val_bndrs)
454 absEval anal rhs rhs_env
456 val_bndrs = filter isId bndrs
457 rhs_env = growAbsValEnvList alts_env (val_bndrs `zip` arg_vals)
459 other -> absEvalAlts anal alts alts_env
462 For @Lets@ we widen the value we get. This is nothing to
463 do with fixpointing. The reason is so that we don't get an explosion
464 in the amount of computation. For example, consider:
476 If we bind @f@ and @g@ to their exact abstract value, then we'll
477 ``execute'' one call to @f@ and {\em two} calls to @g@. This can blow
478 up exponentially. Widening cuts it off by making a fixed
479 approximation to @f@ and @g@, so that the bodies of @f@ and @g@ are
480 not evaluated again at all when they are called.
482 Of course, this can lose useful joint strictness, which is sad. An
483 alternative approach would be to try with a certain amount of ``fuel''
484 and be prepared to bale out.
487 absEval anal (Let (NonRec binder e1) e2) env
489 new_env = addOneToAbsValEnv env binder (widen anal (absEval anal e1 env))
491 -- The binder of a NonRec should *not* be of unboxed type,
492 -- hence no need to strictly evaluate the Rhs.
493 absEval anal e2 new_env
495 absEval anal (Let (Rec pairs) body) env
497 (binders,rhss) = unzip pairs
498 rhs_vals = cheapFixpoint anal binders rhss env -- Returns widened values
499 new_env = growAbsValEnvList env (binders `zip` rhs_vals)
501 absEval anal body new_env
503 absEval anal (Note note expr) env = absEval anal expr env
507 absEvalAlts :: AnalysisKind -> [CoreAlt] -> AbsValEnv -> AbsVal
508 absEvalAlts anal alts env
509 = combine anal (map go alts)
511 combine StrAnal = foldr1 lub -- Diverge only if all diverge
512 combine AbsAnal = foldr1 glb -- Find any poison
515 = absEval anal rhs rhs_env
517 rhs_env = growAbsValEnvList env (filter isId bndrs `zip` repeat AbsTop)
520 %************************************************************************
522 \subsection[absApply]{Apply an abstract function to an abstract argument}
524 %************************************************************************
529 absApply :: AnalysisKind -> AbsVal -> AbsVal -> AbsVal
531 absApply anal AbsBot arg = AbsBot
532 -- AbsBot represents the abstract bottom *function* too
534 absApply StrAnal AbsTop arg = AbsTop
535 absApply AbsAnal AbsTop arg = if anyBot arg
538 -- To be conservative, we have to assume that a function about
539 -- which we know nothing (AbsTop) might look at some part of
543 An @AbsFun@ with only one more argument needed---bind it and eval the
544 result. A @Lam@ with two or more args: return another @AbsFun@ with
545 an augmented environment.
548 absApply anal (AbsFun bndr_ty abs_fn) arg = abs_fn arg
552 absApply StrAnal (AbsApproxFun (d:ds) val) arg
555 other -> AbsApproxFun ds val' -- Result is non-bot if there are still args
557 val' | evalStrictness d arg = AbsBot
560 absApply AbsAnal (AbsApproxFun (d:ds) val) arg
561 = if evalAbsence d arg
562 then AbsBot -- Poison in arg means poison in the application
565 other -> AbsApproxFun ds val
568 absApply anal f@(AbsProd _) arg
569 = pprPanic ("absApply: Duff function: AbsProd." ++ show anal) ((ppr f) <+> (ppr arg))
576 %************************************************************************
578 \subsection[findStrictness]{Determine some binders' strictness}
580 %************************************************************************
584 -> AbsVal -- Abstract strictness value of function
585 -> AbsVal -- Abstract absence value of function
586 -> StrictnessInfo -- Resulting strictness annotation
588 findStrictness id (AbsApproxFun str_ds str_res) (AbsApproxFun abs_ds _)
589 -- You might think there's really no point in describing detailed
590 -- strictness for a divergent function;
591 -- If it's fully applied we get bottom regardless of the
592 -- argument. If it's not fully applied we don't get bottom.
593 -- Finally, we don't want to regard the args of a divergent function
594 -- as 'interesting' for inlining purposes (see Simplify.prepareArgs)
596 -- HOWEVER, if we make diverging functions appear lazy, they
597 -- don't get wrappers, and then we get dreadful reboxing.
598 -- See notes with WwLib.worthSplitting
599 = find_strictness id str_ds str_res abs_ds
601 findStrictness id str_val abs_val
602 | isBot str_val = mkStrictnessInfo ([], True)
603 | otherwise = NoStrictnessInfo
605 -- The list of absence demands passed to combineDemands
606 -- can be shorter than the list of absence demands
608 -- lookup = \ dEq -> letrec {
609 -- lookup = \ key ds -> ...lookup...
612 -- Here the strictness value takes three args, but the absence value
613 -- takes only one, for reasons I don't quite understand (see cheapFixpoint)
615 find_strictness id orig_str_ds orig_str_res orig_abs_ds
616 = mkStrictnessInfo (go orig_str_ds orig_abs_ds, res_bot)
618 res_bot = isBot orig_str_res
620 go str_ds abs_ds = zipWith mk_dmd str_ds (abs_ds ++ repeat wwLazy)
622 mk_dmd str_dmd (WwLazy True)
623 = WARN( not (res_bot || isLazy str_dmd),
624 ppr id <+> ppr orig_str_ds <+> ppr orig_abs_ds )
625 -- If the arg isn't used we jolly well don't expect the function
626 -- to be strict in it. Unless the function diverges.
627 WwLazy True -- Best of all
629 mk_dmd (WwUnpack u str_ds)
630 (WwUnpack _ abs_ds) = WwUnpack u (go str_ds abs_ds)
632 mk_dmd str_dmd abs_dmd = str_dmd
637 findDemand dmd str_env abs_env expr binder
638 = findRecDemand str_fn abs_fn (idType binder)
640 str_fn val = evalStrictness dmd (absEval StrAnal expr (addOneToAbsValEnv str_env binder val))
641 abs_fn val = not (evalAbsence dmd (absEval AbsAnal expr (addOneToAbsValEnv abs_env binder val)))
643 findDemandAlts dmd str_env abs_env alts binder
644 = findRecDemand str_fn abs_fn (idType binder)
646 str_fn val = evalStrictness dmd (absEvalAlts StrAnal alts (addOneToAbsValEnv str_env binder val))
647 abs_fn val = not (evalAbsence dmd (absEvalAlts AbsAnal alts (addOneToAbsValEnv abs_env binder val)))
650 @findRecDemand@ is where we finally convert strictness/absence info
651 into ``Demands'' which we can pin on Ids (etc.).
653 NOTE: What do we do if something is {\em both} strict and absent?
654 Should \tr{f x y z = error "foo"} says that \tr{f}'s arguments are all
655 strict (because of bottoming effect of \tr{error}) or all absent
656 (because they're not used)?
658 Well, for practical reasons, we prefer absence over strictness. In
659 particular, it makes the ``default defaults'' for class methods (the
660 ones that say \tr{defm.foo dict = error "I don't exist"}) come out
661 nicely [saying ``the dict isn't used''], rather than saying it is
662 strict in every component of the dictionary [massive gratuitious
663 casing to take the dict apart].
665 But you could have examples where going for strictness would be better
666 than absence. Consider:
668 let x = something big
673 If \tr{x} is marked absent in \tr{f}, but not strict, and \tr{g} is
674 lazy, then the thunk for \tr{x} will be built. If \tr{f} was strict,
675 then we'd let-to-case it:
677 case something big of
683 findRecDemand :: (AbsVal -> Bool) -- True => function applied to this value yields Bot
684 -> (AbsVal -> Bool) -- True => function applied to this value yields no poison
685 -> Type -- The type of the argument
688 findRecDemand str_fn abs_fn ty
689 = if isUnLiftedType ty then -- It's a primitive type!
692 else if abs_fn AbsBot then -- It's absent
693 -- We prefer absence over strictness: see NOTE above.
696 else if not (opt_AllStrict ||
697 (opt_NumbersStrict && is_numeric_type ty) ||
699 WwLazy False -- It's not strict and we're not pretending
701 else -- It's strict (or we're pretending it is)!
703 case splitProductType_maybe ty of
705 Nothing -> wwStrict -- Could have a test for wwEnum, but
706 -- we don't exploit it yet, so don't bother
708 Just (tycon,_,data_con,cmpnt_tys) -- Single constructor case
709 | isRecursiveTyCon tycon -- Recursive data type; don't unpack
710 -> wwStrict -- (this applies to newtypes too:
711 -- e.g. data Void = MkVoid Void)
713 | null compt_strict_infos -- A nullary data type
716 | otherwise -- Some other data type
717 -> wwUnpack compt_strict_infos
720 prod_len = length cmpnt_tys
724 str_fn (mkMainlyTopProd prod_len i cmpnt_val)
727 abs_fn (mkMainlyTopProd prod_len i cmpnt_val)
730 | (cmpnt_ty, i) <- cmpnt_tys `zip` [1..] ]
734 = case (splitTyConApp_maybe ty) of -- NB: duplicates stuff done above
736 Just (tycon, _) -> tyConUnique tycon `is_elem` numericTyKeys
738 is_elem = isIn "is_numeric_type"
740 -- mkMainlyTopProd: make an AbsProd that is all AbsTops ("n"-1 of
741 -- them) except for a given value in the "i"th position.
743 mkMainlyTopProd :: Int -> Int -> AbsVal -> AbsVal
745 mkMainlyTopProd n i val
747 befores = nOfThem (i-1) AbsTop
748 afters = nOfThem (n-i) AbsTop
750 AbsProd (befores ++ (val : afters))
753 %************************************************************************
755 \subsection[fixpoint]{Fixpointer for the strictness analyser}
757 %************************************************************************
759 The @fixpoint@ functions take a list of \tr{(binder, expr)} pairs, an
760 environment, and returns the abstract value of each binder.
762 The @cheapFixpoint@ function makes a conservative approximation,
763 by binding each of the variables to Top in their own right hand sides.
764 That allows us to make rapid progress, at the cost of a less-than-wonderful
768 cheapFixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
770 cheapFixpoint AbsAnal [id] [rhs] env
771 = [crudeAbsWiden (absEval AbsAnal rhs new_env)]
773 new_env = addOneToAbsValEnv env id AbsTop -- Unsafe starting point!
774 -- In the just-one-binding case, we guarantee to
775 -- find a fixed point in just one iteration,
776 -- because we are using only a two-point domain.
777 -- This improves matters in cases like:
779 -- f x y = letrec g = ...g...
782 -- Here, y isn't used at all, but if g is bound to
783 -- AbsBot we simply get AbsBot as the next
786 cheapFixpoint anal ids rhss env
787 = [widen anal (absEval anal rhs new_env) | rhs <- rhss]
788 -- We do just one iteration, starting from a safe
789 -- approximation. This won't do a good job in situations
791 -- \x -> letrec f = ...g...
795 -- Here, f will end up bound to Top after one iteration,
796 -- and hence we won't spot the strictness in x.
797 -- (A second iteration would solve this. ToDo: try the effect of
798 -- really searching for a fixed point.)
800 new_env = growAbsValEnvList env [(id,safe_val) | id <- ids]
803 = case anal of -- The safe starting point
809 fixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
811 fixpoint anal [] _ env = []
813 fixpoint anal ids rhss env
814 = fix_loop initial_vals
817 = case anal of -- The (unsafe) starting point
820 -- At one stage for StrAnal we said:
821 -- if (returnsRealWorld (idType id))
822 -- then AbsTop -- this is a massively horrible hack (SLPJ 95/05)
823 -- but no one has the foggiest idea what this hack did,
824 -- and returnsRealWorld was a stub that always returned False
825 -- So this comment is all that is left of the hack!
827 initial_vals = [ initial_val id | id <- ids ]
829 fix_loop :: [AbsVal] -> [AbsVal]
831 fix_loop current_widened_vals
833 new_env = growAbsValEnvList env (ids `zip` current_widened_vals)
834 new_vals = [ absEval anal rhs new_env | rhs <- rhss ]
835 new_widened_vals = map (widen anal) new_vals
837 if (and (zipWith sameVal current_widened_vals new_widened_vals)) then
840 -- NB: I was too chicken to make that a zipWithEqual,
841 -- lest I jump into a black hole. WDP 96/02
843 -- Return the widened values. We might get a slightly
844 -- better value by returning new_vals (which we used to
845 -- do, see below), but alas that means that whenever the
846 -- function is called we have to re-execute it, which is
851 -- Return the un-widened values which may be a bit better
852 -- than the widened ones, and are guaranteed safe, since
853 -- they are one iteration beyond current_widened_vals,
854 -- which itself is a fixed point.
856 fix_loop new_widened_vals
859 For absence analysis, we make do with a very very simple approach:
860 look for convergence in a two-point domain.
862 We used to use just one iteration, starting with the variables bound
863 to @AbsBot@, which is safe.
865 Prior to that, we used one iteration starting from @AbsTop@ (which
866 isn't safe). Why isn't @AbsTop@ safe? Consider:
874 Here, if p is @AbsBot@, then we'd better {\em not} end up with a ``fixed
875 point'' of @d@ being @(AbsTop, AbsTop)@! An @AbsBot@ initial value is
876 safe because it gives poison more often than really necessary, and
877 thus may miss some absence, but will never claim absence when it ain't
880 Anyway, one iteration starting with everything bound to @AbsBot@ give
885 Here, f would always end up bound to @AbsBot@, which ain't very
886 clever, because then it would introduce poison whenever it was
887 applied. Much better to start with f bound to @AbsTop@, and widen it
888 to @AbsBot@ if any poison shows up. In effect we look for convergence
889 in the two-point @AbsTop@/@AbsBot@ domain.
891 What we miss (compared with the cleverer strictness analysis) is
892 spotting that in this case
894 f = \ x y -> ...y...(f x y')...
896 \tr{x} is actually absent, since it is only passed round the loop, never
897 used. But who cares about missing that?
899 NB: despite only having a two-point domain, we may still have many
900 iterations, because there are several variables involved at once.