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 dataConSig, 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 PrelInfo ( intTyCon, integerTyCon, doubleTyCon,
34 floatTyCon, wordTyCon, addrTyCon
36 import Pretty ( ppStr )
37 import PrimOp ( PrimOp(..) )
39 import TyCon ( maybeTyConSingleCon, isEnumerationTyCon,
42 import Type ( maybeAppDataTyCon, isPrimType )
43 import Util ( isIn, isn'tIn, nOfThem, zipWithEqual,
44 pprTrace, panic, pprPanic, assertPanic
47 returnsRealWorld = 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 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 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 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 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 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, LitForm _) ->
397 AbsTop -- Literals all terminate, and have no poison
399 (Nothing, NoStrictnessInfo, ConForm _ _) ->
400 AbsTop -- An imported constructor won't have
401 -- bottom components, nor poison!
403 (Nothing, NoStrictnessInfo, GenForm _ _ unfolding _) ->
404 -- We have an unfolding for the expr
405 -- Assume the unfolding has no free variables since it
406 -- came from inside the Id
407 absEval anal (unTagBinders unfolding) env
408 -- Notice here that we only look in the unfolding if we don't
409 -- have strictness info (an unusual situation).
410 -- We could have chosen to look in the unfolding if it exists,
411 -- and only try the strictness info if it doesn't, and that would
412 -- give more accurate results, at the cost of re-abstract-interpreting
413 -- the unfolding every time.
414 -- We found only one place where the look-at-unfolding-first
415 -- method gave better results, which is in the definition of
416 -- showInt in the Prelude. In its defintion, fromIntegral is
417 -- not inlined (it's big) but ab-interp-ing its unfolding gave
418 -- a better result than looking at its strictness only.
419 -- showInt :: Integral a => a -> [Char] -> [Char]
420 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
421 -- "U(U(U(U(SA)AAAAAAAAL)AA)AAAAASAAASA)" {...} _N_ _N_ #-}
423 -- showInt :: Integral a => a -> [Char] -> [Char]
424 -- ! {-# GHC_PRAGMA _A_ 1 _U_ 122 _S_
425 -- "U(U(U(U(SL)LLLLLLLLL)LL)LLLLLSLLLLL)" _N_ _N_ #-}
428 (Nothing, strictness_info, _) ->
429 -- Includes MagicForm, IWantToBeINLINEd, NoUnfoldingDetails
430 -- Try the strictness info
431 absValFromStrictness anal strictness_info
434 -- Done via strictness now
435 -- GenForm _ BottomForm _ _ -> AbsBot
437 -- pprTrace "absId:" (ppBesides [ppr PprDebug var, ppStr "=:", pp_anal anal, ppStr ":=",ppr PprDebug result]) (
441 pp_anal StrAnal = ppStr "STR"
442 pp_anal AbsAnal = ppStr "ABS"
444 absEvalAtom anal (VarArg v) env = absId anal v env
445 absEvalAtom anal (LitArg _) env = AbsTop
449 absEval :: AnalysisKind -> CoreExpr -> AbsValEnv -> AbsVal
451 absEval anal (Var var) env = absId anal var env
453 absEval anal (Lit _) env = AbsTop
454 -- What if an unboxed literal? That's OK: it terminates, so its
455 -- abstract value is AbsTop.
457 -- For absence analysis, a literal certainly isn't the "poison" variable
460 Discussion about \tr{error} (following/quoting Lennart): Any expression
461 \tr{error e} is regarded as bottom (with HBC, with the
462 \tr{-ffail-strict} flag, on with \tr{-O}).
464 Regarding it as bottom gives much better strictness properties for
468 f (x:xs) y = f xs (x+y)
470 f [] _ = error "no match"
472 f (x:xs) y = f xs (x+y)
474 is strict in \tr{y}, which you really want. But, it may lead to
475 transformations that turn a call to \tr{error} into non-termination.
476 (The odds of this happening aren't good.)
479 Things are a little different for absence analysis, because we want
480 to make sure that any poison (?????)
483 absEval StrAnal (Prim SeqOp [TyArg _, e]) env
485 if isBot (absEvalAtom StrAnal e env) then AbsBot else AbsTop
486 -- This is a special case to ensure that seq# is strict in its argument.
487 -- The comments below (for most normal PrimOps) do not apply.
489 absEval StrAnal (Prim op es) env = AbsTop
490 -- The arguments are all of unboxed type, so they will already
491 -- have been eval'd. If the boxed version was bottom, we'll
492 -- already have returned bottom.
494 -- Actually, I believe we are saying that either (1) the
495 -- primOp uses unboxed args and they've been eval'ed, so
496 -- there's no need to force strictness here, _or_ the primOp
497 -- uses boxed args and we don't know whether or not it's
498 -- strict, so we assume laziness. (JSM)
500 absEval AbsAnal (Prim op as) env
501 = if any anyBot [absEvalAtom AbsAnal a env | a <- as, isValArg a]
504 -- For absence analysis, we want to see if the poison shows up...
506 absEval anal (Con con as) env
508 = AbsProd [absEvalAtom anal a env | a <- as, isValArg a]
510 | otherwise -- Not single-constructor
512 StrAnal -> -- Strictness case: it's easy: it certainly terminates
514 AbsAnal -> -- In the absence case we need to be more
515 -- careful: look to see if there's any
516 -- poison in the components
517 if any anyBot [absEvalAtom AbsAnal a env | a <- as, isValArg a]
521 (_,_,_, tycon) = dataConSig con
522 has_single_con = maybeToBool (maybeTyConSingleCon tycon)
526 absEval anal (Lam (ValBinder binder) body) env
527 = AbsFun [binder] body env
528 absEval anal (Lam other_binder expr) env
529 = absEval anal expr env
530 absEval anal (App f a) env | isValArg a
531 = absApply anal (absEval anal f env) (absEvalAtom anal a env)
532 absEval anal (App expr _) env
533 = absEval anal expr env
536 For primitive cases, just GLB the branches, then LUB with the expr part.
539 absEval anal (Case expr (PrimAlts alts deflt)) env
541 expr_val = absEval anal expr env
542 abs_alts = [ absEval anal rhs env | (_, rhs) <- alts ]
543 -- Don't bother to extend envt, because unbound vars
544 -- default to the conservative AbsTop
546 abs_deflt = absEvalDefault anal expr_val deflt env
548 combineCaseValues anal expr_val
549 (abs_deflt ++ abs_alts)
551 absEval anal (Case expr (AlgAlts alts deflt)) env
553 expr_val = absEval anal expr env
554 abs_alts = [ absEvalAlgAlt anal expr_val alt env | alt <- alts ]
555 abs_deflt = absEvalDefault anal expr_val deflt env
559 combineCaseValues anal expr_val
560 (abs_deflt ++ abs_alts)
565 _ -> 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)))
571 For @Lets@ we widen the value we get. This is nothing to
572 do with fixpointing. The reason is so that we don't get an explosion
573 in the amount of computation. For example, consider:
585 If we bind @f@ and @g@ to their exact abstract value, then we'll
586 ``execute'' one call to @f@ and {\em two} calls to @g@. This can blow
587 up exponentially. Widening cuts it off by making a fixed
588 approximation to @f@ and @g@, so that the bodies of @f@ and @g@ are
589 not evaluated again at all when they are called.
591 Of course, this can lose useful joint strictness, which is sad. An
592 alternative approach would be to try with a certain amount of ``fuel''
593 and be prepared to bale out.
596 absEval anal (Let (NonRec binder e1) e2) env
598 new_env = addOneToAbsValEnv env binder (widen anal (absEval anal e1 env))
600 -- The binder of a NonRec should *not* be of unboxed type,
601 -- hence no need to strictly evaluate the Rhs.
602 absEval anal e2 new_env
604 absEval anal (Let (Rec pairs) body) env
606 (binders,rhss) = unzip pairs
607 rhs_vals = cheapFixpoint anal binders rhss env -- Returns widened values
608 new_env = growAbsValEnvList env (binders `zip` rhs_vals)
610 absEval anal body new_env
612 absEval anal (SCC cc expr) env = absEval anal expr env
613 absEval anal (Coerce c ty expr) env = absEval anal expr env
617 absEvalAlgAlt :: AnalysisKind -> AbsVal -> (Id,[Id],CoreExpr) -> AbsValEnv -> AbsVal
619 absEvalAlgAlt anal (AbsProd arg_vals) (con, args, rhs) env
620 = -- The scrutinee is a product value, so it must be of a single-constr
621 -- type; so the constructor in this alternative must be the right one
622 -- so we can go ahead and bind the constructor args to the components
623 -- of the product value.
624 ASSERT(length arg_vals == length args)
626 new_env = growAbsValEnvList env (args `zip` arg_vals)
628 absEval anal rhs new_env
630 absEvalAlgAlt anal other_scrutinee (con, args, rhs) env
631 = -- Scrutinised value is Top or Bot (it can't be a function!)
632 -- So just evaluate the rhs with all constr args bound to Top.
633 -- (If the scrutinee is Top we'll never evaluated this function
639 = case other_scrutinee of {
640 AbsTop -> True; -- i.e., OK
641 AbsBot -> True; -- ditto
642 _ -> False -- party over
646 absEvalDefault :: AnalysisKind
647 -> AbsVal -- Value of scrutinee
650 -> [AbsVal] -- Empty or singleton
652 absEvalDefault anal scrut_val NoDefault env = []
653 absEvalDefault anal scrut_val (BindDefault binder expr) env
654 = [absEval anal expr (addOneToAbsValEnv env binder scrut_val)]
657 %************************************************************************
659 \subsection[absApply]{Apply an abstract function to an abstract argument}
661 %************************************************************************
666 absApply :: AnalysisKind -> AbsVal -> AbsVal -> AbsVal
668 absApply anal AbsBot arg = AbsBot
669 -- AbsBot represents the abstract bottom *function* too
671 absApply StrAnal AbsTop arg = AbsTop
672 absApply AbsAnal AbsTop arg = if anyBot arg
675 -- To be conservative, we have to assume that a function about
676 -- which we know nothing (AbsTop) might look at some part of
680 An @AbsFun@ with only one more argument needed---bind it and eval the
681 result. A @Lam@ with two or more args: return another @AbsFun@ with
682 an augmented environment.
685 absApply anal (AbsFun [binder] body env) arg
686 = absEval anal body (addOneToAbsValEnv env binder arg)
688 absApply anal (AbsFun (binder:bs) body env) arg
689 = AbsFun bs body (addOneToAbsValEnv env binder arg)
693 absApply StrAnal (AbsApproxFun (arg1_demand:ds)) arg
694 = if evalStrictness arg1_demand arg
698 other -> AbsApproxFun ds
700 absApply AbsAnal (AbsApproxFun (arg1_demand:ds)) arg
701 = if evalAbsence arg1_demand arg
705 other -> AbsApproxFun ds
708 absApply anal (AbsApproxFun []) arg = panic ("absApply: Duff function: AbsApproxFun." ++ show anal)
709 absApply anal (AbsFun [] _ _) arg = panic ("absApply: Duff function: AbsFun." ++ show anal)
710 absApply anal (AbsProd _) arg = panic ("absApply: Duff function: AbsProd." ++ show anal)
717 %************************************************************************
719 \subsection[findStrictness]{Determine some binders' strictness}
721 %************************************************************************
723 @findStrictness@ applies the function \tr{\ ids -> expr} to
724 \tr{[bot,top,top,...]}, \tr{[top,bot,top,top,...]}, etc., (i.e., once
725 with @AbsBot@ in each argument position), and evaluates the resulting
726 abstract value; it returns a vector of @Demand@s saying whether the
727 result of doing this is guaranteed to be bottom. This tells the
728 strictness of the function in each of the arguments.
730 If an argument is of unboxed type, then we declare that function to be
731 strict in that argument.
733 We don't really have to make up all those lists of mostly-@AbsTops@;
734 unbound variables in an @AbsValEnv@ are implicitly mapped to that.
736 See notes on @addStrictnessInfoToId@.
739 findStrictness :: StrAnalFlags
740 -> [Type] -- Types of args in which strictness is wanted
741 -> AbsVal -- Abstract strictness value of function
742 -> AbsVal -- Abstract absence value of function
743 -> [Demand] -- Resulting strictness annotation
745 findStrictness strflags [] str_val abs_val = []
747 findStrictness strflags (ty:tys) str_val abs_val
749 demand = findRecDemand strflags [] str_fn abs_fn ty
750 str_fn val = absApply StrAnal str_val val
751 abs_fn val = absApply AbsAnal abs_val val
753 demands = findStrictness strflags tys
754 (absApply StrAnal str_val AbsTop)
755 (absApply AbsAnal abs_val AbsTop)
762 findDemandStrOnly str_env expr binder -- Only strictness environment available
763 = findRecDemand strflags [] str_fn abs_fn (idType binder)
765 str_fn val = absEval StrAnal expr (addOneToAbsValEnv str_env binder val)
766 abs_fn val = AbsBot -- Always says poison; so it looks as if
767 -- nothing is absent; safe
768 strflags = getStrAnalFlags str_env
770 findDemandAbsOnly abs_env expr binder -- Only absence environment available
771 = findRecDemand strflags [] str_fn abs_fn (idType binder)
773 str_fn val = AbsBot -- Always says non-termination;
774 -- that'll make findRecDemand peer into the
775 -- structure of the value.
776 abs_fn val = absEval AbsAnal expr (addOneToAbsValEnv abs_env binder val)
777 strflags = getStrAnalFlags abs_env
780 findDemand str_env abs_env expr binder
781 = findRecDemand strflags [] str_fn abs_fn (idType binder)
783 str_fn val = absEval StrAnal expr (addOneToAbsValEnv str_env binder val)
784 abs_fn val = absEval AbsAnal expr (addOneToAbsValEnv abs_env binder val)
785 strflags = getStrAnalFlags str_env
788 @findRecDemand@ is where we finally convert strictness/absence info
789 into ``Demands'' which we can pin on Ids (etc.).
791 NOTE: What do we do if something is {\em both} strict and absent?
792 Should \tr{f x y z = error "foo"} says that \tr{f}'s arguments are all
793 strict (because of bottoming effect of \tr{error}) or all absent
794 (because they're not used)?
796 Well, for practical reasons, we prefer absence over strictness. In
797 particular, it makes the ``default defaults'' for class methods (the
798 ones that say \tr{defm.foo dict = error "I don't exist"}) come out
799 nicely [saying ``the dict isn't used''], rather than saying it is
800 strict in every component of the dictionary [massive gratuitious
801 casing to take the dict apart].
803 But you could have examples where going for strictness would be better
804 than absence. Consider:
806 let x = something big
811 If \tr{x} is marked absent in \tr{f}, but not strict, and \tr{g} is
812 lazy, then the thunk for \tr{x} will be built. If \tr{f} was strict,
813 then we'd let-to-case it:
815 case something big of
821 findRecDemand :: StrAnalFlags
822 -> [TyCon] -- TyCons already seen; used to avoid
823 -- zooming into recursive types
824 -> (AbsVal -> AbsVal) -- The strictness function
825 -> (AbsVal -> AbsVal) -- The absence function
826 -> Type -- The type of the argument
829 findRecDemand strflags seen str_fn abs_fn ty
830 = if isPrimType ty then -- It's a primitive type!
833 else if not (anyBot (abs_fn AbsBot)) then -- It's absent
834 -- We prefer absence over strictness: see NOTE above.
837 else if not (all_strict ||
838 (num_strict && is_numeric_type ty) ||
839 (isBot (str_fn AbsBot))) then
840 WwLazy False -- It's not strict and we're not pretending
842 else -- It's strict (or we're pretending it is)!
844 case maybeAppDataTyCon ty of
848 Just (tycon,tycon_arg_tys,[data_con]) | tycon `not_elem` seen ->
849 -- Single constructor case, tycon not already seen higher up
851 cmpnt_tys = dataConArgTys data_con tycon_arg_tys
852 prod_len = length cmpnt_tys
855 = [ findRecDemand strflags (tycon:seen)
857 str_fn (mkMainlyTopProd prod_len i cmpnt_val)
860 abs_fn (mkMainlyTopProd prod_len i cmpnt_val)
863 | (cmpnt_ty, i) <- cmpnt_tys `zip` [1..] ]
865 if null compt_strict_infos then
866 if isEnumerationTyCon tycon then wwEnum else wwStrict
868 wwUnpack compt_strict_infos
870 not_elem = isn'tIn "findRecDemand"
873 -- Multi-constr data types, *or* an abstract data
874 -- types, *or* things we don't have a way of conveying
875 -- the info over module boundaries (class ops,
876 -- superdict sels, dfns).
877 if isEnumerationTyCon tycon then
882 (all_strict, num_strict) = strflags
885 = case (maybeAppDataTyCon ty) of -- NB: duplicates stuff done above
889 [intTyCon, integerTyCon,
890 doubleTyCon, floatTyCon,
891 wordTyCon, addrTyCon]
893 _{-something else-} -> False
895 is_elem = isIn "is_numeric_type"
897 -- mkMainlyTopProd: make an AbsProd that is all AbsTops ("n"-1 of
898 -- them) except for a given value in the "i"th position.
900 mkMainlyTopProd :: Int -> Int -> AbsVal -> AbsVal
902 mkMainlyTopProd n i val
904 befores = nOfThem (i-1) AbsTop
905 afters = nOfThem (n-i) AbsTop
907 AbsProd (befores ++ (val : afters))
910 %************************************************************************
912 \subsection[fixpoint]{Fixpointer for the strictness analyser}
914 %************************************************************************
916 The @fixpoint@ functions take a list of \tr{(binder, expr)} pairs, an
917 environment, and returns the abstract value of each binder.
919 The @cheapFixpoint@ function makes a conservative approximation,
920 by binding each of the variables to Top in their own right hand sides.
921 That allows us to make rapid progress, at the cost of a less-than-wonderful
925 cheapFixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
927 cheapFixpoint AbsAnal [id] [rhs] env
928 = [crudeAbsWiden (absEval AbsAnal rhs new_env)]
930 new_env = addOneToAbsValEnv env id AbsTop -- Unsafe starting point!
931 -- In the just-one-binding case, we guarantee to
932 -- find a fixed point in just one iteration,
933 -- because we are using only a two-point domain.
934 -- This improves matters in cases like:
936 -- f x y = letrec g = ...g...
939 -- Here, y isn't used at all, but if g is bound to
940 -- AbsBot we simply get AbsBot as the next
943 cheapFixpoint anal ids rhss env
944 = [widen anal (absEval anal rhs new_env) | rhs <- rhss]
945 -- We do just one iteration, starting from a safe
946 -- approximation. This won't do a good job in situations
948 -- \x -> letrec f = ...g...
952 -- Here, f will end up bound to Top after one iteration,
953 -- and hence we won't spot the strictness in x.
954 -- (A second iteration would solve this. ToDo: try the effect of
955 -- really searching for a fixed point.)
957 new_env = growAbsValEnvList env [(id,safe_val) | id <- ids]
960 = case anal of -- The safe starting point
966 mkLookupFun :: (key -> key -> Bool) -- Equality predicate
967 -> (key -> key -> Bool) -- Less-than predicate
968 -> [(key,val)] -- The assoc list
970 -> Maybe val -- The corresponding value
972 mkLookupFun eq lt alist s
973 = case [a | (s',a) <- alist, s' `eq` s] of
979 fixpoint :: AnalysisKind -> [Id] -> [CoreExpr] -> AbsValEnv -> [AbsVal]
981 fixpoint anal [] _ env = []
983 fixpoint anal ids rhss env
984 = fix_loop initial_vals
987 = case anal of -- The (unsafe) starting point
988 StrAnal -> if (returnsRealWorld (idType id))
989 then AbsTop -- this is a massively horrible hack (SLPJ 95/05)
993 initial_vals = [ initial_val id | id <- ids ]
995 fix_loop :: [AbsVal] -> [AbsVal]
997 fix_loop current_widened_vals
999 new_env = growAbsValEnvList env (ids `zip` current_widened_vals)
1000 new_vals = [ absEval anal rhs new_env | rhs <- rhss ]
1001 new_widened_vals = map (widen anal) new_vals
1003 if (and (zipWith sameVal current_widened_vals new_widened_vals)) then
1004 current_widened_vals
1006 -- NB: I was too chicken to make that a zipWithEqual,
1007 -- lest I jump into a black hole. WDP 96/02
1009 -- Return the widened values. We might get a slightly
1010 -- better value by returning new_vals (which we used to
1011 -- do, see below), but alas that means that whenever the
1012 -- function is called we have to re-execute it, which is
1017 -- Return the un-widened values which may be a bit better
1018 -- than the widened ones, and are guaranteed safe, since
1019 -- they are one iteration beyond current_widened_vals,
1020 -- which itself is a fixed point.
1022 fix_loop new_widened_vals
1025 For absence analysis, we make do with a very very simple approach:
1026 look for convergence in a two-point domain.
1028 We used to use just one iteration, starting with the variables bound
1029 to @AbsBot@, which is safe.
1031 Prior to that, we used one iteration starting from @AbsTop@ (which
1032 isn't safe). Why isn't @AbsTop@ safe? Consider:
1040 Here, if p is @AbsBot@, then we'd better {\em not} end up with a ``fixed
1041 point'' of @d@ being @(AbsTop, AbsTop)@! An @AbsBot@ initial value is
1042 safe because it gives poison more often than really necessary, and
1043 thus may miss some absence, but will never claim absence when it ain't
1046 Anyway, one iteration starting with everything bound to @AbsBot@ give
1051 Here, f would always end up bound to @AbsBot@, which ain't very
1052 clever, because then it would introduce poison whenever it was
1053 applied. Much better to start with f bound to @AbsTop@, and widen it
1054 to @AbsBot@ if any poison shows up. In effect we look for convergence
1055 in the two-point @AbsTop@/@AbsBot@ domain.
1057 What we miss (compared with the cleverer strictness analysis) is
1058 spotting that in this case
1060 f = \ x y -> ...y...(f x y')...
1062 \tr{x} is actually absent, since it is only passed round the loop, never
1063 used. But who cares about missing that?
1065 NB: despite only having a two-point domain, we may still have many
1066 iterations, because there are several variables involved at once.