Sebastian Hunt and Chris Hankin. Approximate fixed points in abstract interpretation. In Fourth European Symposium on Programming, Rennes, France, 1992. LNCS 582.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in model checking. Otherwise, one can always represent properties as terms although this is not quite adequate in practice since powerful widenings are based on the semantics and the geometry of the fixpoint computation. Widenings based on thresholds (for example the widening to a finite domain [53] in static analysis or the limitation of reachability at a certain depth in model checking [9] are equivalent to static abstraction so are not very expressive [34] Dynamic widenings could be better exploited in model checking to cope with the state space explosion problem, the same model being ....

C. Hankin and S. Hunt. Approximate fixed points in abstract interpretation. Sci. Comput. Programming, 22(3):283--306, 1994. Erratum: Sci. Comput. Program# ming 23(1): 103 (1994).

....= rType(t) if fun(t) aTypes : Type [T ype] aTypes(t) if nonfun(t) aTypes(t1 t2 ) t1 : aTypes(t2 ) aTypes(P rocess t1 t2 ) t1 : aTypes(t2) aTypes(8fi:t) aTypes(t) if fun(t) Fig. 10. Functions nArgs , rType and aTypes [CP85,JC87,MH87] and widening narrowing operators [CC77,CC79,HH92,PP93] Here, we will represent functions by signatures in a way similar to [PP93] A signature for a function is obtained by probing such function with some explicitly chosen combinations of arguments. For example, in the strictness analysis of [PP93] a function f with m arguments was probed ....

....1 For each type t, 2 In Proposition 1 we will prove that W t is an upper closure operator. The definition of a widening operator is more general [CC77,NNH99] but given an upper closure operator W t w idD 2t , we can define a corresponding widening operator r t = x; y) x tW t (y) as done in [HH92] So we will use the word widening operator instead, as in [PP93] 10 (a) The functions t , t , and W t are monotone and continuous. b) W t w id D 2 t . c) t Delta t = id S t . Proof. Proposition 1) We prove first 1(a) We will prove that t and t are monotone by structural ....

C. Hankin and S. Hunt. Approximate fixed points in abstract interpretation. In B. Krieg-Bruckner, editor, ESOP '92, 4th European Symposium on Programming, volume 582 of Lecture Notes in Computer Science, pages 219--232, Rennes, France, February 26--28, 1992. Springer, Berlin.

....analysis, although this presentation was restricted to the two point, first order, monomorphic case. Further work showed what a versatile beast it was: higher order analysis [HH91] and arbitrary non flat datatypes [Sew91] were subsequently incorporated. Recently, Hankin and Hunt showed a variant [HH92] which greatly increased controllability by allowing arbitrary tradeoffs between work and quality of result. What remains missing is an effective way to deal with parametric polymorphism. Polymorphic strictness analysis in the large has until recently been a grey area. Investigations of the ....

....seems to suggest that even a single, well chosen embedding closure pair gives better results than Conc. It will be interesting to see if this technology can be used to good effect in replacing uses of Abs and Conc for the purpose for which Hunt originally developed them: approximate fixed points [HH92]. One place in the Haskell Prelude where subsetting is essential to get any results at all in reasonable time is the definition of partition: select p x (ts, fs) p x = x:ts, fs) otherwise = ts, x:fs) partition p = foldr (select p) This requires an instance of foldr where both ....

Sebastian Hunt and Chris Hankin. Approximate fixed points in abstract interpretation. In Fourth European Symposium on Programming, Rennes, France, 1992. LNCS 582.

....finite domain for abstract interpretation, since apparently more information can be obtained from an interpretation over an infinite domain. The answer is that if uniform termination of the abstract interpretation is required, no more information can be obtained by choosing an infinite domain . In [HH90], a fixpoint approximation method is considered which consists in an upwards iteration using a safe approximation ff (F ) of the function F 2 L con 7 Gamma L in a finite small lattice L such that L ( Gamma Gamma fl ff L and in which the problem of finding fixpoints is tractable, followed ....

.... F 2 L con 7 Gamma L in a finite small lattice L such that L ( Gamma Gamma fl ff L and in which the problem of finding fixpoints is tractable, followed by a downwards iteration from fl Gamma lfp ff( ff (F ) Delta in L (or in a sequence of intermediate lattices larger than L) [HH90] claim that We have now shown the equivalence of step 1 of that process and the Cousot s notion of widening. For step 2, which consists in working in a larger lattice, HH90] claim that the refinement of the upper bound in intermediate lattice corresponds to narrowing . 7 Comparing the Two ....

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C. Hankin and S. Hunt. Approximate fixed points in abstract interpretation. In B. Krieg-Bruckner, editor, Proceedings of the 4 th European Symposium on Programming, ESOP '92, pages 219--232. Springer-Verlag, Berlin, Germany, Rennes, France, February 26--28 1990.

....(1987; 1989) and Hunt and Hankin (1989; 1991) with emphasis on applications to strictness analysis. Recent progresses in the development of abstract interpretation, not all of them based on least fixed point finding, abound as well in the literature. See, for example, Ferguson and Hughes (1993) Hankin and Hunt (1992), Hankin and Le Metayer (1994) Nocker (1993) and Seward (1993) We will briefly describe their work, and compare our approach to theirs, in section 6. For now, let us briefly describe how the frontier method works. Take a function s strictness property as an example. For the moment, assume that ....

....giving an explicit proof strategy, the augmented, simply typed # calculus in our approach provides a simple way to compute the desired results. Recent work has shown progress in the development of fast strictness analyzers for higher order functions. See, for example, Ferguson and Hughes (1993) Hankin and Hunt (1992), Hankin and Le Metayer (1994) Nocker (1993) and Seward (1993) Ferguson and Hughes formulate abstract interpretations as sequential algorithms on concrete data structures (CDS) CDS are trees with labeled edges, representing the states of computation. Hankin and Hunt provide techniques to reduce ....

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Hankin, C. and Hunt, S. (1992) Approximate fixed points in abstract interpretation. In B. Krieg--Bruckner, editor,<F3.683e+05> 4th European Symposium on<F4.106e+05> Programming, pp. 219--232.

....of algorithms has not kept pace with the theoretical developments. This is now a major barrier that is preventing the inclusion of the most advanced techniques in compilers. The most significant contributions for improving the efficiency of abstract interpretation include widening techniques [9, 14], chaotic iteration sequences [8, 34] and the related minimal function graphs [25] and frontiers based algorithms [33, 21] The latter has unacceptable performance for some commonly occurring higher order programs. The first two are general approaches for accelerating convergence in fixed point ....

....[4, 28, 35, 36] The abstract interpretation and the projections approaches have led to the construction of analyses based on rich domains which make them intractable even for some simple examples. Techniques striving for a better representation of the domains do not really solve the problem [14, 21]. The main feature of our approach is the notion of lazy types (or lazily evaluated types) which allows us to compute only the information required to answer a particular question about the strictness of a function. One significant advantage of the approach is that it extends naturally to domains ....

C. L. Hankin and L. S. Hunt, Approximate fixed points in abstract interpretation, in B. Krieg-Bruckner (ed), Proceedings of the 4th European Symposium on Programming, LNCS 582, Springer Verlag, 1992.

....with the theoretical developments. This is now a major barrier that is preventing the inclusion of the most advanced techniques in compilers. The majority of the effort on improving the efficiency of abstract interpretation has concentrated on frontiers based algorithms [13] or widening techniques [6, 9]. The former still has unacceptable performance for some commonly occurring higher order programs. The latter is a general approach for accelerating convergence in fixed point computations which, in the finite case, leads to some loss in accuracy. In contrast to abstract interpretation, type ....

....frontiers optimisation can be described as a particular restriction on types. The main technical contribution of the paper is the notion of lazy types and the corresponding type system and algorithm. This addresses an issue that has taxed the abstract interpretation community greatly. The papers [4, 5, 7, 8, 9, 13, 16, 18] all tackle the same issue. The basic problem is that the choice to abstract functions by functions is a disastrous one for the efficiency of the analysis. We can classify the various proposals to circumvent the problem into two categories: 1) some of them [4, 8, 13, 16] strive for a better ....

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C. L. Hankin and L. S. Hunt, Approximate fixed points in abstract interpretation, in B. Krieg-Bruckner (ed), Proceedings of the 4th European Symposium on Programming, LNCS 582, Springer Verlag, 1992.

....issue in this paper. The abstract interpretation and the projections approaches have led to the construction of analyses based on rich domains which make them intractable even for some simple examples. Techniques striving for a better representation of the domains do not really solve the problem [12, 17]. This observation has motivated some researchers, 2, 18, 19, 20] to develop non standard type inference systems for strictness analysis. Kuo and Mishra, 20] proposed a type inference system for strictness information; they developed a sound and complete inference algorithm but did not show ....

C. L. Hankin and L. S. Hunt, Approximate fixed points in abstract interpretation, in B. Krieg-Bruckner (ed), Proceedings of the 4th European Symposium on Programming, LNCS 582, Springer Verlag, 1992.

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Sebastian Hunt and Chris Hankin. Approximate fixed points in abstract interpretation. In Fourth European Symposium on Programming, Rennes, France, 1992. LNCS 582.

No context found.

C. Hankin and S. Hunt. Approximate fixed points in abstract interpretation. In B. Krieg-Bruckner, editor, ESOP '92, 4th European Symposium on Programming, volume 582 of LNCS, pages 219--232. Springer, Berlin, 1992.

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