On termination problems for finitely interpreted ALGOL-like programs

Langmaack, Hans

doi:10.1007/bf00625282

Cited by 17 publications

(4 citation statements)

References 21 publications

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“…Consider the class of all programs from YP which disallow selfapplication and global simple variables in procedure bodies. Langmaack [34] proved that this class of programs satisfies condition l of Theorem 6 in the case of the ALGOL 60 copy rule. By Theorem 6 there exists a sound and complete Hoare's logic for this class of programs.…”

Section: Ten Years Of Hoare's Logic: a Survey 477mentioning

confidence: 96%

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Ten Years of Hoare's Logic: A Survey—Part I

Apt

1981

ACM Trans. Program. Lang. Syst.

420

218

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A survey of various results concerning Hoare's approach to proving partial and total correctness of programs is presented. Emphasis is placed on the soundness and completeness issues. Various proof systems for while programs, recursive procedures, local variable declarations, and procedures with parameters, together with the corresponding soundness, completeness, and incompleteness results, are discussed.

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Section: Ten Years Of Hoare's Logic: a Survey 477mentioning

confidence: 96%

“…But (29) implies that q[x + I/x] ~ x + 1 = z is true; so, by (33), q~x+I=z is true. From (29) and (34) we get that…”

Section: Insufficiency Of the Recursion Rulementioning

confidence: 99%

Ten Years of Hoare's Logic: A Survey—Part I

Apt

1981

ACM Trans. Program. Lang. Syst.

420

218

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“…As a first step, Langmaack proved in [Lan82] that for all Algol-like programs in L 4 the divergence problem is decidable for finite interpretations. This is a necessary condition for the existence of a sound and relatively complete Hoare-like proof system according to Lemma A.…”

Section: Clarke's Language Lmentioning

confidence: 99%

Fifty years of Hoare’s logic

Apt

Olderog

2019

Form. Asp. Comput.

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“…For several years the question of whether there existed a natural Hoare proof system for L4 that was sound and complete in the sense of Cook remained open. Langmaack (1979) proved that the halting problem for L4 was decidable and hence, by the characterization theorem given in §6, such a proof system should exist (although perhaps not a natural one!). Olderog (1982) and Damm & Josko (1982) devised proof systems for L4, which were based on the use of a higher order assertion language and the addition of relation variables to the programming language.…”

Section: Natural Axiomatizations For New Programming Languagesmentioning

confidence: 99%

The characterization problem for Hoare logics

Clarke

1984

Phil. Trans. R. Soc. Lond. A

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Research by myself and by others has shown that there are natural programming language control structures that are impossible to describe adequately by means of Hoare axioms. Specifically, we have shown that there are control structures for which it is impossible to obtain axiom systems that are sound and relatively complete in the sense of Cook. These constructs include procedures with procedure parameters under standard ALGOL 60 scope rules and coroutines in a language with parameterless recursive procedures. A natural question to ask is whether it is possible to characterize those programming languages for which sound and complete proof systems can be obtained. For a wide class of programming languages and interpretations, it can be shown that P has a sound and relatively complete proof system for every expressive interpretation iff the halting problem for language P is decidable for all finite interpretations. Nevertheless, we are still far from a completely satisfactory characterization of the programming languages that can be axiomatized in this manner. The proof system that is generated in proving the above result does not have the property of being ‘syntax-directed’, which is distinctive of the Hoare axioms. Moreoever, theoretical considerations suggest that good axioms for total correctness may exist for a wider spectrum of languages than for partial correctness. In this paper we discuss these questions and others that still need to be addressed before the characterization problem can be considered solved.

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On termination problems for finitely interpreted ALGOL-like programs

Cited by 17 publications

References 21 publications

Ten Years of Hoare's Logic: A Survey—Part I

Ten Years of Hoare's Logic: A Survey—Part I

Fifty years of Hoare’s logic

The characterization problem for Hoare logics

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