Formulas as Programs

Apt, Krzysztof R.; Bezem, Marc

doi:10.1007/978-3-642-60085-2_4

Cited by 6 publications

(2 citation statements)

References 17 publications

(15 reference statements)

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“…This is not adequate for most programs where variables have sorts ("types") and are organized in arrays and other data structures. Proposals for such an extension are presented in Apt and Bezem [2].…”

Section: Discussionmentioning

confidence: 99%

Beyond Structured Programming

van Emden

2018

Preprint

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The correctness of a structured program is, at best, plausible. Though this is a step forward compared to what came before, it falls short of verified correctness. To verify a structured program according to Hoare's method one is faced with the problem of finding assertions to fit existing code. In 1971 this mode of verification was declared by Dijkstra as too hard to be of practical use-he advised that proof and code were to grow together. A method for doing this was independently published by Reynolds in 1978 and by van Emden in 1979. The latter was further developed to attain the form of matrix code. This form of code not only obviates the need of fitting assertions to existing code, but helps in discovering an algorithm that reaches a given postcondition from a fixed precondition. In this paper a keyboard-editable version of matrix code is presented that uses E.W. Dijkstra's guarded commands as starting point. The result is reached by using Floyd's method rather than Hoare's as starting point.

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Section: Discussionmentioning

confidence: 99%

Beyond Structured Programming

van Emden

2018

Preprint

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“…Others have grafted constraint satisfying onto a functional programming host in the form of the "setof" construct. More recently there have been attempts to subsume both idioms within a unified system based on term rewriting, for example, Michael Hanus's integrated functional logic programming language Curry [25], the Vesper formalism of Robinson and Barklund (in [23]), the Escher system of Lloyd (in [23]) and the Alma system of Apt and Bezem [24]. These unified systems have hitherto been mere experiments, and have attracted few if any actual users.…”

Section: To Integrate Functional Programming With Logic Programmingmentioning

confidence: 99%

Computational Logic: Memories of the Past and Challenges for the Future

Robinson

2000

Computational Logic — CL 2000

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Abstract. The development of computational logic since the introduction of Frege's modern logic in 1879 is presented in some detail. The rapid growth of the field and its proliferation into a wide variety of subfields is noted and is attributed to a proliferation of subject matter rather than to a proliferation of logic itself. Logic is stable and universal, and is identified with classical first order logic. Other logics are here considered to be first order theories, syntactically sugared in notationally convenient forms. From this point of view higher order logic is essentially first order set theory. The paper ends by presenting several challenging problems which the computational logic community now faces and whose solution will shape the future of the field.

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First-Order Logic as a Constraint Programming Language

Apt

Vermeulen

2002

Logic for Programming, Artificial Intelligence, and Reasoning

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We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic maintenance of the constraint store takes place. We prove that the resulting semantics is sound with respect to the truth definition. By instantiating it by specific forms of constraint management policies we obtain several sound evaluation policies of first-order formulas. This semantics can also be used a basis for sound implementation of constraint maintenance in presence of block declarations and conditionals.

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Formulas as Programs

Cited by 6 publications

References 17 publications

Beyond Structured Programming

Beyond Structured Programming

Computational Logic: Memories of the Past and Challenges for the Future

First-Order Logic as a Constraint Programming Language

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