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International Workshop on Functional and Constraint Logic Programming

Workshop on Logic Programming

International Conference on Applications of Declarative Programming and Knowledge Management

WFLP 2017, WLP 2017, INAP 2017: Declarative Programming and Knowledge Management pp 64–80Cite as

An Operational Semantics for Constraint-Logic Imperative Programming

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10997))

Abstract

Object-oriented (OO) languages such as Java are the dominating programming languages nowadays, among other reasons due to their ability to encapsulate data and operations working on them, as well as due to their support of inheritance. However, in contrast to constraint-logic languages, they are not particularly suited for solving search problems. During development of enterprise software, which occasionally requires some search, one option is to produce components in different languages and let them communicate. However, this can be clumsy.

As a remedy, we have developed the constraint-logic OO language Muli, which augments Java with logic variables and encapsulated search. Its implementation is based on a symbolic Java virtual machine that supports constraint solving and backtracking. In the present paper, we focus on the non-deterministic operational semantics of an imperative core language.

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Notes

  1. 1.

    In other problems the return value could be a symbolic expressions if the accumulated constraints do not reduce the return value’s domain to a concrete value.

  2. 2.

    Nevertheless, Muli’s symbolic JVM supports these features exactly according to the JVM specification [12] (but does not add interesting details w.r.t. non-determinism).

  3. 3.

    In fact they are functions, since we ignore object-orientation in this presentation.

  4. 4.

    A very simple constraint solver could just take equality constraints into account. In this case, \(\gamma \models x == v\), if \(\gamma = b_1 \wedge \ldots \wedge b_k\) and for some \(j\in \{1,\ldots ,k\}~~b_k = (x == v)\).

  5. 5.

    In the implementation, the applicability of these rules will depend on the constraint propagation abilities of the employed constraint solver. We discuss the implications in Sect. 5.

  6. 6.

    https://github.com/wwu-pi/muli-env.

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Author information

Authors and Affiliations

  1. ERCIS, University of Münster, Münster, Germany

    Jan C. Dageförde & Herbert Kuchen

Authors
  1. Jan C. Dageförde
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  2. Herbert Kuchen
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Corresponding author

Correspondence to Jan C. Dageförde .

Editor information

Editors and Affiliations

  1. Universität Würzburg, Wuerzburg, Germany

    Dietmar Seipel

  2. Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Michael Hanus

  3. Universidade de Èvora, Evora, Portugal

    Salvador Abreu

Appendix: Full Example Evaluation

Appendix: Full Example Evaluation

In addition to \(\rho _0\), \(\sigma _0\), and \(\gamma _1\) defined in section Sect. 4, the following auxiliary definitions will be needed as intermediate results: \(\rho _1 = \rho _0[x/\alpha _1, y/\alpha _2]\), \(\rho _2 = \rho _0[b/\alpha _3, y/\alpha _4]\), \(\rho _3 = \rho _2[i/\alpha _5,r/\alpha _6]\), \(\rho _4 = \rho _3[i/\alpha _7, r/\alpha _8]\), \(\sigma _1 = \sigma _0[\alpha _1/1, \alpha _2/\alpha _2]\), \(\sigma _2 = \sigma _1[\alpha _3/2, \alpha _4/\alpha _2]\), \(\sigma _3 = \sigma _2[\alpha _7/0, \alpha _8/1]\), \(\sigma _4 = \sigma _3[\alpha _0/1]\), \(\sigma _5 = \sigma _4[\alpha _0/\!\perp ]\), \(\sigma _6 = \sigma _5[\alpha _0/0]\), \(\gamma _2 = \gamma _1 \wedge \alpha _2 \le 0\), and \(\gamma _3 = \gamma _2 \wedge \alpha _2 == 0 \). To simplify the understanding of the full computation provided in Sect. 4, we have decomposed it into a couple of lemmas. We present the computation in a top-down fashion. If you prefer a bottom-up fashion, just read the lemmas in reverse order. The names of the applied rules are specified in each step.

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Dageförde, J.C., Kuchen, H. (2018). An Operational Semantics for Constraint-Logic Imperative Programming. In: Seipel, D., Hanus, M., Abreu, S. (eds) Declarative Programming and Knowledge Management. WFLP WLP INAP 2017 2017 2017. Lecture Notes in Computer Science(), vol 10997. Springer, Cham. https://doi.org/10.1007/978-3-030-00801-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-00801-7_5

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