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International Symposium on Practical Aspects of Declarative Languages

PADL 2017: Practical Aspects of Declarative Languages pp 68–85Cite as

Extending Answer Set Programs with Interpreted Functions as First-Class Citizens

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10137))

Abstract

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. Existing approaches towards integrating function terms into ASP can be organized in two classes: uninterpreted function symbols and interpreted functions; we focus on the latter. Existing approaches usually define interpreted functions in the program (e.g. using term equations), while evaluation wrt. to a pre-existing external semantics is neglected. However, this is useful if existing function libraries shall be accessed or if a function is more naturally implemented in procedural code. In this paper, we propose the declarative language of \(\textsc {hex}^{\textsc {ifu}}\) -programs which extends answer set programs (ASP) with such interpreted functions. However, rather than just providing a means for evaluating functions, it further turns interpreted functions into first-class citizens, i.e., functions are represented by accessible objects in the program. This paves the way for functionals (higher-order functions), i.e., functions that take other functions as arguments or return them. We provide then a rewriting of such programs to hex-programs, an extension of ASP with external sources, and an implementation based on this rewriting. Afterwards we present applications which motivated our work, e.g. the adoption of design pattern from software engineering. Finally, we discuss properties of the formalism and differences to related work.

This research has been supported by the Austrian Science Fund (FWF) project P27730.

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Notes

  1. 1.

    We let \(\bar{T}\) denote a meta-variable (not to be confused with ASP variables in the object language) which represents a constant from \(\mathscr {C}\), an ASP variable from \(\mathscr {V}\), or a ground or non-ground functional terms (e.g. f(a), g(X)).

  2. 2.

    For ordinary \(\varPi \), these are Gelfond & Lifschitz’s answer sets.

  3. 3.

    The external atom is intended to return the neighbors Y of X in a fixed finite graph, thus \(\varPi \) computes the nodes which are reachable from a given start node s.

  4. 4.

    http://www.lua.org.

  5. 5.

    To see that this is always possible, let \( runTM (m, i)\) be a function which maps the definition of a turing machine m and an input string i to the tape content after the machine encoded by m under input i terminates. Then any function \(f(\mathbf{x})\) can be defined as \( runTM (m_f, i)\), where i encodes arguments \(\mathbf{x}\) and \(m_f\) is a turing machine which computes f.

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Authors and Affiliations

  1. Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Christoph Redl

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  1. Christoph Redl
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Correspondence to Christoph Redl .

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  1. University of Nebraska, Omaha, Nebraska, USA

    Yuliya Lierler

  2. Halmstad University, Halmstad, Sweden

    Walid Taha

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Redl, C. (2017). Extending Answer Set Programs with Interpreted Functions as First-Class Citizens. In: Lierler, Y., Taha, W. (eds) Practical Aspects of Declarative Languages. PADL 2017. Lecture Notes in Computer Science(), vol 10137. Springer, Cham. https://doi.org/10.1007/978-3-319-51676-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-51676-9_5

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