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Functional Synthesis with Examples

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Principles and Practice of Constraint Programming (CP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11802))

Abstract

Functional synthesis (FS) aims at generating an implementation from a declarative specification over sets of designated input and output variables. Traditionally, FS tasks are formulated as \(\forall \exists \)-formulas, where input variables are universally quantified and output variables are existentially quantified. State-of-the-art approaches to FS proceed by eliminating existential quantifiers and extracting Skolem functions, which are then turned into implementations. Related applications benefit from having concise (i.e., compact and comprehensive) Skolem functions. In this paper, we present an approach for extracting concise Skolem functions for FS tasks specified as examples, i.e., tuples of concrete values of integer variables. Our approach builds a decision tree from relationships between inputs and outputs and preconditions that classify all examples into subsets that share the same input-output relationship. We also present an extension that is applied to hybrid FS tasks, which are formulated in part by examples and in part by arbitrary declarative specifications. Our approach is implemented on top of a functional synthesizer AE-VAL and evaluated on a set of reactive synthesis benchmarks enhanced with examples. Solutions produced by our tool are an order of magnitude smaller than ones produced by the baseline AE-VAL.

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Notes

  1. 1.

    With the required support for quantifier elimination, it can be immediately adapted to rational arithmetic, nonlinear arithmetic, and bitvectors. But to achieve more compact solutions, these algorithms could benefit from additional adjustments in method connect which are left for future work.

  2. 2.

    We refer the reader to Sect. 5 that describes a process of learning from partial examples.

  3. 3.

    The source code and benchmarks are available at https://github.com/grigoryfedyukovich/aeval.

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Acknowledgments

This work was supported in part by NSF Grant 1525936. Any opinions, findings, and conclusions expressed herein are those of the authors and do not necessarily reflect those of the NSF.

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Authors and Affiliations

  1. Princeton University, Princeton, USA

    Grigory Fedyukovich & Aarti Gupta

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  1. Grigory Fedyukovich
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  2. Aarti Gupta
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Correspondence to Grigory Fedyukovich .

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  1. INRA, Castanet Tolosan, France

    Thomas Schiex

  2. INRA, Castanet Tolosan, France

    Simon de Givry

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Fedyukovich, G., Gupta, A. (2019). Functional Synthesis with Examples. In: Schiex, T., de Givry, S. (eds) Principles and Practice of Constraint Programming. CP 2019. Lecture Notes in Computer Science(), vol 11802. Springer, Cham. https://doi.org/10.1007/978-3-030-30048-7_32

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  • DOI: https://doi.org/10.1007/978-3-030-30048-7_32

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