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Random generation of closed simply typed λ-terms: A synergy between logic programming and Boltzmann samplers*

Published online by Cambridge University Press:  13 October 2017

MACIEJ BENDKOWSKI ,
KATARZYNA GRYGIEL  and
PAUL TARAU
MACIEJ BENDKOWSKI
Affiliation:
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. Łojasiewicza 6, 30-348 Kraków, Poland (e-mail: bendkowski@tcs.uj.edu.pl, grygiel@tcs.uj.edu.pl)
KATARZYNA GRYGIEL
Affiliation:
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. Łojasiewicza 6, 30-348 Kraków, Poland (e-mail: bendkowski@tcs.uj.edu.pl, grygiel@tcs.uj.edu.pl)
PAUL TARAU
Affiliation:
Department of Computer Science and Engineering, University of North Texas, Denton, TX, USA (e-mail: paul.tarau@unt.edu)
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Abstract

A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature, a great body of work has been devoted to tools and techniques automating this labour-intensive process. A prominent example is the successful use of randomness, in particular, random typable λ-terms, in testing functional programming compilers such as the Glasgow Haskell Compiler. Unfortunately, due to the intrinsically difficult combinatorial structure of typable λ-terms, no effective uniform sampling method is known, setting it as a fundamental open problem in the random software testing approach. In this paper, we combine the framework of Boltzmann samplers, a powerful technique of random combinatorial structure generation, with today's Prolog systems offering a synergy between logic variables, unification with occurs check and efficient backtracking. This allows us to develop a novel sampling mechanism able to construct uniformly random closed simply typed λ-terms of up size 120. We apply our techniques to the generation of uniformly random closed simply typed normal forms and design a parallel execution mechanism pushing forward the achievable term size to 140.

Keywords

Boltzmann samplersrandom generation of simply typed λ-termstype inferencecombinatorics of λ-termsrandom generation of simply typed normal formsparallel implementation of Boltzmann samplers
Type
Technical Note
Information
Theory and Practice of Logic Programming , Volume 18 , Issue 1 , January 2018 , pp. 97 - 119
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

*

The first two authors have been partially supported by the Polish National Science Center grant 2013/11/B/ST6/00975. The third author has been supported by NSF grant 1423324. A conference version of the present paper appears in the proceedings of PADL 2017 (PC chairs: Yuliya Lierler and Walid Taha).

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