Structural Resolution with Co-inductive Loop Detection

Li, Yue

doi:10.4204/eptcs.258.4

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Related Work. The related paper by Li (2017) shows that an algorithm embedding the CoLP loop detection rule into S-resolution is sound relative to greatest complete Herbrand models. However, that work does not consider conditions on which such embedding would be sound relative to SLD-computations at infinity.…”

Section: Conclusion Discussion Related and Future Workmentioning

confidence: 99%

Productive corecursion in logic programming

Komendantskaya¹,

Li²

2017

Theory and Practice of Logic Programming

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Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing.Recently, an algorithm was presented that semi-decides a weaker property -of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.

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Section: Conclusion Discussion Related and Future Workmentioning

confidence: 99%

Productive corecursion in logic programming

Komendantskaya¹,

Li²

2017

Theory and Practice of Logic Programming

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“…While these results show that there are cases where S-resolution works better than Co-LP as inference engine for abstract compilation, we leave for further development the possibility of extending such a claim to prove that structural resolution always leads to analysis results which, if not improved, are at least comparable to those obtained with Co-LP as inference engine of abstract compilation. In particular, the recent results [20,18] show that it is possible to integrate Co-LP loop detection into S-resolution, and thus to identify regular patterns and infer regular terms like Co-LP does. For example, it is possible to infer the answer X = cons(0, X) for a query of Example 2 rather than giving a lazy answer (X = cons(0, X ), X = cons(0, X ), .…”

Section: Discussionmentioning

confidence: 99%

Structural Resolution for Abstract Compilation of Object-Oriented Languages

Franceschini

Ancona

Komendantskaya

2017

Electron. Proc. Theor. Comput. Sci.

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We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries to be solved with respect to the resulting logic program. We exploit a coinductive semantics to deal with infinite terms and proofs produced by recursive types and methods. Thanks to the recent notion of structural resolution for coinductive logic programming, we are able to infer very precise type information, including a class of irrational recursive types causing non-termination for previously considered coinductive semantics. We also show how to transform logic programs to make them satisfy the preconditions for the operational semantics of structural resolution, and we prove this step does not affect the semantics of the logic program.

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“…While coSLD resolution and its proposed extensions are limited by the fact that cycles must be detected in derivations to allow resolution to succeed, a stream of work based on the notion of structural resolution (Komendantskaya et al 2016;) (S-resolution for short) aims to make coinductive resolution more powerful, by allowing to lazily detect infinite derivations which do not have cycles. In particular, recent results (Li 2017;Komendantskaya and Li 2017;Basold et al 2019) investigate how it is possible to integrate coLP cycle detection into Sresolution, by proposing a comprehensive theory. Trying to integrate S-resolution with coclauses is an interesting topic for future work aiming to make coLP even more flexible.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Flexible coinductive logic programming

Dagnino

Ancona

Zucca

2020

Theory and Practice of Logic Programming

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Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations, necessary in some cases to get the correct meaning. We provide a detailed formal account of an extension of logic programming supporting flexible coinduction. Syntactically, programs are enriched by coclauses, clauses with a special meaning used to tune the interpretation of predicates. As usual, the declarative semantics can be expressed as a fixed point which, however, is not necessarily the least, nor the greatest one, but is determined by the coclauses. Correspondingly, the operational semantics is a combination of standard SLD resolution and coSLD resolution. We prove that the operational semantics is sound and complete with respect to declarative semantics restricted to finite comodels.

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Structural Resolution with Co-inductive Loop Detection

Cited by 4 publications

References 19 publications

Productive corecursion in logic programming

Productive corecursion in logic programming

Structural Resolution for Abstract Compilation of Object-Oriented Languages

Flexible coinductive logic programming

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