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Fred Mesnard

Publications and source records attributed to Fred Mesnard.

At least 19 recordsLinked to original sources
arXiv2026

Case study: solving P-99 with LPTP and an LLM

Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.

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arXiv2026

Case study: proving sqrt(2) irrational with LPTP and an LLM

We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP (Logic Program Theorem Prover) system for stating and proving properties about logic programs. As the proof language of LPTP is based on natural deduction, the proofs are human readable. In our case study, we sketch in LPTP the usual proof showing the irrationality of the square root of 2. Then we describe the interactions we had with the LLM. We end up with a complete formal proof, partially generated by an LLM and fully proof-checked by LPTP.

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arXiv2026

Towards Relating Ciao Assertions and LPTP Theorems

Abstract interpretation-based verification is a central component of the Ciao Prolog system, enabling expressive specifications of properties of programs, predicates, and execution states. Independently, the LPTP (Logic Programming Theorem Proving) framework offers a first-order logical formalism for expressing and proving properties of predicates. In this paper, we address a fundamental issue in relating these two frameworks: studying the translation of Ciao assertions into LPTP formulae and identifying a partial correspondence between assertion-based and logic-based specifications. We introduce a systematic translation scheme, characterize assertion classes according to their logical encodability, and propose approximation strategies and auxiliary constructs for non-translatable cases, and finally analyze the resulting soundness and completeness trade-offs. We argue that our proposal enables a tight integration of Ciao's assertion checking with LPTP-based deductive verification, thereby leveraging their complementary capabilities.

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arXiv2026

Automated Theorem Proving for Prolog Verification

LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates. With LPTP, one can formally prove termination and partial correctness of such Prolog programs. LPTP was designed in the mid-1990's by Robert F. Staerk. It is written in ISO-Prolog and comes with an Emacs user-interface. From a theoretical point of view, in his publications about LPTP, Staerk associates a set of first-order axioms IND(P) to the considered Prolog program P. IND(P) contains the Clark's equality theory for P, definitions of success, failure and termination for each user-defined logic procedure in P, axioms relating these three points of view, and an axiom schema for proving inductive properties. LPTP is thus a dedicated proof editor where these axioms are hard-wired. We propose to translate these axioms as first-order formulas (FOFs), and apply automated theorem provers to check the property of interest. Using FOF as an intermediary language, we experiment the use of automated theorem provers for Prolog program verification. We evaluate the approach over a benchmark of about 400 properties of Prolog programs from the library available with LPTP. Both the compiler which generates a set of FOF files from a given input Prolog program together with its properties and the benchmark are publicly available.

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arXiv2020

Concolic Testing in CLP

Concolic testing is a popular software verification technique based on a combination of concrete and symbolic execution. Its main focus is finding bugs and generating test cases with the aim of maximizing code coverage. A previous approach to concolic testing in logic programming was not sound because it only dealt with positive constraints (by means of substitutions) but could not represent negative constraints. In this paper, we present a novel framework for concolic testing of CLP programs that generalizes the previous technique. In the CLP setting, one can represent both positive and negative constraints in a natural way, thus giving rise to a sound and (potentially) more efficient technique. Defining verification and testing techniques for CLP programs is increasingly relevant since this framework is becoming popular as an intermediate representation to analyze programs written in other programming paradigms.

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arXiv2020

An SMT-Based Concolic Testing Tool for Logic Programs

Concolic testing mixes symbolic and concrete execution to generate test cases covering paths effectively. Its benefits have been demonstrated for more than 15 years to test imperative programs. Other programming paradigms, like logic programming, have received less attention. In this paper, we present a concolic-based test generation method for logic programs. Our approach exploits SMT-solving for constraint resolution. We then describe the implementation of a concolic testing tool for Prolog and validate it on some selected benchmarks.

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arXiv2018

Pre-proceedings of the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018)

This volume constitutes the pre-proceedings of the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), held on 4-6th September 2018 in Frankfurt am Main, Germany and co-located with the 20th International Symposium on Principles and Practice of Declarative Programming (PPDP 2018) and the 26th International Workshop on Functional and Logic Programming (WFLP 2018).

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arXiv2016

On the Completeness of Selective Unification in Concolic Testing of Logic Programs

Concolic testing is a popular dynamic validation technique that can be used for both model checking and automatic test case generation. We have recently introduced concolic testing in the context of logic programming. In contrast to previous approaches, the key ingredient in this setting is a technique to generate appropriate run-time goals by considering all possible ways an atom can unify with the heads of some program clauses. This is called "selective" unification. In this paper, we show that the existing algorithm is not complete and explore different alternatives in order to have a sound and complete algorithm for selective unification.

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arXiv2015

Concolic Testing in Logic Programming

Software testing is one of the most popular validation techniques in the software industry. Surprisingly, we can only find a few approaches to testing in the context of logic programming. In this paper, we introduce a systematic approach for dynamic testing that combines both concrete and symbolic execution. Our approach is fully automatic and guarantees full path coverage when it terminates. We prove some basic properties of our technique and illustrate its practical usefulness through a prototype implementation.

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arXiv2014

A Second-Order Formulation of Non-Termination

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is generally undecidable. However, by restricting the language to known decidable cases, we exhibit new classes of loops, the non-termination of which is decidable. We present a bunch of examples.

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arXiv2014

Non-termination of Dalvik bytecode via compilation to CLP

We present a set of rules for compiling a Dalvik bytecode program into a logic program with array constraints. Non-termination of the resulting program entails that of the original one, hence the techniques we have presented before for proving non-termination of constraint logic programs can be used for proving non-termination of Dalvik programs.

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arXiv2014

Non-Termination Analysis of Java Bytecode

We introduce a fully automated static analysis that takes a sequential Java bytecode program P as input and attempts to prove that there exists an infinite execution of P. The technique consists in compiling P into a constraint logic program P_CLP and in proving non-termination of P_CLP; when P consists of instructions that are exactly compiled into constraints, the non-termination of P_CLP entails that of P. Our approach can handle method calls; to the best of our knowledge, it is the first static approach for Java bytecode able to prove the existence of infinite recursions. We have implemented our technique inside the Julia analyser. We have compared the results of Julia on a set of 113 programs with those provided by AProVE and Invel, the only freely usable non-termination analysers comparable to ours that we are aware of. Only Julia could detect non-termination due to infinite recursion.

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arXiv2013

Eventual Linear Ranking Functions

Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These systems are largely based on techniques and tools coming from the field of declarative constraint programming. In this paper, we first recall an algorithm based on Farkas' Lemma for discovering linear ranking functions proving termination of a certain class of loops. Then we propose an extension of this method for showing the existence of eventual linear ranking functions, i.e., linear functions that become ranking functions after a finite unrolling of the loop. We show correctness and completeness of this algorithm.

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arXiv2010

The Automatic Synthesis of Linear Ranking Functions: The Complete Unabridged Version

The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many terminating loops admit one and algorithms exist to automatically synthesize it. In this paper we present two such algorithms: one based on work dated 1991 by Sohn and Van Gelder; the other, due to Podelski and Rybalchenko, dated 2004. Remarkably, while the two algorithms will synthesize a linear ranking function under exactly the same set of conditions, the former is mostly unknown to the community of termination analysis and its general applicability has never been put forward before the present paper. In this paper we thoroughly justify both algorithms, we prove their correctness, we compare their worst-case complexity and experimentally evaluate their efficiency, and we present an open-source implementation of them that will make it very easy to include termination-analysis capabilities in automatic program verifiers.

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arXiv2009

A Non-Termination Criterion for Binary Constraint Logic Programs

On the one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide this line of research into two kinds of approaches: dynamic versus static analysis, this paper belongs to the latter. It proposes a criterion for detecting non-terminating atomic queries with respect to binary CLP rules, which strictly generalizes our previous works on this subject. We give a generic operational definition and an implemented logical form of this criterion. Then we show that the logical form is correct and complete with respect to the operational definition.

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arXiv2005

An Improved Non-Termination Criterion for Binary Constraint Logic Programs

On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide this line of research into two kinds of approaches: dynamic versus static analysis, this paper belongs to the latter. It proposes a criterion for detecting non-terminating atomic queries with respect to binary CLP clauses, which strictly generalizes our previous works on this subject. We give a generic operational definition and a logical form of this criterion. Then we show that the logical form is correct and complete with respect to the operational definition.

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