Formalizing the dependency pair criterion for innermost termination

Almeida, Ariane Alves; Ayala-Rincón, Maurício

doi:10.1016/j.scico.2020.102474

Cited by 4 publications

(3 citation statements)

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“…Other related formalizations that use or connect to the one presented in this paper have been previously presented. For example, Alves Almeida and Ayala-Rincón formalized a notion of termination for term rewriting systems based on dependency pairs and showed how it can be related to the notions explained in this paper [2]. Also, Ferreira Ramos et.…”

Section: :13mentioning

confidence: 88%

“…While the formalization itself has been available for some time as part of the NASA PVS Library, the goal of this paper is to report the main results. These results, which have been used in other works such as [2] and [12], have not been properly published before. Furthermore, this paper also presents a practical contribution: a mechanizable technique to automate (some) termination proofs of user-defined recursive functions in PVS.…”

Section: Introductionmentioning

confidence: 99%

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Formal Verification of Termination Criteria for First-Order Recursive Functions

Muñoz,

Ayala-Rincón,

Moscato

et al. 2023

J Autom Reasoning

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This paper presents a formalization of several termination criteria for first-order recursive functions. The formalization, which is developed in the Prototype Verification System (PVS), includes the specification and proof of equivalence of semantic termination, Turing termination, size change principle, calling context graphs, and matrix-weighted graphs. These termination criteria are defined on a computational model that consists of a basic functional language called PVS0, which is an embedding of recursive first-order functions. Through this embedding, the native mechanism for checking termination of recursive functions in PVS could be soundly extended with semi-automatic termination criteria such as calling contexts graphs.

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Section: :13mentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Formal Verification of Termination Criteria for First-Order Recursive Functions

Muñoz,

Ayala-Rincón,

Moscato

et al. 2023

J Autom Reasoning

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“…CoLoR/Rainbow [5] does include a formalization of an early definition of HORPO [21], but none of the other techniques in higher-order rewriting. See [2,21,27] for more formalization results in rewriting.…”

Section: Introductionmentioning

confidence: 99%

Certifying Higher-Order Polynomial Interpretations

Weide¹,

Vale²,

Kop³

2023

Preprint

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Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an output. Several tools have been developed to check whether higher-order rewriting systems are terminating. However, developing such tools is difficult and can be error-prone. In this paper, we present a way of certifying termination proofs of higher-order term rewriting systems. We formalize a specific method, namely the polynomial interpretation method, that is used to prove termination. In addition, we give a program that turns the output of Wanda, a termination analysis tool for higher-order rewriting systems, into a Coq script, so that we can check whether the output is a valid proof of termination.

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