Interactive Matching Logic Proofs in Coq

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00131889" target="_blank" >RIV/00216224:14330/23:00131889 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-031-47963-2_10" target="_blank" >http://dx.doi.org/10.1007/978-3-031-47963-2_10</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-47963-2_10" target="_blank" >10.1007/978-3-031-47963-2_10</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interactive Matching Logic Proofs in Coq

Popis výsledku v původním jazyce

Matching logic (ML) is a formalism for specifying and reasoning about mathematical structures by means of patterns and pattern matching. Previously, it has been used to capture a number of other logics, e.g., separation logic with recursive definitions and linear temporal logic. ML has also been formalized in the Coq Proof Assistant, and the soundness of its Hilbert-style proof system has been mechanized. However, using a Hilbert-style system for interactive reasoning is challenging - even more so in ML, which lacks a general deduction theorem. Therefore, we propose a single-conclusion sequent calculus for ML that is more amenable to interactive proving. Based on this sequent calculus, we implement a proof mode for interactive reasoning in ML, which significantly simplifies the construction of ML proofs in Coq. The proof mode is a mechanism for displaying intermediate proof states and an extensible set of proof tactics that implement the rules of the sequent calculus. We evaluate our proof mode on a collection of examples, showing a substantial improvement in proof script size and readability.

Název v anglickém jazyce

Interactive Matching Logic Proofs in Coq

Popis výsledku anglicky

Matching logic (ML) is a formalism for specifying and reasoning about mathematical structures by means of patterns and pattern matching. Previously, it has been used to capture a number of other logics, e.g., separation logic with recursive definitions and linear temporal logic. ML has also been formalized in the Coq Proof Assistant, and the soundness of its Hilbert-style proof system has been mechanized. However, using a Hilbert-style system for interactive reasoning is challenging - even more so in ML, which lacks a general deduction theorem. Therefore, we propose a single-conclusion sequent calculus for ML that is more amenable to interactive proving. Based on this sequent calculus, we implement a proof mode for interactive reasoning in ML, which significantly simplifies the construction of ML proofs in Coq. The proof mode is a mechanism for displaying intermediate proof states and an extensible set of proof tactics that implement the rules of the sequent calculus. We evaluate our proof mode on a collection of examples, showing a substantial improvement in proof script size and readability.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Theoretical Aspects of Computing (ICTAC 2023)

ISBN

9783031479625

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

19

Strana od-do

139-157

Název nakladatele

Springer Nature Switzerland AG

Místo vydání

Lima, Peru

Místo konání akce

Lima, Peru

Datum konání akce

1. 1. 2023

Typ akce podle státní příslušnosti

CST - Celostátní akce

Kód UT WoS článku

001160556100010