Rewriting Induction for Existentially Quantified Equations in Logically Constrained Rewriting (Full Version)

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Hauptverfasser: Nishida, Naoki, Nishie, Kazushi, Kojima, Misaki
Format: Preprint
Veröffentlicht: 2026
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_version_ 1866914331896053760
author Nishida, Naoki
Nishie, Kazushi
Kojima, Misaki
author_facet Nishida, Naoki
Nishie, Kazushi
Kojima, Misaki
contents Rewriting Induction (RI) is a principle to prove that an equation over terms is an inductive theorem of a rewrite system, i.e., that any ground instance of the equation is a theorem of the rewrite system. RI has been adapted to several kinds of rewrite systems, and RI for constrained rewrite systems has been extended to inequalities. In this paper, we extend RI for constrained equations to existentially quantified equations in logically constrained rewriting. To this end, we first extend constrained equations by introducing existential quantification to the equation part of constrained equations. Then, in applying a constrained rewrite rule to such extended constrained equations, we introduce existential quantification to extra variables of the applied rule. Finally, using the extended application of constrained rewrite rules, we extend RI for constrained equations to existentially quantified equations.
format Preprint
id arxiv_https___arxiv_org_abs_2602_14636
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Rewriting Induction for Existentially Quantified Equations in Logically Constrained Rewriting (Full Version)
Nishida, Naoki
Nishie, Kazushi
Kojima, Misaki
Logic in Computer Science
68Q42
F.4.2
Rewriting Induction (RI) is a principle to prove that an equation over terms is an inductive theorem of a rewrite system, i.e., that any ground instance of the equation is a theorem of the rewrite system. RI has been adapted to several kinds of rewrite systems, and RI for constrained rewrite systems has been extended to inequalities. In this paper, we extend RI for constrained equations to existentially quantified equations in logically constrained rewriting. To this end, we first extend constrained equations by introducing existential quantification to the equation part of constrained equations. Then, in applying a constrained rewrite rule to such extended constrained equations, we introduce existential quantification to extra variables of the applied rule. Finally, using the extended application of constrained rewrite rules, we extend RI for constrained equations to existentially quantified equations.
title Rewriting Induction for Existentially Quantified Equations in Logically Constrained Rewriting (Full Version)
topic Logic in Computer Science
68Q42
F.4.2
url https://arxiv.org/abs/2602.14636