Nominal syntax with atom substitutions

Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal s...

Full description

Saved in:
Bibliographic Details
Published inJournal of computer and system sciences Vol. 119; pp. 34 - 59
Main Authors Domínguez, Jesús, Fernández, Maribel
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2021
Subjects
Matching
Nominal syntax
Non-capturing substitution
Rewriting
Unification
Matching
Non-capturing substitution
Nominal syntax
Rewriting
Unification
Online AccessGet full text
ISSN0022-0000
1090-2724
DOI10.1016/j.jcss.2021.01.002

Cover

More Information
Summary:Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal syntax. We consider an extension of nominal syntax with non-capturing atom substitutions and show that matching is decidable and finitary but unification is undecidable in general. The proof of undecidability of unification is obtained by reducing Hilbert's tenth problem to unification of extended nominal terms. We provide a general matching algorithm and characterise a class of problems for which matching is unitary, giving rise to expressive and efficient rewriting systems.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2021.01.002