Paper Info
Title
A Formalisation of Nominal α-equivalence with A and AC Function Symbols.
Abstract
A formalisation of soundness of the notion of α-equivalence in nominal abstract syntax modulo associative (A) and associative-commutative (AC) equational theories is described. Initially, the notion of α-equivalence is specified based on a so called “weak” nominal relation as suggested by Urban in his nominal development in Isabelle/HOL. Then, it is formalised in Coq that this equality is indeed an equivalence relation. After that, general α-equivalence with A and AC function symbols is specified and formally proved to be an equivalence relation. As corollaries, the soundness α-equivalence modulo A and modulo AC is obtained. Finally, an algorithm for checking α-equivalence modulo A and AC is proposed. General α-equivalence problems are log-linearly solved while AC and the combination of A and AC α-equivalence problems have the same complexity as standard first-order approaches. This development is a first step towards verification of nominal matching, unification and narrowing algorithms modulo equational theories in general.
Year
DOI
Venue
2017
10.1016/j.entcs.2017.04.003
Electronic Notes in Theoretical Computer Science
Keywords
Field
DocType
Nominal logic,Alpha Equivalence,Equivalence modulo A and AC
HOL,Discrete mathematics,Equivalence relation,Associative property,Modulo,Unification,Equivalence (measure theory),Abstract syntax,Soundness,Mathematics
Journal
Volume
ISSN
Citations 
332
1571-0661
0
PageRank 
References 
Authors
0.34
7
4
Name
Order
Citations
PageRank
M. Ayala-Rincón1105.38
Washington de Carvalho Segundo201.69
Maribel Fernández303.72
Daniele Nantes Sobrinho423.08