Equational specifications: design, implementation, and reasoning

Texts and Monographs in Symbolic Computation - Advances in the Design of Symbolic Computation Systems ◽

10.1007/978-3-7091-6531-7_8 ◽

1997 ◽

pp. 126-144 ◽

Cited By ~ 1

Author(s):

S. Antoy ◽

P. Forcheri ◽

J. Gannon ◽

M. T. Molfino

Keyword(s):

Equational Specifications

Download Full-text

Proving Ground Confluence of Equational Specifications Modulo Axioms

Rewriting Logic and Its Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-99840-4_11 ◽

2018 ◽

pp. 184-204 ◽

Cited By ~ 2

Author(s):

Francisco Durán ◽

José Meseguer ◽

Camilo Rocha

Keyword(s):

Equational Specifications

Download Full-text

Ground term confluence in parametric conditional equational specifications

STACS 87 - Lecture Notes in Computer Science ◽

10.1007/bfb0039613 ◽

2006 ◽

pp. 286-298 ◽

Cited By ~ 20

Author(s):

Harald Ganzinger

Keyword(s):

Ground Term ◽

Equational Specifications

Download Full-text

A duality between proof systems for cyclic term graphs

Mathematical Structures in Computer Science ◽

10.1017/s0960129507006111 ◽

2007 ◽

Vol 17 (3) ◽

pp. 439-484 ◽

Cited By ~ 2

Author(s):

CLEMENS GRABMAYER

Keyword(s):

Close Connection ◽

Proof System ◽

Consistency Checking ◽

Duality Result ◽

First Order ◽

Proof Systems ◽

Similar Proof ◽

Equational Specifications ◽

Cyclic Term

This paper presents a proof-theoretic observation about two kinds of proof systems for bisimilarity between cyclic term graphs.First we consider proof systems for demonstrating that μ term specifications of cyclic term graphs have the same tree unwinding. We establish a close connection between adaptations for μ terms over a general first-order signature of the coinductive axiomatisation of recursive type equivalence by Brandt and Henglein (Brandt and Henglein 1998) and of a proof system by Ariola and Klop (Ariola and Klop 1995) for consistency checking. We show that there exists a simple duality by mirroring between derivations in the former system and formalised consistency checks, which are called ‘consistency unfoldings', in the latter. This result sheds additional light on the axiomatisation of Brandt and Henglein: it provides an alternative soundness proof for the adaptation considered here.We then outline an analogous duality result that holds for a pair of similar proof systems for proving that equational specifications of cyclic term graphs are bisimilar.

Download Full-text