scholarly journals Proving Ground Confluence of Equational Specifications Modulo Axioms

2018 ◽  
pp. 184-204 ◽  
Author(s):  
Francisco Durán ◽  
José Meseguer ◽  
Camilo Rocha
Keyword(s):  
Equational Specifications

scholarly journals A duality between proof systems for cyclic term graphs

2007 ◽  
Vol 17 (3) ◽  
pp. 439-484 ◽  
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.

Completeness of Proof Systems for Equational Specifications

1985 ◽  
Vol SE-11 (5) ◽  
pp. 454-461 ◽  
Author(s):  
D.B. MacQueen ◽  
D.T. Sannella
Keyword(s):  
Proof Systems ◽  
Equational Specifications

Turning Inductive into Equational Specifications

2009 ◽  
pp. 131-146 ◽  
Author(s):  
Stefan Berghofer ◽  
Lukas Bulwahn ◽  
Florian Haftmann
Keyword(s):  
Equational Specifications
Sign in / Sign up

Export Citation Format

Share Document