Proving Operational Termination of Membership Equational Programs

Francisco Durán (1) , Salvador Lucas (2) , Claude Marché (3, 4) , José Meseguer (5) , Xavier Urbain (6)

1 LCC - Departamento Lenguajes y Ciencias de la Computación [Malaga]
2 Departamento de Sistemas Informáticos y Computación [Valencia]
3 LRI - Laboratoire de Recherche en Informatique
4 PROVAL - Proof of Programs
5 UIUC - University of Illinois at Urbana-Champaign [Urbana]
6 CEDRIC - Centre d'études et de recherche en informatique et communications

Reasoning about the termination of equational programs in sophisticated equational languages such as ELAN, MAUDE, OBJ, CAFEOBJ, HASKELL, and so on, requires support for advanced features such as evaluation strategies, rewriting modulo, use of extra variables in conditions, partiality, and expressive type systems (possibly including polymorphism and higher-order). However, many of those features are, at best, only partially supported by current term rewriting termination tools (for instance MU-TERM, CiME, APROVE, TTT, TERMPTATION, etc.) while they may be essential to ensure termination. We present a sequence of theory transformations that can be used to bridge the gap between expressive membership equational programs and such termination tools, and prove the correctness of such transformations. We also discuss a prototype tool performing the transformations on MAUDE equational programs and sending the resulting transformed theories to some of the aforementioned standard termination tools.

Domaines: Logique en informatique [cs.LO]

Francisco Durán, Salvador Lucas, Claude Marché, José Meseguer, Xavier Urbain. Proving Operational Termination of Membership Equational Programs. Higher-Order and Symbolic Computation, 2008, 21 (1-2), pp.59-88. ⟨inria-00431474⟩