, Volume 21, Issue 1-2, pp 59-88
Date: 26 Apr 2008

Proving operational termination of membership equational programs

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Abstract

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, C i ME, 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.

This research was partly supported by bilateral CNRS-DSTIC/UIUC research project “Rewriting calculi, logic and behavior”, and by ONR Grant N00014-02-1-0715 and NSF Grant CCR-0234524; Francisco Durán was partially supported by the EU (FEDER) and the Spanish MEC, under grant TIN2005-09405-C02-01; Salvador Lucas was partially supported by the EU (FEDER) and the Spanish MEC, under grant TIN 2004-7943-C04-02, the Generalitat Valenciana under grant GV06/285, and the ICT for EU-India Cross-Cultural Dissemination ALA/95/23/2003/077-054 project.