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Operational Termination of Membership Equational Programs: the Order-Sorted Way

Summary: WRLA 2008
Operational Termination of Membership
Equational Programs: the Order-Sorted Way
Salvador Lucas
DSIC, Universidad Polit´ecnica de Valencia, Spain
Jos´e Meseguer
CS Dept., University of Illinois at Urbana-Champaign, USA
Our main goal is automating termination proofs for programs in rewriting-based languages with features
such as: (i) expressive type structures, (ii) conditional rules, (iii) matching modulo axioms, and (iv) context-
sensitive rewriting. Specifically, we present a new operational termination method for membership equa-
tional programs with features (i)-(iv) that can be applied to programs in membership equational logic
(MEL). The method first transforms a MEL program into a simpler, yet semantically equivalent, condi-
tional order-sorted (OS) program. Subsequent trasformations make the OS-program unconditonal, and,
finally, unsorted. In particular, we extend and generalize to this richer setting an order-sorted termination
technique for unconditional OS programs proposed by ¨Olveczky and Lysne. An important advantage of our
method is that it minimizes the use of conditional rules and produces simpler transformed programs whose
termination is often easier to prove automatically.
Keywords: Term rewriting, program analysis, operational termination, membership equational logic,
order-sorted equational logic, rewriting logic.


Source: Alpuente, María - Departamento de Sistemas Informáticos y Computación, Universitat Politècnica de València


Collections: Computer Technologies and Information Sciences