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Declarative languages such as OBJ, CafeOBJ, and Maude use syntactic annotations to introduce replacement restrictions aimed at improving termination or efficiency of computations. Unfortunately, there is a lack of formal techniques for proving such benefits. We show that context-sensitive rewriting and <i>on-demand rewriting</i> provide a suitable framework… (More)

Reasoning about the termination of equational programs in sophisticated equa-tional 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… (More)

Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed… (More)

The concept of deenitional tree by Antoy serves to introduce control information into the bare set of rules of a constructor-based term rewriting system (TRS). TRSs whose rules can be arranged into a deenitional tree are called inductively sequential. By relying on the existence of such a deenitional tree, an optimal rewriting strategy, the outermost-needed… (More)

Restrictions of rewriting can eventually achieve termination by pruning all infinite rewrite sequences issued from every term. Context-sensitive rewriting (CSR) is an example of such a restriction. In CSR, the replacements in some arguments of the function symbols are permanently forbidden. This paper describes mu-term, a tool which can be used to… (More)

c 1998 Massachusetts Institute of Technology. Subscribers are licensed to use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal's World Wide Web site for further details. The Journal of Functional and Logic Programming… (More)

We present a generic scheme for the declarative debugging of functional programs modeled as term rewriting systems. We associate to our programs a semantics based on a (continuous) immediate consequence operator, T R , which models the (values/normal forms) semantics of R. Then, we develop an effective debugging methodology which is based on abstract… (More)

Polynomials over the real numbers were proposed as an alternative to polynomials over the naturals in termination proofs. We have recently shown how to use an arbitrary polynomial interpretation over the reals to generate well-founded and stable term orderings. Monotonicity can, then, be gradually introduced in the interpretations to deal with different… (More)