Term rewriting for normalization by evaluation

Lecture Notes in Computer Science, 1987

Mathematical Structures in Computer Science, 2006

We present a formalism called Addressed Term Rewriting Systems, which can be used to model implementations of theorem proving, symbolic computation, and programming languages, especially aspects of sharing, recursive computations and cyclic data structures. Addressed Term Rewriting Systems are therefore well suited for describing object-based languages, and as an example we present a language called λOb a , incorporating both functional and object-based features. As a case study in how reasoning about languages is supported in the ATRS formalism a type system for λOb a is defined and a type soundness result is proved.

Electronic Notes in Theoretical Computer Science, 2005

Reduction strategies in rewriting and programming continue to attract attention. As new strategies are discovered and investigated, new results on rewriting and on computation under particular strategies become available. A number of programming languages, e.g., Elan, Maude, *OBJ* and Stratego, and systems, e.g., Clean, Curry, and Haskell, permit the explicit definition or modification of the computational reduction strategy. Research in this field ranges from primarily theoretical questions about reduction strategies to very practical application and implementation issues. There is a need for a deeper understanding of reduction strategies in rewriting and programming, both in theory and practice, since they bridge the gap between unrestricted general rewriting rewriting with particular strategies. Moreover, reduction strategies bridge investigations of operational principles, e.g., graph and term rewriting, narrowing and lambda-calculus, and semantics, e.g., normalization, computation of values, infinitary normalization and head-normalization, with implementations of programming languages. The workshop is the fourth edition in a series of events intended to provide a forum for presenting and discussing cutting-edge ideas and new results, recent developments, research directions and surveys on existing knowledge in this area. The previous WRS editions were:

African Journal of Mathematics and Computer Science Research, 2012

It is well-known that termination of finite term of rewriting systems is generally undecidable. Notwithstanding, a remarkable result is that, rewriting systems are Turing complete. A number of methods have been developed to establish termination for certain term of rewriting systems, particularly occurring in practical situations. In this paper, we present an overview of the existing methods used for termination proofs. We also outline areas of applications of term rewriting systems along with recent developments in regard to automated termination proofs.

IEICE Transactions on Information and Systems, 2009

A static dependency pair method, proposed by us, can effectively prove termination of simply-typed term rewriting systems (STRSs). The theoretical basis is given by the notion of strong computability. This method analyzes a static recursive structure based on definition dependency. By solving suitable constraints generated by the analysis result, we can prove the termination. Since this method is not applicable to every system, we proposed a class, namely, plain function-passing, as a restriction. In this paper, we first propose the class of safe function-passing, which relaxes the restriction by plain function-passing. To solve constraints, we often use the notion of reduction pairs, which is designed from a reduction order by the argument filtering method. Next, we improve the argument filtering method for STRSs. Our argument filtering method does not destroy type structure unlike the existing method for STRSs. Hence, our method can effectively apply reduction orders which make use of type information. To reduce constraints, the notion of usable rules is proposed. Finally, we enhance the effectiveness of reducing constraints by incorporating argument filtering into usable rules for STRSs.

Language definitions are often based on significant tacit knowledge. Here, we define a theory of term rewriting systems and an entire programming language without any prerequisites other than precision. All code is available at Github (https://github.com/BabelfishNL/Tram.git)

Journal of Symbolic Computation, 1991

We discuss tenn rewriting in conjunction with sprfn, a Prolog-based theorem prover. Two techniques for theorem proving that utilize tenn rewriting are presented. We demonstrate their effectiveness by exhibiting the results of our experiments in proving some theorems of von Neumann-Bemays-Godel set theory. Some outstanding problems associated with tenn rewriting are also addressed.

We define an efficient rewriting strategy for general term rewriting systems. Several strategies have been proposed over the last two decades for rewriting, the most efficient of all being the natural rewriting strategy of Escobar. All the strategies so far, including natural rewriting, assume that the given term rewriting system is left-linear and constructor-based. Although these restrictions are reasonable for some functional programming languages, they limit the expressive power of equational programming languages, and they preclude certain applications of rewriting to equational theorem proving and to languages combining equational and logic programming. In [5], we proposed a conservative generalization of the natural rewriting strategy that does not require the previous assumptions for the rules and we established its soundness and completeness.

Information and Computation, 1990

It is undecidable whether or not a finite Noetherian term rewriting system is ground-confluent. This undecidability result holds even when systems involving only unary function symbols and one constant are being considered, or when left-linear or right-linear ...

In this paper we propose a method to automatically infer algebraic property-oriented specifications from Term Rewriting Systems. Namely, having three semantics with suitable properties, given the source code of a TRS we infer a specification which consists of a set of \emph{most general} equations relating terms that rewrite, for all possible instantiations, to the same set of constructor terms. The semantic-based inference method that we propose can cope with non-constructor-based TRSs, and considers non-ground terms.