Homological Computations for Term Rewriting Systems

Decidable Call by Need Computations in term Rewriting (Extended Abstract)

In this paper we study decidable approximations to call by need computations to normal and root-stable forms in term rewriting. We obtain uniform decidability proofs by making use of elementary tree automata techniques. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of term rewriting systems.

Call by need computations in orthogonal term rewriting systems

Term Rewriting Systems : Syntax , Semantics , and Pragmatics Extended

We present a formalism called Addressed Term Rewriting Systems, which can be used to define the operational semantics of programming languages, especially those involving sharing, recursive computations and cyclic data structures. Addressed Term Rewriting Systems are therefore well suited for describing object-based languages, as for instance the family of languages called λObja, involving both...

Combining Computer Algebra and Rule Based Reasoning

We present extended term rewriting systems as a means to describe a simpliication relation for an equational speciication with a built-in domain of external objects. Even if the extended term rewriting system is canonical, the combined relation including built-in computations of`ground terms' needs neither be terminating nor connuent. We investigate restrictions on the extended term rewriting s...

Term Graph Narrowing 3

We introduce term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uniication. Our main result is that this mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and connuent. This includes, in particular, all convergent term rewriting syste...