Term rewriting system is a helpful tool for implementing functional programming languages. We focus upon a transformation of term rewriting systems called currying. Currying transforms a term rewriting system with symbols of arbitrary arity into another one, which contains only nullary symbols with a single binary symbol called application. Currying in single-sorted case is explored in [1] but ...

A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P if and only if its underlying term rewriting system Θ(R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort.

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that weak normalization is persistent for term rewriting systems. Furthermore we obtain that semi-completeness is persistent for term rewriting systems and we give the exampl...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for non-overlapping term rewriting systems and we give the example as application of this result. Furthermore we obtain that completeness...

We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions ...

A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort. This is the posit...

We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. We present three such transformations, and prove for all of them that ...

String rewriting systems have been originally introduced by Thue [21] in order to study word problems in monoids. A string rewriting system (Σ,R) consists of a set Σ, called the alphabet, and a set R ⊆ Σ∗×Σ∗ of rules. The monoid Σ∗/≡R, obtained by quotienting the free monoid Σ∗ over Σ by the smallest congruence (wrt concatenation) containing R, is called the monoid presented by the rewriting sy...

BDDs provide an established technique for propositional formula manipulation. In this paper we re-develop the basic BDD theory using standard rewriting techniques. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical ROBDDs can be obtained. For this rewriting system a layerwise strategy is ...

It is well-known that a term rewriting system can be faithfully described by a cartesian 2-category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2-categorical presentation for term graph rewriting. Building on a result presented in 8], which shows that term graphs over a given signature are in one-to-one correspo...