A rewrite system is called uniformly normalising if all its steps are perpetual, i.e. are such that if s → t and s has an infinite reduction, then t has one too. For such systems termination (SN) is equivalent to normalisation (WN). A well-known fact is uniform normalisation of orthogonal non-erasing term rewrite systems, e.g. the λI-calculus. In the present paper both restrictions are analysed...

This paper studies termination properties of rewrite systems that are typeable using intersection types. It introduces a notion of partial type assignment on Curryfied Term Rewrite Systems, that consists of assigning intersection types to function symbols, and specifying the way in which types can be assigned to nodes and edges between nodes in the tree representation of terms. Two operations o...

In earlier work, we have shown that for confluent term rewrite systems, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise this result to full rewriting. For that, we again exploit graph rewriting. We give a new proof of the adequacy of graph rewriting for full rewriting that allows for a precise control of the resources...

In this paper, we describe XQuery compilation and rewrite optimization in DB2 pureXML, a hybrid relational and XML database management system. DB2 pureXML has been designed to scale to large collections of XML data. In such a system, effective filtering of XML documents and efficient execution of XML navigation are vital for high throughput. Hence the focus of rewrite optimization is to consoli...

We show how one can use rewriting logic to faithfully capture (not implement) various operational semantic frameworks as rewrite logic theories, namely big-step and small-step semantics, reduction semantics using evaluation contexts, and continuation-based semantics. There is a one-to-one correspondence between an original operational semantics and its associated rewrite logic theory, both nota...

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper P.A. Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinit...

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value betareduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, ...

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value betareduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, ...