On Constructor Rewrite Systems and the Lambda Calculus

On Constructor Rewrite Systems and the Lambda-Calculus

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, ...

On Constructor Rewrite Systems and the Lambda-Calculus (Long Version)

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, ...

On Termination and Confluence Properties of Disjoint and Constructor-Sharing Conditional Rewrite Systems

We investigate the modularity behaviour of termination and connuence properties of (join) conditional term rewriting systems. We give counterexamples showing that the properties weak termination, weak innermost termination and (strong) innermost termination are not preserved in general under signature extensions. Then we develop suucient conditions for the preservation of these properties under...

Notes on Lambda Calculus

Infinitary Lambda Calculus Innnitary Lambda Calculus

In a previous paper we have established the theory of transsnite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of innnitary rewriting, the BB ohm model of the lambda calculus can be seen as an innnitary term model. In contrast to term rewriting, there are several diierent possible notions of innnite term, whic...