Church-Rosser theorem for a rewriting system on categorial combinators

Church-Rosser for Borrowed Context Rewriting

Modelling distributed and mobile systems at a suitable level of abstraction maybe considered the main application area of process calculi and graph transformation systems. Analysis and verification methods for the resulting models abound. Here we focus on two lines of research: on the one hand the work following the influential theory of Reactive Systems (rs) [6] (originally developed for proce...

An effective one-step Church-Rosser strategy for combinators

Church-Rosser Properties of Normal Rewriting

We prove a general purpose abstract Church-Rosser result that captures most existing such results that rely on termination of computations. This is achieved by studying abstract normal rewriting in a way that allows to incorporate positions at the abstract level. New concrete Church-Rosser results are obtained, in particular for higher-order rewriting at higher types. 1998 ACM Subject Classific...

Partial Categorical Multi-Combinators and Church-Rosser Theorems

Categorical Multi Combinators form a rewriting system developed with the aim of providing e cient implementations of lazy functional languages The core of the system of Categorical Multi Combinators consists of only four rewriting laws with a very low pattern matching complexity This system allows the equivalent of several reductions to be performed at once as functions form frames with all the...

On Upper Bounds on the Church-Rosser Theorem

The Church-Rosser theorem in the type-free λ-calculus is well investigated both for β-equality and β-reduction. We provide a new proof of the theorem for β-equality with no use of parallel reductions, but simply with Takahashi's translation (Gross-Knuth strategy). Based on this, upper bounds for reduction sequences on the theorem are obtained as the fourth level of the Grzegorczyk hierarchy.