Certifying Term Rewriting Proofs in ELAN

Automated Incremental Termination Proofs for Hierarchically Defined Term Rewriting Systems

We propose the notion of rewriting modules in order to provide a structural and hierarchical approach of TRS. We define then relative dependency pairs built upon these modules which allow us to perform termination proofs incrementally. Important results can be expressed in that new framework (regarding CE -termination for instance), and with help of extendable orderings, we give effective new i...

Certifying and Synthesizing Membership Equational Proofs

As the systems we have to specify and verify become larger and more complex, there is a mounting need to combine different tools and decision procedures to accomplish large proof tasks. The problem, then, is how to be sure that we can trust the correctness of a heterogeneous proof. In this work we focus on certification and synthesis of equational proofs, that are pervasive in most proof tasks ...

Observational proofs by rewriting

Rewriting and Multisets in ρ-calculus and ELAN

The ρ-calculus is a new calculus that integrates in a uniform and simple setting first-order rewriting, λ-calculus and non-deterministic computations. The main design concept of the ρ-calculus is to make all the basic ingredients of rewriting explicit objects, in particular the notions of rule application and multisets of results. This paper describes the calculus from its syntax to its basic p...

Rewriting with Strategies in ELAN: A Functional Semantics

In this work, we consider term rewriting from a functional point of view. A rewrite rule is a function that can be applied to a term using an explicit application function. From this starting point, we show how to build more elaborated functions, describing first rewrite derivations, then sets of derivations. These functions, that we call strategies, can themselves be defined by rewrite rules a...