A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455

An Isabelle formalization of protocol-independent secrecy with an application to e-commerce

A protocol-independent secrecy theorem is established and applied to several nontrivial protocols. In particular, it is applied to protocols proposed for protecting the computation results of free-roaming mobile agents doing comparison shopping. All the results presented here have been formally proved in Isabelle by building on Larry Paulson's inductive approach. This therefore provides a library of general theorems that can be applied to other protocols

THEORIE DES TYPES ET RECRITURE

ORSAY-PARIS 11-BU Sciences (914712101) / SudocNANCY-INRIA Lorraine LORIA (545472304) / SudocSudocFranceF

On the Confluence of λ-Calculus with Conditional Rewriting

The confluence of untyped #-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of #-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Muller and Dougherty for unconditional rewriting. Two cases are considered, whether beta-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing #-reduction to weakly normalizing #-reduction. We also provide examples showing that outside these conditions, modularity of confluence is di#cult to achieve