This paper describes some formal tools to support distributed cooperative software engineering. Workers at diierent sites can collaborate on tasks including speci-cation, reenement, proving and documentation. A design record database supports alternative and incomplete development activities, and is read using any web browser; remote proof execution, animation, and informal explanation are supp...

We present a new set of reductions for derivations in natural deduction that can extract witnesses from closed derivations of simply existential formulas in Heyting Arithmetic (HA) plus the Excluded Middle Law restricted to simply existential formulas (EM1), a system motivated by its interest in proof mining. The reduction we have for classical logic are quite different from all existing ones. ...

The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor component, both for collaborative editing of documents, and for embedding in the resulting documents. This paper describes the design of Agora’s asynchronous edi...

Design patterns are reuse artifacts meant to improve the quality of software designs as well as the productivity of designers. Patterns (and their relationships) are mostly described in an informal fashion which leads to ambiguity and limits tools support. This has worsened with the growing number of well-established and candidate patterns. This paper discusses how to formally specify the "solu...

The proofs of universally quantiied statements, in mathematics, are given as \schemata" or as \prototypes" which may be applied to each speciic instance of the quantiied variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Her-brand. In this constructive approach where propositions are types, proofs are viewed as terms of ?calculus and...

Traditionally many proofs in real time scheduling theory were informal and lacked the rigor usually required for good mathematical proofs. Some attempts have been made towards making the proofs more reliable, including using formal logics to specify scheduling algorithms and verify their properties. In particular, Duration Calculus, a real time interval temporal logic, has been used since timin...

— This informal article is an expanded version of two lectures given in Padova during the “Dwork Trimester” in June 2001. Their goal was to explain the proof of the p-adic monodromy theorem for de Rham representations and to give some background on p-adic representations. Résumé. — Cet article informel est une version longue de deux exposés donnés à Padoue en Juin 2001 au “Trimestre Dwork”. Leu...

We characterize the defining equation of a plane algebraic curve with exactly one rational place Q at infinity, then give a basis of L(mQ) with pairwise distinct pole orders at Q. The defining equation can be regarded as a generalization of the Weierstrass form of a hyperelliptic curve. In this informal note I give an English proof of the results of the Cab curve found by Miura [4, 5, 6]. Throu...

This is a tutorial on some of the main ideas in KAM theory. The goal is to present the background and to explain and compare somewhat informally some of the main methods of proof. It is an expanded version of the lectures given by the author in the Summer Research Institute on Smooth Ergodic Theory Seattle, 1999. The style is somewhat informal and expository and it only aims to be an introducti...