Fairouz Kamareddine

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Mathematical texts can be computerized in many ways that capture differing amounts of the mathematical meaning. At one end, there is document imaging, which captures the arrangement of black marks on paper, while at the other end there are proof assistants (e.g., Mizar, Isabelle, Coq, etc.), which capture the full mathematical meaning and have proofs(More)
The aim of this paper is to present the s-calculus which is a very simple-calculus with explicit substitutions and to prove its connuence on closed terms and the preservation of strong normalisation of-terms. We shall prove strong normalisation of the corresponding calculus of substitution by translating it into the-calculus ACCL91], and therefore the(More)
This article is a brief review of the type-free -calculus and its basic rewriting notions, and of the pure type system framework which generalises many type systems. Both the type-free -calculus and the pure type systems are presented using variable names and de Bruijn indices. Using the presentation of the -calculus with de Bruijn indices, we illustrate(More)
We explain in this paper the gradual computerisation process of an ordinary mathematical text into more formal versions ending with a fully formalised Mizar text. The process is part of the MathLang–Mizar project and is divided into a number of steps (called aspects). The first three aspects (CGa, TSa and DRa) are the same for any MathLang–TP project where(More)
Abstract. We provide a syntax and a derivation system for a formal language of mathematics called Weak Type Theory (WTT). We give the metatheory of WTT and a number of illustrative examples. WTT is a refinement of de Bruijn’s Mathematical Vernacular (MV) and hence: WTT is faithful to the mathematician’s language yet is formal and avoids ambiguities. WTT is(More)