Fairouz Kamareddine

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Typed-calculus uses two abstraction symbols (and) which are usually treated in diierent ways: x: :x has as type the abstraction x: : yet x: : has type 2 rather than an abstraction; moreover, (x:A :B)C is allowed and-reduction evaluates it, but ((x:A :B)C is rarely allowed. Furthermore, there is a general consensus that and are diierent abstraction(More)
  • Fairouz Kamareddine, Manuel Maarek, Krzysztof Retel, J B Wells, F Kamareddine, M Maarek +1 other
  • 2007
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)
Motivations 1 To handle the structure of a mathematical document as it appears on paper and at the same time allowing further computerisation and analysis. 2 To allow the presentation of a text with different layouts. 3 To allow further formalisation. Different font styles used to emphasize important parts of text. Relations between mathematical labels(More)
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 close to(More)
In this article, we introduce a-notation that is useful for many concepts of the-calculus. The new notation is a simple translation of the classical one. Yet, it provides many nice advantages. First, we show that deenitions such as compatibility, the heart of a term and-redexes become simpler in item notation. Second, we show that with this item notation,(More)
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)
This document is an appendix to [KMW]. It is composed by the translation of the Foundations of Analysis' first chapter into MathLang (Section A) and by E. Landau's original text (Section B). References [KMW] Fairouz Kamareddine, Manuel Maarek, and J B Wells. MathLang: experience-driven development of a new mathematical language. This section includes the(More)