#### Filter Results:

- Full text PDF available (131)

#### Publication Year

1992

2017

- This year (1)
- Last 5 years (18)
- Last 10 years (62)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Fairouz Kamareddine, Joe B. Wells
- Electr. Notes Theor. Comput. Sci.
- 2008

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)

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
- J. Funct. Program.
- 2005

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)

- Tijn Borghuis, Fairouz Kamareddine, Rob Nederpelt
- Logic Journal of the IGPL
- 2002

- F. Kamareddine
- 2006

In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computerbased formalisation for mathematical authoring habits and we present an… (More)

- Fairouz Kamareddine, Rob Nederpelt
- Journal of Logic, Language and Information
- 2004

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)

- Roel Bloo, Fairouz Kamareddine, Rob Nederpelt
- Inf. Comput.
- 1996

In this paper, we propose to extend the Barendregt Cube by generalising reduction and by adding definition mechanisms. We sho;' that this extension satisfies all the original properties of the Cube including Church Rosser, Subject Reduction and Strong Normalisation.