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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)

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)

Computerizing mathematical texts to allow software access to some or all of the texts' semantic content is a long and tedious process that currently requires much expertise. We believe it is useful to support computerization that adds some structural and semantic information, but does not require jumping directly from the word-processing level believe they… (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)

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)

This paper starts by setting the ground for a lambda calculus notation that strongly mirrors the two fundamental operations of term construction, namely abstraction and application. In particular, we single out those parts of a term, called items in the paper, that are added during abstraction and application. This item notation proves to be a powerful… (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)