There are many styles for the narrative structure of a mathematical document. Each mathematician has its own conventions and traditions about labeling portions of texts (e.g., chapter, section, theorem or proof) and identifying statements according to their logical importance (e.g., theorem is more important than lemma). Such narrative/struc-turing labels… (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)
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 Normali-sation.
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)
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)
First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with and for the helpful remarks received from them. Last but not least, we are grateful to the anonymous referees for their constructive… (More)