RP Rob Nederpelt

TL;DR: Part 1 Motivation and exposition: verification of mathematical proofs by a computer, N.G. de Bruijn the mathematical language automath, its usage, and some of its extensions, and a description of automath and some aspects of its language theory.

TL;DR: This chapter discusses the strong normalization in a typed lambda calculus with lambda structured types, in which the types themselves have lambda structure, and a method for deriving strongnormalization from normalization together with the uniqueness of normal forms is provided.

TL;DR: In this paper, the authors propose to extend the Barendregt Cube by generalisings-reduction and by adding definition mechanisms, which satisfy most of the original properties of the Cube including Church-Rosser, Subject Reduction and Strong Normalisation.

TL;DR: In this article, the authors propose a lambda calculus notation for abstraction and application of a term, called items, which can be used to represent basic substitution steps, giving rise to different versions of β-reduction including local and global.

TL;DR: Weak Type Theory is a refinement of de Bruijn's Mathematical Vernacular and hence WTT is faithful to the mathematician's language yet isformal and avoids ambiguities, and acts as an intermediary between the language of mathematicians and that of logicians.