The Language Theory of Automath: Chapter I, Sections 1–5 (Introduction)

Publisher Summary This chapter discusses the language theory and its role in the Automath project. The preliminary remarks, followed by a survey of the Automath project are also described. An informal introduction to the various Automath languages and how mathematical reasoning can be represented are explained. A comparison with related logical systems and related enterprises is also done. It gives an account of the language theoretical studies on the Automath languages. In Automath, it is attempted to achieve the feasibility of the writing stage by keeping as close as possible to ordinary informal mathematical reasoning, and to existing good mathematical habits. The project can be compared with two other major proof–checking projects: the First Order Logic (FOL) and the Logic of Computable Functions (LCF). When constructing a proof–checking, the total amount of work between the human writer and the machine must be divided. The Automath languages AUT–68 and AUT–QE belong to the pure systems, the language AUT– П belongs to the extended systems and there are no arithmetical Automath languages. The chapter also discusses the aims of the language theory, consequences of closure, a comparison with higher order systems and lower systems, and generalized functionality.