The mathematical language AUTOMATH, its usage, and some of its extensions

Publisher Summary This chapter discusses the mathematical language Automath, its usage, and some of its extensions. Automath is a language suitable for expressing very large parts of mathematics in such a way that the correctness of the mathematical contents is guaranteed as long as the rules of grammar are obeyed. The possibility of building languages defined in terms of Automath but adapted to special purposes are indicated. The chapter also provides a preliminary description of the language, structure of the lines, how to write PAL, how to use it for mathematical reasoning, extending PAL to Automath, how to use Automath for mathematical reasoning, and processors for automath. PAL is a sublanguage of Automath and is quite easy to learn. In PAL, the lambda conversation is not used, and there is no limitation on the variables. The possibilities of superimposed languages, automatic theorem proving, and extensions of Automath are also described in this chapter.