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Journal of Automated Reasoning

, Volume 29, Issue 3–4, pp 365–387 | Cite as

A New Implementation of Automath

  • Freek Wiedijk
Article

Abstract

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features:

• It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds.

• Its implementation of λ-terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder.

• The program can compile an Automath text into one big ‘Automath single line’-style λ-term. It outputs such a term using de Bruijn indices. (These λ-terms cannot be checked by modern systems like Coq or Agda, because the λ-typed λ-calculi of de Bruijn are different from the Π-typed λ-calculi of modern type theory.)

The source of aut is freely available on the Web at the address <http://www.cs.kun.nl/~freek/aut/>.

Automath formalized mathematics proof objects type theory 

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© Kluwer Academic Publishers 2002

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  • Freek Wiedijk

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