### Abstract

We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified proof of standardization for beta reduction that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.

Original language | English |
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Pages (from-to) | 373-409 |

Number of pages | 37 |

Journal | Journal of Automated Reasoning |

Volume | 23 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1999 |

### Keywords

- Formal mathematics
- Lambda calculus
- LEGO proof checker
- Pure Type Systems
- Type theory

### ASJC Scopus subject areas

- Software
- Computational Theory and Mathematics
- Artificial Intelligence

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## Cite this

*Journal of Automated Reasoning*,

*23*(3), 373-409. https://doi.org/10.1023/A:1006294005493