Journal of Automated Reasoning

, Volume 23, Issue 3, pp 373–409 | Cite as

Some Lambda Calculus and Type Theory Formalized

  • James McKinna
  • Robert Pollack


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.

formal mathematics lambda calculus Pure Type Systems type theory LEGO proof checker 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • James McKinna
    • 1
  • Robert Pollack
    • 1
  1. 1.Department of Computer ScienceUniversity of DurhamU.K

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