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Some Lambda Calculus and Type Theory Formalized (1999)

McKinna, James ; Pollack, Robert

Springer

Journal of automated reasoning 23 (1999), S. 373-409

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Details

ISSN: 1573-0670

Schlagwort(e): formal mathematics ; lambda calculus ; Pure Type Systems ; type theory ; LEGO proof checker

Quelle: Springer Online Journal Archives 1860-2000

Thema: Informatik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1006294005493

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