A Formalization of Strong Normalization for Simply-Typed Lambda-Calculus and System F

Authors:
Kevin Donnelly;Hongwei Xi
Affiliations:
Computer Science Department, Boston University, Boston, USA;Computer Science Department, Boston University, Boston, USA
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2007

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Abstract

We formalize in the logical framework ATS/LF a proof based on Tait's method that establishes the simply-typed lambda-calculus being strongly normalizing. In this formalization, we employ higher-order abstract syntax to encode lambda-terms and an inductive datatype to encode the reducibility predicate in Tait's method. The resulting proof is particularly simple and clean when compared to previously formalized ones. Also, we mention briefly how a proof based on Girard's method can be formalized in a similar fashion that establishes System F being strongly normalizing.