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Weak Normalization for the Simply-Typed Lambda-Calculus in Twelf

Summary: Weak Normalization for the Simply-Typed
Lambda-Calculus in Twelf
(Extended Abstract)
Andreas Abel
Department of Computer Science, Chalmers University of Technology
R¨annv¨agen 6, SWE-41296 G¨oteborg, Sweden
Abstract. Weak normalization for the simply-typed -calculus is proven
in Twelf, an implementation of the Edinburgh Logical Framework. Since
due to proof-theoretical restrictions Twelf Tait's computability method
does not seem to be directly usable, a combinatorical proof is adapted
and formalized instead.
1 Introduction
Twelf is an implementation of the Edinburgh Logical Framework which supports
reasoning in full higher-order abstract syntax; therefore it is an ideal candidate
for reasoning comfortably about properties of prototypical programming lan-
guages with binding. Previous work has focused on properties like subject reduc-
tion, confluence, compiler correctness. Even cut elimination for various sequent
calculi has been proven successfully, but until recently, there were no formalized
proofs of normalization in Twelf. The reason might be that normalization is typ-
ically proven by Tait's method, which cannot be applied directly in Twelf. This


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München


Collections: Computer Technologies and Information Sciences