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LFM 2004 Preliminary Version Normalization for the SimplyTyped

Summary: LFM 2004 Preliminary Version
Normalization for the Simply­Typed
Lambda­Calculus in Twelf
Andreas Abel 1
Institut f˜ur Informatik, Ludwig­Maximilians­Universit˜at
Oettingenstr. 67, D­80538 M˜unchen, Germany
Normalization for the simply­typed #­calculus is proven in Twelf, an implementation of the Edinburgh
Logical Framework. Since due to proof­theoretical restrictions Twelf Tait's computability method does not
seem to be directly usable, a syntactical proof is adapted and formalized instead. In this case study, some
boundaries of Twelf current capabilities are touched and discussed.
Keywords: Edinburgh Logical Framework, HOAS, Mechanized Proof, Normalization, Twelf
1 Introduction
Twelf is an implementation of the Edinburgh Logical Framework which supports rea­
soning in full higher­order abstract syntax (HOAS); therefore it is an ideal candidate
for reasoning comfortably about properties of prototypical programming languages
with binding. Previous work has focused on properties like subject reduction, con­
fluence, compiler correctness. Even cut elimination for various sequent calculi has
been proven successfully. But until recently, there were no formalized proofs of nor­
malization 2 in Twelf. The reason might be that normalization is typically proven


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


Collections: Computer Technologies and Information Sciences