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Summary: A Third-Order Representation of the
-Calculus
Andreas Abel ?
Carnegie Mellon University, Department of Computer Science
5000 Forbes Avenue, Pittsburgh, PA 15213, USA
phone: +1(412)268-2582, email: abel@cs.cmu.edu
Abstract. Higher-order logical frameworks provide a powerful technol-
ogy to reason about object languages with binders. This will be demon-
strated for the case of the -calculus with two di erent binders which
can most elegantly be represented using a third-order constant. Since
cases of third- and higher-order encodings are very rare in comparison
with those of second order, a second-order representation is given as well
and equivalence to the third-order representation is proven formally.
1 Introduction
The -calculus [Par92,OS97,Bie98], a proof theory for the implicational frag-
ment of classical logic, has been established as a general tool to reason about
functional programming languages with control, e.g. continuations and excep-
tions. It is basically an extension of the -calculus by a second binder. Some of
its properties like strong normalization and con
uence are very fundamental for
its use in functional programming and proof systems; a formal veri cation of
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