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First-class substitutions in contextual type theory

By Andrew Cave and Brigitte Pientka

Abstract

In this paper, we revisit the theory of first-class substitution in notion of substitution variables. This forms the basis for extending Beluga, a dependently typed proof and programming language which already supports first-class contexts and contextual objects, with first-class substitutions. To illustrate the elegance and power of first-class substitution variables, we describe the implementation of a weak normalization proof for the simply-typed lambda-calculus in Beluga. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.8910
Provided by: CiteSeerX
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