First-class substitutions in contextual type theory

Authors:
Andrew Cave;Brigitte Pientka
Affiliations:
McGill University, Montreal, PQ, Canada;McGill University, Montreal, PQ, Canada
Venue:
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Year:
2013

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Abstract

In this paper, we revisit the theory of first-class substitution in contextual type theory (CTT); in particular, we focus on the abstract 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.