Denotation of syntax and metaprogramming in contextual modal type theory (CMTT).

Authors: Murdoch Gabbay, Aleksandar Nanevski
Subjects: Logic in Computer Science

link: http://arxiv.org/abs/1202.0904
Abstract

The modal logic S4 can be used via a Curry-Howard style correspondence to
obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as
`closed syntax of the calculus'. This lambda-calculus is called modal type
theory --- this is the basic case of a more general contextual modal type
theory, or CMTT.

CMTT has never been given a denotational semantics in which modal types are
given denotation as closed syntax. We show how this can indeed be done, with a
twist. We also use the denotation to prove some properties of the system.

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Denotation of syntax and metaprogramming in contextual modal type theory (CMTT).

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