Denotation of syntax and metaprogramming in contextual modal type theory (CMTT)
Logic in Computer Science
2013-05-28 v1 Logic
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.
Keywords
Cite
@article{arxiv.1202.0904,
title = {Denotation of syntax and metaprogramming in contextual modal type theory (CMTT)},
author = {Murdoch Gabbay and Aleksandar Nanevski},
journal= {arXiv preprint arXiv:1202.0904},
year = {2013}
}