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

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

2012-02-04

arxiv.org/abs/1202.0904v1

Computer Science

Logic in Computer Science

Scientific paper

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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