On the Logical Content of Computational Type Theory: A Solution to Curry's Problem

Authors:
Matt Fairtlough;Michael Mendler
Affiliations:
-;-
Venue:
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Year:
2000

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Abstract

In this paper we relate the lax modality O to Intuitionistic Propositional Logic (IPL) and give a complete characterisation of inhabitation in Computational Type Theory (CTT) as a logic of constraint contexts. This solves a problem open since the 1940's, when Curry was the first to suggest a formal syntactic interpretation of O in terms of contexts.