A cartesian closed category in Martin-Löf's intuitionistic type theory

Authors:
Silvio Valentini
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, via G. Belzoni n.7, I-35131 Padova, Italy
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

First, we briefly recall the main definitions of the theory of Information Bases and Translations. These mathematical structures are the basis to construct the cartesian closed category InfBas, which is equivalent to the category ScDom of Scott domains.Then, we will show that all the definitions and the proof of all the properties that one needs in order to show that InfBas is indeed a cartesian closed category can be formalized within Martin-Löf's intuitionistic type theory.