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Continuous Functionals of Dependent Types and Equilogical Spaces
 

Summary: Continuous Functionals of Dependent
Types and Equilogical Spaces
Andrej Bauer 1 and Lars Birkedal 2
1
Andrej.Bauer@cs.cmu.edu
School of Computer Science, Carnegie Mellon University
5000 Forbes Avenue, Pittsburgh PA 15213, USA
2
birkedal@it≠c.dk
The IT University of Copenhagen
Glentevej 67, DK≠2400 KÝbenhavn NV, Denmark
Abstract. We show that dependent sums and dependent products of
continuous parametrizations on domains with dense, codense, and nat≠
ural totalities agree with dependent sums and dependent products in
equilogical spaces, and thus also in the realizability topos RT(P!).
Keywords: continuous functionals, dependent type theory, domain the≠
ory, equilogical spaces.
1 Introduction
Recently there has been a lot of interest in understanding notions of totality for
domains [3, 23, 4, 18, 21]. There are several reasons for this. Totality is the se≠

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics