Summary: Continuous Functionals of Dependent
Types and Equilogical Spaces
Andrej Bauer 1 and Lars Birkedal 2
School of Computer Science, Carnegie Mellon University
5000 Forbes Avenue, Pittsburgh PA 15213, USA
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.
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≠