Computing with Continuous Objects: A Uniform Co-inductive Approach

Autor:	Spreen, Dieter
Rok vydání:	2020
Předmět:	Computer Science - Logic in Computer Science Mathematics - Dynamical Systems Mathematics - General Topology 03D78 03F60 F.4.1
Zdroj:	Math. Struct. Comp. Sci. 31 (2021) 144-192
Druh dokumentu:	Working Paper
DOI:	10.1017/S0960129521000116
Popis:	A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown how to extract certified algorithms working with the signed digit representation from constructive proofs. Berger and the present author generalised this approach to complete metric spaces and showed how to deal with compact sets. Here, we unify this work and lay the foundations for doing a similar thing for the much more comprehensive class of compact Hausdorff spaces occurring in applications. The approach is of the same computational power as Weihrauch's Type-Two Theory of Effectivity. Comment: 46 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.05392 Zobrazit plný text záznamu View this record from Arxiv