Formally Computing with the Non-computable.

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Church–Turing computability, which is the standard notion of computation, is based on functions for which there is an effective method for constructing their values. However, intuitionistic mathematics, as conceived by Brouwer, extends the notion of effective algorithmic constructions by also admitting constructions corresponding to human experiences of mathematical truths, which are based on temporal intuitions. In particular, the key notion of infinitely proceeding sequences of freely chosen objects, known as free choice sequences, regards functions as being constructed over time. This paper describes how free choice sequences can be embedded in an implemented formal framework, namely the constructive type theory of the Nuprl proof assistant. Some broader implications of supporting such an extended notion of computability in a formal system are then discussed, focusing on formal verification and constructive mathematics.
Original languageEnglish
Title of host publicationConference on Computability in Europe - CiE 2021
EditorsLiesbeth De Mol, Andreas Weiermann, Florin Manea, David Fernández-Duque
Place of PublicationCham
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages11
ISBN (Electronic)978-3-030-80049-9
ISBN (Print)9783030800482
StatePublished - 2 Jul 2021
Event17th Conference on Computability in Europe, CiE 2021 - Virtual, Online
Duration: 5 Jul 20219 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12813 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th Conference on Computability in Europe, CiE 2021
CityVirtual, Online

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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