TY - GEN
T1 - Formally Computing with the Non-computable.
AU - Cohen, Liron
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2021/7/2
Y1 - 2021/7/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85112138944&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-80049-9_12
DO - 10.1007/978-3-030-80049-9_12
M3 - Conference contribution
SN - 9783030800482
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 135
EP - 145
BT - Conference on Computability in Europe - CiE 2021
A2 - De Mol, Liesbeth
A2 - Weiermann, Andreas
A2 - Manea, Florin
A2 - Fernández-Duque, David
PB - Springer Science and Business Media Deutschland GmbH
CY - Cham
T2 - 17th Conference on Computability in Europe, CiE 2021
Y2 - 5 July 2021 through 9 July 2021
ER -