Constructive mathematics in theory and programming practice

&
Philosophia Mathematica 7 (1):65-104 (1999)
  Copy   BIBTEX

Abstract

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.

Categories

Keywords

Reprint years

DOI

10.1093/philmat/7.1.65

Other Versions

original Bridges, Douglas; Reeves, Steeve (1998) "Constructive Mathematics in Theory and Programming Practice". Philosophia Mathematica 6(3):65-104

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

On Farkas' lemma and related propositions in BISH.Josef Berger & Gregor Svindland - 2022 - Annals of Pure and Applied Logic 173 (2):103059.
On the foundations of constructive mathematics – especially in relation to the theory of continuous functions.Franka Arjanne Waaldijk - 2004 - Foundations of Science 10 (3):249-324.
A Definitive Constructive Open Mapping Theorem?Douglas Bridges & Hajime Ishihara - 1998 - Mathematical Logic Quarterly 44 (4):545-552.
Decomposability of ℝ and dense negative subsets of ℝ in constructive reverse mathematics.Mohammad Ardeshir & Mohammad Tahmasbizadeh - 2026 - Logic Journal of the IGPL 34 (1).
Natural Topology.Frank Waaldijk - 2012 - Brouwer Society.
Powers of positive elements in C *-algebras.Hiroki Takamura - 2011 - Mathematical Logic Quarterly 57 (5):481-484.
Reverse Mathematics in Bishop’s Constructive Mathematics.Hajime Ishihara - 2006 - Philosophia Scientiae:43-59.
Did Bishop have a philosophy of mathematics?Helen Billinge - 2003 - Philosophia Mathematica 11 (2):176-194.
Connectedness of the continuum in intuitionistic mathematics.Mark Bickford - 2018 - Mathematical Logic Quarterly 64 (4-5):387-394.
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.

Analytics

Added to PP
2009-01-28

Downloads
271 (#155,934)

6 months
39 (#213,417)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Mathematical Method and Proof.Jeremy Avigad - 2006 - Synthese 153 (1):105-159.
Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.
Limit spaces with approximations.Iosif Petrakis - 2016 - Annals of Pure and Applied Logic 167 (9):737-752.

View all 7 citations / Add more citations

References found in this work

Varieties of constructive mathematics.Douglas Bridges & Fred Richman - 1987 - New York: Cambridge University Press. Edited by Fred Richman.
Over de grondslagen der wiskunde.L. E. J. Brouwer - 1907 - Amsterdam-Leipzig: Maas & van Suchtelen.
Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.

View all 21 references / Add more references