Constructive Mathematics in Theory and Programming Practice

&
Philosophia Mathematica 6 (3):65-104 (1998)
  Copy   BIBTEX

Abstract

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics. 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

reprint Bridges, Douglas; Reeves, Steeve (1999) "Constructive mathematics in theory and programming practice". Philosophia Mathematica 7(1):65-104

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,486

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.Frank 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.
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.
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.
Handbook of Constructive Mathematics.Douglas Bridges, Hajime Ishihara, Michael Rathjen & Helmut Schwichtenberg (eds.) - 2023 - Cambridge: Cambridge University Press.
Bishop's Mathematics: a Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.
Doing and showing.Andrei Rodin - unknown

Analytics

Added to PP
2017-02-21

Downloads
41 (#582,892)

6 months
4 (#909,732)

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.
Did Bishop have a philosophy of mathematics?Helen Billinge - 2003 - Philosophia Mathematica 11 (2):176-194.
Choice principles and constructive logics.David Dedivi - 2004 - Philosophia Mathematica 12 (3):222-243.

View all 7 citations / Add more citations

References found in this work

No references found.

Add more references