Abstract
I shall deal here with conceptual questions concerning two related phenomena: 1) the use of deductive machinery to verify the correctness of computer programs, and 2) the running of programs on computers to produce proofs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Church: Introduction to Mathematical Logic (Princeton University Press, Princeton 1956)
H. Curry, R. Feys: Combinatory Logic, vol. 1 (North Holland, Amsterdam 1958)
M. Detlefsen, M. Luker: The four-color theorem and mathematical proof. The Journal of Philosophy 77 (1980) pp 803–820
G. Gentzen: Untersuchungen ber das logische Schliessen. Mathematische Zeitschrift 39 (1935) pp 176–210, 405-431
A. Heyting: Intuitionism, An Introduction (North Holland, Amsterdam 1956)
W. A. Howard: The formulae-as-types notion of constructions. In: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, ed by J. P. Seldin and J. R. Hindley (Academic Press 1980) pp 479–490
A. N. Kolmogorov: Zur Deutung der intuitionistischen Logik. Mathematische Zeitschrift 35 (1932) pp 58–65
P. Martin-Löf: An intuitionistic theory of types: Predicative part. In: Logic Colloquium’ 73, ed by H. E. Rose and J. C. Shepherdson (North Holland, Amsterdam 1975) pp 73–118
P. Martin-Löf: Constructive mathematics and computer programming. In: Logic, Methodology and Philosophy of Science IV, ed by L. J. Cohen et al. (North-Holland, Amsterdam 1982) pp 153–175
P. Martin-Löf: Intuitionistic Type Theory (Bibliopolis, Napoli 1984)
P. Martin-Löf: On the meanings of the logical constants and the justifications of the logical laws. In: Atti degli Incontri di Logica Matematica 2 Dipartimento di Matematica, Universit di Siena (1985) pp 203–281. Reprinted in Nordic Journal of Philosophical Logic 1 (1996) pp 11-60
D. Prawitz: Natural Deduction. A Proof-Theoretical Study (Almqvist and Wiksell, Stockholm 1965). Reprinted (Dover Publications, New York 2006)
D. Prawitz: Ideas and results in proof theory. In: Proceedings of the Second Scandinavian Logic Symposium, ed by J. Fenstad (North-Holland, Amsterdam, 1971) pp 237–309
D. Prawitz: Validity of inference. In: Proceedings from the 2nd Launer Symposium on the Occasion of the Presentation of the Launer Prize at Bern 2006 (2009) To appear
D. Prawitz, H. Prawitz and N. Voghera: A mechanical proof procedure and its realization in an electronic computer. Journal of the Association for Computing Machinery 7 (1960) pp 102–128
P. Teller: Computer proof. The Journal of Philosophy 77 (1980) pp 797–803
T. Tymoczko: The four-color problem and its philosophical significance. The Journal of Philosophy 76 (1979) pp 57–83
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Italia
About this chapter
Cite this chapter
Prawitz, D. (2008). Proofs Verifying Programs and Programs Producing Proofs: A Conceptual Analysis. In: Lupacchini, R., Corsi, G. (eds) Deduction, Computation, Experiment. Springer, Milano. https://doi.org/10.1007/978-88-470-0784-0_5
Download citation
DOI: https://doi.org/10.1007/978-88-470-0784-0_5
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0783-3
Online ISBN: 978-88-470-0784-0
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)