Program synthesis through Gödel's interpretation

Shigeki Goto

doi:10.1007/3-540-09541-1_32

Program synthesis through Gödel's interpretation

Shigeki Goto^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

This paper develops a program synthesis method based upon intuitionistic logic. This method is essentially an application of Gödel's interpretation which is also called Dialectica interpretation. By the use of Gödel's interpretation, it is possible to transform proof figures of intuitionistic number theory into primitive recursive functionals. The present concept is that primitive recursive functionals can be represented by LISP programs. Consequently, proof figures can be transformed into computer programs. To confirm this idea experimentally, a program synthesizer GDL0, which is a PDP-11 (DEC) program, is implemented. GDL0 experimental applications results are presented.

Original language	English
Title of host publication	Mathematical Studies of Information Processing - Proceedings of the International Conference
Publisher	Springer-Verlag
Pages	302-325
Number of pages	24
ISBN (Print)	9783540095415
DOIs	https://doi.org/10.1007/3-540-09541-1_32
Publication status	Published - 1979 Jan 1
Externally published	Yes
Event	International Conference on Mathematical Studies of Information Processing, 1978 - Kyoto, Japan Duration: 1978 Aug 23 → 1978 Aug 26

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	75 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	International Conference on Mathematical Studies of Information Processing, 1978
Country/Territory	Japan
City	Kyoto
Period	78/8/23 → 78/8/26

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-09541-1_32

Cite this

Goto, S. (1979). Program synthesis through Gödel's interpretation. In Mathematical Studies of Information Processing - Proceedings of the International Conference (pp. 302-325). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 75 LNCS). Springer-Verlag. https://doi.org/10.1007/3-540-09541-1_32

Program synthesis through Gödel's interpretation. / Goto, Shigeki.
Mathematical Studies of Information Processing - Proceedings of the International Conference. Springer-Verlag, 1979. p. 302-325 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 75 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Goto, S 1979, Program synthesis through Gödel's interpretation. in Mathematical Studies of Information Processing - Proceedings of the International Conference. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 75 LNCS, Springer-Verlag, pp. 302-325, International Conference on Mathematical Studies of Information Processing, 1978, Kyoto, Japan, 78/8/23. https://doi.org/10.1007/3-540-09541-1_32

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AB - This paper develops a program synthesis method based upon intuitionistic logic. This method is essentially an application of Gödel's interpretation which is also called Dialectica interpretation. By the use of Gödel's interpretation, it is possible to transform proof figures of intuitionistic number theory into primitive recursive functionals. The present concept is that primitive recursive functionals can be represented by LISP programs. Consequently, proof figures can be transformed into computer programs. To confirm this idea experimentally, a program synthesizer GDL0, which is a PDP-11 (DEC) program, is implemented. GDL0 experimental applications results are presented.

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Program synthesis through Gödel's interpretation

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