### 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 |
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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 | |

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) |
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Volume | 75 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | International Conference on Mathematical Studies of Information Processing, 1978 |
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Country | Japan |

City | Kyoto |

Period | 78/8/23 → 78/8/26 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

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

*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

}

TY - GEN

T1 - Program synthesis through Gödel's interpretation

AU - Goto, Shigeki

PY - 1979/1/1

Y1 - 1979/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84867632620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867632620&partnerID=8YFLogxK

U2 - 10.1007/3-540-09541-1_32

DO - 10.1007/3-540-09541-1_32

M3 - Conference contribution

AN - SCOPUS:84867632620

SN - 9783540095415

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 302

EP - 325

BT - Mathematical Studies of Information Processing - Proceedings of the International Conference

PB - Springer-Verlag

ER -