Towards a mathematical theory of program synthesis

Authors:
Masahiko Sato
Affiliations:
Department of Information Science, Faculty of Science, University of Tokyo, Tokyo, Japan
Venue:
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 2
Year:
1979

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IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1

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Abstract

This paper attempts to set a theoretical foundation for Program Synthesis. A Programming language Progis introduced together with its interpretation in the semantic domain D. A formal system QFT, which is an extension of the Heyting arithmetic, is then introdced in order to express specifications formally. Roughly stated, the main result is: Given a QFT-Proof of the specification A[x,z], it is possible to construct a program p such that A[x,p[x]] is true in D for any input x. Moreover, a formal proof of A[x,p[x]] can also be obtained. Since any program p in Prog always terminates, the above result estabilishes the total correctness of the synthesized program at the same time. Finally, it is shown that any program p in Prog can be faithfully simulated by means of LISP.