Realizability interpretation of coinductive definitions and program synthesis with streams

Abstract

The main aim of the paper is to construct a logical system in which properties of programs can be formalized for verification, synthesis and transformation. The paper has two main points. One point is a realizability interpretation of coinductive definitions of predicates. The other point is extraction of programs which treat streams. An untyped predicative theory TID v is presented, which has the facility of coinductive definitions of predicates and is based on constructive logic. Properties defined by the greatest fixed point, such as streams and the extensional equality of streams, can be formalized by the facility of coinductive definitions of predicates in TID v . A q -realizability interpretation for TID v is defined and the soundness of the interpretation is proved. By the realizability interpretation, a program which treats streams can be extracted from a proof of its specification in TID v . A general program extraction theorem and a stream program extraction theorem are presented.