On Intuitionistic Proof Transformations, their Complexity, and Application to Constructive Program Synthesis

Intuitionistic Proof Transformations and Their Application to Constructive Program Synthesis

Logic-based Program Synthesis via Program Extraction POSITION PAPER

This paper outlines the author’s experiences using the methodology of program extraction within a proof assistant based on constructive type theory. We discuss the feasibility of the methodology and tool support, and suggest some directions for future research.

Program synthesis and transformations in an object-oriented environment

An object-oriented language with automatic synthesis of methods (programs) and transformations of OO descriptions using a logical metalanguage (Horn-clause logic) are considered. Automatic synthesis of methods (Proof-As-Program approach) is based on intuitionistic propositional calculus. The metalanguage expresses general knowledge related to classes and objects and it is used for describing tr...

Guiding Program Development Systems by a Connection Based Proof Strategy

We present an automated proof method for constructive logic based on Wallen’s matrix characterization for intuitionistic validity. The proof search strategy extends Bibel’s connection method for classical predicate logic. It generates a matrix proof which will then be transformed into a proof within a standard sequent calculus. Thus we can use an efficient proof method to guide the development ...

On the computational content of intuitionistic propositional proofs

The intuitionistic calculus was introduced to capture reasoning in constructive mathematics. As such it has much more constructive character than classical logic. This property of the intuitionistic calculus has been extensively studied, but mostly from the point of view of computability and little has been proved about computational complexity. The aim of this paper is to show that the constru...