Abstract

Writing correct programming code is necessary in computer system development, where complete testing is not possible. Intuitionistic type theory leads to a mechanical generation of correct code by using specifications. The idea is that the specification of a program is its type, and the specification can be expressed by logical statements called well-formed formulas (wffs) and therefore proved by using mathematical axioms and inference rules of logic. Then, using the correspondences propositions are types are specifications and proofs are programs are values [16], a proof can be translated into a correct programming code. The fundamental idea of realizability theory is that a proof can be translated into not only correct, but also minimal programming code, which contains only computational values. Based on these theories, a realizability algorithm developed by John Hatcliff defines how the translation can be done. We analyzed Hatcliff's algorithm and implemented it in a system. System ...

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