We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also show how extracted programs can be translated into Haskell. As an application we extract a program converting the signed digit representation of real numbers to infinite Gray code from a proof of inclusion of the corresponding coinductive predicates.

我们研究直觉定点逻辑的系统IFP，这是直觉一阶逻辑通过严格的正归纳和共归定义的扩展。我们定义了IFP的可实现性解释，并使用它来从有关任意任意经典真无相交公式指定的抽象结构的证明中提取计算内容。对于域理论的指称语义和提取的程序的功能语言的相应的惰性运算语义，该解释被证明是合理的。我们还将展示如何将提取的程序转换为Haskell。作为一个应用程序，我们从包含相应共形谓词的证明中提取一个程序，将实数的带符号数字表示转换为无限格雷码。