Intuitionistic fixed point logic

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