The logical system IFP introduced in this paper supports program extraction from proofs, unifying theoretical and practical advantages: Based on first-order logic and powerful strictly positive inductive and coinductive definitions, IFP support abstract axiomatic mathematics with a large amount of classical logic. The Haskell-like target programming language has a denotational and an operational semantics which are linked through a computational adequacy theorem that extends to infinite data. Program extraction is fully verified and highly optimised, thus extracted programs are guaranteed to be correct and free of junk. A case study in exact real number computation underpins IFP's effectiveness
