A fixed point of the second order lambda-calculus: observable equivalences and models

Abstract

The author develops an operational model of an impredicative version of explicit polymorphism, namely, an extension of the second-order lambda-calculus, including a fixed-point combinator and a multisorted first-order algebra. He shows that the typical properties of the lambda -calculus are preserved, and he investigates novel aspects that arise from second-order type structure as well as the relationships with well-known, simply typed, PCF-like languages. A suitable theory of observably equivalent terms is defined, and its complexity is explored. A denotional model suggesting interesting extensions of a language is studied.<>