A Categorical Interpretation of Landin's Correspondence Principle

Many programming languages can be studied by desugaring them into an intermediate language, namely, the simply-typed-calculus. In this manner Landin and Tennent discovered a \correspondence" between the semantics of deenition bindings and parameter bindings such that the semantics of free identiiers becomes independent of their mode of deenition. In this paper we consider programming languages with modules and we desugar modules into records. A categorical model for the simply-typed-calculus with records is then freely generated. The record construction becomes a tensor product, the lambda abstraction construction becomes a function space, and if the language satisses the correspondence principle, then the categorical exponentiation diagram commutes. A converse result is also proved. The framework for deening the model is of interest because it deenes a hierarchy of call-by-value-calculi, of which call-by-name is the weakest form of call-by-value calculus. Applications to compiling are given.