From semantics to types: The case of the imperative λ-calculus

Abstract

We study the logical semantics of an untyped λ-calculus equipped with operators representing read and write operations from and to a global store. Such a logic consists of an intersection type assignment system, which we derive from the denotational semantics of the calculus, based on the monadic approach to model computational λ-calculi.The system is obtained by constructing a filter model in the category of ω-algebraic lattices, such that the typing rules can be recovered out of the term interpretation. By construction, the so-obtained type system satisfies the “type-semantics” property and completeness.