Axiomatics for Data Refinement in Call by Value Programming Languages

Abstract

We give a systematic category theoretic axiomatics for modelling data refinement in call by value programming languages. Our leading examples of call by value languages are extensions of the computational λ-calculus, such as F P C and languages for modelling nondeterminism, and extensions of the first order fragment of the computational λ-calculus, such as a CP S language. We give a category theoretic account of the basic setting, then show how to model contexts, then arbitrary type and term constructors, then signatures, and finally data refinement. This extends and clarifies Kinoshita and Power's work on lax logical relations for call by value languages.

Logical relations for monadic types

“…However, the main topic of this paper is a more complex situation of lax logical relations and data-refinement for the computational lambda calculus. A subsequent paper, Power and Tanaka (2000), develops the ideas of Kinoshita and Power (1999) further. In particular, it addresses lax logical relations for the computational lambda calculus and for the linear lambda calculus.…”