Intersection Types for a Computational Lambda-Calculus with Global State

2021-04-03

arXiv.org

AI Summary

This paper addresses untyped lambda calculus with global read-write state, developing a unified semantic framework for effectful functional computation. Methodologically, it pioneers the integration of intersection type systems with monadic algebraic effects semantics, concurrently defining operational semantics, denotational semantics, and a type system—while proving type preservation under reduction and expansion of state-term configurations. The contributions are threefold: (1) establishing completeness of type safety and convergence characterization; (2) employing intersection types to precisely capture termination behavior of stateful computations; and (3) providing a theoretically rigorous foundation—combining semantic precision and type-based guarantees—for functional languages with global state.

Abstract

We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side-effects and treat read and write as algebraic operations over a monad. We introduce operational and denotational semantics and a type assignment system of intersection types and prove that types are invariant under the reduction and expansion of term and state configurations. Finally, we characterize convergent terms via their typings.

Problem

• Modeling global state operations in lambda-calculus
• Developing intersection type system for stateful computations
• Proving type invariance under term and state reductions

Innovation

• Monadic approach models global state effects
• Intersection types ensure term invariance
• Typings characterize convergent terms