ML Polymorphism of Linear Lambda Calculus with First-class Continuations

Abstract

The Curry-Howard isomorphism shows that an intuitionistic deductive system is similar to a formal computational system; propositions correspond to types, proofs to lambda-terms, and a proof normalization procedure to an evaluation strategy. Furthermore, the duality between computation values and continuations is discovered under the Curry-Howard isomorphism. In the traditional lambda calculus, duplication and erasing of values are allowed but those of continuations prohibited. On the other hand, in the lambda calculus with first-class continuations, both values and continuations are permitted to be duplicated and erased. In our previous paper, we proposed a linear lambda calculus with first-class continuations, in which we cannot duplicate and erase values but can do continuations. In this paper, we propose an ML polymorphic type system for the linear lambda calculus with first-class continuations and design a type inference algorithm of the type system.