Polymorphic Call-by-Value Calculus Based on Classical Proofs

We introduce a polymorphic call-by-value calculus, λexc, based on 2nd order classical logic. The call-by-value computation rules are defined based on proof reductions, in which classical proof reductions are regarded as a logical permutative reduction in the sense of Prawitz and a dual permutative reduction. It is shown that the CPS-translation from the core λexc to the intuitionistic fragment, i.e., the Damas-Milner type system is sound. We discuss that the use of the dual permutative reduction is, in general, uncorrected in polymorphic calculi. We also show the Church-Rosser property of λexc, and the soundness and completeness of the type inference algorithm W. From the subject reduction property, it is obtained that a program whose type is inferred by W never leads to a type-error under the rewriting semantics. Finally, we give a brief comparison with ML plus callcc and some of the existing call-by-value styles.