Polymorphic call-by-value calculus based on classical proofs
We introduce a polymorphic call-by-value calculus, λ exc v , 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 λ exc v 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 λ exc v , 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.
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