Confluency and strong normalizability of call-by-value λμ-calculus

Abstract

This paper proves the confluency and the strong normalizability of the call-by-value Aicalculus with the domain-free style. The confluency of the system is proved by improving the parallel reduction method of Baba, Hirolawa and Fujita. The strong normalizability is proved by using the modified CPS-translation, which preserves the typa.bility and the reduction relation. This paper defines the class of the reductions whose strictness is preserved by the modified CPS-translation to prove the strong normalizability.

Strong normalization proof with CPS-translation for second order classical natural deduction

“…We use the notion of augmentations borrowed from [5] to prevent erasing-continuation of the CPS-translation. By using the notion of augmentations, we translate each 1^-term into a A/i-term of the same meaning in which any ^-abstraction subterm fia.e contains a variable a me.…”

Complete Call-by-Value Calculi of Control Operators II: Strong Termination

“…To this end, we elaborate a syntactic translation that satisfies a kind of soundness with respect to reduction. In the literature, we can find several proofs of strong normalizability by syntactic translations for call-by-value calculi with control operators [Nak03]…”

A call-by-value lambda-calculus with lists and control

“…For Parigot's λ µ-calculus, it is well known that the naive parallel reduction is not preserved under substitution [BHF01]. Instead, a complex parallel reduction that moves subterms located very deeply in a term towards the outside is needed [BHF01,Nak03,GKM12]. For λ ::catch we experience another issue.…”