Domain-Free λµ-Calculus

• Published in: RAIRO. Informatique théorique et applications Vol. 34; no. 6; pp. 433 - 466
• Main Author: Fujita, Ken-Etsu
• Format: Journal Article
• Language: English
• Published: EDP Sciences 01.11.2000
• Subjects: 68N18; 68Q05; call-by-value; Church-Rosser; CPS-translation; domain-free style; polymorphism; strong normalization; subject reduction; type checking; type inference; λµ-calculus
• ISSN: 0988-3754; 1290-385X
• DOI: 10.1051/ita:2000102

We introduce a domain-free λµ-calculus of call-by-value as a short-hand for the second order Church-style. Our motivation comes from the observation that in Curry-style polymorphic calculi, control operators such as callcc-operators cannot, in general, handle correctly the terms placed on the control operator's left, so that the Curry-style system can fail to prove the subject reduction property. Following the continuation semantics, we also discuss the notion of values in classical system, and propose an extended form of values. It is proved that the CPS-translation is sound with respect to domain-free λ2 (second-order λ-calculus). As a by-product, we obtain the strong normalization property for the second-order λµ-calculus of call-by-value in domain-free style. We also study the problems of type inference, typability, and type checking for the call-by-value system. Finally, we give a brief comparison with standard ML plus callcc, and discuss a natural way to avoid the unsoundness of ML with callcc.