Abstract
Λμ-calculus is a Böhm-complete extension of Parigot's Λμ-calculus closely related with delimited control in functional programming. In this article, we investigate the meta-theory of untyped Λμ-calculus by proving confluence of the calculus and characterizing the basic observables for the Separation theorem, canonical normal forms . Then, we define Λ s , a new type system for Λμ-calculus that contains a special type construction for streams, and prove that strong normalization and type preservation hold. Thanks to the new typing discipline of Λ s , new computational behaviors can be observed, which were forbidden in previous type systems for λμ-calculi. Those new typed computational behaviors witness the stream interpretation of Λμ-calculus.
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