Separation with Streams in the ?µ-calculus

Abstract

The /spl lambda//spl mu/-calculus is an extension of the /spl lambda/-calculus introduced in 1992 by Parigot (M. Parigot, 1992) in order to generalize the Curry-Howard isomorphism to classical logic. Two versions of the calculus are usually considered in the literature: Parigot's original syntax and an alternative syntax introduced by de Groote. In 2001, David and Py (R. David, 2001) proved that the Separation Property (also referred to as Bohm theorem) fails for Parigot's /spl lambda//spl mu/-calculus. By analyzing David & Py's result, we exhibit an extension of Parigot's /spl lambda//spl mu/-calculus, the /spl Lambda//spl mu/-calculus, for which the Separation Property holds and which is built as an intermediate language between Parigot's and de Groote's /spl lambda//spl mu/-calculi. We prove the theorem and describe how /spl Lambda//spl mu/-calculus can be considered as a calculus of terms and streams. We then illustrate Separation in showing how in /spl Lambda//spl mu/-calculus it is possible to separate the counter-example used by David & Py.