Abstract
Since Parigot’s seminal article on “an algorithmic interpretation of classical natural deduction” [15], λμ-calculus has been extensively studied both as a typed and an untyped language. Among the studies about the call-by-name lambda-mu-calculus authors used different presentations of the calculus that were usually considered as equivalent from the computational point of view. In particular, most of the papers use one of three variants of the calculus initially introduced by Parigot: (i) Parigot’s syntax, (ii) an extended calculus that satisfies Böhm theorem and (iii) a second variant by de Groote he considered when designing an abstract machine for λμ-calculus that contains one more reduction rule.
In a previous work [20] we showed that contrarily to Parigot’s calculus that does not enjoy separation property as shown by David and Py [3], de Groote’s initial calculus, that we refer to as Λμ-calculus, does enjoy the separation property. This evidence the fact that the calculi are really different and suggest that the relationships between the λμ-calculi should be made clear. This is the purpose of the present work.
We first introduce four variants of call-by-name λμ-calculus, establish some results about reductions in Λμ-calculus and then investigate the relationships between the λμ-calculi. We finally introduce a type system for Λμ-calculus and prove subject reduction and strong normalization.
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Saurin, A. (2008). On the Relations between the Syntactic Theories of λμ-Calculi. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_13
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