Abstract
Λμ-calculus is an extension of Parigot’s λμ-calculus which (i) satisfies Separation theorem: it is Böhm-complete, (ii) corresponds to CBN delimited control and (iii) is provided with a stream interpretation.
In the present paper, we study solvability and investigate Böhm trees for Λμ-calculus. Moreover, we make clear the connections between Λμ-calculus and infinitary λ-calculi. After establishing a standardization theorem for Λμ-calculus, we characterize solvability. Then, we study infinite Λμ-Böhm trees, which are Böhm-like trees for Λμ-calculus; this allows to strengthen the separation results that we established previously for Λμ-calculus and to shed a new light on the failure of separation in Parigot’s original λμ-calculus.
Our construction clarifies Λμ-calculus both as an infinitary calculus and as a core language for dealing with streams as primitive objects.
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Saurin, A. (2010). Standardization and Böhm Trees for Λμ-Calculus. In: Blume, M., Kobayashi, N., Vidal, G. (eds) Functional and Logic Programming. FLOPS 2010. Lecture Notes in Computer Science, vol 6009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12251-4_11
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DOI: https://doi.org/10.1007/978-3-642-12251-4_11
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