FLOPS 2010: Functional and Logic Programming pp 134-149 | Cite as

Standardization and Böhm Trees for Λμ-Calculus

  • Alexis Saurin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6009)

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.

Keywords

Normal Form Reduction Step Natural Deduction Separation Theorem Reduction Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexis Saurin
    • 1
  1. 1.PPS & INRIA π r2 

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