Standardization and Böhm Trees for Λμ-Calculus [chapter]

Alexis Saurin
2010 Lecture Notes in Computer Science  
Λµ-calculus is an extension of Parigot's λµ-calculus which (i) satises 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 Λµcalculus and innitary λ-calculi. After establishing a standardization theorem for Λµ-calculus, we characterize sovalbility in Λµ-calculus. Then, we study
more » ... ite 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 claries Λµ-calculus both as an innitary calculus and as a core language for dealing with streams as primitive objects.
doi:10.1007/978-3-642-12251-4_11 fatcat:niemqq2cf5aczbwgdvortwjoqa