Abstract
We make an argument that, for any study involving computational effects such as divergence or continuations, the traditional syntax of simply typed lambda-calculus cannot be regarded as canonical, because standard arguments for canonicity rely on isomorphisms that may not exist in an effectful setting. To remedy this, we define a “jumbo lambda-calculus” that fuses the traditional connectives together into more general ones, so-called “jumbo connectives”. We provide two pieces of evidence for our thesis that the jumbo formulation is advantageous.
Firstly, we show that the jumbo lambda-calculus provides a “complete” range of connectives, in the sense of including every possible connective that, within the beta-eta theory, possesses a reversible rule.
Secondly, in the presence of effects, we show that there is no decomposition of jumbo connectives into non-jumbo ones that is valid in both call-by-value and call-by-name.
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© 2006 Springer-Verlag Berlin Heidelberg
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Levy, P.B. (2006). Jumbo λ-Calculus. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_38
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DOI: https://doi.org/10.1007/11787006_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35907-4
Online ISBN: 978-3-540-35908-1
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