Jumbo λ-calculus

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. © Springer-Verlag Berlin Heidelberg 2006.