NDLI: The duality of computation

Content Provider	ACM Digital Library
Author	Curien, Pierre-Louis Herbelin, Hugo
Abstract	We present the μ -calculus, a syntax for λ-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus LK, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and programs, we can see LK, or more precisely a formulation called LKμ , as a syntax-directed system of simple types for μ -calculus. For μ -calculus, choosing a call-by-name or call-by-value discipline for reduction amounts to choosing one of the two possible symmetric orientations of a critical pair. Our analysis leads us to revisit the question of what is a natural syntax for call-by-value functional computation. We define a translation of λμ-calculus into μ -calculus and two dual translations back to λ-calculus, and we recover known CPS translations by composing these translations.
Starting Page	233
Ending Page	243
Page Count	11
File Format	PDF
ISBN	1581132026
DOI	10.1145/351240.351262
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2000-09-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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The duality of computation