Continuation calculus

Bram Geron
Herman Geuvers

Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.

In Ugo de'Liguoro and Alexis Saurin: Proceedings First Workshop on Control Operators and their Semantics (COS 2013), Eindhoven, The Netherlands, June 24-25, 2013 , Electronic Proceedings in Theoretical Computer Science 127, pp. 66–85.
Published: 4th September 2013.

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