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The next 700 Krivine machines

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Higher-Order and Symbolic Computation

Abstract

The Krivine machine is a simple and natural implementation of the normal weak-head reduction strategy for pure λ-terms. While its original description has remained unpublished, this machine has served as a basis for many variants, extensions and theoretical studies. In this paper, we present the Krivine machine and some well-known variants in a common framework. Our framework consists of a hierarchy of intermediate languages that are subsets of the λ-calculus. The whole implementation process (compiler + abstract machine) is described via a sequence of transformations all of which express an implementation choice. We characterize the essence of the Krivine machine and locate it in the design space of functional language implementations. We show that, even within the particular class of Krivine machines, hundreds of variants can be designed.

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Authors and Affiliations

  1. École Des Mines De Nantes, 4 rue Alfred Kastler, BP 20722, 44307, Nantes Cedex 3, France

    Rémi Douence

  2. Inria Rhône-Alpes, 655 av. de l’Europe, 38330, Montbonnot, France

    Pascal Fradet

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  1. Rémi Douence
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  2. Pascal Fradet
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Correspondence to Rémi Douence.

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Work performed while at INRIA/IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France.

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Douence, R., Fradet, P. The next 700 Krivine machines. Higher-Order Symb Comput 20, 237–255 (2007). https://doi.org/10.1007/s10990-007-9016-y

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