DIKU IT-C RUC

COPLAS

Copenhagen Programming Language Seminar


THE BETA CUBE

Álvaro García Pérez
IMDEA, Madrid, Spain

March 7th, 11:00 - 11:30
IT University of Copenhagen, Room 4A14

Abstract:
Pure lambda calculus reduction strategies have been thoroughly studied, as they constitute the foundations of evaluation in many programming languages. Sestoft collected and defined several of them as sets of big-step rules, thus clarifying varying and inaccurate definitions in the literature. From Sestoft's work, we present a rule template which can instantiate any of the foremost strategies and some more. Abstracting the parameters of the template, we propose a space of reduction strategies we like to call the Beta Cube. We also formalise a hybridisation operator--informally suggested by Sestoft--which produces new strategies by composing a subsidiary and a base strategy from the cube. Furthermore, we discuss a variant of the hybridisation operator, in which the operand of an application is reduced by the subsidiary instead of the hybrid. This accomplish with the implicit remarks on Plotkin's theorems for the lambda-value calculus. The new hybridisation operator allows to produce a normalising strategy in Plotkin's (pure) lambda-value calculus.

This space gives new and interesting insights about the properties of reduction strategies. We present and prove the Absorption Theorem, which states that subsidiaries are left-identities of their hybrids.

This joint work with Pablo Nogueira and Emilio Jesús Gallego Arias is available at http://iws2010.inria.fr/IWS2010-proceedings.pdf.

Scientific host: Peter Sestoft Administrative host:Renée Korver Michan. All are welcome.
The Copenhagen Programming Language Seminar (COPLAS) is a collaboration between DIKU, ITU and RUC.
COPLAS is sponsored by the FIRST Graduate School.
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For more information about COPLAS, see http://www.coplas.org