Summary: Explicit Substitutions
M. Abadi \Lambda L. Cardelli \Lambda P.­L. Curien y J.­J. L'evy z
May 31, 1991
Abstract
The –oe­calculus is a refinement of the –­calculus where substitu­
tions are manipulated explicitly. The –oe­calculus provides a setting
for studying the theory of substitutions, with pleasant mathematical
properties. It is also a useful bridge between the classical –­calculus
and concrete implementations.
\Lambda Digital Equipment Corporation, Systems Research Center.
y Ecole Normale Sup'erieure; part of this work was completed while at Digital Equipment
Corporation, Systems Research Center.
z INRIA Rocquencourt; part of this work was completed while at Digital Equipment
Corporation, Systems Research Center and Paris Research Laboratory.
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1 Introduction
Substitution is the 'eminence grise of the –­calculus. The classical fi rule,
(–x:a)b ! fi afb=xg
uses substitution crucially though informally. Here a and b denote two

Source: Abadi, Martín - Department of Computer Science, University of California at Santa Cruz

Collections: Computer Technologies and Information Sciences