 
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.
1
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
