Parameterized Aspect Calculus:  A Core Calculus
	  for the Direct Study of Aspect-Oriented Languages
				  by
	  Curtis Clifton, Gary T. Leavens, and Mitchell Wand

			       Abstract

Formal study of aspect-oriented languages is difficult because current
theoretical models provide a range of features that is too limited and
rely on encodings using lower-level abstractions, which involve a
cumbersome level of indirection.  We present a calculus, based on
Abadi and Cardelli's object calculus, that explicitly models a base
language and a variety of point cut description languages.  This
explicit modeling makes clear the aspect-oriented features of the
calculus by removing the indirection of some existing models.  We
demonstrate the generality of our calculus by presenting models for
AspectJ's open classes and advice, and HyperJ's compositions, and
sketching a model for DemeterJ's adaptive methods.

Keywords: Parameterized aspect calculus, object calculus, join point
model, point cut description language, aspect-oriented programming,
AspectJ, advice, HyperJ, hyperslices, DemeterJ, adaptive methods