Although aspect-orientation has gained popularity in recent software development, formal and general definitions of aspects and related concepts are still under development. The important concepts such as aspect, join-point, pointcut, advice, etc. are usually defined on top of specific programming languages or formal systems. Our goal is to formalize these commonly used ‘aspectual’ operations by defining a simple calculus that models the operations independently from other computational activities such as function application or message passing. A specific aspect-oriented language can be formalized by mixing our calculus with the model of the base language. In this paper, we give the definition of our calculus and discuss that how aspectual operations are formalized using it by comparing other formalizations.
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