The overarching goal of a formal specification of design patterns is
to enhance their understandability, address their composability
problem and provide a tool support for their reusability.
Understanding design patterns means uncovering when and how a specific
pattern can be used to resolve a specific design problem. The lack of
completeness of the existing formal specifications motivates this
work. In this paper we start introducing a calculus for design
patterns based on rCOS (Refinement Calculus of Object and Component
Systems) specification which provides a formalization of patterns
addresses the pattern composition mechanism and describes a mechanism
for design refinement to patterns designs. In this first step we are
focusing on the proposition of a formalization model. Thus, a model
for patterns formalization is proposed and an assessment model is
used for the evaluation of the proposed model and comparing it with
the existing ones to show its efficiencies and limitations.