Output details

An algebra of design patterns

<07> This paper gives the algebraic laws obeyed by the design pattern operators that have previously been used to define compositions. It shows that any two expressions defining a composition can be proven to be equal if the expressions denote equivalent patterns. In other words, the operators are complete. A real-world five-way composition of design patterns is effortlessly rewritten to its simplest form, using the rules, and the drawbacks of informal reasoning are thereby demonstrated. This is the first time that algebraic reasoning has been used for this purpose in the case of patterns. All laws are rigorously proved as is the result that the operators are complete.