  Pattern-Oriented Analysis and Design (POAD) is the practice of building
complex software by applying proven designs to specific problem domains.
Although a great deal of research and practice has been devoted to formalizing
existing design patterns and discovering new ones, there has been relatively
little research into methods for combining these patterns into software
applications. This is partly because the creation of complex software
applications is so expensive. This paper proposes a mathematical model of POAD
that may allow future research in pattern-oriented techniques to be performed
using less expensive formal techniques rather than expensive, complex software
development.
