@TechReport{	  it:1999-004,
  author	= {Amnon H. Eden and Yoram Hirshfeld and Amiram Yehudai},
  title		= {Towards a Mathematical Foundation for Design Patterns},
  institution	= {Department of Information Technology, Uppsala University,
		  and Tel Aviv University},
  department	= {Division of Computer Systems},
  year		= {1999},
  number	= {1999-004},
  month		= may,
  abstract	= {We identify a compact and sufficient set of building
		  blocks which constitute most design patterns of the GoF
		  catalog: uniform sets of classes or functions, function
		  clans, class hierarchies, and regularities (morphisms)
		  thereof. The abstractions observed are manifested within a
		  model in symbolic logic and defined in LePUS, a
		  declarative, higher order language. LePUS formulae
		  concisely prescribe design patterns in a general, complete,
		  and accurate manner. We provide a natural, condensed
		  graphic notation for every LePUS formula and demonstrate
		  how design patterns are faithfully portrayed by diagrams in
		  this notation. We conclude by defining refinement
		  (specialization) between patterns by means of predicate
		  calculus and illustrate how the logical formalism of LePUS
		  facilitates tool support for the recognition and
		  implementation of design patterns.}
}