Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey these works and bring them together in a same framework. R'esum'e On appelle habituellement (algorithme d') unification un algorithme de r'esolution d'une 'equation dans une alg`ebre de termes. La r'esolution de formules plus complexes, comportant en particulier des n'egations, est appel'ee ici disunification. Avec une d'efinition aussi 'etendue, de nombreux travaux peuvent etre consid'er'es comme portant sur la disunification. L'objet de cet article de synth`ese est de rassembler tous ces travaux dans un meme formalisme. Laboratoire de Recherche en Informatique, Bat. 490, Universit'e de Paris-Sud, 91405 ORSAY cedex, France. E-mail: comon@lri.lri.fr i Contents 1 Syntax 5 1.1 Basic Defini...

We present a method for compiling pattern matching on lazy languages based on previous work by Laville and Huet-Levy. It consists of coding ambiguous linear sets of patterns using "Term Decomposition," and producing non ambiguous sets over terms with structural constraints on variables. The method can also be applied to strict languages giving a match algorithm that includes only unavoidable tests when such an algorithm exists.

Pattern matching is a key concept for rule-based expert systems. Simple pattern interpreters appear in nearly every book on Lisp. Pattern matching is also a useful tool for case analyses as provided by functional languages such as ML or Miranda TM . These two uses are somewhat different since functional languages emphasize a discrimination based on types while Lisp, or Plasma, make use of S-expressions or segments of S-expressions within patterns. The paper presents an intermediate language for patterns and its denotational semantics. This reduced language is powerful enough to express boolean composition of patterns as well as segment handling and unbounded pattern repetition. A compiler is then defined which translates patterns into functional code. We discuss some compilation variant as well as the integration of the pattern sub-language into Lisp. These capabilities make pattern matching an useful and efficient tool for a wide class of applicative languages and allow to incorpora...