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Functional Modules

  • Manuel Clavel
  • Francisco Durán
  • Steven Eker
  • Patrick Lincoln
  • Narciso Martí-Oliet
  • José Meseguer
  • Carolyn Talcott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4350)

Abstract

Functional modules define data types and operations on them by means of equational theories. The data types consist of elements that can be named by ground terms. Two ground terms denote the same element if and only if they belong to the same equivalence class as determined by the equations. That is, the mathematical semantics of a functional module is its initial algebra. Maude’s functional modules are assumed to have the nice property that equations, considered as simplification rules by using them only in the left to right direction, are Church-Rosser and terminating (see Section 4.7). This means that repeated application of the equations as simplification rules eventually reaches a term to which no further equations apply, and the result, called the canonical form, is the same regardless of the order of application of the equations. Thus each equivalence class has a natural representative, its canonical form, that can be computed by equational simplification. As explained in Section 1.2, this ensures that the initial algebra and the canonical term algebra of the functional module are isomorphic, and therefore that the module’s mathematical and operational semantics coincide.

Keywords

Canonical Form Functional Module Operational Semantic Equational Attribute Ground Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Manuel Clavel
    • 1
  • Francisco Durán
    • 2
  • Steven Eker
    • 3
  • Patrick Lincoln
    • 3
  • Narciso Martí-Oliet
    • 1
  • José Meseguer
    • 4
  • Carolyn Talcott
    • 5
  1. 1.Universidad Complutense de Madrid, Facultad de Informática, Departamento de Sistemas Informáticos y Computación, s/n 28040 MadridSpain
  2. 2.Universidad de Málaga, Departamento de Lenguajes y Ciencias de la Computación, Boulevard Louis Pasteur, s/n. Campus de Teatinos, 29071 MálagaSpain
  3. 3.SRI International, Computer Science Laboratory, 333 Ravenswood Ave., Menlo Park, CA 94025-3493USA
  4. 4.University of Illinois at Urbana-Champaign, Department of Computer Science, Siebel Center for Computer Science, 201 N. Goodwin, Urbana, IL 61801-2302, USA   
  5. 5.SRI InternationalUSA

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