Paper: Order-Sorted Algebra solves the Constructor-Selector, Multiple (at LICS 1987)

Authors: Joseph A. Goguen José Meseguer

Abstract

Structured data are generally composed from constituent parts by constructors and decomposed by selectors. We prove that the usual many-sorted algebra approach to abstract data types cannot capture this simple intuition in a satisfactory way. We also show that order-sorted algebra does solve this problem, and many others concerning ill-defined and erroneous expressions, in a simple and natural way. In particular, we show how order-sorted algebra supports an elegant solution to the problems of multiple representations and coercions. The essence of order-sorted algebra is that sorts have subsorts, whose semantic interpretation is the subset relation on the carriers of algebras.

BibTeX

  @InProceedings{GoguenMeseguer-OrderSortedAlgebras,
    author = 	 {Joseph A. Goguen and José Meseguer},
    title = 	 {Order-Sorted Algebra solves the Constructor-Selector, Multiple},
    booktitle =  {Proceedings of the Second Annual IEEE Symposium on Logic in Computer Science (LICS 1987)},
    year =	 {1987},
    month =	 {June}, 
    pages =      {18--29},
    location =   {Ithaca, NY, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }