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  • Mathematical Structures in Computer Science, Volume 3, Issue 4
  • December 1993, pp. 417-433

Demonic operators and monotype factors

  • Roland Backhouse (a1) and Jaap van der Woude (a1)
  • DOI: http://dx.doi.org/10.1017/S096012950000030X
  • Published online: 01 March 2009
Abstract

This paper tackles the problem of constructing a compact, point-free proof of the associativity of demonic composition of binary relations and its distributivity through demonic choice. In order to achieve this goal, a definition of demonic composition is proposed in which angelic composition is restricted by means of a so-called ‘monotype factor’. Monotype factors are characterised by a Galois connection similar to the Galois connection between composition and factorisation of binary relations. The identification of such a connection is argued to be highly conducive to the desired compactness of calculation.

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R. C. Backhouse and R. K. Lutz (1977) Factor graphs, failure functions and bi-trees. In: A. Salomaa and M. Steinby (eds.) Fourth Colloquium on Automata, Languages and Programming. Springer-Verlag Lecture Notes in Computer Science 52 6175.

R. Berghammer and H. Zierer (1986) Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43 123147.

E. W. Dijkstra and C. S. Scholten (1990) Predicate Calculus and Program Semantics, Springer-Verlag, Berlin.

R. P. Dilworth (1939) Non-commutative residuated lattices. Transactions of the American Mathematical Society 46 426444.

G. Gierz , K. H. Hofmann , K. Keimel , J. D. Lawson , M. Mislove and D. S. Scott (1980) A Compendium of Continuous Lattices, Springer-Verlag.

J. Hartmanis and R. E. Stearns (1964) Pair algebras and their application to automata theory. Information and Control 7 (4) 485507.

H. Herrlich and M. Hušek (1985) Galois connections. In: A. Melton (ed.) Mathematical Foundations of Programming Semantics. Springer-Verlag Lecture Notes in Computer Science 239 122134.

D. E. Knuth , J. H. Morris and V. R. Pratt (1977) Fast pattern matching in strings. SIAM Journal of Computing 6 325350.

J. M. McDill , A. C. Melton and G. E. Strecker (1987) A category of Galois connections. In: D. H. Pitt , A. Poigné and D. E. Rydeheard (eds.) Category Theory and Computer Science. Springer- Verlag Lecture Notes in Computer Science 283 290300.

A. Melton , D. A. Schmidt and G. E. Strecker (1986) Galois connections and computer science applications. In: D. Pitt , A. Abramsky , A. Poigné and D. E. Rydeheard (eds.) Category Theory and Computer Programming. Springer-Verlag Lecture Notes in Computer Science 240 299312.

T. T. Nguyen (1991) A relational model of nondeterministic programs. International J. of Foundations of Computer Science 2 (2) 101131.

O. Ore (1944) Galois connexions. Transactions of the American Mathematical Society 55 493513.

V. Pratt (1990) Action logic and pure induction. In: J. van Eijck (ed.) Proc. Logics in AI: European Workshop JELIA '90. Springer-Verlag Lecture Notes in Computer Science 478 97120.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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