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An axiomatization of partial n-place operations

Published online by Cambridge University Press:  01 June 1997

MARCO FORTI ,
FURIO HONSELL  and
MARINA LENISA
MARCO FORTI
Affiliation:
Dip. di Matematica Applicata ‘U. Dini’, Università di Pisa, Italy. forti@dm.unipi.it.
FURIO HONSELL
Affiliation:
Dip. di Matematica e Informatica, Università di Udine, Italy. honsell@dimi.uniud.it.
MARINA LENISA
Affiliation:
Dip. di Informatica, Università di Pisa, Italy. lenisa@di.unipi.it.
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Abstract

We propose a general theory of partial n-place operations based solely on the primitive notion of the application of a (possibly partial) operation to n objects. This theory is strongly selfdescriptive in that the fundamental manipulations of operations, that is, application, composition, abstraction, union, intersection and so on, are themselves internal operations. We give several applications of this theory, including implementations of partial n-ary λ-calculus, and other operation description languages. We investigate the issue of extensionality and give weakly extensional models of the theory.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 3 , June 1997 , pp. 283 - 302
Copyright
1997 Cambridge University Press

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Footnotes

This work was partially supported by 40% and 60% MURST grants, CNR, EEC Science MASK, BRA Types 6453 contracts. The first author is a member of GNSAGA of CNR.