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Reasoning about Partial Functions with the Aid of a Computer

William M. Farmer
Erkenntnis (1975-)
Vol. 43, No. 3, Varia with a Workshop on the Foundations of Partial Functions and Programming (Nov., 1995), pp. 279-294
Published by: Springer
Stable URL: http://www.jstor.org/stable/20012659
Page Count: 16
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Reasoning about Partial Functions with the Aid of a Computer
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Abstract

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms -- first-order logic, type theory, and set theory -- are usually only adequate for reasoning about partial functions in theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequate in practice. This paper shows how the traditional approach to partial functions can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann-Bernays-Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems.

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