Erkenntnis 43 (3):279 - 294 (1995)

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 functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein 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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DOI 10.1007/BF01135375
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References found in this work BETA

A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
Consistency of the Continuum Hypothesis.Kurt Gödel - 1940 - Princeton University Press;.
The Logic of Existence.Henry S. Leonard - 1956 - Philosophical Studies 7 (4):49 - 64.
Sense Without Denotation.Timothy Smiley - 1959 - Analysis 20 (6):125 - 135.

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The Lazy Logic of Partial Terms.Raymond D. Gumb - 2002 - Journal of Symbolic Logic 67 (3):1065-1077.

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