Kleene equality
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In mathematics, Kleene equality,[1] or strong equality, () is an equality operator on partial functions, that states that on a given argument either both functions are undefined, or both are defined and their values on that arguments are equal.
For example, if we have partial functions and , means that for every :[2]
- and are both defined and
- or and are both undefined.
Some authors[3] are using "quasi-equality", which is defined like this: where the down arrow means that the term on the left side of it is defined. Then it becomes possible to define the strong equality in the following way:
References
[edit]- ^ "Kleene equality in nLab". ncatlab.org.
- ^ Cutland 1980, p. 3.
- ^ Farmer, William M.; Guttman, Joshua D. (2000). "A Set Theory with Support for Partial Functions". Studia Logica: An International Journal for Symbolic Logic. 66 (1): 59–78. JSTOR 20016214.
- Cutland, Nigel (1980). Computability, an introduction to recursive function theory. Cambridge University Press. p. 251. ISBN 978-0-521-29465-2.