Kleene equality

Short description: Equality operator on partial functions

In mathematics, Kleene equality, or strong equality, ([math]\displaystyle{ \simeq }[/math]) 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 [math]\displaystyle{ f }[/math] and [math]\displaystyle{ g }[/math], [math]\displaystyle{ f \simeq g }[/math] means that for every [math]\displaystyle{ x }[/math]:

• [math]\displaystyle{ f(x) }[/math] and [math]\displaystyle{ g(x) }[/math] are both defined and [math]\displaystyle{ f(x) = g(x) }[/math]
• or [math]\displaystyle{ f(x) }[/math] and [math]\displaystyle{ g(x) }[/math] are both undefined.

References

1. Cutland, Nigel (1980). Computability, an introduction to recursive function theory. Cambridge University Press. pp. 251. ISBN 978-0-521-29465-2. https://books.google.com/books?id=wAstOUE36kcC&pg=PP1.