In mathematics, Kleene equality, ^[1] or strong equality, (${\displaystyle \simeq }$) 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 ${\displaystyle f}$ and ${\displaystyle g}$, ${\displaystyle f\simeq g}$ means that for every ${\displaystyle x}$: ^[2]

• ${\displaystyle f(x)}$ and ${\displaystyle g(x)}$ are both defined and ${\displaystyle f(x)=g(x)}$
• or ${\displaystyle f(x)}$ and ${\displaystyle g(x)}$ are both undefined.

References

1. Cutland, Nigel (1980). Computability, an introduction to recursive function theory. Cambridge University Press. p. 251. ISBN  978-0-521-29465-2.

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