Kleene equality

In mathematics, Kleene equality, or strong equality, ($$\simeq$$) 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 $$f$$ and $$g$$, $$f \simeq g$$ means that for every $$x$$:
 * $$f(x)$$ and $$g(x)$$ are both defined and $$f(x) = g(x)$$
 * or $$f(x)$$ and $$g(x)$$ are both undefined.