Kleene equality

In mathematics, Kleene equality, 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 :

• and are both defined and
• or and are both undefined.

Some authors 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