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
means that for every
:[2] 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:
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