Kleene equality
In mathematics, Kleene equality, 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 f {\displaystyle f} and g {\displaystyle g} , f ≃ g {\displaystyle f\simeq g} means that for every x {\displaystyle x} : f ( x ) {\displaystyle f(x)} and g ( x ) {\displaystyle g(x)} are both defined and f ( x ) = g ( x ) {\displaystyle f(x)=g(x)} or f ( x ) {\displaystyle f(x)} and g ( x ) {\displaystyle g(x)} are both undefined.