What would be the equivalent math concept for associative arrays/maps/dictionaries?EDIT: Disregard mutability. FYI,off topic, the reason why I ask this question, is that I want to calculate the distance(or similarity) between two maps given that I have a distance function for each entity(or key) in the map. 
Math term for Associative arrays/Maps/Dictionaries
discrete mathematics
Function ($A \to B$). If that doesn't work for you, try a set of pairs (subset of $A \times B$).Note that something like mutable state is not common in maths, outside of computer science.