An associative array in computer science is a set of keys and values such that each:
- each key is unique
- each key has a value
- each value has one or more keys
For instance, an associative array describing a shape might contain the following, with the keys in italics.
- outline: red
- fill : red
- size: small
- sides: four
Theoretically you could model the associative array as a one-to-many function, but generally an associative array is thought of as holding values rather than manipulating them. It is taken for granted that the key-pair relation exists.
Is there standard term for an associative array in mathematics, such that it is assumed that for any key $a$ there is a value $a'$?
My use case is that I want to use propositional logic to state that following: there exists a key $a$ with value $a'$ in associative array $A$ and a key $b$ with value $b'$ in associative array $B$ such that if $a$ = $b$ then $a'$ = $b'$. I want to say that $A$ and $B$ are [whatever term means associated array] in the descriptive text, and then be able to write something like this, without needing to state that $a' \in A$ and $b' \in B$ because it is assumed:
$\exists(a \in A, b \in B)(a = b \rightarrow a'=b')$