Bidirectional map

In computer science, a bidirectional map, or hash bag, is an associative data structure in which the $(key,value)$ pairs form a one-to-one correspondence. Thus the binary relation is functional in each direction: $value$ can also act as a key to $key$ . A pair $(a,b)$ thus provides a unique coupling between $a$ and $b$ so that $b$ can be found when $a$ is used as a key and $a$ can be found when $b$ is used as a key.

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