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I'm trying to say this in my paper: "$M$ is a key-value store, where 1) all keys are unique, 2) $k \in M$ means that the $k$ key exists in the store, 3) $M + (k, v)$ is a new store equal to $M$ but the key $k$ is assigned to $v$, 4) $M - k$ is a new store equal to $M$ but without the $k$ key.

Is it possible to omit all this text and just say that "$M$ is something," referring to some well-known definition of such structures?

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  • $\begingroup$ The proper technical name for this is Associative Array (as mentioned in an answer below). More common technical names include hash tables, hash, map, dictionary and array (PHP & TCL) $\endgroup$
    – slebetman
    Commented Jan 29, 2023 at 12:21

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You might be looking for a dictionary. Common implementations are hash tables and binary search trees.

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Another common name for such a "map" data structure is Map. That's what it is called in C++, Java, ECMAScript, PHP, Go, Matlab, Rust, Scala, Clojure, Elixir, OCaml, F#, Racket, Kotlin, Dart, Ada, and Haskell, to name just a few.

The name Map is also used in Computer Science.

Yet another common name is Associative Array.

A slightly less common name is Table. That's what it is called in Lua. The term Table also appears in terms like Hash Table.

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