NonemapFlatMap

NonemapFlatMap is a theoretical higher-order operation defined for the Nonemap data structure, a non-empty map variant used in some functional programming libraries. It extends the idea of flatMap from lists to maps, providing a way to transform and flatten entries within a non-empty map while preserving the non-empty invariant.

The operation takes a Nonemap<K,V> and a function f that maps each key-value pair to another Nonemap, i.e., f: (K,V) -> Nonemap<K2,V2>. NonemapFlatMap applies f to every entry in the input Nonemap and then concatenates all resulting inner Nonemaps into a single Nonemap<K2,V2>. This is analogous to flatMap for lists, but it requires that each application of f yields a Nonemap (not an empty map), ensuring the overall result remains non-empty when the input is non-empty.

Key properties and behavior include:

- Result construction: the final Nonemap contains the union of all key-value pairs produced by f for every original entry.

- Collision policy: if multiple inputs produce the same key, a defined merge policy applies (for example, last-wins or a user-supplied merge function).

- Preconditions: f must return a Nonemap for every input entry; the operation preserves the non-empty guarantee of the final map as long as the input map is non-empty.

- Performance: complexity is proportional to the number of original entries plus the total size of all inner maps produced, with runtime depending on the underlying Nonemap implementation and merge rules.

Related concepts include map, flatMap, and monadic bind in functional programming. NonemapFlatMap is primarily of interest in theoretical discussions and libraries that enforce non-emptiness guarantees for map-like structures.