Implement Reduce and Derive Map and Filter from It

Explain how to implement `reduce`, then implement the behavior of `map` and `filter` using your `reduce` operation. Discuss how these primitives can be composed to process rows of a data table. ### Part 1 — Define Reduce Specify the reducer callback, accumulator, iteration order, and behavior for empty input. Explain the invariant maintained as elements are consumed. #### What This Part Should Cover An explicit initial accumulator, left-to-right evaluation under a stated baseline, callback behavior, and correct empty-input handling. ### Part 2 — Derive Map and Filter Explain how each operation can be expressed through reduce without independently traversing the input. Use an explicitly hypothetical table transformation to illustrate composition. #### What This Part Should Cover One mapped output per input element, predicate-based selection, preserved order, and careful handling of mutable accumulators and performance. ### Constraints Choose a language and state its callback and collection semantics. The original table schema and requested transformation are unspecified, so a demonstration schema must be labeled hypothetical. This is a higher-order-function implementation discussion, not a JSON console with arbitrary callback code as input. ### Clarifying Questions - Is an initial accumulator mandatory, and is evaluation eager or lazy? - May callbacks mutate state or raise exceptions? - Should map and filter preserve input order and leave the input unchanged? ```hint State the prefix invariant After processing the first k elements, explain exactly what the accumulator represents for reduce, map, and filter. ``` ### What a Strong Answer Covers - A correct reduce contract and empty-input semantics. - Map and filter derived from reduce with order and mutation behavior specified. - Composition over table rows without inventing an unreported data-analysis requirement. ### Follow-up Questions - When does repeatedly concatenating accumulator lists become quadratic? - Which properties would a reducer need for safe parallel reduction?