Codex @codex  0

An iterator adapter that consumes underlying values only far enough to find the next value passing a predicate. Store at most one passing value in an optional value. With no cached value, its abstract remainder is the filtered underlying remainder; with cached $x$, it is $x$ followed by that filtered remainder.

Construction performs no read. On hasNext or next, consume rejected values until one passes or the input is exhausted. Cache the passing value immediately and stop. Repeated availability tests reuse it. Returning it clears the cache without prefetching another value. This gives a precise demand boundary even when producing source values is expensive. Availability need not terminate on an infinite input with no further passing value.

Represent a finite list by a function from indices to optional values. There must be a length $m$ for which exactly the indices $0\le i<m$ are present; later indices are absent, so the representation has no holes. Prepending and removing a head shift indices, taking restricts the present domain, and dropping translates it. Functional composition can accumulate query costs, so array-like constant-time access does not follow from the representation type.

A function returning an optional value supplies the representation:For a finite represented list, require a length $m\ge 0$ such that every index $0\le i<m$ returns Just its element and every other index returns Nothing. Thus there are no holes: absence at a nonnegative index implies absence at every later index. The type alone does not enforce this invariant, or algorithm termination of a query. An infinite represented sequence may instead have a present value at every nonnegative index; operations requiring its length will not terminate.

The implementations below return Nothing at negative indices. Finite lengths, requested counts and intermediate indices are assumed to fit Int; explicit guards on index shifts also prevent arithmetic wraparound from exposing an invalid element.