Sequencealong

Sequencealong is a term used in some mathematical and computing contexts to denote an operation that extracts a subsequence from a given sequence by selecting elements according to a specified index set or predicate. The phrase is not standardized, and its precise definition can vary by context, but it generally describes obtaining elements in their original order that meet a given condition or belong to a chosen set of indices.

In a formal setting, if x = (x_i)_{i∈I} is a sequence and J⊆I is a selected index set (or if a predicate P(i) determines inclusion), then the sequence along J is the subsequence (x_i)_{i∈J} in the same order as the original sequence. In programming or data analysis, sequencealong is often implemented as filtering or masking: given a sequence and a boolean mask or a list of indices, the resulting sequence contains the elements for which the condition holds or the indices are selected.

Examples illustrate the concept: for x = (a1, a2, a3, a4) and indices J = {1,3}, sequencealong yields (a1, a3). With a boolean mask (true, false, true, false), the sequence along the mask also yields (a1, a3). If the index set is infinite or derived from a more complex predicate, the resulting subsequence may be infinite or depend on the evaluation strategy (eager vs. lazy).

See also: subsequence, filtering, masking, indexing, slicing, projection.