Occurrence-position representation of a sequence ($\mathrm{rep}(xs)(v)=\{i:x{s}_i=v\}$)

Represent a sequence by a function mapping each value to its increasing list of occurrence positions. On finite inputs, querying a value produces every matching index and a terminating tail. On infinite inputs, absence of further occurrences may be uncomputable by a generic scan, as expressed by the absence-detection obstruction for infinite lists. Parity filtering and index rescaling represent alternate-element subsequences, but may fail to preserve productivity.