two-tier function map/assignment writer notation: X1 (ordered list, no repetitious terms) maps termwise-respectively to X2 (ordered list; may be repetitious but must have exactly as many terms as X1)

So named because, in mathematical notation, the domain set of the function is written down in some order in its entirety and then, below it, the range of the function is written so that each image and preimage line up vertically with their appropriate/respective partner. Really useful when mapping from a countable set/object that is either human-small or in which the pattern is clear. Occasionally used for a more explicit form of notation for permutations (in which cycle decomposition is not necessarily as evident, but the structure as a how is, at least, explicit). The ith term of X1 is mapped to the ith term of X2; there is no knowledge of what happens to any value that is not term of list X1. Useful for lambda calculus.