🚿 Map

Theory

map captures the element‑wise transformation pattern.

Type: $\text{map}::(a\to b)\to [a]\to [b]$

Semantics

map _ []     = []
map f (x:xs) = f x : map f xs

Example

squares = map (^2)
shout   = map toUpper

Eta‑contraction often yields point‑free style: shout = map toUpper. Lazy and fusion‑friendly map f (map g xs) rewrites to map (f . g) xs.