➡️ Function Combinators

Theory

Combinators are functions that manipulate functions.

combinator	type	purpose
(.)	$(b\to c)\to (a\to b)\to a\to c$	composition
flip	$(a\to b\to c)\to b\to a\to c$	swap arguments
($)	$(a\to b)\to a\to b$	low‑precedence application
id	$a\to a$	identity

Eta-conversion

• Expansion: $f⟹\lambda x.fx$
• Contraction: $\lambda x.fx⟹f$ (when $x$ not free in $f$)

Implementation

-- Point‑free rewrite
sumOfSquares = sum . map (^2)
 
-- Re‑order for foldl
foldl (flip (:)) [] xs   ==   reverse xs