#98

Equivalence Classes

 

A function f defined on a domain D induces an equivalence relation on D, as follows: a is equivalent to b with respect to f if and only if (f a) is equal to (f b). Write a function with arguments f and D that computes the equivalence classes of D with respect to f.

	(= (__ #(* % %) #{-2 -1 0 1 2}) #{#{0} #{1 -1} #{2 -2}})
	(= (__ #(rem % 3) #{0 1 2 3 4 5 }) #{#{0 3} #{1 4} #{2 5}})
	(= (__ identity #{0 1 2 3 4}) #{#{0} #{1} #{2} #{3} #{4}})
	(= (__ (constantly true) #{0 1 2 3 4}) #{#{0 1 2 3 4}})