This article uses the factorial function on Church numerals as motivation for discussing recursion and the Y-combinator. Yet Church numerals have enough recursi

This article uses the factorial function on Church numerals as motivation for discussing recursion and the Y-combinator. Yet Church numerals have enough recursion "built-in" to compute factorials directly: fac = λn.λf. n F (λx.f) (λx.x) where F = (λc.λn.n(c(λf.λx.n f(f x)))) For example, fac 3 evaluates as (writing Church numerals simply as 1,2...) λf. F (F (F (λx.f))) 1 = λf. 1 (F (F (λx.f)) 2) = λf. 1 (2 (F (λx.f) 3)) = λf. 1 (2 (3 ((λx.f) 4))) = λf. 1 (2 (3 f)) = 6