Peano in Haskell

Peano.hs

$ ghci
GHCi, version 7.10.3: http://www.haskell.org/ghc/  :? for help
Prelude> let z = \s z -> z
Prelude> let s = \n s z -> s $ n s z
Prelude> let unchurch n = n (+1) 0
Prelude> unchurch z
0
Prelude> let n1 = s z
Prelude> let n2 = s $ s z
Prelude> let n3 = s $ s $ s z
Prelude> unchurch n1
1
Prelude> unchurch n2
2
Prelude> unchurch n3
3
Prelude> unchurch $ n2 n3
9
Prelude> unchurch $ n3 n2
8