Peano arithmetic
Giuseppe Peano's system for representing natural numbers inductively using only two symbols, "0" (zero) and "S" (successor).
This system could be expressed as a recursive data type with the following Haskell definition:
data Peano = Zero | Succ Peano
The number three, usually written "SSS0", would be Succ (Succ (Succ Zero)). Addition of Peano numbers can be expressed as a simple syntactic transformation:
plus Zero n = n plus (Succ m) n = Succ (plus m n)