General Computer Science; Problems and Solutions for ... - Kwarc

Problem 1.28 (Unary natural numbers)
Define a datatype nat of unary natural numbers and implement the functions
• add = fn : nat * nat -> nat (adds two numbers)
• mul = fn : nat * nat -> nat (multiplies two numbers)
Solution:
datatype nat = zero | s of nat;
fun add(zero:nat,n2:nat) = n2
| add(n1,zero) = n1
| add(s(n1),s(n2)) = s(add(n1,s(n2)));
fun mult(zero:nat,_) = zero
| mult(_,zero) = zero
| mult(n1,s(zero)) = n1
| mult(s(zero),n2) = n2
| mult(n1,s(n2)) = add(n1,mult(n1,n2));
29