peano

Peano arithmetics

Consider the following type to represent natural numbers:

type nat = Z | S of nat

Write the following functions:

iseven : nat -> bool

detects if a number is even.

halve : nat -> nat

divides a natural number by two (note: this is the integer division, where \eg 3 divided by 2 equals 1).

add : nat -> nat -> nat

adds two numbers.

mul : nat -> nat -> nat

multiplies two numbers.

equals : nat -> nat -> bool

checks equality.

leq : nat -> nat -> bool

checks if a number is less than or equal to another one.