Page 21, Exercise 1

ADT NaturalNumber is objects:
an ordered subrange of the integers starting at zero and ending at the
maximum integer (INT_MAX) on the computer functions: for
all x, y ∈ NaturalNumber; TRUE, FALSE ∈ Boolean
and where +, −, <, and == are the usual integer operations

NaturalNumber Zero( )	::= 0
Boolean IsZero(x)	::= if (x) return FALSE return TRUE
Boolean Equal(x, y)	::= if (x == y) return TRUE return FALSE
NaturalNumber Successor(x)	::= if (x == INT_MAX) return x return x + 1
NaturalNumber Add(x, y)	::= if ((x + y) < INT_MAX) return x + y if ((x + y) == INT_MAX) return x + y return INT_MAX
NaturalNumber Subtract(x, y)	::= if (x < y) return 0 return x − y
NaturalNumber Predecessor(x)	::= if (x < 0) return ERROR if (x == 0) return 0 return x - 1
Boolean IsGreater(x, y)	:= if ((x-y)) < 0) return ERROR if ((x-y)) == 0) return FALSE return TRUE
NaturalNumber mult(x, y)	::= if (x < 0) return ERROR if (y < 0) return ERROR if (y == 1) return x return x + mult(x, y-1)
NaturalNumber div(x, y)	::= if (x < 0) return ERROR if (y < 0) return ERROR if (y == 0) return ERROR if (y == 1) return 1 return x - div(x, y-1)

end NaturalNumber