Exercise 6.1. Simple Arithmetic Operations, . Let there be given just the simple RSL expression constructs: value f: A -> B f(a) if Ptest (a) then Econ else Ealt end pre: Ppre; where Ptest is a simple Boolean value expression which tests whether invocation of f should terminate; where Econ is the consequence expression, a simple expression which does not contain a (recursive) reference to f; where Ealt is the alternative expression, also an expression, also an expression which does contain a (hence recursive) reference to f; and where Ppr is a simple Boolean value expression which tests whether f should be applied, a pre-condition.

Define 1. arithmetic (natural number) multiplication (i x j), and

2. arithmetic (natural number) exponentiation ( )

using just addition and subtraction, or already defined functions. That is: A is the Cartesian of the Natural Number type, and B is that type.

1. Define arithmetic (natural number) multiplication (i x j)

2. Define arithmetic (natural number) exponentiation (i j)