In a similar manner to the function add, define a recursive...

In a similar manner to the function add, define a recursive multiplication function mult :: Nat $\rightarrow$ Nat $\rightarrow$ Nat for the recursive type of natural numbers:
Hint: make use of add in your definition.

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Key Concepts

Recursion

Recursion is a programming and mathematical technique where a function is defined in terms of itself. In the context of defining multiplication for natural numbers, recursion allows the operation to be broken down into a base case and a recursive step that builds on previously computed values.

Recursive Type for Natural Numbers

The recursive type of natural numbers is typically defined using a base case (often called Zero) and a recursive case (using a successor function, such as Succ). This structure is fundamental in proofs and definitions in computer science and mathematics, enabling algorithms like addition and multiplication to be defined inductively.

Addition as Repeated Operation

Addition, when defined recursively over natural numbers, serves as a basic arithmetic operation. In this context, addition is used as a building block to define multiplication as repeated addition, illustrating how complex operations can build on simpler ones.

Multiplication as Repeated Addition

Multiplication for natural numbers can be conceptualized as repeated addition. This means that to multiply two natural numbers, one can add one of the numbers to itself a number of times equal to the other number. This approach naturally lends itself to a recursive definition that utilizes the previously defined addition function.

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