Four Fours

Puzzle
Using exactly $4$ instances of the number $4$, it is possible to write an expression for all positive integers from $0$ to $100$, using whatever arithmetical operations are necessary.

Solution
In the below, let $\map {e_n} m$ be an expression which is effectively shorthand for:


 * $\map {e_n} m :=$ an expression using exactly $n$ instances of $4$ in order to evaluate $m$