Arrange 4 fours into various expressions to generate all integer numbers, from 1 to 112 inclusive like:

1 = 44 ÷ 44
2=sqrt 4 - (4 - 4) x 4
3 = (4 + 4 + 4) ÷ 4
4 = 4 + 4 × (4 - 4)
... ...
7= 44/4-4
... ...
19=4!-4-4/4
... ...
100=4*4!+sqrt(4*4)
etc

Allow use of concatenation, +, -, x, /, sqrt, exponentation, factorial,decimal fractions, overline & brackets.

Source: Inspired by Martin Gardner statement.