Finding an element in a sorted array

Input

1. An array [math]\displaystyle{ A }[/math] of some component type [math]\displaystyle{ S }[/math]
2. A definition of comparison on [math]\displaystyle{ S }[/math]

Prerequisite: The components of [math]\displaystyle{ A }[/math] are sorted in ascending order according to the comparison.

1. An element [math]\displaystyle{ s\in S/math\gt == Output == If \lt math\gt s }[/math] equals at least one of the components of [math]\displaystyle{ A }[/math], the index of one of the occurrences is returned; otherwise, the information is returned that [math]\displaystyle{ s }[/math] is not in [math]\displaystyle{ A }[/math].