Convert boolean test function to pattern?

Question

What is a "reverse" to MatchQ? MatchQ converts pattern into boolean function. So how to convert back?

Suppose I want to use boolean function in Switch.

Answer 1

To convert a Boolean test function such as PrimeQ or IntegerQ into a pattern one typically uses either Condition (/;) or PatternTest (?). There are specific strengths and purposes for each which are described in: Using a PatternTest versus a Condition for pattern matching.

Here is a simple and brief example of each:

Cases[Range@10, _?PrimeQ]

{2, 3, 5, 7}

Cases[Range@10, x_ /; PrimeQ[x]]

{2, 3, 5, 7}

Be aware that the PatternTest operator ? has unusually high binding power as seen in this table and with:

Precedence[PatternTest]

680.