Why is there a difference when formulating patterns for Select and FirstPosition?

Question

Select[{1, 2, 4, 7, 6, 2}, # > 2 &]

Gives {4, 7, 6}. OK!

So one should think that the following would work:

myList = {-2, -1, 0, 1, 2};
FirstPosition[myList, # > 0 &]

But this fails. The correct command is

myList = {-2, -1, 0, 1, 2};
FirstPosition[myList, _?(# > 0 &)]

But why on earth do we have to use different syntax for those two cases??? Why is the _? necessary?

As it was commented by MarcoB:

Select takes a criterion function, while FirstPosition takes a pattern instead.

Can someone give a for dummies explanation what is the difference between both? Literally I would say a criterion is a pattern and a pattern is a criterion...

Answer 1

This question might end up closed as it is hard to know what was in the minds of the language designers in every case. However I think a reasonable answer can be given here so I shall try.

The high-level Mathematica language is arguably built on pattern matching. It it therefore natural that many functions also use, operate on, or work with patterns. For example Cases, Count, Position, Replace, Switch, Collect, Reap and standard definitions all natively use patterns. Patterns allow a generally way to express a specification.

Since one can make any Boolean test function into a pattern using PatternTest or Condition these may be considered a subset of pattern matching however they have their own benefits and conventions:

• They are easily applicable in a procedural style of programming, e.g. they fit naturally into constructs like If, Which, etc.

• They combine with Boolean operators such as And, Or, Xor, Not, etc.

Since Mathematica uses a multi-paradigm language it is entirely reasonable for it to have functions dedicated to the use of Boolean test functions as well as its own pattern matching. Select is one such function. Note that it lacks the levelspec of the more general Cases which I believe is in keeping with the style of programming it is primarily intended for. It should be thought of as a specialized function. Your question could perhaps be recast as "Why isn't there a "BooleanPosition" function?" With the explosion of functions in recent versions I would not be surprised if one appears, but really it is not necessary as it could be simply constructed from the existing Position function.

In summary patterns and Boolean test functions coexist in Mathematica; it is up to the user to choose the programming style and supporting functions that suit him and his application.