Are these two functions equivalent?

Question

I checked several cases and saw that two functions are equivalent in these samples. However, are the two equivalent in all cases? Is there a way to check that?

Explicit function:

  g[x_]= π
  h[_] = π

Answer 1

Yes, they are equivalent.

_ is a pattern that matches any expression.

x_ is the same thing, with a name, x. The pattern name can be used in two ways.

The most common way is to refer to it on the right hand side of the definition or rule. For example, f[x_] := x^2. If we are not using the matched expression in the right hand side, there's no reason to name the pattern.

The other situation is when two sub-patterns have the same name. This is used to require them to match the same expression. For example, {x_, x_} matches {1,1} but not {1,2}. In contrast, {_, _} matches both {1,1} and {1,2}.

Neither situation applies to your example. The pattern name is never used for anything. Thus there's no purpose of naming the pattern.

Further reading:

• http://reference.wolfram.com/language/tutorial/PatternsOverview.html