Naming Pieces of Patterns
Particularly when you use transformation rules, you often need to name pieces of patterns. An object like x_
stands for any expression, but gives the expression the name x
. You can then, for example, use this name on the right-hand side of a transformation rule.
An important point is that when you use x_
requires that all occurrences of blanks with the same name x
in a particular expression must stand for the same expression.
Thus f[x_, x_]
can only stand for expressions in which the two arguments of f
are exactly the same. f[_, _]
, on the other hand, can stand for any expression of the form f[x, y]
, where x
need not be the same.
The transformation rule applies only to cases where the two arguments of f
allows you to give names not just to single blanks, but to any piece of a pattern. The object x:pattern
in general represents a pattern which is assigned the name x
. In transformation rules, you can use this mechanism to name exactly those pieces of a pattern that you need to refer to on the right-hand side of the rule.
|x_||any expression, to be named x|
|x:pattern||an expression to be named x, matching pattern|
Patterns with names.
This gives a name to the complete form _^_
so you can refer to it as a whole on the right-hand side of the transformation rule.
Here the exponent is named n
, while the whole object is x
When you give the same name to two pieces of a pattern, you constrain the pattern to match only those expressions in which the corresponding pieces are identical.
Here the pattern matches both cases.
Now both arguments of f
are constrained to be the same, and only the first case matches.