Specifying Types of Expression in Patterns
You can tell a lot about what "type" of expression something is by looking at its head. Thus, for example, an integer has head Integer, while a list has head List.
In a pattern, _h and x_h represent expressions that are constrained to have head h. Thus, for example, _Integer represents any integer, while _List represents any list.
|x_h||an expression with head h|
|x_Real||an approximate real number|
|x_Complex||a complex number|
Patterns for objects with specified heads.
This replaces just those elements that are integers:
You can think of making an assignment for f[x_Integer] as like defining a function f that must take an argument of "type" Integer.
This defines a value for the function gamma
when its argument is an integer:
The definition applies only when the argument of gamma
is an integer:
The object 4.
has head Real
, so the definition does not apply:
This defines values for expressions with integer exponents:
The definition is used only when the exponent is an integer: