2.3.4 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.

Patterns for objects with specified heads.

This replaces just those elements that are integers.

In[1]:= {a, 4, 5, b} /. x_Integer -> p[x]

Out[1]=

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.

In[2]:= gamma[n_Integer] := (n - 1)!

The definition applies only when the argument of gamma is an integer.

In[3]:= gamma[4] + gamma[x]

Out[3]=

The object 4. has head Real, so the definition does not apply.

In[4]:= gamma[4.]

Out[4]=

This defines values for expressions with integer exponents.

In[5]:= d[x_^n_Integer] := n x^(n-1)

The definition is used only when the exponent is an integer.

In[6]:= d[x^4] + d[(a+b)^3] + d[x^(1/2)]

Out[6]=