SetDelayed

lhs := rhs sets lhs to stand for rhs, with rhs not being evaluated until it is referenced by lhs.

Attributes[SetDelayed] := {HoldAll, Protected, SequenceHold}

Simple examples

SetDelayed can be used to define functions:

In[1]:= testa[x_] := x*2
Out[1]= Null

In[2]:= testa[x_Integer] := x*3
Out[2]= Null

In[3]:= testa[x_Real] := x*4
Out[3]= Null

The more "specific" definitions match first:

In[4]:= testa[2.]
Out[4]= 8.

In[5]:= testa[2]
Out[5]= 6

There is no specific match for testa[k], so the general case matches:

In[6]:= testa[k]
Out[6]= 2 * k

Further examples

Set has the HoldFirst attribute, meaning rhs is evaluated before assignment:

In[1]:= Attributes[Set]
Out[1]= {HoldFirst, Protected, SequenceHold}

SetDelayed has the HoldAll attribute, meaning rhs is not evaluated during assignment:

In[2]:= Attributes[SetDelayed]
Out[2]= {HoldAll, Protected, SequenceHold}