Symbols and Expressions

Symbols

Mathematica has one more basic type than those mentioned before: Symbol

In reality, every variable we’ve used and function we’ve defined (excluding pure functions) has been a symbol.

One thing to keep in mind is that the only things that can have properties or values in Mathematica are symbols, although a symbol need not have any.

All of the following are symbols:

Automatic
AxesLabel
$ModuleNumber
Rule
SetDelayed

(*Out:*)

Automatic

(*Out:*)

AxesLabel

(*Out:*)

1205

(*Out:*)

Rule

(*Out:*)

SetDelayed

Expressions

In Mathematica, they say everything is an expression. What this means, really, is that outside of the primitive types everything has one common form:

(head)[arg1,arg2,arg2,...,argn]

Furthermore, there are tools to parse these structures:

{1,2,3}//FullForm

(*Out:*)

List[1,2,3]

This even applies to things like graphics. Consider the following graphic:

Graphics3D[Sphere[],BoxedFalse,Lighting"Neutral",ImageSizeSmall]

It is, however, still just an expression:

Graphics3D[Sphere[], BoxedFalse, Lighting"Neutral", ImageSizeSmall ]//FullForm

(*Out:*)

Graphics3D[Sphere[List[0,0,0]],Rule[Boxed,False],Rule[Lighting,"Neutral"],Rule[ImageSize,Small]]

Symbols and Expressions