WolframLang: Expression

By Xah Lee. Date: . Last updated: .

WolframLang source code is made of expressions. Every part in source code, is expression. (there is no such thing as “statements”.)

What this means is that, any valid syntactic unit returns a value.

Atom
An atom is a indivisible expression, such as number, Symbol, String. [see Atomic Expression]
Expression

Expression is either a single Atom , or a sequence of atoms in the form

a[b, c etc]

any of the a, b, c, etc, is again an expression.

this syntax is called FullForm

Head of expression
The a in a[…] is called the Head of expression. [see Head of Expression]
List
A list is a expression whose head is List. [see List]
FullForm
  • The form a[…] is called FullForm.
  • Atomic Expression such as number and string, are in FullForm by themself.
  • The WolframEngine convert shortcut syntax to FullForm internally before eval.
  • All Pattern Matching are done against FullForm.

[see WolframLang: FullForm Syntax]

Frequently used functions have syntax shortcuts. Example:

FullFormShortcut
Plus[3,4]3+4
Rational[3,4]3/4
List[3,4]{3,4}
Equal[x,y]x == y
SameQ[x,y]x === y
Greater[x,y]x > y
Set[x,3]x = 3

Expression, Atom, Head