Wolfram: Set, SetDelayed

Set[x, y]

🔸 SHORT SYNTAX: x=y

Create a transformation rule so that left-hand-side becomes the right-hand-side. The right-hand-side is evaluated before the rule is defined.

The rule is associated to the left most symbol of left-hand-side expression.

(* global variable, of current session  *)
x = 5

In most programing languages, this is setting a value to a variable. In WolframLang, it's actually defining a transformation rule. The effect is the same .

Set

The left-hand-side can be any expression.

(* make f[3] to always become 5.
Effectively defining a function's value at 3.
*)
f[3] = 5

f[3]
(* 5 *)

f[4]
(* f[4] *)
(* no change *)

(* clear the rule associated with f *)
Clear[f]

The left-hand-side can be a Pattern.

(* make the pattern g[x_] to always become 5. Effectively defining a constant function. *)
g[x_] = 5

(* all of the following evalutes to 5 *)
g[3]
g[4]
g[{1,2}]
g[y]

(* clear the rule associated with g *)
Clear[g]

SetDelayed[x, y]

🔸 SHORT SYNTAX: x:=y

Like Set, but right-hand-side is evaluated at the time the replacement happens.

This is usually used to define a function by way of pattern matching. 〔see Define Function by Pattern〕

SetDelayed