• ← Set
• → TagSet

SetDelayed (:=)

WMA link

SetDelayed[expr, value]

expr := value

assigns value to expr, without evaluating value.

SetDelayed is like Set, except it has attribute HoldAll, thus it does not evaluate the right-hand side immediately, but evaluates it when needed.

• • Attributes[SetDelayed]

• • a = 1

• • x := a

• • x

Changing the value of a affects x:

• • a = 2

• • x

Condition (/;) can be used with SetDelayed to make an
assignment that only holds if a condition is satisfied:

• • f[x_] := p[x] /; x>0

• • f[3]

• • f[-3]

It also works if the condition is set in the LHS:

• • F[x_, y_] /; x < y /; x>0  := x / y;

• • F[x_, y_] := y / x;

• • F[2, 3]

• • F[3, 2]

• • F[-3, 2]

We can use conditional delayed assignments to define symbols with values conditioned to the context. For example,

• • ClearAll[a,b]; a/; b>0:= 3

Set a to have a value of $3$ if certain variable b is positive. So, if this variable is not set, a stays unevaluated:

• • a

If now we assign a positive value to b, then a is evaluated:

• • b=2; a