TagSetDelayed 
f/:lhs:=rhs
assigns rhs to be the delayed value of lhs, and associates the assignment with the symbol f.
Examples
open allclose allBasic Examples (1)
Scope (7)
Left-Hand Sides (4)
Properties & Relations (7)
^:= defines upvalues in the same way as using a tag does:
A tag defines only one upvalue; ^:= makes definitions for all symbols:
The right side of an immediate definition is evaluated when the definition is made:
The right side of a delayed definition is evaluated each time the definition is used:
Definitions with the same left side overwrite earlier ones:
Definition prints definitions associated with a symbol:
Information prints various information about a symbol, including any definitions:
UpValues returns a list of rules corresponding to any upvalues defined:
Use =. to clear definitions with a particular left-hand side:
Delayed assignment introduces a scope that is not affected by global variables:
Text
Wolfram Research (1988), TagSetDelayed, Wolfram Language function, https://reference.wolfram.com/language/ref/TagSetDelayed.html.
CMS
Wolfram Language. 1988. "TagSetDelayed." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TagSetDelayed.html.
APA
Wolfram Language. (1988). TagSetDelayed. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TagSetDelayed.html