Built-in Mathematica Symbol

TagSetDelayed (/: :=)

f/:lhs:=rhs
assigns rhs to be the delayed value of lhs, and associates the assignment with the symbol f.

An expression with a delayed definition is evaluated every time it is used:

Make definitions for special and general cases using immediate and delayed assignments:

The tag can appear as an argument of the left side:

The tag can appear as the head of an argument of the left side:

For ownvalues, the tag is redundant:

For downvalues, the tag is redundant:

Use a tag to define upvalues:

Implement modular arithmetic:

^:= 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:

Clear all definitions:

Delayed assignment introduces a scope that is not affected by global variables:

Immediate assignment does not introduce a scope: