UpSetDelayed (^:=)

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 definition can be associated with a symbol appearing as an argument of the left side:

The definition can be associated with the head of an argument of the left side:

If several symbols appear in the left-hand side, upvalues for all of them are defined:

^:= defines upvalues:

^:= 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:

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

Immediate assignment does not introduce a scope: