Define an upvalue for a symbol g using TagSetDelayed:

Define an upvalue using UpSetDelayed:

These are the upvalues associated with g:

UpValues returns rules corresponding to upvalues defined for a symbol:

Create several values:

Obtain the upvalues of symbols whose names start with x:

UpValues can be used to set the values directly:

The resulting rules are in the order given:

Now reorder the definitions:

Copy a symbol's definitions to another symbol:

Values can be defined by immediate or delayed assignments:

HoldPattern is used to protect the rules from their own definitions:

UpValues["sym"] will issue a message if the specified symbol does not exist:

If the symbol exists but has no definitions, an empty list is returned:

Definition and Information display upvalues but do not return them as values:

UpValues returns a value that can be used in a program:

Evaluation of an expression involves applying matching upvalues:

Matching upvalues are used before matching downvalues in evaluation:

The upvalue for g is used prior to the downvalue for f:

Compare with a manual application of the upvalue and downvalue:

Define an upvalue for g that applies for all heads:

Even if a function has attribute HoldAll, the upvalue will be applied during evaluation:

If a function has attribute HoldAllComplete, the upvalue will not be applied: