Define a function with a default value for the second argument:

Use the function with both arguments specified explicitly:

The second argument is now taken to have its default value:

Use Optional in any pattern-matching function including ReplaceAll:

Cases:

And MatchQ:

Use Optional with BlankSequence:

The default is used:

The value given is used:

A sequence of values is bound to x:

The first argument to Optional can be any pattern, not just a form of Blank:

Specify a default value for a function:

Define a down value using a default argument:

If the third argument is given, its value is used:

If the third argument is not present, the value is taken from the function's default:

The default value need not match the pattern for the optional argument:

5 matches the pattern:

The string "xyz" does not match the pattern:

When no argument is specified, the default value is returned even though it fails to match the pattern:

The ternary form sym:pat:def has head Optional:

The forms s_:v and s:_:v are identical:

If no explicit default is given, the default is inferred from DefaultValues of the head:

The 1 comes from DefaultValues[Times]:

An explicit default can always be provided:

The short form x_. is equivalent to Optional[Pattern[x,Blank[]]:

When restricting a default argument, the pattern will entirely fail to match a nonconforming argument:

Only if the argument is completely missing will the default value be used:

Optional does not prevent the default value from evaluating:

Thus, all calls f use the same default value:

Use HoldPattern to delay evaluation of the default value until it is used:

Each call to g uses a unique default value:

Define a function using BlankSequence and Optional; the function evaluates using a default value:

Define a function using BlankNullSequence; the function evaluates with no value:

Since BlankNullSequence matches a zero argument length, the form x___:d will never use d:

The input s:v has head Optional only if s is a special input form for Blank[…] or Pattern[sym,Blank[…]]:

BlankSequence[…] and BlankNullSequence[…] are also allowed:

If s is a symbol, then s:v represents Pattern[s,v]:

If s is any other expression, the form is not valid input:

Condition and PatternTest cannot be applied to Optional:

Instead, apply the test to the first argument of Optional:

The functions f and g behave as expected, whether given zero or one argument:

Pattern cannot bind to an Optional object:

Instead, put the pattern inside the first argument to Optional:

The symbol x is bound to the default value if the pattern does not match:

Note that the Optional object can written more compactly using the ternary form s:p:d: