How to specify optional arguments that take functional values made me wonder: Can we come up with a variant of Optional that allows to do the following:

lhs = x_; g[lhs~HeldOptional~RandomReal[]] := x DownValues@g 

and get

{HoldPattern[g[Optional[x_, RandomReal[]]]] :> x}

Specifically, I want HeldOptional to evaluate the left hand side like all pattern construction constructs, while leaving the right argument untouched.

The following attempt does not work:

HeldOptional~SetAttributes~HoldRest HeldOptional[x_, y_] := Optional[x, Unevaluated@y] 

This gives the DownValue

{HoldPattern[g[x_ : Unevaluated[RandomReal[]]]] :> x}

such that g[] gives Unevaluated[RandomReal[]] instead of a random real.

How to specify optional arguments that take functional values made me wonder: Can we come up with a variant of Optional that allows to do the following:

lhs = x_; g[lhs~HeldOptional~RandomReal[]] := x DownValues@g 

and get

{HoldPattern[g[Optional[x_, RandomReal[]]]] :> x}

Specifically, I want HeldOptional to evaluate the left hand side like all pattern construction constructs, while leaving the right argument untouched.

The following attempt does not work:

HeldOptional~SetAttributes~HoldRest HeldOptional[x_, y_] := Optional[x, Unevaluated@y] 

This gives the DownValue

{HoldPattern[g[x_ : Unevaluated[RandomReal[]]]] :> x}

such that g[] gives Unevaluated[RandomReal[]] instead of a random real.