Optional named arguments in Mathematica

Question

What's the best/canonical way to define a function with optional named arguments? To make it concrete, let's create a function foo with named arguments a, b, and c, which default to 1, 2, and 3, respectively. For comparison, here's a version of foo with positional arguments:

foo[a_:1, b_:2, c_:3] := bar[a,b,c]

Here is sample input and output for the named-arguments version of foo:

foo[]                  --> bar[1,2,3]
foo[b->7]              --> bar[1,7,3]
foo[a->6, b->7, c->8]  --> bar[6,7,8]

It should of course also be easy to have positional arguments before the named arguments.

Answer 1

I found the standard way to do it in the Mathematica documentation: http://reference.wolfram.com/mathematica/tutorial/SettingUpFunctionsWithOptionalArguments.html

Options[foo] = {a->1, b->2, c->3};  (* defaults *)
foo[OptionsPattern[]] := bar[OptionValue@a, OptionValue@b, OptionValue@c]

Typing "OptionValue" every time is a little cumbersome. For some reason you can't just make a global abbreviation like ov = OptionValue but you can do this:

foo[OptionsPattern[]] := Module[{ov},
  ov[x___] := OptionValue[x];
  bar[ov@a, ov@b, ov@c]]

Or this:

With[{ov = OptionValue},
  foo[OptionsPattern[]] := bar[ov@a, ov@b, ov@c]
]

Or this:

$PreRead = ReplaceAll[#, "ov" -> "OptionValue"] &;

foo[OptionsPattern[]] := bar[ov@a, ov@b, ov@c]

Answer 2

Yes, OptionValue can be a bit tricky because is relies on a piece of magic so that

OptionValue[name] is equivalent to OptionValue[f,name], where f is the head of the left-hand side of the transformation rule in which OptionValue[name] appears.

Throwing in an explicit Automatic usually does the trick, so in your case I would say that the solution is:

Options[foo] = {a -> 1, b -> 2, c -> 3};
foo[OptionsPattern[]] := 
  bar @@ (OptionValue[Automatic, #] &) /@ First /@ Options[foo] 

By the way, options used to be done by matching to opts:___?OptionQ, and then finding option values manually as {a,b,c}/.Flatten[{opts}]. The pattern check OptionQ is still around (although not documented), but the OptionValue approach has the advantage that you get warnings for non-existing options (e.g. foo[d->3]). This would also be the case for your second response, but not for the one you have accepted.

Answer 3

I'll throw this possible solution into the mix:

foo[opts___Rule] := Module[{f},
  f@a = 1; (* defaults... *)
  f@b = 2;
  f@c = 3;
  each[a_->v_, {opts}, f@a = v];

  Return[bar[f@a, f@b, f@c]]
]

I like it for its terseness but I don't think it's the standard way. Any gotchas with doing it that way?

PS, it uses the following handy utility function:

SetAttributes[each, HoldAll];                (* each[pattern, list, body]     *)
each[pat_, lst_, bod_] :=                    (*  converts pattern to body for *)
  Scan[Replace[#, pat:>bod]&, Evaluate@lst]  (*   each element of list.       *)