Optional named arguments without wrapping them all in "OptionValue"

Question

Suppose I have a function with optional named arguments but I insist on referring to the arguments by their unadorned names.

Consider this function that adds its two named arguments, a and b:

Options[f] = {a->0, b->0};  (* The default values. *)
f[OptionsPattern[]] := 
  OptionValue[a] + OptionValue[b]

How can I write a version of that function where that last line is replaced with simply a+b? (Imagine that that a+b is a whole slew of code.)

The answers to the following question show how to abbreviate OptionValue (easier said than done) but not how to get rid of it altogether: Optional named arguments in Mathematica

Philosophical Addendum: It seems like if Mathematica is going to have this magic with OptionsPattern and OptionValue it might as well go all the way and have a language construct for doing named arguments properly where you can just refer to them by, you know, their names. Like every other language with named arguments does. (And in the meantime, I'm curious what workarounds are possible...)

Answer 1

Why not just use something like:

Options[f] = {a->0, b->0};
f[args___] := (a+b) /. Flatten[{args, Options[f]}]

For more complicated code I'd probably use something like:

Options[f] = {a->0, b->0};
f[OptionsPattern[]] := Block[{a,b}, {a,b} = OptionValue[{a,b}]; a+b]

and use a single call to OptionValue to get all the values at once. (Main reason is that this cuts down on messages if there are unknown options present.)

Update, to programmatically generate the variables from the options list:

Options[f] = {a -> 0, b -> 0};
f[OptionsPattern[]] := 
  With[{names = Options[f][[All, 1]]}, 
    Block[names, names = OptionValue[names]; a + b]]

Answer 2

Here is the final version of my answer, containing the contributions from the answer by Brett Champion.

ClearAll[def];
SetAttributes[def, HoldAll];
def[lhs : f_[args___] :> rhs_] /; !FreeQ[Unevaluated[lhs], OptionsPattern] :=
   With[{optionNames = Options[f][[All, 1]]},
     lhs := Block[optionNames, optionNames = OptionValue[optionNames]; rhs]];
def[lhs : f_[args___] :> rhs_] := lhs := rhs;

The reason why the definition is given as a delayed rule in the argument is that this way we can benefit from the syntax highlighting. Block trick is used because it fits the problem: it does not interfere with possible nested lexical scoping constructs inside your function, and therefore there is no danger of inadvertent variable capture. We check for presence of OptionsPattern since this code wil not be correct for definitions without it, and we want def to also work in that case. Example of use:

Clear[f, a, b, c, d];
Options[f] = {a -> c, b -> d};
(*The default values.*)
def[f[n_, OptionsPattern[]] :> (a + b)^n]

You can look now at the definition:

Global`f
f[n$_,OptionsPattern[]]:=Block[{a,b},{a,b}=OptionValue[{a,b}];(a+b)^n$]

f[n_,m_]:=m+n

Options[f]={a->c,b->d}

We can test it now:

In[10]:= f[2]
Out[10]= (c+d)^2

In[11]:= f[2,a->e,b->q]
Out[11]= (e+q)^2

The modifications are done at "compile - time" and are pretty transparent. While this solution saves some typing w.r.t. Brett's, it determines the set of option names at "compile-time", while Brett's - at "run-time". Therefore, it is a bit more fragile than Brett's: if you add some new option to the function after it has been defined with def, you must Clear it and rerun def. In practice, however, it is customary to start with ClearAll and put all definitions in one piece (cell), so this does not seem to be a real problem. Also, it can not work with string option names, but your original concept also assumes they are Symbols. Also, they should not have global values, at least not at the time when def executes.

Answer 3

Here's a kind of horrific solution:

Options[f] = {a->0, b->0};
f[OptionsPattern[]] := Module[{vars, tmp, ret},
  vars = Options[f][[All,1]];
  tmp = cat[vars];
  each[{var_, val_}, Transpose[{vars, OptionValue[Automatic,#]& /@ vars}],
    var = val];
  ret = 
    a + b;  (* finally! *)
  eval["ClearAll[", StringTake[tmp, {2,-2}], "]"];
  ret]

It uses the following convenience functions:

cat = StringJoin@@(ToString/@{##})&;        (* Like sprintf/strout in C/C++.  *)
eval = ToExpression[cat[##]]&;              (* Like eval in every other lang. *)
SetAttributes[each, HoldAll];               (* each[pattern, list, body]      *)
each[pat_, lst_, bod_] := ReleaseHold[      (*  converts pattern to body for  *)
  Hold[Cases[Evaluate@lst, pat:>bod];]];    (*   each element of list.        *)

Note that this doesn't work if a or b has a global value when the function is called. But that was always the case for named arguments in Mathematica anyway.