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I'd like to make my own "typed function" in WolframScript. Suppose the type we desire is called money, and we'd like to make a function called doubleOurMoney which doubles any money argument but throws an error on everything else. How do we do this?

Attempt: This isn't quite right but perhaps is a good starting point:

doubleOurMoney[money[x_Real]] := money[2 x]
doubleOurMoney[money[2.0]] (* Should return money[4.], and does. *)

doubleOurMoney[money["nonsense"]] (* How do we make this throw an error? *)
doubleOurMoney[2] (* How do we make this throw an error? *)
doubleOurMoney["nonsense"] (* How do we make this throw an error? *)
doubleOurMoney[symbol] (* How do we make this throw an error? *)

Questions:

1. How do we throw "type errors" in this context?


2. Right now money accepts real numbers as arguments; how could we make it take any "number" as an argument (Integer, etc) but throw an error on everything else?


3. Is my attempt at "typed WolframScript" an idiomatic approach to type-checking in Wolfram? If not, what is the idiomatic approach here to check that inputs to a function are sensible?

Here is an idiom used by many built-in functions to achieve this effect:

doubleOurMoney::badarg = "`1` should be of the form money[number]";
doubleOurMoney[money[x_?NumericQ]] := money[2 x];
doubleOurMoney[args___] := (
 Message[doubleOurMoney::badarg, args];
 Null /; False
)

Here I'm using _?NumericQ instead of _Real to make your function work on all numeric input. That first definition will only fire for numeric inputs of the right form, but the second definition will work for any input. The second definition will issue a message telling the user what type of input is needed:

doubleOurMoney[money[2]]
(* money[4] *)

doubleOurMoney[3]

During evaluation of doubleOurMoney::badarg: 3 should be of the form money[number]
(* doubleOurMoney[3] *)

doubleOurMoney["bob"]

During evaluation of doubleOurMoney::badarg: bob should be of the form money[number]
(* doubleOurMoney["bob"] *)

That last bit of trickery is so that your function, after issuing a message, returns unevaluated. You could replace the Null /; False with $Failed just as easily.