Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

Here's a simplified version of what I'm trying to do:

SetAttributes[def, HoldFirst]
def[s_Symbol, v_] := (s[x_] := v)
def[f, x^2]
f[3] (* Expected result: 9 *)
(*
  x^2
*)
?f (* Expected result: f[x_] := x^2 *)
(*
  Global`f

  f[x$_] := x^2
*)

Obviously the x in the x_ pattern gets replaced by x$. Is there a way I can prevent that? That is, from calling def[f,x^2] I want to result the definition f[x_] := x^2. I don't of course care about the name of the variable, so if the resulting function definition reads f[x$_] := x$^2 I'm fine with that, too.

I tried

def[s_Symbol, v_] := With[{x$ = x}, s[x_] := v]
def[s_Symbol, v_] := With[{x = x$}, s[x_] := v]
def[s_Symbol, v_] := (s[x_] := v) /. x :> x$

and

def[s_Symbol, v_] := (s[x_] := v) /. x$ :> x

but none worked.

share|improve this question
2  
How about SetAttributes[def, HoldFirst]; def[s_Symbol, v_] := With[{temp = v}, s = Function @@ {x, temp}]? –  J. M. Aug 31 '12 at 9:28
    
@J.M.: Thanks, I didn't think of anonymous functions; that's a solution that indeed works for my case. –  celtschk Aug 31 '12 at 9:36
    
@J.M.: I have to retract that it works for my problem: I just noticed that anonymous functions don't seem to support optional arguments. –  celtschk Aug 31 '12 at 9:43

3 Answers 3

up vote 15 down vote accepted

With your proposed definition style, the user of that function def has to know that v could/should/must depend on x for this to work; x really should be an argument of def. Perhaps something like this were better suited.

ClearAll[def]
ClearAll[f]
(*SetAttributes[def,HoldFirst]*)

def[s_Symbol, v_, vars_List] := 
 With[{h = s @@ (Pattern[#, Blank[]] & /@ vars)}, (h := v)]
def[f, x^2, {x}]

f[3]
(* 9 *)
share|improve this answer
    
This indirect pattern building did the trick! –  celtschk Aug 31 '12 at 9:51

Try for example

SetAttributes[def, HoldAll]
def[s_Symbol, v_] := Function[Null, s[x_] := #, HoldFirst][v]

Unnamed functions just don't care :)

Other alternatives that should also work (but I would use the previous approach)

def[s_Symbol, v_] := Identity[SetDelayed][HoldPattern@s[x_], v];
def[s_Symbol, v_] := Unevaluated[s[x_] := "Hello"] /. "Hello" -> v
share|improve this answer
    
Elegant! +1. (I edited to better respect the semantics of SetDelayed. If you don't like the result, feel free to revert!) –  Oleksandr R. Aug 31 '12 at 21:33
    
Thanks @OleksandrR. Your edit is fine. I had done it that way based on the question being HoldFirst, but HoldAll makes more sense to me too –  Rojo Sep 1 '12 at 1:21

I propose these:

SetAttributes[def, HoldAllComplete]

def[s_Symbol, v_] := SetDelayed @@ Hold[s[x_], v]

def[s_Symbol, v_] := With[{L := s[x_]}, L := v]

def[s_Symbol, v_] := Reverse @ Unevaluated[v := s[x_]]

The HoldAllComplete (or SequenceHold) attribute is necessary for an assignment such as:

def[q, Sequence[1, 2, x]]

head[q[5]]
head[1, 2, 5]

Also see:

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.