Skip to main content
Mathematica

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

23
  • 1
    $\begingroup$ related to this answer: mathematica.stackexchange.com/a/39936/534 $\endgroup$ Commented Jan 7, 2014 at 13:39
  • 1
    $\begingroup$ I guess Mathematica tries to be smart in some definitions with no patterns on the rhs and sometimes skips them after a couple of iterations in which the rhs didn't change upon evaluation. Let's see if someone digs in and shares a more exact mechanism as to when this happens and when it doesn't $\endgroup$ Commented Jan 7, 2014 at 14:23
  • 5
    $\begingroup$ The Standard Evaluation Procedure "continue[s] reevaluating results until it gets an expression which remains unchanged through the evaluation procedure." So x = x is applied only once (no change); x := Identity[x] leads to infinite recursion: Identity[Identity[…]] because the argument x is evaluated before Identity[x] and becomes Identity[x], in which x is evaluate before Identity[x], ad infinitum. (In other words, Jacob is basically right.) $\endgroup$ Commented Jan 7, 2014 at 15:15
  • 4
    $\begingroup$ @Rojo As you know f[x_] := f[x] has nothing to do with Global`x, so let's use y in f[y]. I think difference is in how pattern replacements are handled. When f[y] is evaluated, M evaluates the head f first, finds the downvalue, applies it. Now, to apply it, M needs to evaluate the rhs, f of the pattern x. After it does the substitution, the result has not been evaluated yet. So even though the result is again f[y], f[y] has to be evaluated once more. Clearly you want this to happen for normal functions. Here you get infinite recursion. $\endgroup$ Commented Jan 7, 2014 at 16:33
  • 2
    $\begingroup$ @JacobAkkerboom I think ReplaceRepeated examines the result of a replacement after evaluation is complete and continues until a fixed point is reached. After the first replacement, the expression is the same as the starting expression, so it stops. $\endgroup$ Commented Jan 7, 2014 at 18:13