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function construction - Another difference between Set and Setdelayed. Evaluation shortcut?



A little while ago I wondered why


f[x_] = f[x]

gives an infinite iteration. I ended up discovering the following difference in evaluation between Set and SetDelayed with Evaluate.


count = 0;
ClearAll@a
a /; (count++ < 20) = {a}
a // OwnValues
count = 0;
a


Output


{{{{{{{{{{{{{{{{{{{{{a}}}}}}}}}}}}}}}}}}}}}
{HoldPattern[a /; count++ < 20] :> {a}}
{a}

and


count = 0;
ClearAll@b
b /; (count++ < 20) := Evaluate@{b}

b // OwnValues
count = 0;
b

Output


{HoldPattern[b /; count++ < 20] :> {b}}
{{{{{{{{{{{{{{{{{{{{b}}}}}}}}}}}}}}}}}}}}

Can somebody explain the difference? Can we say that there is an evaluation shortcut at work here?


Related



This is a follow up question: Strange results of definitions using OwnValues


Why x = x doesn't cause an infinite loop, but f[x_] := f[x] does?


Does Set vs. SetDelayed have any effect after the definition was done?



Answer



I thought to give a bit more insight into why Update is needed, as pointed out in the other answers. Its documentation says Update may be needed when a change in 1 symbol changes another via a condition test.


In Jacob's example, setting count = 0 changes the condition test outcome, and thus a or b on the LHS. Consequently, a or b on the RHS is supposed to change. However, RHS a equals the old LHS a, which was undefined because count>=20, and needs Update to be changed. RHS b behaves the same, but was not evaluated in SetDelayed because Evaluate occurs before SetDelayed, so count is unchanged, and RHS b evaluates to LHS b with count<20. If we now reset count=0, evaluating b will return {b}.


To illustrate, I modify the example to separate LHS and RHS. MMA is clever enough to automatically update LHS declared as a variable, so I have to make a function:


count=0;
ClearAll[LHS,RHS];
LHS[]/;(count++<20)={RHS};

RHS=Unevaluated@LHS[];

count=0;
RHS (* Equals LHS[] with count >= 20 *)

(* Tell Wolfram Language about changes affecting RHS which depends on LHS *)
Update@Unevaluated@LHS;
RHS



LHS[]


{{{{{{{{{{{{{{{{{{{{LHS[]}}}}}}}}}}}}}}}}}}}}



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