Another difference between Set and SetDelayed. Evaluation shortcut?

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[]}}}}}}}}}}}}}}}}}}}}


Extended comment. Also: If Rojo wants to post an answer, I can delete this

It seems Rojo was right, guessing that it had to do with Update.

count = 0;
ClearAll@a2
a2 /; (Update[Unevaluated@a2]; count++ < 20) = {a2}
a2 // OwnValues
count = 0;
a2

Output

{{{{{{{{{{{{{{{{{{{{{a2}}}}}}}}}}}}}}}}}}}}}
{HoldPattern[a2 /; (Update[Unevaluated[a2]]; count++ < 20)] :> {a2}}
{{{{{{{{{{{{{{{{{{{{a2}}}}}}}}}}}}}}}}}}}}

I think user obsolesced rightly pointed out why there is an additional pair of brackets in the first output. This is because there is already a pair of brackets on the right hand side of Set and {a2} is evaluated rather than a2.


Also an extended comment; using Update[] makes the first recursion behave as expected:

count = 0;
ClearAll@a
a /; (count++ < 20) = {a};
count = 0;
Update[]
a
{{{{{{{{{{{{{{{{{{{{a}}}}}}}}}}}}}}}}}}}}

Apparently the LHS condition is affected by the use of Set versus SetDelayed. Certainly worth more exploration, but for me that will have to wait.