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

Question

I was always assuming that the only difference between Set (=) and SetDelayed (:=) is that SetDelayed holds the right argument, so that a := b is effectively the same as a = Unevaluated[b]. Especially I assumed that after the assignment is done, there's no further difference for variables or functions assigned with Set and variables assigned with SetDelayed. Looking at OwnValues resp. DownValues seems to support that assumption.

However I now noticed that when writing ?a, Mathematica displays the type of assignment used for the definition, which means it has to store it somewhere. And I somehow doubt that it only stores it in order to show it with ?.

Therefore my question is: Is there any difference in the behaviour of values assigned with = and with := (apart from the different output of ?), assuming the actual assigned expression is the same (i,e, OwnValues/DownValues have the same value after both assignments)?

Answer 1

Yes, at least in one place.

x = {1, 2, 3}    
x[[2]] = 8;

All right there, but

y := {1, 2, 3}    
y[[2]] = 8

gives Set::noval: Symbol y in part assignment does not have an immediate value

Credit to this old comment by Leonid. Also note the point on memory usage:

[...] I'd guess that delayed definitions may use some intermediate internal variables, while immediate ones point straight to the memory where the data is stored.

Answer 2

Here is another difference

test[a_] = Unevaluated[1 /; a];
test2[a_] := 1 /; a
test[True]
test2[True]

1/;True  
1

I think this has to do with different handling of RuleDelayed and Rule. I actually found this difference between Set and SetDelayed after finding the following difference between those.

True/.a_->  2/;a
True/.a_:>  2/;a
True/.a_:>  Evaluate[2/;a]

2/;True
2
2

Silly note on syntax highlighting

Note that the syntax coloring, which does not connect the as in the case of Rule, can be misleading. Of course (in the case where a does not have a value) the symbols a do correspond and we do not simply replace by the symbol a, but rather by what a_ matches.

True/.a_->  !a,
True/.a_:>  !a

False (*of course this is the right output, and not !a*)
False

So this has nothing to do with the difference.

Root of the difference

The code

True/.a_:> !a

is evaluated using the undocumented function RuleCondition (WReach explains that function nicely here). This can be seen by looking at the trace

Trace[True/.a_:>2/;a]

But in

Trace[True/.a_->2/;a]

no RuleCondition appears. A simple replacement is made, where the pattern is simply replaced by the expression with head Condition. So no "special handling" occurs here and whether we replace or not does not depend on the condition.

Another difference between Rule and RuleDelayed

First I thought the difference was responsible for the difference between Set and SetDelayed. I felt it was worth mentioning anyway.

Hold[2]/.a_Integer-> RuleCondition[a*2]
Hold[2]/.a_Integer:>  RuleCondition[a*2]

Hold[2 2]
Hold[4]

Another difference

Even another difference between Set and SetDelayed, also involving Condition, is given here