Re: Bug with Sequence and Assignment by Part...

*To*: mathgroup at smc.vnet.net*Subject*: [mg121636] Re: Bug with Sequence and Assignment by Part...*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Fri, 23 Sep 2011 03:43:58 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109221126.HAA26759@smc.vnet.net>

I agree with your analysis, but I disagree with your conclusions. > Surely I am not the first to encounter this, Indeed: http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/b7303eafccee6d5a > and surely it constitutes > at least one bug, (and surely it is shouldn't be in Mathematica 8!). I wouldn't be so sure. Using Sequence to insert several elements is not a standard form of assignment. The way I understand idiomatic Mathematica, it is a hack. The fact that you can sort of do it does not mean that all aspects of it must conform to your expectations. Every decent language allows many more things than those for which it was primarily designed. If you are exploring the darker corners, be prepared to face the consequences. As for Mathematica, the observed behavior is in complete agreement with the semantics of Set / SetDelayed (both being SequenceHold) and Sequence, and the evaluation procedure. So, IMO, this is not a bug. In my reply in the quoted thread, I gave some arguments in support of this behavior. One point was that assignments using Sequence in this manner could not be made generally efficient, given that lists are implemented as arrays in Mathematica . It is one thing to assign a pointer to the Sequence object in a pointer array (don't need resizing), and another to shift an array of pointers to accommodate new elements. There is no way around the fact that insertion in an array is a linear-time operation in the size of an array - to avoid that you'd need lists implemented as linked lists. Also, from the language design perspective, adding a special case to Set - Sequence (and complicating the evaluation semantics even more), and silently expanding / shifting arrays (and giving assignment a linear time complexity without giving a clue to the user) would IMO be a terribly bad design decision, for at least two reasons. First, Sequence is a general head, and its semantics are higher level than those of the memory operations needed to truly insert new elements into a list. Second, in Mathematica (being so high - level) it is not always easy to estimate the complexity of code, and I'd at least like to be sure that a single element assignment is always a constant - time operation. > I mean, > it seems to me that FullForm and Length should also detect the > presence of Sequence and act differently than they do here. > IMO, this would also be bad. Sequence splicing is a result of evaluation (a step in evaluation sequence). What you request again requires exceptions to the main evaluation sequence. For such a system as Mathematica, you pay a huge price for exceptions - even in its current general form, evaluation sequence is complex enough. I actually think that it is this generality and consistency of evaluator (and, more generally, the languagte) that makes possible much of further Mathematica development and component integration. Start adding ad hoc stuff that *looks* convenient, and you get what many other systems offer - a bunch of not so well integrated functionality and inelegant languages full of magic and special cases. Regards, Leonid

**References**:**Bug with Sequence and Assignment by Part...***From:*BernieTheJet <berniethejet@gmail.com>