Re: RE: Should Pure Functions Require &

*To*: mathgroup at smc.vnet.net*Subject*: [mg29793] Re: RE: Should Pure Functions Require &*From*: "Orestis Vantzos" <atelesforos at hotmail.com>*Date*: Tue, 10 Jul 2001 20:25:31 -0400 (EDT)*Organization*: National Technical University of Athens, Greece*References*: <9iau96$15r$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Building an expression with #s and applying Function to it, does not always yield the desired effect. I distinctly remember running into serious trouble more than once in this way...although I can't recite specific code right now. Orestis "Andrzej Kozlowski" <andrzej at tuins.ac.jp> wrote in message news:9iau96$15r$1 at smc.vnet.net... > I think in order to do what you would like you would have to add to > Mathematica quite a lot of rules for deciding where to insert & in more > complicated cases, e.g. > > Select[Range[100],Function[x,x>#]]&/@Range[10]; > > The point is that even if Mathematica was able to correctly decide where to > insert the & and even if Mathematica programmers could remember all the > rules which you stated in your message (and which, by the way, I can't > understand because I do not understand what you mean when you write > >where test has " " > and so on), implementing your idea would encourage people to write even more > unreadable code than they do at present. I find the idea of trying to > understand such code quite dreadful. Thus I would strongly oppose your idea > on the grounds of wanting to preserve my sanity. > > By the way, I there is a reasonable use for # without & ( well, sort of). > Here is a somewhat artificial example. > This makes a list of expressions {#,#^2,...} which can be manipulated just > as any algebraic expressions. > > l = Table[#^i, {i, 1, 100}]; > > This converts them to pure functions: > > In[2]:= > v=Function/@l; > > For example: > > In[3]:= > v[[15]][3] > Out[3]= > 14348907 > > -- > Andrzej Kozlowski > Toyama International University > JAPAN > > http://platon.c.u-tokyo.ac.jp/andrzej/ > http://sigma.tuins.ac.jp/~andrzej/ > > > on 01.7.8 2:00 PM, Ersek, Ted R at ErsekTR at navair.navy.mil wrote: > > > Earlier I wrote: > > -------------------- > >> I stated wondering if all would work well if pure functions didn't require > >> & at the end. I am thinking it would be great if a future version of > >> Mathematica would make the use of & optional. > >> > >> So for example we could use > >> Select[data, #!=0] > >> instead of > >> Select[data, #!=0&] > >> > >> > >> and we could use > >> #^2 /@expr > >> instead of > >> #^2& /@expr > >> > >> I would want to have pure functions ending with & optional rather than > >> prohibited for backward compatibility. Wouldn't life be better if we > >> didn't have to use &. Is there a reason why my suggestion would not work? > >> > > ----------------- > > Orestis Vantzos, > > asked whether Select[data, #!=0] > > should do what Select[data, #!=0&] does now, > > or what Select[data, #!0]& does now. > > > > In that case one clearly wants Select[data, #!=0&] > > since the other case is a pure function that always returns an empty > > list. > > > > ---------------- > > The way I would like to see it the kernel would put an & at a > > suitable place in the following situations. > > 1 A head has one or more #, #n, ##, or ##n but no &. > > 2 Use of expr/;test, _?test, __?test, ___?test where test has > > " ". > > 3 The right side of Set, or SetDelayed has " ". > > 4 The second argument of Select, MatrixQ, VectorQ has " ". > > 5 An argument of a functional programming construct includes #, #n, > > ##, or ##n but no & and a function is expected in this argument. > > > > Examples of 5 > > > > In[1]:= g = {##+1, ##+2}; > > Through[ g[{x,y,z}] ] > > > > This would return the same thing as if we had g = {##+1&, ##+2& } > > since Through expects an argument of the form p[func1, func2][x] > > > > > > In[2]:= g= {##+1, ##+2}; > > Apply[ g, {x,y,z} ] > > > > This would return the same thing as if we had g= {##+1, ##+2}& > > since Apply expects the first argument to be a function. > > > > > > In[3]:= Clear[g]; Apply[g, {x,y,z}] > > > > Out[3]= g[x,y,z] > > > > In this case (g) has no #, #n, ##, ##n so an (&) would not be > > assumed. > > > > > > I haven't found a case where the "missing" (&) could go "here" or > > "there" and both decisions would be useful. Also I am not aware of a use for > > #, #n, ##, ##n without an (&). > > > > ------------------ > >> Regards, > >> Ted Ersek > >> Download Mathematica tips, tricks from > >> http://www.verbeia.com/mathematica/tips/Tricks.html > >> > > > > > > >

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