May I write {x,a,b}//Do[…,#]& instead of Do[…,{x,a

问题:

I'm in love with Ruby. In this language all core functions are actually methods. That's why I prefer postfix notation – when the data, which I want to process is placed left from the body of anonymous processing function, for example: array.map{...}. I believe, that it has advantages in how easy is this code to read.

But Mathetica, being functional (yeah, it can be procedural if you want) dictates a style, where Function name is placed left from the data. As we can see in its manuals, // is used only when it's some simple Function, without arguments, like list // MatrixForm. When Function needs a lot of arguments, people who wrote manuals, use syntax F[data].
It would be okay, but my problem is the case F[f,data], for example Do[function, {x, a, b}]. Most of Mathematica functions (if not all) have arguments in exactly this order – [function, data], not [data, function]. As I prefer to use pure functions to keep namespace clean instead of creating a lot of named functions in my notebook, the argument function can be too big – so big, that argument data would be placed on the 5-20th line of code after the line with Function call.

This is why sometimes, when evil Ruby nature takes me under control, I rewrite such functions in postfix way:

Because it's important for me, that pure function (potentially big code) is placed right from processing data. Yeah I do it and I'm happy. But there are two things:

1. this causes Mathematica's highlighting parser problem: the x in postfix notation is highlighted with blue color, not turquoise;
2. everytime when I look into Mathematica manuals, I see examples like this one: Do[x[[i]] = (v[[i]] - U[[i, i + 1 ;; n]].x[[i + 1 ;; n]])/ U[[i, i]], {i, n, 1, -1}];, which means... hell, they think it's easy to read/support/etc.?!

So these two things made me ask this question here: am I so bad boy, that use my Ruby-style, and should I write code like these guys do, or is it OK, and I don't have to worry, and should write as I like to?

回答1:

Mathematica supports 4 ways of applying a function to its arguments:

1. standard function form: f[x]
2. prefix: f@x or g@@{x,y}
3. postfix: x // f, and
4. infix: x~g~y which is equivalent to g[x,y].

What form you choose to use is up to you, and is often an aesthetic choice, more than anything else. Internally, f@x is interpreted as f[x]. Personally, I primarily use postfix, like you, because I view each function in the chain as a transformation, and it is easier to string multiple transformations together like that. That said, my code will be littered with both the standard form and prefix form mostly depending on whim, but I tend to use standard form more as it evokes a feeling of containment with regards to the functions parameters.

I took a little liberty with the prefix form, as I included the shorthand form of Apply (@@) alongside Prefix (@). Of the built in commands, only the standard form, infix form, and Apply allow you easily pass more than one variable to your function without additional work. Apply (e.g. g @@ {x,y}) works by replacing the Head of the expression ({x,y}) with the function, in effect evaluating the function with multiple variables (g@@{x,y} == g[x,y]).

The method I use to pass multiple variables to my functions using the postfix form is via lists. This necessitates a little more work as I have to write

{x,y} // f[ #[[1]], #[[2]] ]&

to specify which element of the List corresponds to the appropriate parameter. I tend to do this, but you could combine this with Apply like

{x,y} // f @@ #&

which involves less typing, but could be more difficult to interpret when you read it later.

Edit: I should point out that f and g above are just placeholders, they can, and often are, replaced with pure functions, e.g. #+1& @ x is mostly equivalent to #+1&[x], see Leonid's answer.

To clarify, per Leonid's answer, the equivalence between f@expr and f[expr] is true if f does not posses an attribute that would prevent the expression, expr, from being evaluated before being passed to f. For instance, one of the Attributes of Do is HoldAll which allows it to act as a scoping construct which allows its parameters to be evaluated internally without undo outside influence. The point is expr will be evaluated prior to it being passed to f, so if you need it to remain unevaluated, extra care must be taken, like creating a pure function with a Hold style attribute.

回答2:

The style you propose is frequently possible, but is inadvisable in the case of Do. The problem is that Do has the attribute HoldAll. This is important because the loop variable (x in the example) must remain unevaluated and be treated as a local variable. To see this, try evaluating these expressions:

x = 123;

Do[Print[x], {x, 1, 2}]
(* prints 1 and 2 *)

{x, 1, 2} // Do[Print[x], #]&
(* error: Do::itraw: Raw object 123 cannot be used as an iterator.
   Do[Print[x], {123, 1, 2}]
*)

The error occurs because the pure function Do[Print[x], #]& lacks the HoldAll attribute, causing {x, 1, 2} to be evaluated. You could solve the problem by explicitly defining a pure function with the HoldAll attribute, thus:

{x, 1, 2} // Function[Null, Do[Print[x], #], HoldAll]

... but I suspect that the cure is worse than the disease :)

Thus, when one is using "binding" expressions like Do, Table, Module and so on, it is safest to conform with the herd.

回答3:

I think you need to learn to use the styles that Mathematica most naturally supports. Certainly there is more than one way, and my code does not look like everyone else's. Nevertheless, if you continue to try to beat Mathematica syntax into your own preconceived style, based on a different language, I foresee nothing but continued frustration for you.

Whitespace is not evil, and you can easily add line breaks to separate long arguments:

Do[
  x[[i]] = (v[[i]] - U[[i, i + 1 ;; n]].x[[i + 1 ;; n]]) / U[[i, i]]
  , {i, n, 1, -1}
];

---

This said, I like to write using more prefix (f @ x) and infix (x ~ f ~ y) notation that I usually see, and I find this valuable because it is easy to determine that such functions are receiving one and two arguments respectively. This is somewhat nonstandard, but I do not think it is kicking over the traces of Mathematica syntax. Rather, I see it as using the syntax to advantage. Sometimes this causes syntax highlighting to fail, but I can live with that:

f[x] ~Do~ {x, 2, 5} 

---

When using anything besides the standard form of f[x, y, z] (with line breaks as needed), you must be more careful of evaluation order, and IMHO, readability can suffer. Consider this contrived example:

{x, y} // # + 1 & @@ # &

I do not find this intuitive. Yes, for someone intimate with Mathematica's order of operations, it is readable, but I believe it does not improve clarity. I tend to reserve // postfix for named functions where reading is natural:

Do[f[x], {x, 10000}] //Timing //First

回答4:

I'd say it is one of the biggest mistakes to try program in a language B in ways idiomatic for a language A, only because you happen to know the latter well and like it. There is nothing wrong in borrowing idioms, but you have to make sure to understand the second language well enough so that you know why other people use it the way they do.

In the particular case of your example, and generally, I want to draw attention to a few things others did not mention. First, Do is a scoping construct which uses dynamic scoping to localize its iterator symbols. Therefore, you have:

In[4]:= 
x=1;
{x,1,5}//Do[f[x],#]&

During evaluation of In[4]:= Do::itraw: Raw object 
1 cannot be used as an iterator. >>

Out[5]= Do[f[x],{1,1,5}]

What a surprise, isn't it. This won't happen when you use Do in a standard fashion.

Second, note that, while this fact is largely ignored, f[#]&[arg] is NOT always the same as f[arg]. Example:

ClearAll[f];
SetAttributes[f, HoldAll];
f[x_] := Print[Unevaluated[x]]

f[5^2]

5^2

f[#] &[5^2]

25

This does not affect your example, but your usage is close enough to those cases affected by this, since you manipulate the scopes.

回答5:

You can certainly do it, as you evidently know. Personally, I would not worry about how the manuals write code, and just write it the way I find natural and memorable.

However, I have noticed that I usually fall into definite patterns. For instance, if I produce a list after some computation and incidentally plot it to make sure it's what I expected, I usually do

prodListAfterLongComputation[
    args,
]//ListPlot[#,PlotRange->Full]&

If I have a list, say lst, and I am now focusing on producing a complicated plot, I'll do

ListPlot[
    lst,
    Option1->Setting1,
    Option2->Setting2
]

So basically, anything that is incidental and perhaps not important to be readable (I don't need to be able to instantaneously parse the first ListPlot as it's not the point of that bit of code) ends up being postfix, to avoid disrupting the already-written complicated code it is applied to. Conversely, complicated code I tend to write in the way I find easiest to parse later, which, in my case, is something like

f[
    g[
        a,
        b,
        c
    ]
]

even though it takes more typing and, if one does not use the Workbench/Eclipse plugin, makes it more work to reorganize code.

So I suppose I'd answer your question with "do whatever is most convenient after taking into account the possible need for readability and the possible loss of convenience such as code highlighting, extra work to refactor code etc".

Of course all this applies if you're the only one working with some piece of code; if there are others, it is a different question alltogether.

But this is just an opinion. I doubt it's possible for anybody to offer more than this.

回答6:

For one-argument functions (f@(arg)), ((arg)//f) and f[arg] are completely equivalent even in the sense of applying of attributes of f. In the case of multi-argument functions one may write f@Sequence[args] or Sequence[args]//f with the same effect:

In[1]:= SetAttributes[f,HoldAll];
In[2]:= arg1:=Print[];
In[3]:= f@arg1
Out[3]= f[arg1]
In[4]:= f@Sequence[arg1,arg1]
Out[4]= f[arg1,arg1]

So it seems that the solution for anyone who likes postfix notation is to use Sequence:

x=123;
Sequence[Print[x],{x,1,2}]//Do
(* prints 1 and 2 *)

Some difficulties can potentially appear with functions having attribute SequenceHold or HoldAllComplete:

In[18]:= Select[{#, ToExpression[#, InputForm, Attributes]} & /@ 
   Names["System`*"], 
  MemberQ[#[[2]], SequenceHold | HoldAllComplete] &][[All, 1]]

Out[18]= {"AbsoluteTiming", "DebugTag", "EvaluationObject", \
"HoldComplete", "InterpretationBox", "MakeBoxes", "ParallelEvaluate", \
"ParallelSubmit", "Parenthesize", "PreemptProtect", "Rule", \
"RuleDelayed", "Set", "SetDelayed", "SystemException", "TagSet", \
"TagSetDelayed", "Timing", "Unevaluated", "UpSet", "UpSetDelayed"}