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I can edit a notebook within the mathematica front end and then Save As a .m file, which produces output like this:

(* ::Package:: *)

(* ::Section::Closed:: *)
(*Preliminaries*)

(* ::Input:: *)
(*ClearAll["Global`*"]*)

(* ::Text:: *)
(*Some text here.*)

(* ::Input:: *)
(*u[d_,v_]:=v-t d;*)
(*Solve[u[x,v1]==u[1-x,v2],x][[1]];*)
(*x/.%;*)
(*x[v1_,v2_]=%;*)

The same thing is a .nb file looks like this:

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[      1786,         74]
NotebookOptionsPosition[      1395,         55]
NotebookOutlinePosition[      1750,         71]
CellTagsIndexPosition[      1707,         68]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Preliminaries", "Section"],

Cell[BoxData[
 RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell["Some text here.", "Text"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"u", "[", 
    RowBox[{"d_", ",", "v_"}], "]"}], ":=", 
   RowBox[{"v", "-", 
    RowBox[{"t", " ", "d"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"u", "[", 
       RowBox[{"x", ",", "v1"}], "]"}], "==", 
      RowBox[{"u", "[", 
       RowBox[{
        RowBox[{"1", "-", "x"}], ",", "v2"}], "]"}]}], ",", "x"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"x", "/.", "%"}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"x", "[", 
    RowBox[{"v1_", ",", "v2_"}], "]"}], "=", "%"}], ";"}]}], "Input"]
}, Closed]]
},
WindowSize->{740, 840},
WindowMargins->{{4, Automatic}, {Automatic, 4}},
FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (November 20, \
2012)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 32, 0, 80, "Section"],
Cell[614, 24, 76, 1, 22, "Input"],
Cell[693, 27, 31, 0, 30, "Text"],
Cell[727, 29, 652, 23, 80, "Input"]
}, Closed]]
}
]
*)

(* End of internal cache information *)

Whilst the fact that everything in the .m file gets put inside of a comment seems kind of odd, this format has the significant advantage that the result is a readable and editable plain text file. Moreover, I can load the .m file back into the mathematica front end and interact with it as normal. This also leaves all of my formatted section headings etc. as they would be in the .nb file.

This leads me to ask: what are the advantages to saving in the proprietary .nb format when one can store code and formatted text in a human readable .m file that also works interactively within the Mathematica front end?

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1  
I don't work directly with .m files, so I have questions rather than answers. Q1. Can you use multiple cells that are variously formatted in .m files? Q2. Can you display two dimensional input? Q3 Can you leave output in the file? I suspect that the answer is "no" to each of these questions. –  David Carraher Aug 9 '13 at 10:00
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3 Answers

up vote 12 down vote accepted

Usually, a so-called notebook is an ascii file which contains exactly one Notebook expression which itself contains a list of Cell expressions. Additionally to that, the notebook stores some meta data in comments at the beginning and the end of the file. Although one could claim that a notebook file is human readable because it contains only Mathematica code, in reality it is not because even simple input lines are stored in very obfuscated box expressions to preserve the formatting. So the most simple notebook containing only 1+1 is stored as (without the meta data comments)

Notebook[{
  Cell[BoxData[
    RowBox[{"1", "+", "1"}]], "Input",
    CellChangeTimes->{{3.5850786760953827`*^9, 3.585078676635056*^9}}]
  },
  WindowSize->{740, 867},
  WindowMargins->{{Automatic, 1084}, {72, Automatic}},
  FrontEndVersion->"9.0 for Linux x86 (64-bit) (January 25, 2013)",
  StyleDefinitions->"Default.nb"
]

The notebook becomes really unreadable, when you have used for instance images, graphics or dynamic content. If you view a notebook in the front end, which is the only meaningful way, all those cell expressions are interpreted and rendered very nicely. To quote your main question:

what are the advantages to saving in the proprietary .nb format when one can store code and formatted text in a human readable .m file that also works interactively within the Mathematica front end?

A notebook file can store different kinds of cells. Some examples are:

  • evaluating an input creates usually an output cell
  • sections, subsections, text, etc are stored as text cells like Cell["hello", "Section"]
  • if you write text, you can create inline cells for formulas which are cells inside cells

In a package all this is not possible and you can test this yourself. By is not possible I mean here, that you cannot use Cell expressions to format code. To see this create a new package file type some input and evaluate it to get the output. Make a text cell (Alt+7) write something and create a new inline cell with Ctrl+Shift+(. Now change the type of this inline cell to e.g. subsection (Alt+5) and type some more. Now save this *.m file and reopen it. We created different kinds of cells and it might have looked like this when in the front end:

enter image description here

After re-opening it all cells are gone, so you don't have the output and the inline cells anymore. Therefore, package files are very different from notebooks because they contain only pure input code, while when you create and edit a notebook in the front end, it contains a list of cells which support all kinds of formatting.

As you see after re-opening your package the sections and the text are not lost. They are preserved which brings us to another sentence of yours

Whilst the fact that everything in the .m file gets put inside of a comment seems kind of odd

It is only odd at first glance. The most important thing you have to know is, that when you save an .nb file as .m package, only initialization input cells become package code. Therefore, when you want to create a package from a normal notebook you have to mark the input cells and make a right click to set change them to initialization cells.

The other thing is, that a package (as already seen) does not store text cells. To provide a convenient way to have explaining text and a section structure beside the pure code, sections, subsections, etc are converted to special comments which you have already seen:

(* ::Section:: *)
(*Hello*)

(* ::Text:: *)
(*Normal text subsection inline cell normal text again*)

Before coming to the end with my answer let me say some words to the comment of David

Q1. Can you use multiple cells that are variously formatted in .m files?

I think I showed already that this is not possible. Although, there is a but here which is that Mathematica will not complain when you change the file suffix of a notebook to .m. When you re-open this, you'll see the usual notebook interface and not the gray package view.

Q2. Can you display two dimensional input?

Yes, but it is a horror to view this with any other editor than the Mathematica front end. The reason is, that 2d input is not some kind of special cell, but it is done by using special functions like Underoverscript which is then interpreted by the front end. To give an example, try to copy this in a notebook or package

\!\(\*UnderoverscriptBox[\(\[Sum]\), \(x = 0\), \(n\)]\(f[x]\)\)

Q3. Can you leave output in the file?

No, because without cells there is no way to distinguish for instance input from output. Loading the package later with Get would be a mess because your output would be evaluated as well. You might wanna try to put a plot or an image into a text-cell but you will be disappointed when you open the file the next time since you'll only see pure input text and no graphic.

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Useful. Good material for "Mathematica The Missing Manual" - I couldn't find this in the reference... –  cormullion Aug 10 '13 at 7:00
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It's important to understand the guiding motivation for notebooks (.nb files) and packages (.m files).

A notebook file is a full fidelity version of your document content. Nothing will be thrown away; every last twiddle and style is saved into the notebook. The resulting file has two primary purposes. One, of course, is to reconstitute your document at the highest fidelity when you load it into Mathematica. The second is to be able to load the file into the kernel for various kinds of document processing. This is done much less frequently but, for example, one could imagine a notebook file being used as a template for report generation, or content which is programmatically manipulated to personalize (or randomize) content for a classroom of students, or many other sorts of manipulations. These changes happen at the document level, so loading the file using Get into the kernel represents it as a document expression, not as the evaluated version of its contents.

A package file is, first and foremost, a conveniently evaluatable form of the code you designate. Code is found in Code-style cells, which are the default cell type when you're editing in a package, as well as the style you get by using Cmd+8 or Alt+8 in a regular notebook. Input cells might also contain code that you might use in the notebook environment, but not code you wish to deploy (for example, test cases or boostrapping code). The most critical thing is that, when you call Get on a package, it evaluates your code and ignores your comments.

Secondary purposes of package files include creating a serialized form which is readable by humans in other package editors (such as Workbench, or any text editor you might choose) and to reconstitute as much of the document as is reasonable without violating the other purposes. That explains many of the design decisions we made in package files.

  • Why do packages strip output cells? Because it makes the package easier to read in a text editor, and stripping output cells will never affect evaluation.
  • Why are Input and textual cells in comments? Because they should not be evaluated.
  • Why does inline formatting get stripped? It's preserved, if necessary, to preserve evaluation semantics, but it otherwise so contributes to lack of readability in a text editor that it's just not worth it.
  • Why does some typesetting get converted from 2D to 1D (for example, superscripts are converted to ^)? Because it preserves evaluation semantics while increasing readability in a text editor.
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Actually, both .m and .nb files have "proprietary" format and both are "human readable". The difference is the purpose. Packages use .m files, notebooks use .nb files. A package is reusable code. A notebook is more like calculations in scrap paper where you put notes, graphs, and computations. That is, a notebook is something that the end user would employ for daily calculations. A package is something that a developer writes. Further, when you load a package, all of the code in the package is interpreted at once. While you could execute all of a notebook at once, usually you interact with the kernel through the notebook (which is managed by the front end).

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I would agree with Hector but would like to sharpen it up a little. I believe many users would benefit if they did not think of a notebook as a calculator scratch pad, or as a programming sheet, but more as a document in which one is writing one's ideas backed up with calculations, discussion, displays, and sectional groupings. Similarly anyone can write .m files, not just developers. Write them directly, also with Text and Sectional groupings. Put them all together in your $UserBaseDirectory/Applications Folder. –  David Park Aug 10 '13 at 3:16
1  
@DavidPark I would rephrase "anyone can write .m files, not just developers" as "anyone can be a developer" ;-) –  Hector Aug 10 '13 at 5:10
    
I would say developing in a notebook is a valid option as well. For example a notebook might generate a .m file. Or you could generate C code using a notebook. Why bother sticking to coding in a less flexible .m file (editor), while you only use your Mathematica code once to generate your C code? I would argue that a notebook can also "be" reusable code. –  Jacob Akkerboom Aug 17 '13 at 21:47
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