What are "\<" and "\>" delimiters in box expressions?

Question

If I enter a string (say, "abc") in a cell, and then switch to box representation (Shift+Ctrl+E or menu item Cell ► Show Expression), I see the following:

Cell[BoxData["\"\<abc\>\""], "Input",
 CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]

I understand everything in this expression except the delimiters \< and \>. They look like escape sequences (e.g. \\, \") or like symbols used in string representation of boxes (e.g. \(, \!, \*, etc), but I could not find their description anywhere. I experimented a little, and it looks they are ignored within strings (for example StringLength["\<"] evaluates to 0) and rejected as an incorrect input elsewhere.

What do \< and \> mean inside of a string? For what purpose they are automatically added into the low-level representation of a cell? What are their use cases?

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$Version 

"10.2.0 for Microsoft Windows (64-bit) (July 7, 2015)"

Answer 1

This syntax was deprecated in the version 6.0 era. According to the legacy documentation,

For example, in version 5.2, the following strings are interpreted differently

string1 = "first line
  second line"

string2 = "\<first line
  second line\>"

Answer 2

Thanks to andre's comment (where this link is provided), I now see the effect of those delimiters (I tested it in Mathematica 11 and also some earlier versions). When I add 2 newlines to the box representation of the cell:

Cell[BoxData["\"\<a

bc\>\""], "Input",
 CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]

and switch back using Shift+Ctrl+E, then the cell look like this:

"a

bc"

But if I remove those delimiters:

Cell[BoxData["\"a

bc\""], "Input",
 CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]

and switch back, then the cell looks like this:

"a  bc"

It seems that the purpose of \<,\> is to delimit ranges within string literals in raw box representations of cells where newlines should be exactly preserved. It looks like they only have effect in that context and are ignored in normal input in newer versions of Mathematica. The legacy documentation suggests that in Mathematica 5 they were significant in all string literals.

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Update: I found an old discussion on this topic: [1],[2],[3].

Answer 3

Summary of the all available information

In the hoarier days space-like characters (spaces, newlines, tabs) inside strings were interpreted on input in an odd way: for example single newlines followed by spaces or tabs were converted to a single space. The \<\> syntax was introduced as a way to avoid this: between \< and \> the space-like characters are interpreted literally with the only exception to line-ending backslash whish escapes the newline. This syntax was standardized in the modern Mathematica notebook format (introduced in 1996).

The kernel simply ignores the \<\> delimiters on input and also when you Get or Import a notebook file:

FullForm@"\<1\n2\>"

"1\n2"

"\<\>" // StringLength

0

Note that FrontEnd doesn't remove them on normal input:

"\<\>";
InString[-1]

"RowBox[{\"\\\"\\\\<\\\\>\\\"\", \";\"}]"

Starting from version 6 the behavior of strings on normal input was changed and the \<\> syntax is no longer needed for preserving space-like characters. But for direct editing of the low-level box representation of cells in the special cell editing mode of the FrontEnd (which is toggled by pressing Shift+Ctrl+E) it is still necessary as Vladimir showed. These delimiters aren't needed however when you programmatically work with the low-level representation (and the kernel simply removes them anyway!).

These delimiters are also added automatically when you Export as "NB", but not added when you Export as "Package":

StringCases[ExportString["1\n2", "NB"], "Cell[" ~~ Shortest@__ ~~ "\"Input\"]"] // First //
  ImportString[#, "Text"] &

Cell["\<\
1
2\
\>", "Input"]

ExportString["1\n2", "Package"]

(* Created with the Wolfram Language : www.wolfram.com *)

"1\n2"

Despite this a Notebook exported as a "Package" can be correctly opened or imported as "NB" preserving space-like characters:

nb = ImportString[ExportString["1\n2", "NB"], "NB"];
ImportString[ExportString[nb, "Package"], "NB"] === nb

True

NotebookPut[nb];

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Further elaboration

Let us consider the example given by John Fultz (please copy the code exactly as written!):

CellPrint@Cell["abc\
         d"]

abc         d

It is easy to check that there are 9 spaces between abc and d in the printed cell (and so are before d in the code). But the newline and the backslash are absent because the backslash at the end of line simply escapes the newline.

After pressing Shift+Ctrl+E we can see the code of the printed cell:

Cell["abc         d",
 GeneratedCell->True,
 CellAutoOverwrite->True,
 CellChangeTimes->{3.680677305471143*^9}]

Now let us add a space after the backslash (it isn't visible, but it is there!):

CellPrint@Cell["abc\ 
         d"]

abc 
          d

Now we got our newline but the backslash is absent (the next space is present). I think that the absence of the backslash can be related to the series of bugs I discuss in this answer. The code of the printed cell:

Cell["\<\
abc 
         d\
\>",
 GeneratedCell->True,
 CellAutoOverwrite->True,
 CellChangeTimes->{3.6806776850508537`*^9}]

Note that similar things happen when we write \n instead of entering the newline:

CellPrint@Cell["abc\\n         d"]
CellPrint@Cell["abc\ \n         d"]

abc\n         d

abc 
          d

In the first case here the newline character \n is escaped by the backslash and is present in the output literally. In the second case the backslash is absent again but the space at the first line is preserved.

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An old discussion on MathGroup

A closely related (but not identical) question was asked by user kj and answered by John Fultz in the official newsgroup in 2010, so I'll cite here both the question and the answer completely:

The question:

When I examine the source code of Mathematica notebooks, I often see Cell objects whose first argument is preceded by

"\<\

and followed by

\
\>"

E.g.

Cell["\<\
Yet another undocumented item.\
\>", "Text"...

What do these delimiters mean? And how do they differ from the TextData symbol? (The latter is also undocumented, but at least I've seen "cameo appearances" of it in the documentation.)

TIA!
~kj

The answer:

Cell[_String] is equivalent to Cell[TextData[{_String}]] as far as the front end is concerned. The former is just an abbreviation of the latter syntax, which is necessarily used when the contents are more complex (e.g., contain styles or buttons).

The \<\> business dates back to a hoarier day (in my opinion) in the design of strings in Mathematica. Once upon a time, Mathematica had an odd interpretation of newlines which I probably made more sense in the days of 80 character terminal usage. You'll have to forgive me...my memory is fuzzy here, and I don't have an old Mathematica text to double-check this from my current location...but I believe the issue was something like this...

"abc\
         d"

...with the newlines and spaces as shown, being equivalent to "abc d" (with just the single space). The \<\> business forced everything inside the string to really be interpreted literally, with backslash at the end of a line meaning to simply escape the newline, and do nothing special to leading spaces. Since the Mathematica notebook format generally wraps at about 70 characters, the non-literal interpretation would have made the representation of more than 70 consecutive spaces difficult.

The modern Mathematica notebook format (introduced in 1996) was always made to be interpreted properly as a Mathematica expression should you call Get[] on it from the kernel. So this syntax was standardized, and is still used today. Now, the kernel simply ignores the \<\> delimiters as you can see below:

In[1]:== StringLength["\<x\>"]

Out[1]== 1

Sincerely,

John Fultz
jfultz at wolfram.com
User Interface Group
Wolfram Research, Inc.