Question

Could anyone please provide an explanation of the syntax in the following example, or post me a link where there is a more general explanation of the individual symbols used in this expression? I found Vim help to be incomplete in this regard.

:set foldexpr=getline(v:lnum)=~'^\\s*$'&&getline(v:lnum+1)=~'\\S'?'<1':1

What is unclear to me is the following.

1. Why are strings enclosed in single quotes instead of double quotes? Is it a matter of choice?
2. What does the explanation mark mean in =~'\\S'?'<1':1?
3. What does the expression 'string1'string2'string3 mean?
4. What does :1 mean?

Answer 1

The foldexpr option supposed to contain an expression that evaluates
into an integer or a string of particular format that specifies the folding
level of the line which number is stored in the v:lnum global variable
at the moment of evaluation.

Let us follow the logic of this foldexpr example from top to bottom.

getline(v:lnum)=~'^\\s*$'&&getline(v:lnum+1)=~'\\S'?'<1':1

At the top level, the whole expression is an instance of the ternary
operator A ? B : C. The result of the operator is the value of the
B expression if A evaluates to non-zero, and the value of the
C expression otherwise (see :help expr1). In this case, B is
the string literal '<1', and C is the number 1 (for meaning
of '<1' and 1 as fold level specifiers see :help fold-expr).

The A expression consists of two conditions joined by the
&& operator:

getline(v:lnum) =~ '^\\s*$' && getline(v:lnum+1) =~ '\\S'

Both conditions have the same form:

getline(N) =~ S

The getline function returns contents of the line (in the current
buffer) that is referenced by the line number passed as an argument
(see :help getline). When the foldexpr is evaluated, the v:lnum
variable contains number of the line for which folding level should
be calculated.

The =~ operator tests whether its left operand matches a regular
expression given by its right string operand, and returns boolean value
(see :help expr4, in particular, near the end of the expr4 section).
Thus, the A condition is intended to check that the v:lnum-th line
matches the '^\\s*$' pattern, and the line following that v:lnum-th
line matches the '\\S' pattern.

The regular expression patterns are specified in the expression as
string literals. String literals have two syntactic forms and can be
quoted using double or single quotes. The difference between these
forms is that double quoted string could contain various control
sequences which start with backslash. That sequences allow to specify
special characters that cannot be easily typed otherwise (double
quote, for example—it writes \"). Single quoted strings, at the
other hand, do not allow such backslash-sequences. (For complete
description of single and double quoted strings see :help expr-string
and :help literal-string.)

The notable consequence of the double quoted strings syntax is that
backslash symbol itself must be escaped (\\). That is why single
quoted strings are often used to specify regular expressions: there
is no need to escape constantly demanded backslash symbol. One can
notice, though, that backslashes are nevertheless escaped in those
patterns above. This is due to that some symbols (including backslash)
have special meaning when in Ex commands (including :set, of
course). When you hit Enter to start the command

:set foldexpr=...

Vim interprets some character sequences first (see :help cmdline-special).
In particular, the \\ sequence is treated as a single backslash.

Putting it all together, the expression tests whether the line number
v:lnum contains only blank characters and whether the following line
(number v:lnum+1) has any non-blank character (see :help pattern
to grasp the meaning of the patterns). If so, the expression evaluates
to the string '<1', otherwise it evaluates to the number 1.