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The let* expression

The next line of the forward-paragraph function begins a let* expression. This is a different kind of expression than we have seen so far. The symbol is let* not let.

The let* special form is like let except that Emacs sets each variable in sequence, one after another, and variables in the latter part of the varlist can make use of the values to which Emacs set variables in the earlier part of the varlist.

In the let* expression in this function, Emacs binds two variables: fill-prefix-regexp and paragraph-separate. The value to which paragraph-separate is bound depends on the value of fill-prefix-regexp.

Let's look at each in turn. The symbol fill-prefix-regexp is set to the value returned by evaluating the following list:

(and fill-prefix
     (not (equal fill-prefix ""))
     (not paragraph-ignore-fill-prefix)
     (regexp-quote fill-prefix))

This is an expression whose first element is the and special form.

As we learned earlier (see The kill-new function), the and special form evaluates each of its arguments until one of the arguments returns a value of nil, in which case the and expression returns nil; however, if none of the arguments returns a value of nil, the value resulting from evaluating the last argument is returned. (Since such a value is not nil, it is considered true in Lisp.) In other words, an and expression returns a true value only if all its arguments are true.

In this case, the variable fill-prefix-regexp is bound to a non-nil value only if the following four expressions produce a true (i.e., a non-nil) value when they are evaluated; otherwise, fill-prefix-regexp is bound to nil.

When this variable is evaluated, the value of the fill prefix, if any, is returned. If there is no fill prefix, this variable returns nil.
(not (equal fill-prefix "")
This expression checks whether an existing fill prefix is an empty string, that is, a string with no characters in it. An empty string is not a useful fill prefix.
(not paragraph-ignore-fill-prefix)
This expression returns nil if the variable paragraph-ignore-fill-prefix has been turned on by being set to a true value such as t.
(regexp-quote fill-prefix)
This is the last argument to the and special form. If all the arguments to the and are true, the value resulting from evaluating this expression will be returned by the and expression and bound to the variable fill-prefix-regexp,

The result of evaluating this and expression successfully is that fill-prefix-regexp will be bound to the value of fill-prefix as modified by the regexp-quote function. What regexp-quote does is read a string and return a regular expression that will exactly match the string and match nothing else. This means that fill-prefix-regexp will be set to a value that will exactly match the fill prefix if the fill prefix exists. Otherwise, the variable will be set to nil.

The second local variable in the let* expression is paragraph-separate. It is bound to the value returned by evaluating the expression:

(if fill-prefix-regexp
    (concat paragraph-separate
            "\\|^" fill-prefix-regexp "[ \t]*$")

This expression shows why let* rather than let was used. The true-or-false-test for the if depends on whether the variable fill-prefix-regexp evaluates to nil or some other value.

If fill-prefix-regexp does not have a value, Emacs evaluates the else-part of the if expression and binds paragraph-separate to its local value. (paragraph-separate is a regular expression that matches what separates paragraphs.)

But if fill-prefix-regexp does have a value, Emacs evaluates the then-part of the if expression and binds paragraph-separate to a regular expression that includes the fill-prefix-regexp as part of the pattern.

Specifically, paragraph-separate is set to the original value of the paragraph separate regular expression concatenated with an alternative expression that consists of the fill-prefix-regexp followed by a blank line. The ^ indicates that the fill-prefix-regexp must begin a line, and the optional whitespace to the end of the line is defined by "[ \t]*$".) The \\| defines this portion of the regexp as an alternative to paragraph-separate.

Now we get into the body of the let*. The first part of the body of the let* deals with the case when the function is given a negative argument and is therefore moving backwards. We will skip this section.