more nil docs

* doc/ref/api-languages.texi (Nil): Be a bit more thorough, and
  positive.

doc/ref/api-languages.texi

@@ -107,8 +107,8 @@ code to maintain their current semantics. @code{nil}, which in Elisp
 would just be written and read as @code{nil}, in Scheme has the external
 representation @code{#nil}.
 
-This decision to have @code{nil} as a low-level distinct value does
+This decision to have @code{nil} as a low-level distinct value
-complicate interoperability between the two languages. Guile has chosen
+facilitates interoperability between the two languages. Guile has chosen
 to have Scheme deal with @code{nil} as follows:
 
 @example
@@ -117,17 +117,62 @@ to have Scheme deal with @code{nil} as follows:
 (null? #nil) @result{} #t
 @end example
 
+And in C, one has:
+
+@example
+scm_is_bool (SCM_ELISP_NIL) @result{} 1
+scm_is_false (SCM_ELISP_NIL) @result{} 1
+scm_is_null (SCM_ELISP_NIL) @result{} 1
+@end example
+
+In this way, a version of @code{fold} written in Scheme can correctly
+fold a function written in Elisp (or in fact any other language) over a
+nil-terminated list, as Elisp makes. The converse holds as well; a
+version of @code{fold} written in Elisp can fold over a
+@code{'()}-terminated list, as made by Scheme.
+
+On a low level, the bit representations for @code{#f}, @code{#t},
+@code{nil}, and @code{'()} are made in such a way that the differ by
+only one bit, and so a test for, for example, @code{#f}-or-@code{nil}
+may be made very efficiently. See @code{libguile/boolean.h}, for more
+information.
+
+@subsubsection Equality
+
 Since Scheme's @code{equal?} must be transitive, and @code{'()}
 is not @code{equal?} to @code{#f}, to Scheme @code{nil} is not
 @code{equal?} to @code{#f} or @code{'()}.
 
+@example
+(eq? #f '()) @result{} #f
+(eq? #nil '()) @result{} #f
+(eq? #nil #f) @result{} #f
+(eqv? #f '()) @result{} #f
+(eqv? #nil '()) @result{} #f
+(eqv? #nil #f) @result{} #f
+(equal? #f '()) @result{} #f
+(equal? #nil '()) @result{} #f
+(equal? #nil #f) @result{} #f
+@end example
+
 However, in Elisp, @code{'()}, @code{#f}, and @code{nil} are all
-@code{eqv} (though not @code{eq}).
+@code{equal} (though not @code{eq}).
+
+@example
+(defvar f (make-scheme-false))
+(defvar eol (make-scheme-null))
+(eq f eol) @result{} nil
+(eq nil eol) @result{} nil
+(eq nil f) @result{} nil
+(equal f eol) @result{} t
+(equal nil eol) @result{} t
+(equal nil f) @result{} t
+@end example
 
 These choices facilitate interoperability between Elisp and Scheme code,
-but they are not perfect. Some code that is historically correct
+but they are not perfect. Some code that is correct standard Scheme is
-standard Scheme is not correct in the presence of a second false and
+not correct in the presence of a second false and null value. For
-null value. For example:
+example:
 
 @example
 (define (truthiness x)
@@ -156,9 +201,12 @@ Here, @code{my-length} will raise an error if @var{l} is a
 Both of these examples are correct standard Scheme, but, depending on
 what they really want to do, they are not correct Guile Scheme.
 Correctly written, they would test the @emph{properties} of falsehood or
-nullity, not the individual members of that set. That is to say, use
+nullity, not the individual members of that set. That is to say, they
-@code{not} or @code{null?} to test for falsehood or nullity, not
+should use @code{not} or @code{null?} to test for falsehood or nullity,
-@code{eq?} or @code{memv} or the like.
+not @code{eq?} or @code{memv} or the like.
+
+Fortunately, using @code{not} and @code{null?} is in good style, so all
+well-written standard Scheme programs are correct, in Guile Scheme.
 
 Here are correct versions of the above examples:
 
@@ -189,11 +237,6 @@ This problem has a mirror-image case in Elisp:
 Guile can warn when compiling code that has equality comparisons with
 @code{#f}, @code{'()}, or @code{nil}. @xref{Compilation}, for details.
 
-On a low level, the bit representations for @code{#f}, @code{#t},
-@code{nil}, and @code{'()} are made in such a way that the differ by
-only one bit, and so a test for, for example, @code{#f}-or-@code{nil}
-may be made very efficiently.
-
 @node Dynamic Binding
 @subsubsection Dynamic Binding