Legitimate uses of (\+)//1 - prolog

Question

In grammar rules (dcg), there are several predefined constructs: (',')//2 meaning concatenation, ('|')//2 meaning alternation etc. One construct which is supported by several but not all Prolog systems is (\+)//1.
Personally, I have used it only for the sake of using it. I have never seen it in code written by others.
So, are there legitimate uses of (\+)//1?
Edit: And additionally, are there legitimate uses of (\+)//1 within a query phrase(nt, L) with L an uninstantiated variable.

Answer 1

\+ can be used to create grammars that are less ambiguous.
The advantage of using \+ over ! for example, is a certain
declarativity of \+, so that for example the resulting DCG
rules can be reordered.
Lets make an example, consider the following grammar:
s([X|Y]) --> t(X), s(Y). % 1
s([]) --> []. % 2
t(2) --> [a,a]. % 3
t(1) --> [a]. % 4
The above grammar is highly ambiguous, for example I get multiple
parses for the following input:
?- phrase(s(A),[a,a,a,a,a]).
A = [2,2,1] ;
A = [2,1,2] ;
A = [2,1,1,1] ;
etc..
Now assume I want to prefer the long parse of t over the
short parse of t. I can do this with a cut as follows:
t(2) --> [a,a], !. % 5
t(1) --> [a]. % 6
?- phrase(s(A),[a,a,a,a,a]).
A = [2,2,1] ;
No
Unfortunately I cannot reorder. Since doing the following
does not give the desired result. Although s(A) now yields
the results in a different order, we are back to square one,
since the grammar is ambiguous again:
t(1) --> [a]. % 7
t(2) --> [a,a], !. % 8
?- phrase(s(A),[a,a,a,a,a]).
A = [1,1,1,1,1] ;
A = [1,1,1,2] ;
A = [1,1,2,1] ;
etc...
Now lets try the same with \+. We can replace the cut
by the following negation:
t(2) --> [a,a]. % 9
t(1) --> [a], \+ [a]. % 10
?- phrase(s(A),[a,a,a,a,a]).
A = [2,2,1] ;
No
Now lets try whether we can reorder. We reorder the
grammar rules of t//1:
t(1) --> [a], \+ [a]. % 11
t(2) --> [a,a]. % 12
?- phrase(s(A),[a,a,a,a,a]).
A = [2,2,1] ;
No
The declarativity is very useful. It means for example
that we can use \+ in a right-to-left chart parser that
picks the grammar rules in an arbitrary order. The
declarativity assures that the bottom up forward chaining
of the chart parser yields the same result independently of
the input order of the DCG rules.
It is then possible to apply the DCG technique in large
natural language (NL) projects and it scales well. The
NL grammars can be empirically tuned into determinism.
The more deterministic a grammar the more efficient
its parsing. Complex NL grammars that are otherwise
intractable become feasible.
Bye

Answer 2

When L is not instantiated then the grammar is used for text generation. Then
you don't need the grammar \+ at all. Since there is no more problem of ambiguity
from some text.
Lets make an example, consider the following grammar:
s([X|Y]) --> t(X), s(Y). % 1
s([]) --> []. % 2
t(2) --> [a,a]. % 3
t(1) --> [a]. % 4
Each different parse has a different parse tree. And there is no ambiguity in
using phrase/2 to generate text. The following queries give exactly one
answer:
?- phrase(s([2,1]),L).
L = [a,a,a]
?- phrase(s([1,2]),L).
L = [a,a,a]
?- phrase(s([1,1,1]),L).
L = [a,a,a]
But there is a little reuse problem. Assume I have a NL grammar with \+ for
parsing. I then cannot use it for unparsing. Since the instantiation pattern
of the \+ goal will be different, and therefore the semantic of the construct
changes.
The way out is probably just to use two grammars. One for parsing and one for
unparsing. I guess parsing and unparsing are two different cognitive capabilities.
Remember in school, there were reading exercises and writting exercises. The
same happens in computer science.
I think it is also in some cases possible to use a single grammar, and view \+ as
an annotation for disambiguation, that is dropped during unparse or differently
handled. One could build such a mechanism. But the issues with unparsing versus
parsing are deeper: Bidirectionallity of auxiliary conditions ({}/1), left recursion
during unparsing, etc...
Bye