fix nth and nth0 to accept unbound first argument.

git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@144 b08c6af1-5177-4d33-ba66-4b1c6b8b522a

docs/yap.tex

@@ -6655,7 +6655,7 @@ As @code{member/2}, but may only be used to test whether a known
 @var{Element} occurs in a known Set.  In return for this limited use, it
 is more efficient when it is applicable.
 
-@item nth0(+@var{N}, +@var{List}, ?@var{Elem})
+@item nth0(?@var{N}, +@var{List}, ?@var{Elem})
 @findex nth0/2
 @syindex nth0/2
 @cnindex nth0/2
@@ -6665,14 +6665,14 @@ N elements and unify @var{Elem} with the next.)  It can only be used to
 select a particular element given the list and index.  For that
 task it is more efficient than @code{member/2}
 
-@item nth(+@var{N}, +@var{List}, ?@var{Elem})
+@item nth(?@var{N}, +@var{List}, ?@var{Elem})
 @findex nth/2
 @syindex nth/2
 @cnindex nth/2
 The same as @code{nth0/3}, except that it counts from
 1, that is @code{nth(1, [H|_], H)}.
 
-@item nth0(+@var{N}, ?@var{List}, ?@var{Elem}, ?@var{Rest})
+@item nth0(?@var{N}, ?@var{List}, ?@var{Elem}, ?@var{Rest})
 @findex nth0/4
 @syindex nth0/4
 @cnindex nth0/4
@@ -6681,8 +6681,20 @@ counting from 0, and @var{Rest} with the other elements.  It can be used
 to select the Nth element of @var{List} (yielding @var{Elem} and @var{Rest}), or to
 insert @var{Elem} before the Nth (counting from 1) element of @var{Rest}, when
 it yields @var{List}, e.g. @code{nth0(2, List, c, [a,b,d,e])} unifies List with
-@code{[a,b,c,d,e]}.  nth is the same except that it counts from 1.  nth
+@code{[a,b,c,d,e]}.  @code{nth/4} is the same except that it counts from 1.  @code{nth0/4}
-can be used to insert Elem after the Nth element of Rest.
+can be used to insert @var{Elem} after the Nth element of @var{Rest}.
+
+@item nth(?@var{N}, ?@var{List}, ?@var{Elem}, ?@var{Rest})
+@findex nth/4
+@syindex nth/4
+@cnindex nth/4
+Unifies @var{Elem} with the Nth element of @var{List}, counting from 1,
+and @var{Rest} with the other elements.  It can be used to select the
+Nth element of @var{List} (yielding @var{Elem} and @var{Rest}), or to
+insert @var{Elem} before the Nth (counting from 1) element of
+@var{Rest}, when it yields @var{List}, e.g. @code{nth(1, List, c,
+[a,b,d,e])} unifies List with @code{[a,b,c,d,e]}.  @code{nth/4}
+can be used to insert @var{Elem} after the Nth element of @var{Rest}.
 
 @item permutation(+@var{List},?@var{Perm})
 @findex permutation/2

library/lists.yap

@@ -100,7 +100,7 @@ nextto(X,Y, [X,Y|_]).
 nextto(X,Y, [_|List]) :-
 	nextto(X,Y, List).
 
-%   nth0(+N, +List, ?Elem) is true when Elem is the Nth member of List,
+%   nth0(?N, +List, ?Elem) is true when Elem is the Nth member of List,
 %   counting the first as element 0.  (That is, throw away the first
 %   N elements and unify Elem with the next.)  It can only be used to
 %   select a particular element given the list and index.  For that
@@ -108,29 +108,45 @@ nextto(X,Y, [_|List]) :-
 %   nth(+N, +List, ?Elem) is the same as nth0, except that it counts from
 %   1, that is nth(1, [H|_], H).
 
+nth0(V, In, Element) :- var(V), !,
+	generate_nth0(V, In, Element).
 nth0(0, [Head|_], Head) :- !.
-
 nth0(N, [_|Tail], Elem) :-
-	nonvar(N), !,
 	M is N-1,
-	nth0(M, Tail, Elem).
+	find_nth0(M, Tail, Elem).
 
-nth0(N,[_|T],Item) :-		% Clause added KJ 4-5-87 to allow mode
+find_nth0(0, [Head|_], Head) :- !.
-	nth0(M,T,Item),
+find_nth0(N, [_|Tail], Elem) :-
-	N is M + 1.
+	M is N-1,
+	find_nth0(M, Tail, Elem).
 
 
+generate_nth0(0, [Head|_], Head).
+generate_nth0(I, [_|List], El) :-
+	generate_nth0(I1, List, El),
+	I is I1+1.
+
+
+nth(V, In, Element) :- var(V), !,
+	generate_nth(V, In, Element).
 nth(1, [Head|_], Head) :- !.
-
 nth(N, [_|Tail], Elem) :-
 	nonvar(N), !,
 	M is N-1,			% should be succ(M, N)
-	nth(M, Tail, Elem).
+	find_nth(M, Tail, Elem).
+
+find_nth(1, [Head|_], Head) :- !.
+find_nth(N, [_|Tail], Elem) :-
+	M is N-1,
+	find_nth(M, Tail, Elem).
+
+
+generate_nth(1, [Head|_], Head).
+generate_nth(I, [_|List], El) :-
+	generate_nth(I1, List, El),
+	I is I1+1.
+
 
-nth(N,[_|T],Item) :-		% Clause added KJ 4-5-87 to allow mode
-				% nth(-,+,+)
-	nth(M,T,Item),
-	N is M + 1.
 
 %   nth0(+N, ?List, ?Elem, ?Rest) unifies Elem with the Nth element of List,
 %   counting from 0, and Rest with the other elements.  It can be used
@@ -140,30 +156,44 @@ nth(N,[_|T],Item) :-		% Clause added KJ 4-5-87 to allow mode
 %   [a,b,c,d,e].  nth is the same except that it counts from 1.  nth
 %   can be used to insert Elem after the Nth element of Rest.
 
+nth0(V, In, Element, Tail) :- var(V), !,
+	generate_nth0(V, In, Element, Tail).
 nth0(0, [Head|Tail], Head, Tail) :- !.
-
 nth0(N, [Head|Tail], Elem, [Head|Rest]) :-
-	nonvar(N),
 	M is N-1,
 	nth0(M, Tail, Elem, Rest).
 
-nth0(N, [Head|Tail], Elem, [Head|Rest]) :-	% Clause added KJ 4-5-87
+find_nth0(0, [Head|Tail], Head, Tail) :- !.
-	var(N),					% to allow mode
+find_nth0(N, [Head|Tail], Elem, [Head|Rest]) :-
-	nth0(M, Tail, Elem, Rest),		% nth0(-,+,+,?).
+	M is N-1,
-	N is M+1.
+	find_nth0(M, Tail, Elem, Rest).
 
 
+generate_nth0(0, [Head|Rest], Head, Rest).
+generate_nth0(I, [Head|List], El, [Head|Rest]) :-
+	generate_nth0(I1, List, El, Rest),
+	I is I1+1.
+
+
+nth(V, In, Element, Tail) :- var(V), !,
+	generate_nth(V, In, Element, Tail).
 nth(1, [Head|Tail], Head, Tail) :- !.
-
 nth(N, [Head|Tail], Elem, [Head|Rest]) :-
-	nonvar(N),
 	M is N-1,
 	nth(M, Tail, Elem, Rest).
 
-nth(N, [Head|Tail], Elem, [Head|Rest]) :-	% Clause added KJ 4-5-87
+find_nth(1, [Head|Tail], Head, Tail) :- !.
-	var(N),					% to allow mode
+find_nth(N, [Head|Tail], Elem, [Head|Rest]) :-
-	nth(M, Tail, Elem, Rest),		% nth(-,+,+,?).
+	M is N-1,
-	N is M+1.
+	find_nth(M, Tail, Elem, Rest).
+
+
+generate_nth(1, [Head|Rest], Head, Rest).
+generate_nth(I, [Head|List], El, [Head|Rest]) :-
+	generate_nth(I1, List, El, Rest),
+	I is I1+1.
+
+
 
 
 %   permutation(List, Perm)