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<H2><A NAME="sec:4.29"><SPAN class="sec-nr">4.29</SPAN> <SPAN class="sec-title">Finding 
all Solutions to a Goal</SPAN></A></H2>

<A NAME="sec:allsolutions"></A>

<DL class="latex">
<DT class="pubdef"><span class="pred-tag">[ISO]</span><A NAME="findall/3"><STRONG>findall</STRONG>(<VAR>+Template, 
:Goal, -Bag</VAR>)</A></DT>
<DD class="defbody">
Creates a list of the instantiations <VAR>Template</VAR> gets 
successively on backtracking over <VAR>Goal</VAR> and unifies the result 
with <VAR>Bag</VAR>. Succeeds with an empty list if <VAR>Goal</VAR> has 
no solutions. <A NAME="idx:findall3:1057"></A><A class="pred" href="allsolutions.html#findall/3">findall/3</A> 
is equivalent to <A NAME="idx:bagof3:1058"></A><A class="pred" href="allsolutions.html#bagof/3">bagof/3</A> 
with all free variables bound with the existential operator (<STRONG><CODE>^</CODE></STRONG>), 
except that <A NAME="idx:bagof3:1059"></A><A class="pred" href="allsolutions.html#bagof/3">bagof/3</A> 
fails when goal has no solutions.</DD>
<DT class="pubdef"><A NAME="findall/4"><STRONG>findall</STRONG>(<VAR>+Template, 
:Goal, -Bag, +Tail</VAR>)</A></DT>
<DD class="defbody">
As <A NAME="idx:findall3:1060"></A><A class="pred" href="allsolutions.html#findall/3">findall/3</A>, 
but returns the result as the difference-list
<VAR>Bag</VAR>-<VAR>Tail</VAR>. The 3-argument version is defined as

<PRE class="code">
findall(Templ, Goal, Bag) :-
        findall(Templ, Goal, Bag, [])
</PRE>

</DD>
<DT class="pubdef"><span class="pred-tag">[ISO]</span><A NAME="bagof/3"><STRONG>bagof</STRONG>(<VAR>+Template, 
:Goal, -Bag</VAR>)</A></DT>
<DD class="defbody">
Unify <VAR>Bag</VAR> with the alternatives of <VAR>Template</VAR>, if <VAR>Goal</VAR> 
has free variables besides the one sharing with <VAR>Template</VAR> 
bagof will backtrack over the alternatives of these free variables, 
unifying
<VAR>Bag</VAR> with the corresponding alternatives of <VAR>Template</VAR>. 
The construct <CODE>+<VAR>Var</VAR><CODE>^</CODE><VAR>Goal</VAR></CODE> 
tells bagof not to bind
<VAR>Var</VAR> in <VAR>Goal</VAR>. <A NAME="idx:bagof3:1061"></A><A class="pred" href="allsolutions.html#bagof/3">bagof/3</A> 
fails if <VAR>Goal</VAR> has no solutions.

<P>The example below illustrates <A NAME="idx:bagof3:1062"></A><A class="pred" href="allsolutions.html#bagof/3">bagof/3</A> 
and the <STRONG><CODE>^</CODE></STRONG> operator. The variable bindings 
are printed together on one line to save paper.

<PRE class="code">
2 ?- listing(foo).

foo(a, b, c).
foo(a, b, d).
foo(b, c, e).
foo(b, c, f).
foo(c, c, g).

Yes
3 ?- bagof(C, foo(A, B, C), Cs).

A = a, B = b, C = G308, Cs = [c, d] ;
A = b, B = c, C = G308, Cs = [e, f] ;
A = c, B = c, C = G308, Cs = [g] ;

No
4 ?- bagof(C, A^foo(A, B, C), Cs).

A = G324, B = b, C = G326, Cs = [c, d] ;
A = G324, B = c, C = G326, Cs = [e, f, g] ;

No
5 ?-
</PRE>

</DD>
<DT class="pubdef"><span class="pred-tag">[ISO]</span><A NAME="setof/3"><STRONG>setof</STRONG>(<VAR>+Template, 
+Goal, -Set</VAR>)</A></DT>
<DD class="defbody">
Equivalent to <A NAME="idx:bagof3:1063"></A><A class="pred" href="allsolutions.html#bagof/3">bagof/3</A>, 
but sorts the result using <A NAME="idx:sort2:1064"></A><A class="pred" href="builtinlist.html#sort/2">sort/2</A> 
to get a sorted list of alternatives without duplicates.
</DD>
</DL>

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