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 Symbolic constraints
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<TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#66dbff"><DIV ALIGN=center><TABLE>
<TR><TD><FONT SIZE=4><B><A NAME="htoc330">8.8</A></B></FONT></TD>
<TD WIDTH="100%" ALIGN=center><FONT SIZE=4><B>Symbolic constraints</B></FONT></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE><UL>
<LI><A HREF="manual062.html#toc270"> <TT>fd_all_different/1</TT></A>
<LI><A HREF="manual062.html#toc271"> <TT>fd_element/3</TT></A>
<LI><A HREF="manual062.html#toc272"> <TT>fd_element_var/3</TT></A>
<LI><A HREF="manual062.html#toc273"> <TT>fd_atmost/3</TT>,
 <TT>fd_atleast/3</TT>,
 <TT>fd_exactly/3</TT></A>
<LI><A HREF="manual062.html#toc274"> <TT>fd_relation/2</TT>,
 <TT>fd_relationc/2</TT></A>
</UL>
<BR>
<A NAME="toc270"></A><TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#98e7ff"><DIV ALIGN=center><TABLE>
<TR><TD><B><A NAME="htoc331">8.8.1</A></B></TD>
<TD WIDTH="100%" ALIGN=center><TT><B>fd_all_different/1</B></TT></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE>
 <BR>
<B>Templates</B>
<DL COMPACT=compact><DT><DD><TT>
fd_all_different(+fd_variable_list)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_all_different(List)</TT> constrains all variables in <TT>List</TT>
to take distinct values. This is equivalent to posting an inequality
constraint for each pair of variables. This constraint is triggered when a
variable becomes ground, removing its value from the domain of the other
variables.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc271"></A><TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#98e7ff"><DIV ALIGN=center><TABLE>
<TR><TD><B><A NAME="htoc332">8.8.2</A></B></TD>
<TD WIDTH="100%" ALIGN=center><TT><B>fd_element/3</B></TT></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE>
<A NAME="fd-element/3"></A>
 <BR>
<B>Templates</B>
<DL COMPACT=compact><DT><DD><TT>
fd_element(?fd_variable, +integer_list, ?fd_variable)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_element(I, List, X)</TT> constraints <TT>X</TT> to be equal to the
<TT>I</TT><EM>th</EM> integer (from 1) of <TT>List</TT>.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>I</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, I)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>X</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, X)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list or a list with an element
<TT>E</TT> which is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc272"></A><TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#98e7ff"><DIV ALIGN=center><TABLE>
<TR><TD><B><A NAME="htoc333">8.8.3</A></B></TD>
<TD WIDTH="100%" ALIGN=center><TT><B>fd_element_var/3</B></TT></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE>
 <BR>
<B>Templates</B>
<DL COMPACT=compact><DT><DD><TT>
fd_element_var(?fd_variable, +fd_variable_list, ?fd_variable)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_element_var(I, List, X)</TT> constraints <TT>X</TT> to be equal to
the <TT>I</TT><EM>th</EM> variable (from 1) of <TT>List</TT>. This
constraint is similar to <TT>fd_element/3</TT> (section&nbsp;<A HREF="#fd-element/3">8.8.2</A>) but
<TT>List</TT> can also contain FD variables (rather than just integers).<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>I</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, I)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>X</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, X)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc273"></A><TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#98e7ff"><DIV ALIGN=center><TABLE>
<TR><TD><B><A NAME="htoc334">8.8.4</A></B></TD>
<TD WIDTH="100%" ALIGN=center><B><TT>fd_atmost/3</TT>,
 <TT>fd_atleast/3</TT>,
 <TT>fd_exactly/3</TT></B></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE>
 
 
 <BR>
<B>Templates</B>
<DL COMPACT=compact><DT><DD><TT>
fd_atmost(+integer, +fd_variable_list, +integer)<BR>
fd_atleast(+integer, +fd_variable_list, +integer)<BR>
fd_exactly(+integer, +fd_variable_list, +integer)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_atmost(N, List, V)</TT> posts the constraint that at most <TT>N</TT>
variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
<TT>fd_atleast(N, List, V)</TT> posts the constraint that at least
<TT>N</TT> variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
<TT>fd_exactly(N, List, V)</TT> posts the constraint that at exactly
<TT>N</TT> variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
These constraints are special cases of <TT>fd_cardinality/2</TT>
(section&nbsp;<A HREF="manual061.html#fd-cardinality/2">8.7.3</A>) but their implementation is more efficient.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>N</TT> is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>N</TT> is neither a variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, N)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>V</TT> is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>V</TT> is neither a variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, V)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicates.<BR>
<BR>
<A NAME="toc274"></A><TABLE CELLPADDING=0 CELLSPACING=0 WIDTH="100%">
<TR><TD BGCOLOR="#98e7ff"><DIV ALIGN=center><TABLE>
<TR><TD><B><A NAME="htoc335">8.8.5</A></B></TD>
<TD WIDTH="100%" ALIGN=center><B><TT>fd_relation/2</TT>,
 <TT>fd_relationc/2</TT></B></TD>
</TR></TABLE></DIV></TD>
</TR></TABLE>
 
 <BR>
<B>Templates</B>
<DL COMPACT=compact><DT><DD><TT>
fd_relation(+integer_list_list, ?fd_variable_list)<BR>
fd_relationc(+integer_list_list, ?fd_variable_list)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_relation(Relation, Vars)</TT> constraints the tuple of variables
<TT>Vars</TT> to be equal to one tuple of the list <TT>Relation</TT>. A
tuple is represented by a list.<BR>
<BR>
Example: definition of the boolean AND relation so that X AND Y
&lt;=&gt; Z:
<DL COMPACT=compact><DT><DD>
<PRE>
and(X,Y,Z):-
        fd_relation([[0,0,0],[0,1,0],[1,0,0],[1,1,1]], [X,Y,Z]).
</PRE></DL>
<TT>fd_relationc(Columns, Vars)</TT> is similar to <TT>fd_relation/2</TT>
except that the relation is not given as the list of tuples but as the list
of the columns of the relation. A column is represented by a list.<BR>
<BR>
Example:
<DL COMPACT=compact><DT><DD>
<PRE>
and(X,Y,Z):-
        fd_relationc([[0,0,1,1],[0,1,0,1],[0,0,0,1]], [X,Y,Z]).
</PRE></DL>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Relation</TT> is a partial list or a list with a sub-term
<TT>E</TT> which is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Relation</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, Relation)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>Relation</TT> list is neither a
variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Vars</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Vars</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, Vars)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>Vars</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP>&nbsp;&nbsp;</TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicates.<BR>
<BR>

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Copyright (C) 1999-2002 Daniel Diaz
<BR>
<BR>
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