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Prolog

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% clp(q,r) version 1.3.3 %
% %
% (c) Copyright 1992,1993,1994,1995 %
% Austrian Research Institute for Artificial Intelligence (OFAI) %
% Schottengasse 3 %
% A-1010 Vienna, Austria %
% %
% File: ordering.pl %
% Author: Christian Holzbaur christian@ai.univie.ac.at %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Collect ordering constraints
% Produce an arrangement via toplogical sorting
%
%
:- use_module( library(lists), [append/3]).
:- use_module( library(ugraphs),
[
top_sort/2,
add_edges/3,
add_vertices/3
]).
ordering( X) :- var(X), !, fail.
ordering( A>B) :- !, ordering( B<A).
ordering( A<B) :-
join_class( [A,B], Class),
class_get_prio( Class, Ga),
!,
add_edges( [], [A-B], Gb), % [] = empty graph
combine( Ga, Gb, Gc),
class_put_prio( Class, Gc).
ordering( Pb) :- Pb = [_|Xs],
join_class( Pb, Class),
class_get_prio( Class, Ga),
!,
( Xs=[],
add_vertices( [], Pb, Gb)
; Xs=[_|_],
gen_edges( Pb, Es, []),
add_edges( [], Es, Gb)
),
combine( Ga, Gb, Gc),
class_put_prio( Class, Gc).
ordering( _).
arrangement( Class, Arr) :-
class_get_prio( Class, G),
normalize( G, Gn),
top_sort( Gn, Arr),
!.
arrangement( _, _) :-
raise_exception( unsatisfiable_ordering).
join_class( [], _).
join_class( [X|Xs], Class) :-
( var(X), get_or_add_class( X, Class)
; nonvar(X)
),
join_class( Xs, Class).
combine( Ga, Gb, Gc) :-
normalize( Ga, Gan),
normalize( Gb, Gbn),
ugraphs:graph_union( Gan, Gbn, Gc).
%
% both Ga and Gb might have their internal ordering invalidated
% because of bindings and aliasings
%
normalize( [], []).
normalize( G, Gsgn) :-
G=[_|_],
keysort( G, Gs),
group( Gs, Gsg),
normalize_vertices( Gsg, Gsgn).
normalize_vertices( [], []).
normalize_vertices( [X-Xnb|Xs], Res) :-
( normalize_vertex( X, Xnb, Xnorm) ->
Res = [Xnorm|Xsn],
normalize_vertices( Xs, Xsn)
;
normalize_vertices( Xs, Res)
).
%
% get rid of nonvar vertices/edges, and turn V-[V] into V-[]
%
normalize_vertex( X, Nbs, X-Nbsss) :-
var(X),
sort( Nbs, Nbss),
strip_nonvar( Nbss, X, Nbsss).
strip_nonvar( [], _, []).
strip_nonvar( [X|Xs], Y, Res) :-
( X==Y -> strip_nonvar( Xs, Y, Res)
; var(X) ->
Res=[X|Stripped],
strip_nonvar( Xs, Y, Stripped)
; nonvar(X),
Res=[] % because Vars<anything
).
gen_edges( []) --> [].
gen_edges( [X|Xs]) -->
gen_edges( Xs, X),
gen_edges( Xs).
gen_edges( [], _) --> [].
gen_edges( [Y|Ys], X) -->
[ X-Y ],
gen_edges( Ys, X).
%
% map k-La,k-Lb.... into k-LaLb
%
group( [], []).
group( [K-Kl|Ks], Res) :-
group( Ks, K, Kl, Res).
group( [], K, Kl, [K-Kl]).
group( [L-Ll|Ls], K, Kl, Res) :-
( K==L ->
append( Kl, Ll, KLl),
group( Ls, K, KLl, Res)
;
Res = [K-Kl|Tail],
group( Ls, L, Ll, Tail)
).