/*  Part of ClioPatria SeRQL and SPARQL server

    Author:        Jan Wielemaker
    E-mail:        J.Wielemaker@cs.vu.nl
    WWW:           http://www.swi-prolog.org
    Copyright (C): 2013, University of Amsterdam,
		   VU University Amsterdam

    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License
    as published by the Free Software Foundation; either version 2
    of the License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public
    License along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    As a special exception, if you link this library with other files,
    compiled with a Free Software compiler, to produce an executable, this
    library does not by itself cause the resulting executable to be covered
    by the GNU General Public License. This exception does not however
    invalidate any other reasons why the executable file might be covered by
    the GNU General Public License.
*/

:- module(graph_properties,
	  [ empty_graph/1,		% +Graph
	    ground_graph/1,		% +Graph
	    lean_graph/1,		% +Graph
	    isomorphic_graphs/2,	% +Graph1, +Graph2
	    is_subgraph/2,		% +SubGraph, +Graph
	    is_proper_subgraph/2,	% +SubGraph, +Graph
	    is_instance_of_graph/2,	% +Instance, +Graph
	    is_proper_instance_of_graph/2, % +Instance, +Graph
	    simply_entails/2		% +Graph, E
	  ]).
:- use_module(library(apply)).
:- use_module(library(lists)).
:- use_module(library(terms)).
:- use_module(library(pairs)).
:- use_module(library(ordsets)).

/** <module> Predicates that prove properties about RDF graphs
*/

		 /*******************************
		 *	 GRAPH PROPERTIES	*
		 *******************************/

%%	empty_graph(?Graph)
%
%	True when Graph is the empty graph

empty_graph([]).

%%	ground_graph(?Graph)
%
%	True if Graph is ground (holds no blank nodes)

ground_graph(Graph) :-
	ground(Graph).

%%	lean_graph(Graph) is semidet.

lean_graph(Graph) :-
	partition(ground, Graph, Ground, NonGround),
	\+ (   member(Gen, NonGround),
	       (   member(Spec, Ground)
	       ;   member(Spec, NonGround)
	       ),
	       Gen \== Spec,
	       subsumes_term(Gen, Spec)
	   ).


		 /*******************************
		 *	  GRAPH RELATIONS	*
		 *******************************/

%%	equal_graphs(Graph1, Graph2) is semidet.
%
%	True if both graphs are equal.

equal_graphs(Graph1, Graph2) :-
	sort(Graph1, Graph),
	sort(Graph2, Graph).

%%	isomorphic_graphs(+Graph1, +Graph2)
%
%	Is true if there is a consistent  mapping between of blank nodes
%	in Graph1 to blank nodes in Graph2 that makes both graphs equal.
%	This maps to the Prolog  notion  of   _variant_  if  there was a
%	canonical ordering of triples.

isomorphic_graphs(Graph1, Graph2) :-
	once(graph_permutation(Graph1, Ordered1)),
	graph_permutation(Graph2, Ordered2),
	variant(Ordered1, Ordered2), !.

graph_permutation(Graph1, Graph) :-
	partition(ground, Graph1, Ground, NonGround),
	sort(Ground, Sorted),
	append(Sorted, NonGroundPermutation, Graph),
	permutation(NonGround, NonGroundPermutation).

%%	is_subgraph(+Sub, +Super) is semidet.

is_subgraph(Sub, Super) :-
	sort(Sub, SubSorted),
	sort(Super, SuperSorted),
	ord_subset(SubSorted, SuperSorted).

%%	subgraph(+Sub, +Super) is nondet.

subgraph([], _).
subgraph([H|T0], [H|T]) :-
	subgraph(T0, T).
subgraph(T0, [_|T]) :-
	subgraph(T0, T).

%%	is_proper_subgraph(+Sub, +Super) is semidet.

is_proper_subgraph(Sub, Super) :-
	sort(Sub, SubSorted),
	sort(Super, SuperSorted),
	ord_subset(SubSorted, SuperSorted),
	length(SubSorted, SubLen),
	length(SuperSorted, SuperLen),
	SubLen < SuperLen.

%%	is_instance_of_graph(+Instance, +Graph) is semidet.
%
%	Instance is an instance of Graph, which   means that there is an
%	assignment of blank nodes in Instance   that makes it equivalent
%	to Graph. This is cose to  subsumes_term/2 with similar ordering
%	issues as with isomorphic_graphs/2.  First, we remove the ground
%	part of the Graph from Instance.

is_instance_of_graph(Instance, Graph) :-
	partition(ground, Graph, Ground, GNonGround),
	sort(Instance, ISorted),
	ord_subtract(ISorted, Ground, RestInstance),
	permutation(RestInstance, Permutation),
	subsumes_term(GNonGround, Permutation), !.

%%	is_proper_instance_of_graph(+Instance, +Graph) is semidet.

is_proper_instance_of_graph(Instance, Graph) :-
	\+ equal_graphs(Instance, Graph),
	is_instance_of_graph(Instance, Graph).


		 /*******************************
		 *	    ENTAILMENT		*
		 *******************************/

%%	simply_entails(+Graph1, +Graph2) is semidet.

simply_entails(G, E) :-
	length(E, Len),
	length(Sub, Len),
	subgraph(Sub, G),
	is_instance_of_graph(Sub, E), !.