This file is indexed.

/usr/share/Yap/clpq/fourmotz_q.pl is in yap 5.1.3-6.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
/*  $Id: fourmotz_q.pl,v 1.1 2008/03/13 17:16:43 vsc Exp $

    Part of CLP(Q) (Constraint Logic Programming over Rationals)

    Author:        Leslie De Koninck
    E-mail:        Leslie.DeKoninck@cs.kuleuven.be
    WWW:           http://www.swi-prolog.org
		   http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09
    Copyright (C): 2006, K.U. Leuven and
		   1992-1995, Austrian Research Institute for
		              Artificial Intelligence (OFAI),
			      Vienna, Austria
			      
    This software is based on CLP(Q,R) by Christian Holzbaur for SICStus
    Prolog and distributed under the license details below with permission from
    all mentioned authors.

    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 Lesser 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(fourmotz_q,
	[
	    fm_elim/3
	]).
:- use_module(bv_q,
	[
	    allvars/2,
	    basis_add/2,
	    detach_bounds/1,
	    pivot/5,	
	    var_with_def_intern/4
	]).
:- use_module('../clpqr/class',
	[
	    class_allvars/2
	]).
:- use_module('../clpqr/project',
	[
	    drop_dep/1,
	    drop_dep_one/1,
	    make_target_indep/2
	]).
:- use_module('../clpqr/redund',
	[
	    redundancy_vars/1
	]).
:- use_module(store_q,
	[
	    add_linear_11/3,
	    add_linear_f1/4,
	    indep/2,
	    nf_coeff_of/3,
	    normalize_scalar/2
	]).
		


fm_elim(Vs,Target,Pivots) :-
	prefilter(Vs,Vsf),
	fm_elim_int(Vsf,Target,Pivots).

% prefilter(Vars,Res)
%
% filters out target variables and variables that do not occur in bounded linear equations. 
% Stores that the variables in Res are to be kept independent.

prefilter([],[]).
prefilter([V|Vs],Res) :-
	(   get_attr(V,itf,Att),
	    arg(9,Att,n),
	    occurs(V)
	->  % V is a nontarget variable that occurs in a bounded linear equation 
	    Res = [V|Tail],
	    setarg(10,Att,keep_indep),
	    prefilter(Vs,Tail)
	;   prefilter(Vs,Res)
	).

%
% the target variables are marked with an attribute, and we get a list
% of them as an argument too
%
fm_elim_int([],_,Pivots) :-	% done
	unkeep(Pivots).
fm_elim_int(Vs,Target,Pivots) :-
	Vs = [_|_],
	(   best(Vs,Best,Rest)
	->  occurences(Best,Occ),
	    elim_min(Best,Occ,Target,Pivots,NewPivots)
	;   % give up
	    NewPivots = Pivots,
	    Rest = []
	),
	fm_elim_int(Rest,Target,NewPivots).

% best(Vs,Best,Rest)
%
% Finds the variable with the best result (lowest Delta) in fm_cp_filter
% and returns the other variables in Rest.

best(Vs,Best,Rest) :-
	findall(Delta-N,fm_cp_filter(Vs,Delta,N),Deltas),
	keysort(Deltas,[_-N|_]),
	select_nth(Vs,N,Best,Rest).

% fm_cp_filter(Vs,Delta,N)
%
% For an indepenent variable V in Vs, which is the N'th element in Vs,
% find how many inequalities are generated when this variable is eliminated.
% Note that target variables and variables that only occur in unbounded equations
% should have been removed from Vs via prefilter/2

fm_cp_filter(Vs,Delta,N) :-
	length(Vs,Len),	% Len = number of variables in Vs
	mem(Vs,X,Vst),	% Selects a variable X in Vs, Vst is the list of elements after X in Vs
	get_attr(X,itf,Att),
	arg(4,Att,lin(Lin)),
	arg(5,Att,order(OrdX)),
	arg(9,Att,n),	% no target variable
	indep(Lin,OrdX),	% X is an independent variable
	occurences(X,Occ),	
	Occ = [_|_],
	cp_card(Occ,0,Lnew),
	length(Occ,Locc),
	Delta is Lnew-Locc,
	length(Vst,Vstl),
	N is Len-Vstl.	% X is the Nth element in Vs

% mem(Xs,X,XsT)
%
% If X is a member of Xs, XsT is the list of elements after X in Xs.

mem([X|Xs],X,Xs).
mem([_|Ys],X,Xs) :- mem(Ys,X,Xs).

% select_nth(List,N,Nth,Others)
%
% Selects the N th element of List, stores it in Nth and returns the rest of the list in Others.

select_nth(List,N,Nth,Others) :-
	select_nth(List,1,N,Nth,Others).

select_nth([X|Xs],N,N,X,Xs) :- !.
select_nth([Y|Ys],M,N,X,[Y|Xs]) :-
	M1 is M+1,
	select_nth(Ys,M1,N,X,Xs).

%
% fm_detach + reverse_pivot introduce indep t_none, which
% invalidates the invariants
%
elim_min(V,Occ,Target,Pivots,NewPivots) :-
	crossproduct(Occ,New,[]),
	activate_crossproduct(New),
	reverse_pivot(Pivots),
	fm_detach(Occ),
	allvars(V,All),
	redundancy_vars(All),			% only for New \== []
	make_target_indep(Target,NewPivots),
	drop_dep(All).

%
% restore NF by reverse pivoting
%
reverse_pivot([]).
reverse_pivot([I:D|Ps]) :-
	get_attr(D,itf,AttD),
	arg(2,AttD,type(Dt)),
	setarg(11,AttD,n), % no longer
	get_attr(I,itf,AttI),
	arg(2,AttI,type(It)),
	arg(5,AttI,order(OrdI)),
	arg(6,AttI,class(ClI)),
	pivot(D,ClI,OrdI,Dt,It),
	reverse_pivot(Ps).

% unkeep(Pivots)
%
% 

unkeep([]).
unkeep([_:D|Ps]) :-
	get_attr(D,itf,Att),
	setarg(11,Att,n),
	drop_dep_one(D),
	unkeep(Ps).


%
% All we drop are bounds
%
fm_detach( []).
fm_detach([V:_|Vs]) :-
	detach_bounds(V),
	fm_detach(Vs).

% activate_crossproduct(Lst)
%
% For each inequality Lin =< 0 (or Lin < 0) in Lst, a new variable is created:
% Var = Lin and Var =< 0 (or Var < 0). Var is added to the basis. 

activate_crossproduct([]).
activate_crossproduct([lez(Strict,Lin)|News]) :-
	var_with_def_intern(t_u(0),Var,Lin,Strict),
	% Var belongs to same class as elements in Lin
	basis_add(Var,_),
	activate_crossproduct(News).

% ------------------------------------------------------------------------------

% crossproduct(Lst,Res,ResTail)
%
% See crossproduct/4
% This predicate each time puts the next element of Lst as First in crossproduct/4
% and lets the rest be Next.

crossproduct([]) --> [].
crossproduct([A|As]) -->
	crossproduct(As,A),
	crossproduct(As).

% crossproduct(Next,First,Res,ResTail)
% 
% Eliminates a variable in linear equations First + Next and stores the generated
% inequalities in Res.
% Let's say A:K1 = First and B:K2 = first equation in Next.
% A = ... + K1*V + ...
% B = ... + K2*V + ...
% Let K = -K2/K1
% then K*A + B = ... + 0*V + ...
% from the bounds of A and B, via cross_lower/7 and cross_upper/7, new inequalities
% are generated. Then the same is done for B:K2 = next element in Next.

crossproduct([],_) --> [].
crossproduct([B:Kb|Bs],A:Ka) -->
	{
	    get_attr(A,itf,AttA),
	    arg(2,AttA,type(Ta)),
	    arg(3,AttA,strictness(Sa)),
	    arg(4,AttA,lin(LinA)),
	    get_attr(B,itf,AttB),
	    arg(2,AttB,type(Tb)),
	    arg(3,AttB,strictness(Sb)),
	    arg(4,AttB,lin(LinB)),
	    K is -Kb rdiv Ka,
	    add_linear_f1(LinA,K,LinB,Lin)	% Lin doesn't contain the target variable anymore
	},
	(   { K > 0 }	% K > 0: signs were opposite
	->  { Strict is Sa \/ Sb },
	    cross_lower(Ta,Tb,K,Lin,Strict),
	    cross_upper(Ta,Tb,K,Lin,Strict)
	;   % La =< A =< Ua -> -Ua =< -A =< -La
    	    {
		flip(Ta,Taf),
		flip_strict(Sa,Saf),
		Strict is Saf \/ Sb
	    },
	    cross_lower(Taf,Tb,K,Lin,Strict),
	    cross_upper(Taf,Tb,K,Lin,Strict)
	),
	crossproduct(Bs,A:Ka).

% cross_lower(Ta,Tb,K,Lin,Strict,Res,ResTail)
%
% Generates a constraint following from the bounds of A and B.
% When A = LinA and B = LinB then Lin = K*LinA + LinB. Ta is the type
% of A and Tb is the type of B. Strict is the union of the strictness 
% of A and B. If K is negative, then Ta should have been flipped (flip/2).
% The idea is that if La =< A =< Ua and Lb =< B =< Ub (=< can also be <)
% then if K is positive, K*La + Lb =< K*A + B =< K*Ua + Ub.
% if K is negative, K*Ua + Lb =< K*A + B =< K*La + Ub.
% This predicate handles the first inequality and adds it to Res in the form
% lez(Sl,Lhs) meaning K*La + Lb - (K*A + B) =< 0 or K*Ua + Lb - (K*A + B) =< 0
% with Sl being the strictness and Lhs the lefthandside of the equation.
% See also cross_upper/7

cross_lower(Ta,Tb,K,Lin,Strict) -->
	{
	    lower(Ta,La),
	    lower(Tb,Lb),
	    !,
	    L is K*La+Lb,
	    normalize_scalar(L,Ln),
	    add_linear_f1(Lin,-1,Ln,Lhs),
	    Sl is Strict >> 1			% normalize to upper bound
	},
	[ lez(Sl,Lhs) ].
cross_lower(_,_,_,_,_) --> [].

% cross_upper(Ta,Tb,K,Lin,Strict,Res,ResTail)
%
% See cross_lower/7
% This predicate handles the second inequality:
% -(K*Ua + Ub) + K*A + B =< 0 or -(K*La + Ub) + K*A + B =< 0

cross_upper(Ta,Tb,K,Lin,Strict) -->
	{
	    upper(Ta,Ua),
	    upper(Tb,Ub),
	    !,
	    U is -(K*Ua+Ub),
	    normalize_scalar(U,Un),
	    add_linear_11(Un,Lin,Lhs),
	    Su is Strict /\ 1			% normalize to upper bound
	},
	[ lez(Su,Lhs) ].
cross_upper(_,_,_,_,_) --> [].

% lower(Type,Lowerbound)
%
% Returns the lowerbound of type Type if it has one.
% E.g. if type = t_l(L) then Lowerbound is L,
%      if type = t_lU(L,U) then Lowerbound is L,
%      if type = t_u(U) then fails

lower(t_l(L),L).
lower(t_lu(L,_),L).
lower(t_L(L),L).
lower(t_Lu(L,_),L).
lower(t_lU(L,_),L).

% upper(Type,Upperbound)
%
% Returns the upperbound of type Type if it has one.
% See lower/2

upper(t_u(U),U).
upper(t_lu(_,U),U).
upper(t_U(U),U).
upper(t_Lu(_,U),U).
upper(t_lU(_,U),U).

% flip(Type,FlippedType)
%
% Flips the lower and upperbound, so the old lowerbound becomes the new upperbound and
% vice versa.

flip(t_l(X),t_u(X)).
flip(t_u(X),t_l(X)).
flip(t_lu(X,Y),t_lu(Y,X)).
flip(t_L(X),t_u(X)).
flip(t_U(X),t_l(X)).
flip(t_lU(X,Y),t_lu(Y,X)).
flip(t_Lu(X,Y),t_lu(Y,X)).

% flip_strict(Strict,FlippedStrict)
%
% Does what flip/2 does, but for the strictness.

flip_strict(0,0).
flip_strict(1,2).
flip_strict(2,1).
flip_strict(3,3).

% cp_card(Lst,CountIn,CountOut)
%
% Counts the number of bounds that may generate an inequality in
% crossproduct/3

cp_card([],Ci,Ci).
cp_card([A|As],Ci,Co) :-
	cp_card(As,A,Ci,Cii),
	cp_card(As,Cii,Co).

% cp_card(Next,First,CountIn,CountOut)
% 
% Counts the number of bounds that may generate an inequality in
% crossproduct/4.

cp_card([],_,Ci,Ci).
cp_card([B:Kb|Bs],A:Ka,Ci,Co) :-
	get_attr(A,itf,AttA),
	arg(2,AttA,type(Ta)),
	get_attr(B,itf,AttB),
	arg(2,AttB,type(Tb)),
	(   sign(Ka) =\= sign(Kb)
	->  cp_card_lower(Ta,Tb,Ci,Cii),
	    cp_card_upper(Ta,Tb,Cii,Ciii)
	;   flip(Ta,Taf),
	    cp_card_lower(Taf,Tb,Ci,Cii),
	    cp_card_upper(Taf,Tb,Cii,Ciii)
	),
	cp_card(Bs,A:Ka,Ciii,Co).

% cp_card_lower(TypeA,TypeB,SIn,SOut)
%
% SOut = SIn + 1 if both TypeA and TypeB have a lowerbound.

cp_card_lower(Ta,Tb,Si,So) :-
	lower(Ta,_),
	lower(Tb,_),
	!,
	So is Si+1.
cp_card_lower(_,_,Si,Si).

% cp_card_upper(TypeA,TypeB,SIn,SOut)
%
% SOut = SIn + 1 if both TypeA and TypeB have an upperbound.

cp_card_upper(Ta,Tb,Si,So) :-
	upper(Ta,_),
	upper(Tb,_),
	!,
	So is Si+1.
cp_card_upper(_,_,Si,Si).

% ------------------------------------------------------------------------------

% occurences(V,Occ)
%
% Returns in Occ the occurrences of variable V in the linear equations of dependent variables
% with bound =\= t_none in the form of D:K where D is a dependent variable and K is the scalar
% of V in the linear equation of D.

occurences(V,Occ) :-
	get_attr(V,itf,Att),
	arg(5,Att,order(OrdV)),
	arg(6,Att,class(C)),
	class_allvars(C,All),
	occurences(All,OrdV,Occ).

% occurences(De,OrdV,Occ)
%
% Returns in Occ the occurrences of variable V with order OrdV in the linear equations of 
% dependent variables De with bound =\= t_none in the form of D:K where D is a dependent
% variable and K is the scalar of V in the linear equation of D.

occurences(De,_,[]) :- 
	var(De),
	!.
occurences([D|De],OrdV,Occ) :-
	(   get_attr(D,itf,Att),
	    arg(2,Att,type(Type)),
	    arg(4,Att,lin(Lin)),
	    occ_type_filter(Type),
	    nf_coeff_of(Lin,OrdV,K)
	->  Occ = [D:K|Occt],
	    occurences(De,OrdV,Occt)
	;   occurences(De,OrdV,Occ)
	).

% occ_type_filter(Type)
% 
% Succeeds when Type is any other type than t_none. Is used in occurences/3 and occurs/2

occ_type_filter(t_l(_)).
occ_type_filter(t_u(_)).
occ_type_filter(t_lu(_,_)).
occ_type_filter(t_L(_)).
occ_type_filter(t_U(_)).
occ_type_filter(t_lU(_,_)).
occ_type_filter(t_Lu(_,_)).

% occurs(V)
%
% Checks whether variable V occurs in a linear equation of a dependent variable with a bound
% =\= t_none.

occurs(V) :-
	get_attr(V,itf,Att),
	arg(5,Att,order(OrdV)),
	arg(6,Att,class(C)),
	class_allvars(C,All),
	occurs(All,OrdV).

% occurs(De,OrdV)
%
% Checks whether variable V with order OrdV occurs in a linear equation of any dependent variable
% in De with a bound =\= t_none.

occurs(De,_) :- 
	var(De),
	!,
	fail.
occurs([D|De],OrdV) :-
	(   get_attr(D,itf,Att),
	    arg(2,Att,type(Type)),
	    arg(4,Att,lin(Lin)),
	    occ_type_filter(Type),
	    nf_coeff_of(Lin,OrdV,_)
	->  true
	;   occurs(De,OrdV)
	).