| 1 | /* This file is part of the project "Hilbert II" - http://www.qedeq.org |
| 2 | * |
| 3 | * Copyright 2000-2014, Michael Meyling <mime@qedeq.org>. |
| 4 | * |
| 5 | * "Hilbert II" is free software; you can redistribute |
| 6 | * it and/or modify it under the terms of the GNU General Public |
| 7 | * License as published by the Free Software Foundation; either |
| 8 | * version 2 of the License, or (at your option) any later version. |
| 9 | * |
| 10 | * This program is distributed in the hope that it will be useful, |
| 11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 13 | * GNU General Public License for more details. |
| 14 | */ |
| 15 | |
| 16 | package org.qedeq.kernel.bo.logic.common; |
| 17 | |
| 18 | import org.qedeq.base.utility.Enumerator; |
| 19 | import org.qedeq.base.utility.EqualsUtility; |
| 20 | import org.qedeq.kernel.se.base.list.Atom; |
| 21 | import org.qedeq.kernel.se.base.list.Element; |
| 22 | import org.qedeq.kernel.se.base.list.ElementList; |
| 23 | import org.qedeq.kernel.se.dto.list.DefaultAtom; |
| 24 | import org.qedeq.kernel.se.dto.list.DefaultElementList; |
| 25 | import org.qedeq.kernel.se.dto.list.ElementSet; |
| 26 | |
| 27 | |
| 28 | /** |
| 29 | * Some useful static methods for formulas and terms. |
| 30 | * |
| 31 | * @author Michael Meyling |
| 32 | */ |
| 33 | public final class FormulaUtility implements Operators { |
| 34 | |
| 35 | /** |
| 36 | * Constructor. |
| 37 | * |
| 38 | */ |
| 39 | private FormulaUtility() { |
| 40 | // nothing to do here |
| 41 | } |
| 42 | |
| 43 | /** |
| 44 | * Is {@link Element} a subject variable? |
| 45 | * |
| 46 | * @param element Element to look onto. |
| 47 | * @return Is it a subject variable? |
| 48 | */ |
| 49 | public static final boolean isSubjectVariable(final Element element) { |
| 50 | if (element == null || !element.isList() || element.getList() == null) { |
| 51 | return false; |
| 52 | } |
| 53 | final ElementList list = element.getList(); |
| 54 | if (list.getOperator().equals(SUBJECT_VARIABLE)) { |
| 55 | if (list.size() != 1) { |
| 56 | return false; |
| 57 | } |
| 58 | final Element first = element.getList().getElement(0); |
| 59 | if (first == null || !first.isAtom() || first.getAtom() == null) { |
| 60 | return false; |
| 61 | } |
| 62 | final Atom atom = first.getAtom(); |
| 63 | if (atom.getString() == null || atom.getAtom().getString() == null |
| 64 | || atom.getString().length() == 0) { |
| 65 | return false; |
| 66 | } |
| 67 | } else { |
| 68 | return false; |
| 69 | } |
| 70 | return true; |
| 71 | } |
| 72 | |
| 73 | /** |
| 74 | * Is {@link Element} a predicate variable? |
| 75 | * |
| 76 | * @param element Element to look onto. |
| 77 | * @return Is it a predicate variable? |
| 78 | */ |
| 79 | public static final boolean isPredicateVariable(final Element element) { |
| 80 | return isOperator(PREDICATE_VARIABLE, element); |
| 81 | } |
| 82 | |
| 83 | /** |
| 84 | * Is {@link Element} a proposition variable? |
| 85 | * |
| 86 | * @param element Element to look onto. |
| 87 | * @return Is it a proposition variable? |
| 88 | */ |
| 89 | public static final boolean isPropositionVariable(final Element element) { |
| 90 | return isOperator(PREDICATE_VARIABLE, element) && element.getList().size() <= 1; |
| 91 | } |
| 92 | |
| 93 | /** |
| 94 | * Is {@link Element} a function variable? |
| 95 | * |
| 96 | * @param element Element to look onto. |
| 97 | * @return Is it a function variable? |
| 98 | */ |
| 99 | public static final boolean isFunctionVariable(final Element element) { |
| 100 | return isOperator(FUNCTION_VARIABLE, element); |
| 101 | } |
| 102 | |
| 103 | /** |
| 104 | * Is {@link Element} a predicate constant? |
| 105 | * |
| 106 | * @param element Element to look onto. |
| 107 | * @return Is it a predicate constant? |
| 108 | */ |
| 109 | public static final boolean isPredicateConstant(final Element element) { |
| 110 | return isOperator(PREDICATE_CONSTANT, element); |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | * Is {@link Element} a function constant? |
| 115 | * |
| 116 | * @param element Element to look onto. |
| 117 | * @return Is it a function constant? |
| 118 | */ |
| 119 | public static final boolean isFunctionConstant(final Element element) { |
| 120 | return isOperator(FUNCTION_CONSTANT, element); |
| 121 | } |
| 122 | |
| 123 | /** |
| 124 | * Is the given element an list with given operator and has as first element an non empty |
| 125 | * string atom? |
| 126 | * |
| 127 | * @param operator Operator. |
| 128 | * @param element Check this element. |
| 129 | * @return Check successful? |
| 130 | */ |
| 131 | public static boolean isOperator(final String operator, |
| 132 | final Element element) { |
| 133 | return isOperator(operator, element, 0); |
| 134 | } |
| 135 | |
| 136 | /** |
| 137 | * Is the given element an list with given operator and has as first element an non empty |
| 138 | * string atom? |
| 139 | * |
| 140 | * @param operator Operator. |
| 141 | * @param element Check this element. |
| 142 | * @param minArguments Minimum number of arguments (beside the first string atom). |
| 143 | * @return Check successful? |
| 144 | */ |
| 145 | private static boolean isOperator(final String operator, |
| 146 | final Element element, final int minArguments) { |
| 147 | if (element == null || !element.isList() || element.getList() == null) { |
| 148 | return false; |
| 149 | } |
| 150 | final ElementList list = element.getList(); |
| 151 | if (list.getOperator().equals(operator)) { |
| 152 | if (list.size() < 1 + minArguments) { |
| 153 | return false; |
| 154 | } |
| 155 | final Element first = element.getList().getElement(0); |
| 156 | if (first == null || !first.isAtom() || first.getAtom() == null) { |
| 157 | return false; |
| 158 | } |
| 159 | final Atom atom = first.getAtom(); |
| 160 | if (atom.getString() == null || atom.getAtom().getString() == null |
| 161 | || atom.getString().length() == 0) { |
| 162 | return false; |
| 163 | } |
| 164 | } else { |
| 165 | return false; |
| 166 | } |
| 167 | return true; |
| 168 | } |
| 169 | |
| 170 | /** |
| 171 | * Return all free subject variables of an element. |
| 172 | * |
| 173 | * @param element Work on this element. |
| 174 | * @return All free subject variables. |
| 175 | */ |
| 176 | public static final ElementSet getFreeSubjectVariables(final Element element) { |
| 177 | final ElementSet free = new ElementSet(); |
| 178 | if (isSubjectVariable(element)) { |
| 179 | free.add(element); |
| 180 | } else if (element.isList()) { |
| 181 | final ElementList list = element.getList(); |
| 182 | if (isBindingOperator(list)) { |
| 183 | for (int i = 1; i < list.size(); i++) { |
| 184 | free.union(getFreeSubjectVariables(list.getElement(i))); |
| 185 | } |
| 186 | free.remove(list.getElement(0)); |
| 187 | } else { |
| 188 | for (int i = 0; i < list.size(); i++) { |
| 189 | free.union(getFreeSubjectVariables(list.getElement(i))); |
| 190 | } |
| 191 | } |
| 192 | } |
| 193 | return free; |
| 194 | } |
| 195 | |
| 196 | /** |
| 197 | * Return all bound subject variables of an element. |
| 198 | * |
| 199 | * @param element Work on this element. |
| 200 | * @return All bound subject variables. |
| 201 | */ |
| 202 | public static final ElementSet getBoundSubjectVariables(final Element element) { |
| 203 | final ElementSet bound = new ElementSet(); |
| 204 | if (element.isList()) { |
| 205 | ElementList list = element.getList(); |
| 206 | // if operator is quantifier or class term |
| 207 | if (isBindingOperator(list)) { |
| 208 | // add subject variable to bound list |
| 209 | bound.add(list.getElement(0)); |
| 210 | // add all bound variables of sub-elements |
| 211 | for (int i = 1; i < list.size(); i++) { |
| 212 | bound.union(getBoundSubjectVariables( |
| 213 | list.getElement(i))); |
| 214 | } |
| 215 | } else { |
| 216 | // add all bound variables of sub-elements |
| 217 | for (int i = 0; i < list.size(); i++) { |
| 218 | bound.union(getBoundSubjectVariables(list.getElement(i))); |
| 219 | } |
| 220 | } |
| 221 | } |
| 222 | return bound; |
| 223 | } |
| 224 | |
| 225 | /** |
| 226 | * Return all subject variables of an element. |
| 227 | * |
| 228 | * @param element Work on this element. |
| 229 | * @return All subject variables. |
| 230 | */ |
| 231 | public static final ElementSet getSubjectVariables(final Element element) { |
| 232 | final ElementSet all = new ElementSet(); |
| 233 | if (isSubjectVariable(element)) { |
| 234 | all.add(element); |
| 235 | } else if (element.isList()) { |
| 236 | final ElementList list = element.getList(); |
| 237 | for (int i = 1; i < list.size(); i++) { |
| 238 | all.union(getSubjectVariables(list.getElement(i))); |
| 239 | } |
| 240 | } |
| 241 | return all; |
| 242 | } |
| 243 | |
| 244 | /** |
| 245 | * Return all predicate variables of an element. The arguments are normalized to subject |
| 246 | * variables "x_1", "x_2" and so on. |
| 247 | * |
| 248 | * @param element Work on this element. |
| 249 | * @return All predicate variables of that formula. |
| 250 | */ |
| 251 | public static final ElementSet getPredicateVariables(final Element element) { |
| 252 | final ElementSet all = new ElementSet(); |
| 253 | if (isPredicateVariable(element)) { |
| 254 | final ElementList pred = element.getList(); |
| 255 | final DefaultElementList normalized = new DefaultElementList(pred.getOperator()); |
| 256 | normalized.add(pred.getElement(0)); |
| 257 | for (int i = 1; i < pred.size(); i++) { |
| 258 | normalized.add(createSubjectVariable("x_" + i)); |
| 259 | } |
| 260 | all.add(normalized); |
| 261 | } else if (element.isList()) { |
| 262 | final ElementList list = element.getList(); |
| 263 | for (int i = 0; i < list.size(); i++) { |
| 264 | all.union(getPredicateVariables(list.getElement(i))); |
| 265 | } |
| 266 | } |
| 267 | return all; |
| 268 | } |
| 269 | |
| 270 | /** |
| 271 | * Return all proposition variables of an element. That are predicate variables with |
| 272 | * arity zero. |
| 273 | * |
| 274 | * @param element Work on this element. |
| 275 | * @return All proposition variables of that formula. |
| 276 | */ |
| 277 | public static final ElementSet getPropositionVariables(final Element element) { |
| 278 | final ElementSet all = new ElementSet(); |
| 279 | if (isPropositionVariable(element)) { |
| 280 | all.add(element); |
| 281 | } else if (element.isList()) { |
| 282 | final ElementList list = element.getList(); |
| 283 | for (int i = 0; i < list.size(); i++) { |
| 284 | all.union(getPropositionVariables(list.getElement(i))); |
| 285 | } |
| 286 | } |
| 287 | return all; |
| 288 | } |
| 289 | |
| 290 | /** |
| 291 | * Return all part formulas of an element. |
| 292 | * |
| 293 | * @param element Work on this element. |
| 294 | * @return All part formulas of that element. |
| 295 | */ |
| 296 | public static final ElementSet getPartFormulas(final Element element) { |
| 297 | final ElementSet all = new ElementSet(); |
| 298 | if (element == null || element.isAtom()) { |
| 299 | return all; |
| 300 | } |
| 301 | final ElementList list = element.getList(); |
| 302 | if (isPredicateVariable(list)) { |
| 303 | all.add(element); |
| 304 | } else if (isPredicateConstant(list)) { |
| 305 | all.add(list); |
| 306 | } else if (Operators.CONJUNCTION_OPERATOR.equals(list.getOperator()) |
| 307 | || Operators.DISJUNCTION_OPERATOR.equals(list.getOperator()) |
| 308 | || Operators.NEGATION_OPERATOR.equals(list.getOperator()) |
| 309 | || Operators.IMPLICATION_OPERATOR.equals(list.getOperator()) |
| 310 | || Operators.EQUIVALENCE_OPERATOR.equals(list.getOperator()) |
| 311 | ) { |
| 312 | all.add(list); |
| 313 | for (int i = 0; i < list.size(); i++) { |
| 314 | all.union(getPartFormulas(list.getElement(i))); |
| 315 | } |
| 316 | } else if (isBindingOperator(list)) { |
| 317 | all.add(list); |
| 318 | for (int i = 0; i < list.size(); i++) { |
| 319 | all.union(getPartFormulas(list.getElement(i))); |
| 320 | } |
| 321 | } else if (isSubjectVariable(list)) { |
| 322 | // this is no formula |
| 323 | } else if (isFunctionVariable(list)) { |
| 324 | // this is no formula |
| 325 | } else if (isFunctionConstant(list)) { |
| 326 | // this is no formula |
| 327 | } else { |
| 328 | for (int i = 0; i < list.size(); i++) { |
| 329 | all.union(getPartFormulas(list.getElement(i))); |
| 330 | } |
| 331 | } |
| 332 | return all; |
| 333 | } |
| 334 | |
| 335 | /** |
| 336 | * Has the given list an operator that binds a subject variable? |
| 337 | * |
| 338 | * @param list Check for this operator. |
| 339 | * @return Has it an binding operator with subject variable? |
| 340 | */ |
| 341 | public static boolean isBindingOperator(final ElementList list) { |
| 342 | final String operator = list.getOperator(); |
| 343 | if (operator == null || list.size() <= 0 || !isSubjectVariable(list.getElement(0))) { |
| 344 | return false; |
| 345 | } |
| 346 | return operator.equals(EXISTENTIAL_QUANTIFIER_OPERATOR) |
| 347 | || operator.equals(UNIQUE_EXISTENTIAL_QUANTIFIER_OPERATOR) |
| 348 | || operator.equals(UNIVERSAL_QUANTIFIER_OPERATOR) |
| 349 | || operator.equals(CLASS_OP); |
| 350 | } |
| 351 | |
| 352 | /** |
| 353 | * Get relative context of the first difference between the given elements. |
| 354 | * |
| 355 | * @param first First element. |
| 356 | * @param second Second element. |
| 357 | * @return Relative path (beginning with ".") of first difference. |
| 358 | */ |
| 359 | public static String getDifferenceLocation(final Element first, final Element second) { |
| 360 | final StringBuffer diff = new StringBuffer(); |
| 361 | equal(diff, first, second); |
| 362 | return diff.toString(); |
| 363 | } |
| 364 | |
| 365 | /** |
| 366 | * Is there any difference between the two elements? If so, the context has the difference |
| 367 | * position. |
| 368 | * |
| 369 | * @param firstContext Context (might be relative) for first element. |
| 370 | * @param first First element. |
| 371 | * @param second Second element. |
| 372 | * @return Are both elements equal? |
| 373 | */ |
| 374 | private static boolean equal(final StringBuffer firstContext, |
| 375 | final Element first, final Element second) { |
| 376 | if (first == null) { |
| 377 | return second == null; |
| 378 | } |
| 379 | if (second == null) { |
| 380 | return false; |
| 381 | } |
| 382 | if (first.isAtom()) { |
| 383 | if (!second.isAtom()) { |
| 384 | return false; |
| 385 | } |
| 386 | return EqualsUtility.equals(first.getAtom().getString(), second.getAtom().getString()); |
| 387 | } |
| 388 | if (second.isAtom()) { |
| 389 | return false; |
| 390 | } |
| 391 | if (!EqualsUtility.equals(first.getList().getOperator(), second.getList().getOperator())) { |
| 392 | return false; |
| 393 | } |
| 394 | if (first.getList().size() != second.getList().size()) { |
| 395 | return false; |
| 396 | } |
| 397 | for (int i = 0; i < first.getList().size(); i++) { |
| 398 | final int length = firstContext.length(); |
| 399 | firstContext.append(".getList().getElement(" + i + ")"); |
| 400 | if (!equal(firstContext, first.getList().getElement(i), |
| 401 | second.getList().getElement(i))) { |
| 402 | return false; |
| 403 | } |
| 404 | firstContext.setLength(length); |
| 405 | } |
| 406 | return true; |
| 407 | } |
| 408 | |
| 409 | /** |
| 410 | * Replace bound subject variables at given occurrence by another one. |
| 411 | * If goal occurrence number is below number of occurrences within the formula nothing is |
| 412 | * changed. Original parts are used, so don't modify the formulas directly. |
| 413 | * |
| 414 | * @param originalSubjectVariable Replace this subject variable. |
| 415 | * @param replacementSubjectVariable By this subject variable. |
| 416 | * @param formulaElement This is the formula we work on. |
| 417 | * @param occurrenceGoal This is the binding occurrence number. |
| 418 | * @param occurreneCurrent Counter how much occurrences we already had. |
| 419 | * @return Formula with replaced subject variables. |
| 420 | */ |
| 421 | public static Element replaceSubjectVariableQuantifier(final Element originalSubjectVariable, |
| 422 | final Element replacementSubjectVariable, final Element formulaElement, |
| 423 | final int occurrenceGoal, final Enumerator occurreneCurrent) { |
| 424 | if (formulaElement.isAtom()) { |
| 425 | return formulaElement; |
| 426 | } |
| 427 | final ElementList formula = formulaElement.getList(); |
| 428 | if (occurreneCurrent.getNumber() > occurrenceGoal) { |
| 429 | return formula.copy(); |
| 430 | } |
| 431 | final ElementList result = new DefaultElementList(formula.getOperator()); |
| 432 | if (isBindingOperator(formula) |
| 433 | && formula.getElement(0).equals(originalSubjectVariable)) { |
| 434 | occurreneCurrent.increaseNumber(); |
| 435 | // System.out.println("found: " + occurreneCurrent); |
| 436 | if (occurrenceGoal == occurreneCurrent.getNumber()) { |
| 437 | // System.out.println("match: " + occurrenceGoal); |
| 438 | return formula.replace(originalSubjectVariable, |
| 439 | replacementSubjectVariable); |
| 440 | } |
| 441 | } |
| 442 | for (int i = 0; i < formula.size(); i++) { |
| 443 | result.add(replaceSubjectVariableQuantifier(originalSubjectVariable, |
| 444 | replacementSubjectVariable, formula.getElement(i), occurrenceGoal, |
| 445 | occurreneCurrent)); |
| 446 | } |
| 447 | return result; |
| 448 | } |
| 449 | |
| 450 | /** |
| 451 | * Replace function or predicate variable by given term or formula. Old parts are not copied |
| 452 | * but taken directly - so don't modify the formulas! |
| 453 | * |
| 454 | * @param formula Formula we want the replacement take place. |
| 455 | * @param operatorVariable Predicate variable or function variable with only subject |
| 456 | * variables as arguments. |
| 457 | * @param replacement Replacement formula or term with matching subject variables. |
| 458 | * <code>operatorVariable</code> might have some subject variables |
| 459 | * that are not in <code>replacement</code> and vice versa. |
| 460 | * @return Formula where operatorVariable was replaced. |
| 461 | */ |
| 462 | public static Element replaceOperatorVariable(final Element formula, |
| 463 | final Element operatorVariable, final Element replacement) { |
| 464 | if (formula == null || operatorVariable == null || replacement == null |
| 465 | || formula.isAtom() || operatorVariable.isAtom() || replacement.isAtom()) { |
| 466 | return formula; |
| 467 | } |
| 468 | final ElementList f = formula.getList(); |
| 469 | final ElementList ov = operatorVariable.getList(); |
| 470 | final ElementList r = replacement.getList(); |
| 471 | // check elementary preconditions |
| 472 | // System.out.println("ov.size=" + ov.size()); |
| 473 | if (f.size() < 1 || ov.size() < 1) { |
| 474 | // System.out.println("failed elementary conditions"); |
| 475 | return formula; |
| 476 | } |
| 477 | // construct replacement formula with meta variables |
| 478 | Element rn = r; |
| 479 | for (int i = 1; i < ov.size(); i++) { |
| 480 | rn = rn.replace(ov.getElement(i), createMeta(ov.getElement(i))); |
| 481 | } |
| 482 | return replaceOperatorVariableMeta(formula, operatorVariable, rn); |
| 483 | } |
| 484 | |
| 485 | /** |
| 486 | * Replace function or predicate variable by given term or formula. Original parts are used - |
| 487 | * so don't modify them! |
| 488 | * |
| 489 | * @param formula Formula we want the replacement take place. |
| 490 | * @param operatorVariable Predicate variable or function variable with only subject |
| 491 | * variables as arguments. |
| 492 | * @param replacement Replacement formula or term with meta variables instead of |
| 493 | * subject variables to replace (matching |
| 494 | * <code>operatorVariable</code>). |
| 495 | * @return Formula where operatorVariable was replaced. |
| 496 | */ |
| 497 | private static Element replaceOperatorVariableMeta(final Element formula, |
| 498 | final Element operatorVariable, final Element replacement) { |
| 499 | if (formula.isAtom() || operatorVariable.isAtom() || replacement.isAtom()) { |
| 500 | return formula; |
| 501 | } |
| 502 | final ElementList f = formula.getList(); |
| 503 | final ElementList ov = operatorVariable.getList(); |
| 504 | final ElementList r = replacement.getList(); |
| 505 | if (f.size() < 1 || ov.size() < 1) { |
| 506 | return formula.copy(); |
| 507 | } |
| 508 | ElementList result; |
| 509 | if (EqualsUtility.equals(f.getOperator(), ov.getOperator()) && f.size() == ov.size() |
| 510 | && f.getElement(0).equals(ov.getElement(0))) { |
| 511 | // replace meta variables by matching entries |
| 512 | result = r; |
| 513 | for (int i = 1; i < ov.size(); i++) { |
| 514 | result = (ElementList) result.replace(createMeta(ov.getElement(i)), |
| 515 | replaceOperatorVariableMeta(f.getElement(i), operatorVariable, replacement)); |
| 516 | } |
| 517 | } else { |
| 518 | result = new DefaultElementList(f.getOperator()); |
| 519 | for (int i = 0; i < f.size(); i++) { |
| 520 | result.add(replaceOperatorVariableMeta(f.getElement(i), operatorVariable, |
| 521 | replacement)); |
| 522 | } |
| 523 | } |
| 524 | return result; |
| 525 | } |
| 526 | |
| 527 | /** |
| 528 | * Checks if a given term or formula contains a given function or predicate variable with same |
| 529 | * size. |
| 530 | * |
| 531 | * @param formula Formula we want the replacement take place. |
| 532 | * @param operatorVariable Predicate variable or function variable with only subject |
| 533 | * variables as arguments. |
| 534 | * @return Do we have any occurrence? |
| 535 | */ |
| 536 | public static boolean containsOperatorVariable(final Element formula, |
| 537 | final Element operatorVariable) { |
| 538 | if (formula == null || formula.isAtom() || operatorVariable == null |
| 539 | || operatorVariable.isAtom()) { |
| 540 | return false; |
| 541 | } |
| 542 | final ElementList f = formula.getList(); |
| 543 | final ElementList ov = operatorVariable.getList(); |
| 544 | if (f.size() < 1 || ov.size() < 1) { |
| 545 | return f.equals(ov); |
| 546 | } |
| 547 | if (EqualsUtility.equals(f.getOperator(), ov.getOperator()) && f.size() == ov.size() |
| 548 | && f.getElement(0).equals(ov.getElement(0))) { |
| 549 | return true; |
| 550 | } |
| 551 | for (int i = 0; i < f.size(); i++) { |
| 552 | if (containsOperatorVariable(f.getElement(i), operatorVariable)) { |
| 553 | return true; |
| 554 | } |
| 555 | } |
| 556 | return false; |
| 557 | } |
| 558 | |
| 559 | /** |
| 560 | * Test if operator occurrence in formula matches always to a formula that contains no subject |
| 561 | * variable that is in the given ElementSet of bound subject variables.. |
| 562 | * |
| 563 | * @param formula Formula we want to test the condition. |
| 564 | * @param operatorVariable Predicate variable or function variable with only subject |
| 565 | * variables as arguments. |
| 566 | * @param bound Set of subject variables that are tabu. |
| 567 | * @return Formula test was successful. |
| 568 | */ |
| 569 | public static boolean testOperatorVariable(final Element formula, |
| 570 | final Element operatorVariable, final ElementSet bound) { |
| 571 | if (formula.isAtom() || operatorVariable.isAtom()) { |
| 572 | return true; |
| 573 | } |
| 574 | final ElementList f = formula.getList(); |
| 575 | final ElementList ov = operatorVariable.getList(); |
| 576 | if (f.size() < 1 || ov.size() < 1) { |
| 577 | return true; |
| 578 | } |
| 579 | boolean ok = true; |
| 580 | if (EqualsUtility.equals(f.getOperator(), ov.getOperator()) && f.size() == ov.size() |
| 581 | && f.getElement(0).equals(ov.getElement(0))) { |
| 582 | if (!getSubjectVariables(f).intersection(bound).isEmpty()) { |
| 583 | return false; |
| 584 | } |
| 585 | } else { |
| 586 | for (int i = 0; ok && i < f.size(); i++) { |
| 587 | ok = testOperatorVariable(f.getElement(i), operatorVariable, bound); |
| 588 | } |
| 589 | } |
| 590 | return ok; |
| 591 | } |
| 592 | |
| 593 | /** |
| 594 | * Is the given formula a simple implication like A => B. |
| 595 | * |
| 596 | * @param formula Check this formula. |
| 597 | * @return Is the formula a simple implication? |
| 598 | */ |
| 599 | public static boolean isImplication(final Element formula) { |
| 600 | if (formula.isAtom()) { |
| 601 | return false; |
| 602 | } |
| 603 | final ElementList f = formula.getList(); |
| 604 | return Operators.IMPLICATION_OPERATOR.equals(f.getList().getOperator()) |
| 605 | && f.getList().size() == 2; |
| 606 | } |
| 607 | |
| 608 | /** |
| 609 | * Create meta variable for subject variable. |
| 610 | * |
| 611 | * @param subjectVariable Subject variable, we want to have a meta variable for. |
| 612 | * @return Resulting meta variable. If we didn't got a subject variable we just |
| 613 | * return the original. |
| 614 | */ |
| 615 | public static Element createMeta(final Element subjectVariable) { |
| 616 | if (!isSubjectVariable(subjectVariable)) { |
| 617 | return subjectVariable; |
| 618 | } |
| 619 | final DefaultElementList result = new DefaultElementList(META_VARIABLE); |
| 620 | result.add(subjectVariable.getList().getElement(0)); |
| 621 | return result; |
| 622 | } |
| 623 | |
| 624 | /** |
| 625 | * Create subject variable out of variable name. |
| 626 | * |
| 627 | * @param subjectVariableName Subject variable name. |
| 628 | * @return Resulting subject variable. |
| 629 | */ |
| 630 | public static Element createSubjectVariable(final String subjectVariableName) { |
| 631 | final DefaultElementList result = new DefaultElementList(SUBJECT_VARIABLE); |
| 632 | result.add(new DefaultAtom(subjectVariableName)); |
| 633 | return result; |
| 634 | } |
| 635 | |
| 636 | /** |
| 637 | * Create predicate variable out of variable name with no further arguments. |
| 638 | * |
| 639 | * @param predicateVariableName Predicate variable name. |
| 640 | * @return Resulting predicate variable. |
| 641 | */ |
| 642 | public static Element createPredicateVariable(final String predicateVariableName) { |
| 643 | final DefaultElementList result = new DefaultElementList(PREDICATE_VARIABLE); |
| 644 | result.add(new DefaultAtom(predicateVariableName)); |
| 645 | return result; |
| 646 | } |
| 647 | |
| 648 | } |