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.model; |
17 | |
18 | |
19 | /** |
20 | * A model for our mathematical world. It has entities, functions and predicates. |
21 | * There are also predicate and function constants. |
22 | * |
23 | * @author Michael Meyling |
24 | */ |
25 | public final class FourDynamicModel extends DynamicModel { |
26 | |
27 | /** "Zero" or empty set. */ |
28 | public static final Entity ZERO = new Entity(0, "{}", "{} or empty set"); |
29 | |
30 | /** "One" or set that contains the empty set. */ |
31 | public static final Entity ONE = new Entity(1, "{{}}", "{{}} or 1"); |
32 | |
33 | /** "Two" or set that contains "zero" and "one". */ |
34 | public static final Entity TWO = new Entity(2, "{{}, {{}}}", "{{}, {{}}} or 2"); |
35 | |
36 | /** "Three" or set that contains "one". */ |
37 | public static final Entity THREE = new Entity(3, "{{{}}}", "{{{}}} or 3"); |
38 | |
39 | /** Map to empty class. */ |
40 | public static final Function FUNCTION_ZERO = Function.createConstant(ZERO); |
41 | |
42 | /** Map to 1. */ |
43 | public static final Function FUNCTION_ONE = Function.createConstant(ONE); |
44 | |
45 | /** Map to 2. */ |
46 | public static final Function FUNCTION_TWO = Function.createConstant(TWO); |
47 | |
48 | /** Map to 2. */ |
49 | public static final Function FUNCTION_THREE = Function.createConstant(THREE); |
50 | |
51 | /** Return true if all values are zero. */ |
52 | public static final Predicate IS_ZERO = Predicate.isEntity(ZERO); |
53 | |
54 | /** Return true if all values are 1. */ |
55 | public static final Predicate IS_ONE = Predicate.isEntity(ONE); |
56 | |
57 | /** Return true if all values are 2. */ |
58 | public static final Predicate IS_TWO = Predicate.isEntity(TWO); |
59 | |
60 | /** Return true if all values are 2. */ |
61 | public static final Predicate IS_THREE = Predicate.isEntity(THREE); |
62 | |
63 | /** Map to one. */ |
64 | /** Modulo 3. */ |
65 | private final Function functionModulo3 = new Function(0, 99, "% 3", "modulo 3") { |
66 | public Entity map(final Entity[] entities) { |
67 | int result = 0; |
68 | for (int i = 0; i < entities.length; i++) { |
69 | result += entities[i].getValue() % 3; |
70 | } |
71 | result = result % 3; |
72 | return getEntity(result); |
73 | } |
74 | }; |
75 | |
76 | /** +1 Modulo 3. */ |
77 | private final Function functionPlus1Modulo3 = new Function(0, 99, "+1 % 3", "plus 1 modulo 3") { |
78 | public Entity map(final Entity[] entities) { |
79 | int result = 1; |
80 | for (int i = 0; i < entities.length; i++) { |
81 | result += entities[i].getValue() % 3; |
82 | } |
83 | result = result % 3; |
84 | return getEntity(result); |
85 | } |
86 | }; |
87 | |
88 | |
89 | /** |
90 | * Constructor. |
91 | */ |
92 | public FourDynamicModel() { |
93 | super("four elements"); |
94 | |
95 | addEntity(ZERO); |
96 | addEntity(ONE); |
97 | addEntity(TWO); |
98 | addEntity(THREE); |
99 | |
100 | addFunction(0, FUNCTION_ZERO); |
101 | addFunction(0, FUNCTION_ONE); |
102 | addFunction(0, FUNCTION_TWO); |
103 | addFunction(0, FUNCTION_THREE); |
104 | |
105 | addFunction(1, FUNCTION_ZERO); |
106 | addFunction(1, FUNCTION_ONE); |
107 | addFunction(0, FUNCTION_TWO); |
108 | addFunction(0, FUNCTION_THREE); |
109 | addFunction(1, functionModulo3); |
110 | addFunction(1, functionPlus1Modulo3); |
111 | |
112 | addFunction(2, FUNCTION_ZERO); |
113 | addFunction(2, FUNCTION_ONE); |
114 | addFunction(0, FUNCTION_TWO); |
115 | addFunction(0, FUNCTION_THREE); |
116 | addFunction(2, functionModulo3); |
117 | addFunction(2, functionPlus1Modulo3); |
118 | |
119 | addPredicate(0, FALSE); |
120 | addPredicate(0, TRUE); |
121 | |
122 | addPredicate(1, FALSE); |
123 | addPredicate(1, TRUE); |
124 | addPredicate(1, EVEN); |
125 | addPredicate(1, IS_ZERO); |
126 | addPredicate(1, IS_ONE); |
127 | addPredicate(1, IS_TWO); |
128 | addPredicate(1, IS_THREE); |
129 | |
130 | addPredicate(2, FALSE); |
131 | addPredicate(2, TRUE); |
132 | addPredicate(2, EVEN); |
133 | addPredicate(2, LESS); |
134 | addPredicate(2, EQUAL); |
135 | addPredicate(2, IS_ZERO); |
136 | addPredicate(2, IS_ONE); |
137 | addPredicate(2, IS_TWO); |
138 | addPredicate(2, IS_THREE); |
139 | |
140 | addPredicateConstant(new ModelPredicateConstant("in", 2), new Predicate(2, 2, "in", "Element of") { |
141 | public boolean calculate(final Entity[] entities) { |
142 | if (entities.length != 2) { |
143 | return false; |
144 | } |
145 | final int element = entities[0].getValue(); |
146 | switch (entities[1].getValue()) { |
147 | case 0: return false; |
148 | case 1: if (element == 0) { |
149 | return true; |
150 | } |
151 | return false; |
152 | case 2: if (element < 2) { |
153 | return true; |
154 | } |
155 | return false; |
156 | case 3: if (element == 1) { |
157 | return true; |
158 | } |
159 | return false; |
160 | default: return false; |
161 | } |
162 | } |
163 | }); |
164 | } |
165 | |
166 | public String getDescription() { |
167 | return "This model has four entities: {}, {{}}, {{}, {{}}}, {{{}}}."; |
168 | } |
169 | |
170 | public Entity comprehension(final Entity[] array) { |
171 | Entity result = ZERO; |
172 | for (int i = 0; i < array.length; i++) { |
173 | final int element = array[i].getValue(); |
174 | switch (result.getValue()) { |
175 | case 0: |
176 | if (element == 0) { |
177 | result = ONE; |
178 | } else if (element == 1) { |
179 | result = THREE; |
180 | } |
181 | break; |
182 | case 1: |
183 | if (element == 1) { |
184 | result = TWO; |
185 | } |
186 | break; |
187 | case 2: |
188 | break; |
189 | case 3: |
190 | if (element == 0) { |
191 | result = TWO; |
192 | } |
193 | break; |
194 | default: throw new RuntimeException("unknown value for entity " + array[i]); |
195 | } |
196 | } |
197 | return result; |
198 | } |
199 | |
200 | } |