31 \item axioms |
31 \item axioms |
32 \subitem Peano, 54 |
32 \subitem Peano, 54 |
33 |
33 |
34 \indexspace |
34 \indexspace |
35 |
35 |
36 \item {\tt ba}, 30 |
36 \item {\tt ba}, 31 |
37 \item {\tt back}, 59, 62 |
37 \item {\tt back}, 59, 62 |
38 \item backtracking |
38 \item backtracking |
39 \subitem Prolog style, 62 |
39 \subitem Prolog style, 62 |
40 \item {\tt bd}, 30 |
40 \item {\tt bd}, 31 |
41 \item {\tt be}, 30 |
41 \item {\tt be}, 31 |
42 \item {\tt br}, 30 |
42 \item {\tt br}, 31 |
43 \item {\tt by}, 30 |
43 \item {\tt by}, 30 |
44 |
44 |
45 \indexspace |
45 \indexspace |
46 |
46 |
47 \item {\tt choplev}, 36, 37, 64 |
47 \item {\tt choplev}, 37, 64 |
48 \item classes, 3 |
48 \item classes, 3 |
49 \subitem built-in, \bold{25} |
49 \subitem built-in, \bold{25} |
50 \item classical reasoner, 39 |
50 \item classical reasoner, 39 |
51 \item {\tt conjunct1} theorem, 27 |
51 \item {\tt conjunct1} theorem, 28 |
52 \item constants, 1 |
52 \item constants, 3 |
53 \subitem clashes with variables, 9 |
53 \subitem clashes with variables, 9 |
54 \subitem declaring, \bold{48} |
54 \subitem declaring, \bold{48} |
55 \subitem overloaded, 53 |
55 \subitem overloaded, 53 |
56 \subitem polymorphic, 3 |
56 \subitem polymorphic, 3 |
|
57 \item {\tt CPure} theory, 47 |
57 |
58 |
58 \indexspace |
59 \indexspace |
59 |
60 |
60 \item definitions, 6, \bold{48} |
61 \item definitions, 6, \bold{48} |
61 \subitem and derived rules, 43--46 |
62 \subitem and derived rules, 43--46 |
62 \item {\tt DEPTH_FIRST}, 64 |
63 \item {\tt DEPTH_FIRST}, 64 |
63 \item destruct-resolution, 22, 30 |
64 \item destruct-resolution, 22, 30 |
64 \item {\tt disjE} theorem, 31 |
65 \item {\tt disjE} theorem, 31 |
65 \item {\tt dres_inst_tac}, 57 |
66 \item {\tt dres_inst_tac}, 57 |
66 \item {\tt dresolve_tac}, 30, 32, 38 |
67 \item {\tt dresolve_tac}, 30, 32, 33, 38 |
67 |
68 |
68 \indexspace |
69 \indexspace |
69 |
70 |
70 \item eigenvariables, \see{parameters}{8} |
71 \item eigenvariables, \see{parameters}{8} |
71 \item elim-resolution, \bold{20}, 30 |
72 \item elim-resolution, \bold{20}, 30 |
72 \item equality |
73 \item equality |
73 \subitem polymorphic, 3 |
74 \subitem polymorphic, 3 |
74 \item {\tt eres_inst_tac}, 57 |
75 \item {\tt eres_inst_tac}, 57 |
75 \item {\tt eresolve_tac}, 30, 32, 38, 47 |
76 \item {\tt eresolve_tac}, 30, 32, 33, 39, 47 |
76 \item examples |
77 \item examples |
77 \subitem of deriving rules, 41 |
78 \subitem of deriving rules, 41 |
78 \subitem of induction, 57, 58 |
79 \subitem of induction, 57, 58 |
79 \subitem of simplification, 59 |
80 \subitem of simplification, 59 |
80 \subitem of tacticals, 37 |
81 \subitem of tacticals, 37 |
81 \subitem of theories, 48, 50--55, 61 |
82 \subitem of theories, 48, 50--55, 61 |
82 \subitem propositional, 17, 31, 32 |
83 \subitem propositional, 17, 31, 32 |
83 \subitem with quantifiers, 18, 33, 35, 37 |
84 \subitem with quantifiers, 18, 34, 35, 38 |
84 \item {\tt exE} theorem, 38 |
85 \item {\tt exE} theorem, 38 |
85 |
86 |
86 \indexspace |
87 \indexspace |
87 |
88 |
88 \item {\tt FalseE} theorem, 45 |
89 \item {\tt FalseE} theorem, 45 |
89 \item {\tt fast_tac}, 39 |
90 \item {\tt fast_tac}, 39 |
90 \item first-order logic, 1 |
91 \item first-order logic, 1 |
91 \item flex-flex constraints, 6, 25, \bold{28} |
92 \item flex-flex constraints, 6, 25, \bold{28} |
92 \item {\tt flexflex_rule}, 28 |
93 \item {\tt flexflex_rule}, 29 |
93 \item forward proof, 21, 24--30 |
94 \item forward proof, 21, 24--30 |
94 \item {\tt fun} type, 1, 4 |
95 \item {\tt fun} type, 1, 4 |
95 \item function applications, 1, 8 |
96 \item function applications, 1, 8 |
96 |
97 |
97 \indexspace |
98 \indexspace |
136 \item meta-quantifiers, \bold{5}, 8, 25 |
137 \item meta-quantifiers, \bold{5}, 8, 25 |
137 \item meta-rewriting, 43 |
138 \item meta-rewriting, 43 |
138 \item mixfix declarations, 52, 53, 56 |
139 \item mixfix declarations, 52, 53, 56 |
139 \item ML, i |
140 \item ML, i |
140 \item {\tt ML} section, 47 |
141 \item {\tt ML} section, 47 |
141 \item {\tt mp} theorem, 27 |
142 \item {\tt mp} theorem, 27, 28 |
142 |
143 |
143 \indexspace |
144 \indexspace |
144 |
145 |
145 \item {\tt Nat} theory, 55 |
146 \item {\tt Nat} theory, 55 |
146 \item {\tt nat} type, 1, 3 |
147 \item {\tt nat} type, 3 |
147 \item {\tt not_def} theorem, 44 |
148 \item {\tt not_def} theorem, 44 |
148 \item {\tt notE} theorem, \bold{45}, 58 |
149 \item {\tt notE} theorem, \bold{45}, 57 |
149 \item {\tt notI} theorem, \bold{44}, 58 |
150 \item {\tt notI} theorem, \bold{44}, 57 |
150 |
151 |
151 \indexspace |
152 \indexspace |
152 |
153 |
153 \item {\tt o} type, 1, 4 |
154 \item {\tt o} type, 3, 4 |
154 \item {\tt ORELSE}, 37 |
155 \item {\tt ORELSE}, 38 |
155 \item overloading, \bold{4}, 53 |
156 \item overloading, \bold{4}, 53 |
156 |
157 |
157 \indexspace |
158 \indexspace |
158 |
159 |
159 \item parameters, \bold{8}, 33 |
160 \item parameters, \bold{8}, 34 |
160 \subitem lifting over, 15 |
161 \subitem lifting over, 15 |
161 \item {\tt Prolog} theory, 61 |
162 \item {\tt Prolog} theory, 61 |
162 \item Prolog interpreter, \bold{60} |
163 \item Prolog interpreter, \bold{60} |
163 \item proof state, 16 |
164 \item proof state, 16 |
164 \item proofs |
165 \item proofs |
165 \subitem commands for, 30 |
166 \subitem commands for, 30 |
166 \item {\tt PROP} symbol, 26 |
167 \item {\tt PROP} symbol, 26 |
167 \item {\tt prop} type, 6, 25, 26 |
168 \item {\tt prop} type, 6, 25, 26 |
168 \item {\tt prth}, 27 |
169 \item {\tt prth}, 27 |
169 \item {\tt prthq}, 27, 28 |
170 \item {\tt prthq}, 27, 29 |
170 \item {\tt prths}, 27 |
171 \item {\tt prths}, 27 |
171 \item {\tt Pure} theory, 47 |
172 \item {\tt Pure} theory, 47 |
172 |
173 |
173 \indexspace |
174 \indexspace |
174 |
175 |
175 \item quantifiers, 5, 8, 33 |
176 \item {\tt qed}, 31, 42, 46 |
|
177 \item quantifiers, 5, 8, 34 |
176 |
178 |
177 \indexspace |
179 \indexspace |
178 |
180 |
179 \item {\tt read_instantiate}, 29 |
181 \item {\tt read_instantiate}, 29 |
180 \item {\tt refl} theorem, 29 |
182 \item {\tt refl} theorem, 29 |
181 \item {\tt REPEAT}, 33, 37, 62, 64 |
183 \item {\tt REPEAT}, 33, 38, 62, 64 |
182 \item {\tt res_inst_tac}, 57, 60 |
184 \item {\tt res_inst_tac}, 57, 59 |
183 \item reserved words, 24 |
185 \item reserved words, 24 |
184 \item resolution, 10, \bold{12} |
186 \item resolution, 10, \bold{12} |
185 \subitem in backward proof, 15 |
187 \subitem in backward proof, 15 |
186 \subitem with instantiation, 57 |
188 \subitem with instantiation, 57 |
187 \item {\tt resolve_tac}, 30, 31, 46, 58 |
189 \item {\tt resolve_tac}, 30, 31, 46, 58 |
188 \item {\tt result}, 30, 42, 46 |
190 \item {\tt result}, 31 |
189 \item {\tt rewrite_goals_tac}, 44 |
191 \item {\tt rewrite_goals_tac}, 44 |
190 \item {\tt rewrite_rule}, 45, 46 |
192 \item {\tt rewrite_rule}, 45, 46 |
191 \item {\tt RL}, 29 |
193 \item {\tt RL}, 29 |
192 \item {\tt RLN}, 29 |
194 \item {\tt RLN}, 29 |
193 \item {\tt RS}, 27, 29, 46 |
195 \item {\tt RS}, 27, 29, 46 |
220 |
222 |
221 \indexspace |
223 \indexspace |
222 |
224 |
223 \item tacticals, \bold{19}, 37 |
225 \item tacticals, \bold{19}, 37 |
224 \item tactics, \bold{19} |
226 \item tactics, \bold{19} |
225 \subitem assumption, 29 |
227 \subitem assumption, 30 |
226 \subitem resolution, 30 |
228 \subitem resolution, 30 |
227 \item {\tt term} class, 3 |
229 \item {\tt term} class, 3 |
228 \item terms |
230 \item terms |
229 \subitem syntax of, 1, \bold{25} |
231 \subitem syntax of, 1, \bold{25} |
230 \item theorems |
232 \item theorems |
231 \subitem basic operations on, \bold{26} |
233 \subitem basic operations on, \bold{27} |
232 \subitem printing of, 27 |
234 \subitem printing of, 27 |
233 \item theories, \bold{9} |
235 \item theories, \bold{9} |
234 \subitem defining, 47--57 |
236 \subitem defining, 47--56 |
235 \item {\tt thm} ML type, 26 |
237 \item {\tt thm} ML type, 27 |
236 \item {\tt topthm}, 42 |
238 \item {\tt topthm}, 42 |
237 \item {\tt Trueprop} constant, 6, 7, 25 |
239 \item {\tt Trueprop} constant, 6, 7, 25 |
238 \item type constraints, 25 |
240 \item type constraints, 25 |
239 \item type constructors, 1 |
241 \item type constructors, 1 |
240 \item type identifiers, 24 |
242 \item type identifiers, 24 |