1 \begin{theindex} |
1 \begin{theindex} |
2 |
2 |
3 \item \ttall, \bold{199} |
3 \item \ttall, \bold{201} |
4 \item \texttt{?}, \bold{199} |
4 \item \texttt{?}, \bold{201} |
5 \item \isasymuniqex, \bold{199} |
5 \item \isasymuniqex, \bold{201} |
6 \item \ttuniquex, \bold{199} |
6 \item \ttuniquex, \bold{201} |
7 \item {\texttt {\&}}, \bold{199} |
7 \item {\texttt {\&}}, \bold{201} |
8 \item \verb$~$, \bold{199} |
8 \item \verb$~$, \bold{201} |
9 \item \verb$~=$, \bold{199} |
9 \item \verb$~=$, \bold{201} |
10 \item \ttor, \bold{199} |
10 \item \ttor, \bold{201} |
11 \item \texttt{[]}, \bold{9} |
11 \item \texttt{[]}, \bold{9} |
12 \item \texttt{\#}, \bold{9} |
12 \item \texttt{\#}, \bold{9} |
13 \item \texttt{\at}, \bold{10}, 199 |
13 \item \texttt{\at}, \bold{10}, 201 |
14 \item \isasymnotin, \bold{199} |
14 \item \isasymnotin, \bold{201} |
15 \item \verb$~:$, \bold{199} |
15 \item \verb$~:$, \bold{201} |
16 \item \isasymInter, \bold{199} |
16 \item \isasymInter, \bold{201} |
17 \item \isasymUnion, \bold{199} |
17 \item \isasymUnion, \bold{201} |
18 \item \isasyminverse, \bold{199} |
18 \item \isasyminverse, \bold{201} |
19 \item \verb$^-1$, \bold{199} |
19 \item \verb$^-1$, \bold{201} |
20 \item \isactrlsup{\isacharasterisk}, \bold{199} |
20 \item \isactrlsup{\isacharasterisk}, \bold{201} |
21 \item \verb$^$\texttt{*}, \bold{199} |
21 \item \verb$^$\texttt{*}, \bold{201} |
22 \item \isasymAnd, \bold{12}, \bold{199} |
22 \item \isasymAnd, \bold{12}, \bold{201} |
23 \item \ttAnd, \bold{199} |
23 \item \ttAnd, \bold{201} |
24 \item \isasymrightleftharpoons, 26 |
24 \item \isasymrightleftharpoons, 55 |
25 \item \isasymrightharpoonup, 26 |
25 \item \isasymrightharpoonup, 55 |
26 \item \isasymleftharpoondown, 26 |
26 \item \isasymleftharpoondown, 55 |
27 \item \emph {$\Rightarrow $}, \bold{5} |
27 \item \emph {$\Rightarrow $}, \bold{5} |
28 \item \ttlbr, \bold{199} |
28 \item \ttlbr, \bold{201} |
29 \item \ttrbr, \bold{199} |
29 \item \ttrbr, \bold{201} |
30 \item \texttt {\%}, \bold{199} |
30 \item \texttt {\%}, \bold{201} |
31 \item \texttt {;}, \bold{7} |
31 \item \texttt {;}, \bold{7} |
32 \item \isa {()} (constant), 24 |
32 \item \isa {()} (constant), 24 |
33 \item \isa {+} (tactical), 89 |
33 \item \isa {+} (tactical), 91 |
34 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
34 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
35 \item \isa {?} (tactical), 89 |
35 \item \isa {?} (tactical), 91 |
36 \item \texttt{|} (tactical), 89 |
36 \item \texttt{|} (tactical), 91 |
37 |
37 |
38 \indexspace |
38 \indexspace |
39 |
39 |
40 \item \isa {0} (constant), 22, 23, 140 |
40 \item \isa {0} (constant), 22, 23, 142 |
41 \item \isa {1} (constant), 23, 140, 141 |
41 \item \isa {1} (constant), 23, 142, 143 |
42 |
42 |
43 \indexspace |
43 \indexspace |
44 |
44 |
45 \item abandoning a proof, \bold{13} |
45 \item abandoning a proof, \bold{13} |
46 \item abandoning a theory, \bold{16} |
46 \item abandoning a theory, \bold{16} |
47 \item \isa {abs} (constant), 143 |
47 \item \isa {abs} (constant), 145 |
48 \item \texttt {abs}, \bold{199} |
48 \item \texttt {abs}, \bold{201} |
49 \item absolute value, 143 |
49 \item absolute value, 145 |
50 \item \isa {add} (modifier), 29 |
50 \item \isa {add} (modifier), 29 |
51 \item \isa {add_ac} (theorems), 142 |
51 \item \isa {add_ac} (theorems), 144 |
52 \item \isa {add_assoc} (theorem), \bold{142} |
52 \item \isa {add_assoc} (theorem), \bold{144} |
53 \item \isa {add_commute} (theorem), \bold{142} |
53 \item \isa {add_commute} (theorem), \bold{144} |
54 \item \isa {add_mult_distrib} (theorem), \bold{141} |
54 \item \isa {add_mult_distrib} (theorem), \bold{143} |
55 \item \texttt {ALL}, \bold{199} |
55 \item \texttt {ALL}, \bold{201} |
56 \item \isa {All} (constant), 99 |
56 \item \isa {All} (constant), 101 |
57 \item \isa {allE} (theorem), \bold{71} |
57 \item \isa {allE} (theorem), \bold{73} |
58 \item \isa {allI} (theorem), \bold{70} |
58 \item \isa {allI} (theorem), \bold{72} |
59 \item append function, 10--14 |
59 \item append function, 10--14 |
60 \item \isacommand {apply} (command), 15 |
60 \item \isacommand {apply} (command), 15 |
61 \item \isa {arg_cong} (theorem), \bold{86} |
61 \item \isa {arg_cong} (theorem), \bold{88} |
62 \item \isa {arith} (method), 23, 139 |
62 \item \isa {arith} (method), 23, 141 |
63 \item arithmetic operations |
63 \item arithmetic operations |
64 \subitem for \protect\isa{nat}, 23 |
64 \subitem for \protect\isa{nat}, 23 |
65 \item \textsc {ascii} symbols, \bold{199} |
65 \item \textsc {ascii} symbols, \bold{201} |
66 \item associative-commutative function, 166 |
66 \item associative-commutative function, 168 |
67 \item \isa {assumption} (method), 59 |
67 \item \isa {assumption} (method), 61 |
68 \item assumptions |
68 \item assumptions |
69 \subitem of subgoal, 12 |
69 \subitem of subgoal, 12 |
70 \subitem renaming, 72--73 |
70 \subitem renaming, 74--75 |
71 \subitem reusing, 73 |
71 \subitem reusing, 75 |
72 \item \isa {auto} (method), 38, 82 |
72 \item \isa {auto} (method), 38, 84 |
73 \item \isa {axclass}, 154--160 |
73 \item \isa {axclass}, 156--162 |
74 \item axiom of choice, 76 |
74 \item axiom of choice, 78 |
75 \item axiomatic type classes, 154--160 |
75 \item axiomatic type classes, 156--162 |
76 |
76 |
77 \indexspace |
77 \indexspace |
78 |
78 |
79 \item \isacommand {back} (command), 68 |
79 \item \isacommand {back} (command), 70 |
80 \item \isa {Ball} (constant), 99 |
80 \item \isa {Ball} (constant), 101 |
81 \item \isa {ballI} (theorem), \bold{98} |
81 \item \isa {ballI} (theorem), \bold{100} |
82 \item \isa {best} (method), 82 |
82 \item \isa {best} (method), 84 |
83 \item \isa {Bex} (constant), 99 |
83 \item \isa {Bex} (constant), 101 |
84 \item \isa {bexE} (theorem), \bold{98} |
84 \item \isa {bexE} (theorem), \bold{100} |
85 \item \isa {bexI} (theorem), \bold{98} |
85 \item \isa {bexI} (theorem), \bold{100} |
86 \item \isa {bij_def} (theorem), \bold{100} |
86 \item \isa {bij_def} (theorem), \bold{102} |
87 \item bijections, 100 |
87 \item bijections, 102 |
88 \item binary trees, 18 |
88 \item binary trees, 18 |
89 \item binomial coefficients, 99 |
89 \item binomial coefficients, 101 |
90 \item bisimulations, 106 |
90 \item bisimulations, 108 |
91 \item \isa {blast} (method), 79--80, 82 |
91 \item \isa {blast} (method), 81--82, 84 |
92 \item \isa {bool} (type), 4, 5 |
92 \item \isa {bool} (type), 4, 5 |
93 \item boolean expressions example, 20--22 |
93 \item boolean expressions example, 20--22 |
94 \item \isa {bspec} (theorem), \bold{98} |
94 \item \isa {bspec} (theorem), \bold{100} |
95 \item \isacommand{by} (command), 63 |
95 \item \isacommand{by} (command), 65 |
96 |
96 |
97 \indexspace |
97 \indexspace |
98 |
98 |
99 \item \isa {card} (constant), 99 |
99 \item \isa {card} (constant), 101 |
100 \item \isa {card_Pow} (theorem), \bold{99} |
100 \item \isa {card_Pow} (theorem), \bold{101} |
101 \item \isa {card_Un_Int} (theorem), \bold{99} |
101 \item \isa {card_Un_Int} (theorem), \bold{101} |
102 \item cardinality, 99 |
102 \item cardinality, 101 |
103 \item \isa {case} (symbol), 32, 33 |
103 \item \isa {case} (symbol), 32, 33 |
104 \item \isa {case} expressions, 5, 6, 18 |
104 \item \isa {case} expressions, 5, 6, 18 |
105 \item case distinctions, 19 |
105 \item case distinctions, 19 |
106 \item case splits, \bold{31} |
106 \item case splits, \bold{31} |
107 \item \isa {case_tac} (method), 19, 91, 147 |
107 \item \isa {case_tac} (method), 19, 93, 149 |
108 \item \isa {cases} (method), 152 |
108 \item \isa {cases} (method), 154 |
109 \item \isa {clarify} (method), 81, 82 |
109 \item \isa {clarify} (method), 83, 84 |
110 \item \isa {clarsimp} (method), 81, 82 |
110 \item \isa {clarsimp} (method), 83, 84 |
111 \item \isa {classical} (theorem), \bold{63} |
111 \item \isa {classical} (theorem), \bold{65} |
112 \item coinduction, \bold{106} |
112 \item coinduction, \bold{108} |
113 \item \isa {Collect} (constant), 99 |
113 \item \isa {Collect} (constant), 101 |
114 \item compiling expressions example, 36--38 |
114 \item compiling expressions example, 36--38 |
115 \item \isa {Compl_iff} (theorem), \bold{96} |
115 \item \isa {Compl_iff} (theorem), \bold{98} |
116 \item complement |
116 \item complement |
117 \subitem of a set, 95 |
117 \subitem of a set, 97 |
118 \item composition |
118 \item composition |
119 \subitem of functions, \bold{100} |
119 \subitem of functions, \bold{102} |
120 \subitem of relations, \bold{102} |
120 \subitem of relations, \bold{104} |
121 \item conclusion |
121 \item conclusion |
122 \subitem of subgoal, 12 |
122 \subitem of subgoal, 12 |
123 \item conditional expressions, \see{\isa{if} expressions}{1} |
123 \item conditional expressions, \see{\isa{if} expressions}{1} |
124 \item conditional simplification rules, 31 |
124 \item conditional simplification rules, 31 |
125 \item \isa {cong} (attribute), 166 |
125 \item \isa {cong} (attribute), 168 |
126 \item congruence rules, \bold{165} |
126 \item congruence rules, \bold{167} |
127 \item \isa {conjE} (theorem), \bold{61} |
127 \item \isa {conjE} (theorem), \bold{63} |
128 \item \isa {conjI} (theorem), \bold{58} |
128 \item \isa {conjI} (theorem), \bold{60} |
129 \item \isa {Cons} (constant), 9 |
129 \item \isa {Cons} (constant), 9 |
130 \item \isacommand {constdefs} (command), 25 |
130 \item \isacommand {constdefs} (command), 25 |
131 \item \isacommand {consts} (command), 10 |
131 \item \isacommand {consts} (command), 10 |
132 \item contrapositives, 63 |
132 \item contrapositives, 65 |
133 \item converse |
133 \item converse |
134 \subitem of a relation, \bold{102} |
134 \subitem of a relation, \bold{104} |
135 \item \isa {converse_iff} (theorem), \bold{102} |
135 \item \isa {converse_iff} (theorem), \bold{104} |
136 \item CTL, 111--116, 181--183 |
136 \item CTL, 113--118, 183--185 |
137 |
137 |
138 \indexspace |
138 \indexspace |
139 |
139 |
140 \item \isacommand {datatype} (command), 9, 38--43 |
140 \item \isacommand {datatype} (command), 9, 38--43 |
141 \item datatypes, 17--22 |
141 \item datatypes, 17--22 |
142 \subitem and nested recursion, 40, 44 |
142 \subitem and nested recursion, 40, 44 |
143 \subitem mutually recursive, 38 |
143 \subitem mutually recursive, 38 |
144 \subitem nested, 170 |
144 \subitem nested, 172 |
145 \item \isacommand {defer} (command), 16, 90 |
145 \item \isacommand {defer} (command), 16, 92 |
146 \item Definitional Approach, 26 |
146 \item Definitional Approach, 26 |
147 \item definitions, \bold{25} |
147 \item definitions, \bold{25} |
148 \subitem unfolding, \bold{30} |
148 \subitem unfolding, \bold{30} |
149 \item \isacommand {defs} (command), 25 |
149 \item \isacommand {defs} (command), 25 |
150 \item \isa {del} (modifier), 29 |
150 \item \isa {del} (modifier), 29 |
151 \item description operators, 75--77 |
151 \item description operators, 77--79 |
152 \item descriptions |
152 \item descriptions |
153 \subitem definite, 75 |
153 \subitem definite, 77 |
154 \subitem indefinite, 76 |
154 \subitem indefinite, 78 |
155 \item \isa {dest} (attribute), 92 |
155 \item \isa {dest} (attribute), 94 |
156 \item destruction rules, 61 |
156 \item destruction rules, 63 |
157 \item \isa {diff_mult_distrib} (theorem), \bold{141} |
157 \item \isa {diff_mult_distrib} (theorem), \bold{143} |
158 \item difference |
158 \item difference |
159 \subitem of sets, \bold{96} |
159 \subitem of sets, \bold{98} |
160 \item \isa {disjCI} (theorem), \bold{64} |
160 \item \isa {disjCI} (theorem), \bold{66} |
161 \item \isa {disjE} (theorem), \bold{60} |
161 \item \isa {disjE} (theorem), \bold{62} |
162 \item \isa {div} (symbol), 23 |
162 \item \isa {div} (symbol), 23 |
163 \item divides relation, 74, 85, 91--94, 142 |
163 \item divides relation, 76, 87, 93--96, 144 |
164 \item division |
164 \item division |
165 \subitem by negative numbers, 143 |
165 \subitem by negative numbers, 145 |
166 \subitem by zero, 142 |
166 \subitem by zero, 144 |
167 \subitem for type \protect\isa{nat}, 141 |
167 \subitem for type \protect\isa{nat}, 143 |
168 \item domain |
168 \item domain |
169 \subitem of a relation, 102 |
169 \subitem of a relation, 104 |
170 \item \isa {Domain_iff} (theorem), \bold{102} |
170 \item \isa {Domain_iff} (theorem), \bold{104} |
171 \item \isacommand {done} (command), 13 |
171 \item \isacommand {done} (command), 13 |
172 \item \isa {drule_tac} (method), 66, 86 |
172 \item \isa {drule_tac} (method), 68, 88 |
173 \item \isa {dvd_add} (theorem), \bold{142} |
173 \item \isa {dvd_add} (theorem), \bold{144} |
174 \item \isa {dvd_anti_sym} (theorem), \bold{142} |
174 \item \isa {dvd_anti_sym} (theorem), \bold{144} |
175 \item \isa {dvd_def} (theorem), \bold{142} |
175 \item \isa {dvd_def} (theorem), \bold{144} |
176 |
176 |
177 \indexspace |
177 \indexspace |
178 |
178 |
179 \item \isa {elim!} (attribute), 121 |
179 \item \isa {elim!} (attribute), 123 |
180 \item elimination rules, 59--60 |
180 \item elimination rules, 61--62 |
181 \item \isacommand {end} (command), 14 |
181 \item \isacommand {end} (command), 14 |
182 \item \isa {Eps} (constant), 99 |
182 \item \isa {Eps} (constant), 101 |
183 \item equality, 5 |
183 \item equality, 5 |
184 \subitem of functions, \bold{99} |
184 \subitem of functions, \bold{101} |
185 \subitem of records, 151 |
185 \subitem of records, 153 |
186 \subitem of sets, \bold{96} |
186 \subitem of sets, \bold{98} |
187 \item \isa {equalityE} (theorem), \bold{96} |
187 \item \isa {equalityE} (theorem), \bold{98} |
188 \item \isa {equalityI} (theorem), \bold{96} |
188 \item \isa {equalityI} (theorem), \bold{98} |
189 \item \isa {erule} (method), 60 |
189 \item \isa {erule} (method), 62 |
190 \item \isa {erule_tac} (method), 66 |
190 \item \isa {erule_tac} (method), 68 |
191 \item Euclid's algorithm, 91--94 |
191 \item Euclid's algorithm, 93--96 |
192 \item even numbers |
192 \item even numbers |
193 \subitem defining inductively, 117--121 |
193 \subitem defining inductively, 119--123 |
194 \item \texttt {EX}, \bold{199} |
194 \item \texttt {EX}, \bold{201} |
195 \item \isa {Ex} (constant), 99 |
195 \item \isa {Ex} (constant), 101 |
196 \item \isa {exE} (theorem), \bold{72} |
196 \item \isa {exE} (theorem), \bold{74} |
197 \item \isa {exI} (theorem), \bold{72} |
197 \item \isa {exI} (theorem), \bold{74} |
198 \item \isa {ext} (theorem), \bold{99} |
198 \item \isa {ext} (theorem), \bold{101} |
199 \item \isa {extend} (constant), 153 |
199 \item \isa {extend} (constant), 155 |
200 \item extensionality |
200 \item extensionality |
201 \subitem for functions, \bold{99, 100} |
201 \subitem for functions, \bold{101, 102} |
202 \subitem for records, 151 |
202 \subitem for records, 153 |
203 \subitem for sets, \bold{96} |
203 \subitem for sets, \bold{98} |
204 \item \ttEXU, \bold{199} |
204 \item \ttEXU, \bold{201} |
205 |
205 |
206 \indexspace |
206 \indexspace |
207 |
207 |
208 \item \isa {False} (constant), 5 |
208 \item \isa {False} (constant), 5 |
209 \item \isa {fast} (method), 82, 114 |
209 \item \isa {fast} (method), 84, 116 |
210 \item Fibonacci function, 47 |
210 \item Fibonacci function, 47 |
211 \item \isa {fields} (constant), 153 |
211 \item \isa {fields} (constant), 155 |
212 \item \isa {finite} (symbol), 99 |
212 \item \isa {finite} (symbol), 101 |
213 \item \isa {Finites} (constant), 99 |
213 \item \isa {Finites} (constant), 101 |
214 \item fixed points, 106 |
214 \item fixed points, 108 |
215 \item flags, 5, 6, 33 |
215 \item flags, 5, 6, 33 |
216 \subitem setting and resetting, 5 |
216 \subitem setting and resetting, 5 |
217 \item \isa {force} (method), 81, 82 |
217 \item \isa {force} (method), 83, 84 |
218 \item formulae, 5--6 |
218 \item formulae, 5--6 |
219 \item forward proof, 82--88 |
219 \item forward proof, 84--90 |
220 \item \isa {frule} (method), 73 |
220 \item \isa {frule} (method), 75 |
221 \item \isa {frule_tac} (method), 66 |
221 \item \isa {frule_tac} (method), 68 |
222 \item \isa {fst} (constant), 24 |
222 \item \isa {fst} (constant), 24 |
223 \item function types, 5 |
223 \item function types, 5 |
224 \item functions, 99--101 |
224 \item functions, 101--103 |
225 \subitem partial, 172 |
225 \subitem partial, 174 |
226 \subitem total, 11, 46--52 |
226 \subitem total, 11, 46--52 |
227 \subitem underdefined, 173 |
227 \subitem underdefined, 175 |
228 |
228 |
229 \indexspace |
229 \indexspace |
230 |
230 |
231 \item \isa {gcd} (constant), 83--84, 91--94 |
231 \item \isa {gcd} (constant), 85--86, 93--96 |
232 \item generalizing for induction, 119 |
232 \item generalizing for induction, 121 |
233 \item generalizing induction formulae, 35 |
233 \item generalizing induction formulae, 35 |
234 \item Girard, Jean-Yves, \fnote{61} |
234 \item Girard, Jean-Yves, \fnote{63} |
235 \item Gordon, Mike, 3 |
235 \item Gordon, Mike, 3 |
236 \item grammars |
236 \item grammars |
237 \subitem defining inductively, 130--135 |
237 \subitem defining inductively, 132--137 |
238 \item ground terms example, 125--130 |
238 \item ground terms example, 127--132 |
239 |
239 |
240 \indexspace |
240 \indexspace |
241 |
241 |
242 \item \isa {hd} (constant), 17, 37 |
242 \item \isa {hd} (constant), 17, 37 |
243 \item Hilbert's $\varepsilon$-operator, 76 |
243 \item Hilbert's $\varepsilon$-operator, 78 |
244 \item HOLCF, 43 |
244 \item HOLCF, 43 |
245 \item Hopcroft, J. E., 135 |
245 \item Hopcroft, J. E., 137 |
246 \item \isa {hypreal} (type), 145 |
246 \item \isa {hypreal} (type), 147 |
247 |
247 |
248 \indexspace |
248 \indexspace |
249 |
249 |
250 \item \isa {Id_def} (theorem), \bold{102} |
250 \item \isa {Id_def} (theorem), \bold{104} |
251 \item \isa {id_def} (theorem), \bold{100} |
251 \item \isa {id_def} (theorem), \bold{102} |
252 \item identifiers, \bold{6} |
252 \item identifiers, \bold{6} |
253 \subitem qualified, \bold{4} |
253 \subitem qualified, \bold{4} |
254 \item identity function, \bold{100} |
254 \item identity function, \bold{102} |
255 \item identity relation, \bold{102} |
255 \item identity relation, \bold{104} |
256 \item \isa {if} expressions, 5, 6 |
256 \item \isa {if} expressions, 5, 6 |
257 \subitem simplification of, 33 |
257 \subitem simplification of, 33 |
258 \subitem splitting of, 31, 49 |
258 \subitem splitting of, 31, 49 |
259 \item if-and-only-if, 6 |
259 \item if-and-only-if, 6 |
260 \item \isa {iff} (attribute), 80, 92, 120 |
260 \item \isa {iff} (attribute), 82, 94, 122 |
261 \item \isa {iffD1} (theorem), \bold{84} |
261 \item \isa {iffD1} (theorem), \bold{86} |
262 \item \isa {iffD2} (theorem), \bold{84} |
262 \item \isa {iffD2} (theorem), \bold{86} |
263 \item image |
263 \item image |
264 \subitem under a function, \bold{101} |
264 \subitem under a function, \bold{103} |
265 \subitem under a relation, \bold{102} |
265 \subitem under a relation, \bold{104} |
266 \item \isa {image_def} (theorem), \bold{101} |
266 \item \isa {image_def} (theorem), \bold{103} |
267 \item \isa {Image_iff} (theorem), \bold{102} |
267 \item \isa {Image_iff} (theorem), \bold{104} |
268 \item \isa {impI} (theorem), \bold{62} |
268 \item \isa {impI} (theorem), \bold{64} |
269 \item implication, 62--63 |
269 \item implication, 64--65 |
270 \item \isa {ind_cases} (method), 121 |
270 \item \isa {ind_cases} (method), 123 |
271 \item \isa {induct_tac} (method), 12, 19, 52, 180 |
271 \item \isa {induct_tac} (method), 12, 19, 52, 182 |
272 \item induction, 176--183 |
272 \item induction, 178--185 |
273 \subitem complete, 178 |
273 \subitem complete, 180 |
274 \subitem deriving new schemas, 180 |
274 \subitem deriving new schemas, 182 |
275 \subitem on a term, 177 |
275 \subitem on a term, 179 |
276 \subitem recursion, 51--52 |
276 \subitem recursion, 51--52 |
277 \subitem structural, 19 |
277 \subitem structural, 19 |
278 \subitem well-founded, 105 |
278 \subitem well-founded, 107 |
279 \item induction heuristics, 34--36 |
279 \item induction heuristics, 34--36 |
280 \item \isacommand {inductive} (command), 117 |
280 \item \isacommand {inductive} (command), 119 |
281 \item inductive definition |
281 \item inductive definition |
282 \subitem simultaneous, 131 |
282 \subitem simultaneous, 133 |
283 \item inductive definitions, 117--135 |
283 \item inductive definitions, 119--137 |
284 \item \isacommand {inductive\_cases} (command), 121, 129 |
284 \item \isacommand {inductive\_cases} (command), 123, 131 |
285 \item infinitely branching trees, 43 |
285 \item infinitely branching trees, 43 |
286 \item \isacommand{infixr} (annotation), 10 |
286 \item \isacommand{infixr} (annotation), 10 |
287 \item \isa {inj_on_def} (theorem), \bold{100} |
287 \item \isa {inj_on_def} (theorem), \bold{102} |
288 \item injections, 100 |
288 \item injections, 102 |
289 \item \isa {insert} (constant), 97 |
289 \item \isa {insert} (constant), 99 |
290 \item \isa {insert} (method), 87--88 |
290 \item \isa {insert} (method), 89--90 |
291 \item instance, \bold{155} |
291 \item instance, \bold{158} |
292 \item \texttt {INT}, \bold{199} |
292 \item \texttt {INT}, \bold{201} |
293 \item \texttt {Int}, \bold{199} |
293 \item \texttt {Int}, \bold{201} |
294 \item \isa {int} (type), 143--144 |
294 \item \isa {int} (type), 145--146 |
295 \item \isa {INT_iff} (theorem), \bold{98} |
295 \item \isa {INT_iff} (theorem), \bold{100} |
296 \item \isa {IntD1} (theorem), \bold{95} |
296 \item \isa {IntD1} (theorem), \bold{97} |
297 \item \isa {IntD2} (theorem), \bold{95} |
297 \item \isa {IntD2} (theorem), \bold{97} |
298 \item integers, 143--144 |
298 \item integers, 145--146 |
299 \item \isa {INTER} (constant), 99 |
299 \item \isa {INTER} (constant), 101 |
300 \item \texttt {Inter}, \bold{199} |
300 \item \texttt {Inter}, \bold{201} |
301 \item \isa {Inter_iff} (theorem), \bold{98} |
301 \item \isa {Inter_iff} (theorem), \bold{100} |
302 \item intersection, 95 |
302 \item intersection, 97 |
303 \subitem indexed, 98 |
303 \subitem indexed, 100 |
304 \item \isa {IntI} (theorem), \bold{95} |
304 \item \isa {IntI} (theorem), \bold{97} |
305 \item \isa {intro} (method), 64 |
305 \item \isa {intro} (method), 66 |
306 \item \isa {intro!} (attribute), 118 |
306 \item \isa {intro!} (attribute), 120 |
307 \item \isa {intro_classes} (method), 155 |
307 \item \isa {intro_classes} (method), 158 |
308 \item introduction rules, 58--59 |
308 \item introduction rules, 60--61 |
309 \item \isa {inv} (constant), 76 |
309 \item \isa {inv} (constant), 78 |
310 \item \isa {inv_image_def} (theorem), \bold{105} |
310 \item \isa {inv_image_def} (theorem), \bold{107} |
311 \item inverse |
311 \item inverse |
312 \subitem of a function, \bold{100} |
312 \subitem of a function, \bold{102} |
313 \subitem of a relation, \bold{102} |
313 \subitem of a relation, \bold{104} |
314 \item inverse image |
314 \item inverse image |
315 \subitem of a function, 101 |
315 \subitem of a function, 103 |
316 \subitem of a relation, 104 |
316 \subitem of a relation, 106 |
317 \item \isa {itrev} (constant), 34 |
317 \item \isa {itrev} (constant), 34 |
318 |
318 |
319 \indexspace |
319 \indexspace |
320 |
320 |
321 \item \isacommand {kill} (command), 16 |
321 \item \isacommand {kill} (command), 16 |
322 |
322 |
323 \indexspace |
323 \indexspace |
324 |
324 |
325 \item $\lambda$ expressions, 5 |
325 \item $\lambda$ expressions, 5 |
326 \item LCF, 43 |
326 \item LCF, 43 |
327 \item \isa {LEAST} (symbol), 23, 75 |
327 \item \isa {LEAST} (symbol), 23, 77 |
328 \item least number operator, \see{\protect\isa{LEAST}}{75} |
328 \item least number operator, \see{\protect\isa{LEAST}}{77} |
329 \item \isacommand {lemma} (command), 13 |
329 \item \isacommand {lemma} (command), 13 |
330 \item \isacommand {lemmas} (command), 83, 92 |
330 \item \isacommand {lemmas} (command), 85, 94 |
331 \item \isa {length} (symbol), 18 |
331 \item \isa {length} (symbol), 18 |
332 \item \isa {length_induct}, \bold{180} |
332 \item \isa {length_induct}, \bold{182} |
333 \item \isa {less_than} (constant), 104 |
333 \item \isa {less_than} (constant), 106 |
334 \item \isa {less_than_iff} (theorem), \bold{104} |
334 \item \isa {less_than_iff} (theorem), \bold{106} |
335 \item \isa {let} expressions, 5, 6, 31 |
335 \item \isa {let} expressions, 5, 6, 31 |
336 \item \isa {Let_def} (theorem), 31 |
336 \item \isa {Let_def} (theorem), 31 |
337 \item \isa {lex_prod_def} (theorem), \bold{105} |
337 \item \isa {lex_prod_def} (theorem), \bold{107} |
338 \item lexicographic product, \bold{105}, 168 |
338 \item lexicographic product, \bold{107}, 170 |
339 \item {\texttt{lfp}} |
339 \item {\texttt{lfp}} |
340 \subitem applications of, \see{CTL}{106} |
340 \subitem applications of, \see{CTL}{108} |
341 \item Library, 4 |
341 \item Library, 4 |
342 \item linear arithmetic, 22--24, 139 |
342 \item linear arithmetic, 22--24, 141 |
343 \item \isa {List} (theory), 17 |
343 \item \isa {List} (theory), 17 |
344 \item \isa {list} (type), 5, 9, 17 |
344 \item \isa {list} (type), 5, 9, 17 |
345 \item \isa {list.split} (theorem), 32 |
345 \item \isa {list.split} (theorem), 32 |
346 \item \isa {lists_mono} (theorem), \bold{127} |
346 \item \isa {lists_mono} (theorem), \bold{129} |
347 \item Lowe, Gavin, 186--187 |
347 \item Lowe, Gavin, 188--189 |
348 |
348 |
349 \indexspace |
349 \indexspace |
350 |
350 |
351 \item \isa {Main} (theory), 4 |
351 \item \isa {Main} (theory), 4 |
352 \item major premise, \bold{65} |
352 \item major premise, \bold{67} |
353 \item \isa {make} (constant), 153 |
353 \item \isa {make} (constant), 155 |
354 \item \isa {max} (constant), 23, 24 |
354 \item \isa {max} (constant), 23, 24 |
355 \item measure functions, 47, 104 |
355 \item measure functions, 47, 106 |
356 \item \isa {measure_def} (theorem), \bold{105} |
356 \item \isa {measure_def} (theorem), \bold{107} |
357 \item meta-logic, \bold{70} |
357 \item meta-logic, \bold{72} |
358 \item methods, \bold{16} |
358 \item methods, \bold{16} |
359 \item \isa {min} (constant), 23, 24 |
359 \item \isa {min} (constant), 23, 24 |
360 \item \isa {mod} (symbol), 23 |
360 \item \isa {mod} (symbol), 23 |
361 \item \isa {mod_div_equality} (theorem), \bold{141} |
361 \item \isa {mod_div_equality} (theorem), \bold{143} |
362 \item \isa {mod_mult_distrib} (theorem), \bold{141} |
362 \item \isa {mod_mult_distrib} (theorem), \bold{143} |
363 \item model checking example, 106--116 |
363 \item model checking example, 108--118 |
364 \item \emph{modus ponens}, 57, 62 |
364 \item \emph{modus ponens}, 59, 64 |
365 \item \isa {mono_def} (theorem), \bold{106} |
365 \item \isa {mono_def} (theorem), \bold{108} |
366 \item monotone functions, \bold{106}, 129 |
366 \item monotone functions, \bold{108}, 131 |
367 \subitem and inductive definitions, 127--128 |
367 \subitem and inductive definitions, 129--130 |
368 \item \isa {more} (constant), 148--150 |
368 \item \isa {more} (constant), 150, 152 |
369 \item \isa {mp} (theorem), \bold{62} |
369 \item \isa {mp} (theorem), \bold{64} |
370 \item \isa {mult_ac} (theorems), 142 |
370 \item \isa {mult_ac} (theorems), 144 |
371 \item multiple inheritance, \bold{159} |
371 \item multiple inheritance, \bold{161} |
372 \item multiset ordering, \bold{105} |
372 \item multiset ordering, \bold{107} |
373 |
373 |
374 \indexspace |
374 \indexspace |
375 |
375 |
376 \item \isa {nat} (type), 4, 22, 141--143 |
376 \item \isa {nat} (type), 4, 22, 143--145 |
377 \item \isa {nat_less_induct} (theorem), 178 |
377 \item \isa {nat_less_induct} (theorem), 180 |
378 \item natural deduction, 57--58 |
378 \item natural deduction, 59--60 |
379 \item natural numbers, 22, 141--143 |
379 \item natural numbers, 22, 143--145 |
380 \item Needham-Schroeder protocol, 185--187 |
380 \item Needham-Schroeder protocol, 187--189 |
381 \item negation, 63--65 |
381 \item negation, 65--67 |
382 \item \isa {Nil} (constant), 9 |
382 \item \isa {Nil} (constant), 9 |
383 \item \isa {no_asm} (modifier), 29 |
383 \item \isa {no_asm} (modifier), 29 |
384 \item \isa {no_asm_simp} (modifier), 30 |
384 \item \isa {no_asm_simp} (modifier), 30 |
385 \item \isa {no_asm_use} (modifier), 30 |
385 \item \isa {no_asm_use} (modifier), 30 |
386 \item non-standard reals, 145 |
386 \item non-standard reals, 147 |
387 \item \isa {None} (constant), \bold{24} |
387 \item \isa {None} (constant), \bold{24} |
388 \item \isa {notE} (theorem), \bold{63} |
388 \item \isa {notE} (theorem), \bold{65} |
389 \item \isa {notI} (theorem), \bold{63} |
389 \item \isa {notI} (theorem), \bold{65} |
390 \item numbers, 139--145 |
390 \item numbers, 141--147 |
391 \item numeric literals, 140 |
391 \item numeric literals, 142 |
392 \subitem for type \protect\isa{nat}, 141 |
392 \subitem for type \protect\isa{nat}, 143 |
393 \subitem for type \protect\isa{real}, 145 |
393 \subitem for type \protect\isa{real}, 147 |
394 |
394 |
395 \indexspace |
395 \indexspace |
396 |
396 |
397 \item \isa {O} (symbol), 102 |
397 \item \isa {O} (symbol), 104 |
398 \item \texttt {o}, \bold{199} |
398 \item \texttt {o}, \bold{201} |
399 \item \isa {o_def} (theorem), \bold{100} |
399 \item \isa {o_def} (theorem), \bold{102} |
400 \item \isa {OF} (attribute), 85--86 |
400 \item \isa {OF} (attribute), 87--88 |
401 \item \isa {of} (attribute), 83, 86 |
401 \item \isa {of} (attribute), 85, 88 |
402 \item \isa {only} (modifier), 29 |
402 \item \isa {only} (modifier), 29 |
403 \item \isacommand {oops} (command), 13 |
403 \item \isacommand {oops} (command), 13 |
404 \item \isa {option} (type), \bold{24} |
404 \item \isa {option} (type), \bold{24} |
405 \item ordered rewriting, \bold{166} |
405 \item ordered rewriting, \bold{168} |
406 \item overloading, 23, 154--157 |
406 \item overloading, 23, 157--159 |
407 \subitem and arithmetic, 140 |
407 \subitem and arithmetic, 142 |
408 |
408 |
409 \indexspace |
409 \indexspace |
410 |
410 |
411 \item pairs and tuples, 24, 145--148 |
411 \item pairs and tuples, 24, 147--150 |
412 \item parent theories, \bold{4} |
412 \item parent theories, \bold{4} |
413 \item pattern matching |
413 \item pattern matching |
414 \subitem and \isacommand{recdef}, 47 |
414 \subitem and \isacommand{recdef}, 47 |
415 \item patterns |
415 \item patterns |
416 \subitem higher-order, \bold{167} |
416 \subitem higher-order, \bold{169} |
417 \item PDL, 108--110 |
417 \item PDL, 110--112 |
418 \item \isacommand {pr} (command), 16, 90 |
418 \item \isacommand {pr} (command), 16, 92 |
419 \item \isacommand {prefer} (command), 16, 90 |
419 \item \isacommand {prefer} (command), 16, 92 |
420 \item primitive recursion, \see{recursion, primitive}{1} |
420 \item primitive recursion, \see{recursion, primitive}{1} |
421 \item \isacommand {primrec} (command), 10, 18, 38--43 |
421 \item \isacommand {primrec} (command), 10, 18, 38--43 |
422 \item product type, \see{pairs and tuples}{1} |
422 \item product type, \see{pairs and tuples}{1} |
423 \item Proof General, \bold{7} |
423 \item Proof General, \bold{7} |
424 \item proof state, 12 |
424 \item proof state, 12 |
425 \item proofs |
425 \item proofs |
426 \subitem abandoning, \bold{13} |
426 \subitem abandoning, \bold{13} |
427 \subitem examples of failing, 77--79 |
427 \subitem examples of failing, 79--81 |
428 \item protocols |
428 \item protocols |
429 \subitem security, 185--195 |
429 \subitem security, 187--197 |
430 |
430 |
431 \indexspace |
431 \indexspace |
432 |
432 |
433 \item quantifiers, 6 |
433 \item quantifiers, 6 |
434 \subitem and inductive definitions, 125--127 |
434 \subitem and inductive definitions, 127--129 |
435 \subitem existential, 72 |
435 \subitem existential, 74 |
436 \subitem for sets, 98 |
436 \subitem for sets, 100 |
437 \subitem instantiating, 74 |
437 \subitem instantiating, 76 |
438 \subitem universal, 69--72 |
438 \subitem universal, 71--74 |
439 |
439 |
440 \indexspace |
440 \indexspace |
441 |
441 |
442 \item \isa {r_into_rtrancl} (theorem), \bold{102} |
442 \item \isa {r_into_rtrancl} (theorem), \bold{104} |
443 \item \isa {r_into_trancl} (theorem), \bold{103} |
443 \item \isa {r_into_trancl} (theorem), \bold{105} |
444 \item range |
444 \item range |
445 \subitem of a function, 101 |
445 \subitem of a function, 103 |
446 \subitem of a relation, 102 |
446 \subitem of a relation, 104 |
447 \item \isa {range} (symbol), 101 |
447 \item \isa {range} (symbol), 103 |
448 \item \isa {Range_iff} (theorem), \bold{102} |
448 \item \isa {Range_iff} (theorem), \bold{104} |
449 \item \isa {Real} (theory), 145 |
449 \item \isa {Real} (theory), 147 |
450 \item \isa {real} (type), 144--145 |
450 \item \isa {real} (type), 146--147 |
451 \item real numbers, 144--145 |
451 \item real numbers, 146--147 |
452 \item \isacommand {recdef} (command), 46--52, 104, 168--176 |
452 \item \isacommand {recdef} (command), 46--52, 106, 170--178 |
453 \subitem and numeric literals, 140 |
453 \subitem and numeric literals, 142 |
454 \item \isa {recdef_cong} (attribute), 172 |
454 \item \isa {recdef_cong} (attribute), 174 |
455 \item \isa {recdef_simp} (attribute), 49 |
455 \item \isa {recdef_simp} (attribute), 49 |
456 \item \isa {recdef_wf} (attribute), 170 |
456 \item \isa {recdef_wf} (attribute), 172 |
457 \item \isacommand {record} (command), 149 |
457 \item \isacommand {record} (command), 151 |
458 \item records, 148--154 |
458 \item records, 150--156 |
459 \subitem extensible, 150 |
459 \subitem extensible, 152 |
460 \item recursion |
460 \item recursion |
461 \subitem guarded, 173 |
461 \subitem guarded, 175 |
462 \subitem primitive, 18 |
462 \subitem primitive, 18 |
463 \subitem well-founded, \bold{169} |
463 \subitem well-founded, \bold{171} |
464 \item recursion induction, 51--52 |
464 \item recursion induction, 51--52 |
465 \item \isacommand {redo} (command), 16 |
465 \item \isacommand {redo} (command), 16 |
466 \item reflexive and transitive closure, 102--104 |
466 \item reflexive and transitive closure, 104--106 |
467 \item reflexive transitive closure |
467 \item reflexive transitive closure |
468 \subitem defining inductively, 122--125 |
468 \subitem defining inductively, 124--127 |
469 \item \isa {rel_comp_def} (theorem), \bold{102} |
469 \item \isa {rel_comp_def} (theorem), \bold{104} |
470 \item relations, 101--104 |
470 \item relations, 103--106 |
471 \subitem well-founded, 104--105 |
471 \subitem well-founded, 106--107 |
472 \item \isa {rename_tac} (method), 72--73 |
472 \item \isa {rename_tac} (method), 74--75 |
473 \item \isa {rev} (constant), 10--14, 34 |
473 \item \isa {rev} (constant), 10--14, 34 |
474 \item rewrite rules, \bold{27} |
474 \item rewrite rules, \bold{27} |
475 \subitem permutative, \bold{166} |
475 \subitem permutative, \bold{168} |
476 \item rewriting, \bold{27} |
476 \item rewriting, \bold{27} |
477 \item \isa {rotate_tac} (method), 30 |
477 \item \isa {rotate_tac} (method), 30 |
478 \item \isa {rtrancl_refl} (theorem), \bold{102} |
478 \item \isa {rtrancl_refl} (theorem), \bold{104} |
479 \item \isa {rtrancl_trans} (theorem), \bold{102} |
479 \item \isa {rtrancl_trans} (theorem), \bold{104} |
480 \item rule induction, 118--120 |
480 \item rule induction, 120--122 |
481 \item rule inversion, 120--121, 129--130 |
481 \item rule inversion, 122--123, 131--132 |
482 \item \isa {rule_format} (attribute), 177 |
482 \item \isa {rule_format} (attribute), 179 |
483 \item \isa {rule_tac} (method), 66 |
483 \item \isa {rule_tac} (method), 68 |
484 \subitem and renaming, 73 |
484 \subitem and renaming, 75 |
485 |
485 |
486 \indexspace |
486 \indexspace |
487 |
487 |
488 \item \isa {safe} (method), 81, 82 |
488 \item \isa {safe} (method), 83, 84 |
489 \item safe rules, \bold{80} |
489 \item safe rules, \bold{82} |
490 \item \isa {set} (type), 5, 95 |
490 \item selector |
491 \item set comprehensions, 97--98 |
491 \subitem record, 151 |
492 \item \isa {set_ext} (theorem), \bold{96} |
492 \item \isa {set} (type), 5, 97 |
493 \item sets, 95--99 |
493 \item set comprehensions, 99--100 |
494 \subitem finite, 99 |
494 \item \isa {set_ext} (theorem), \bold{98} |
495 \subitem notation for finite, \bold{97} |
495 \item sets, 97--101 |
|
496 \subitem finite, 101 |
|
497 \subitem notation for finite, \bold{99} |
496 \item settings, \see{flags}{1} |
498 \item settings, \see{flags}{1} |
497 \item \isa {show_brackets} (flag), 6 |
499 \item \isa {show_brackets} (flag), 6 |
498 \item \isa {show_types} (flag), 5, 16 |
500 \item \isa {show_types} (flag), 5, 16 |
499 \item \isa {simp} (attribute), 11, 28 |
501 \item \isa {simp} (attribute), 11, 28 |
500 \item \isa {simp} (method), \bold{28} |
502 \item \isa {simp} (method), \bold{28} |
501 \item \isa {simp} del (attribute), 28 |
503 \item \isa {simp} del (attribute), 28 |
502 \item \isa {simp_all} (method), 29, 38 |
504 \item \isa {simp_all} (method), 29, 38 |
503 \item simplification, 27--33, 165--168 |
505 \item simplification, 27--33, 167--170 |
504 \subitem of \isa{let}-expressions, 31 |
506 \subitem of \isa{let}-expressions, 31 |
505 \subitem with definitions, 30 |
507 \subitem with definitions, 30 |
506 \subitem with/of assumptions, 29 |
508 \subitem with/of assumptions, 29 |
507 \item simplification rule, 167--168 |
509 \item simplification rule, 169--170 |
508 \item simplification rules, 28 |
510 \item simplification rules, 28 |
509 \subitem adding and deleting, 29 |
511 \subitem adding and deleting, 29 |
510 \item \isa {simplified} (attribute), 83, 86 |
512 \item \isa {simplified} (attribute), 85, 88 |
511 \item \isa {size} (constant), 17 |
513 \item \isa {size} (constant), 17 |
512 \item \isa {snd} (constant), 24 |
514 \item \isa {snd} (constant), 24 |
513 \item \isa {SOME} (symbol), 76 |
515 \item \isa {SOME} (symbol), 78 |
514 \item \texttt {SOME}, \bold{199} |
516 \item \texttt {SOME}, \bold{201} |
515 \item \isa {Some} (constant), \bold{24} |
517 \item \isa {Some} (constant), \bold{24} |
516 \item \isa {some_equality} (theorem), \bold{76} |
518 \item \isa {some_equality} (theorem), \bold{78} |
517 \item \isa {someI} (theorem), \bold{76} |
519 \item \isa {someI} (theorem), \bold{78} |
518 \item \isa {someI2} (theorem), \bold{76} |
520 \item \isa {someI2} (theorem), \bold{78} |
519 \item \isa {someI_ex} (theorem), \bold{77} |
521 \item \isa {someI_ex} (theorem), \bold{79} |
520 \item sorts, 159 |
522 \item sorts, 162 |
521 \item \isa {spec} (theorem), \bold{70} |
523 \item \isa {spec} (theorem), \bold{72} |
522 \item \isa {split} (attribute), 32 |
524 \item \isa {split} (attribute), 32 |
523 \item \isa {split} (constant), 146 |
525 \item \isa {split} (constant), 148 |
524 \item \isa {split} (method), 31, 146 |
526 \item \isa {split} (method), 31, 148 |
525 \item \isa {split} (modifier), 32 |
527 \item \isa {split} (modifier), 32 |
526 \item split rule, \bold{32} |
528 \item split rule, \bold{32} |
527 \item \isa {split_if} (theorem), 32 |
529 \item \isa {split_if} (theorem), 32 |
528 \item \isa {split_if_asm} (theorem), 32 |
530 \item \isa {split_if_asm} (theorem), 32 |
529 \item \isa {ssubst} (theorem), \bold{67} |
531 \item \isa {ssubst} (theorem), \bold{69} |
530 \item structural induction, \see{induction, structural}{1} |
532 \item structural induction, \see{induction, structural}{1} |
531 \item subclasses, 154, 158 |
533 \item subclasses, 156, 161 |
532 \item subgoal numbering, 46 |
534 \item subgoal numbering, 46 |
533 \item \isa {subgoal_tac} (method), 88 |
535 \item \isa {subgoal_tac} (method), 90 |
534 \item subgoals, 12 |
536 \item subgoals, 12 |
535 \item subset relation, \bold{96} |
537 \item subset relation, \bold{98} |
536 \item \isa {subsetD} (theorem), \bold{96} |
538 \item \isa {subsetD} (theorem), \bold{98} |
537 \item \isa {subsetI} (theorem), \bold{96} |
539 \item \isa {subsetI} (theorem), \bold{98} |
538 \item \isa {subst} (method), 67 |
540 \item \isa {subst} (method), 69 |
539 \item substitution, 67--69 |
541 \item substitution, 69--71 |
540 \item \isa {Suc} (constant), 22 |
542 \item \isa {Suc} (constant), 22 |
541 \item \isa {surj_def} (theorem), \bold{100} |
543 \item \isa {surj_def} (theorem), \bold{102} |
542 \item surjections, 100 |
544 \item surjections, 102 |
543 \item \isa {sym} (theorem), \bold{84} |
545 \item \isa {sym} (theorem), \bold{86} |
544 \item syntax, 6, 11 |
546 \item syntax, 6, 11 |
545 \item syntax translations, 26 |
547 \item syntax translations, 55--56 |
546 |
548 |
547 \indexspace |
549 \indexspace |
548 |
550 |
549 \item tacticals, 89 |
551 \item tacticals, 91 |
550 \item tactics, 12 |
552 \item tactics, 12 |
551 \item \isacommand {term} (command), 16 |
553 \item \isacommand {term} (command), 16 |
552 \item term rewriting, \bold{27} |
554 \item term rewriting, \bold{27} |
553 \item termination, \see{functions, total}{1} |
555 \item termination, \see{functions, total}{1} |
554 \item terms, 5 |
556 \item terms, 5 |
555 \item \isa {THE} (symbol), 75 |
557 \item \isa {THE} (symbol), 77 |
556 \item \isa {the_equality} (theorem), \bold{75} |
558 \item \isa {the_equality} (theorem), \bold{77} |
557 \item \isa {THEN} (attribute), \bold{84}, 86, 92 |
559 \item \isa {THEN} (attribute), \bold{86}, 88, 94 |
558 \item \isacommand {theorem} (command), \bold{11}, 13 |
560 \item \isacommand {theorem} (command), \bold{11}, 13 |
559 \item theories, 4 |
561 \item theories, 4 |
560 \subitem abandoning, \bold{16} |
562 \subitem abandoning, \bold{16} |
561 \item \isacommand {theory} (command), 16 |
563 \item \isacommand {theory} (command), 16 |
562 \item theory files, 4 |
564 \item theory files, 4 |
563 \item \isacommand {thm} (command), 16 |
565 \item \isacommand {thm} (command), 16 |
564 \item \isa {tl} (constant), 17 |
566 \item \isa {tl} (constant), 17 |
565 \item \isa {ToyList} example, 9--14 |
567 \item \isa {ToyList} example, 9--14 |
566 \item \isa {trace_simp} (flag), 33 |
568 \item \isa {trace_simp} (flag), 33 |
567 \item tracing the simplifier, \bold{33} |
569 \item tracing the simplifier, \bold{33} |
568 \item \isa {trancl_trans} (theorem), \bold{103} |
570 \item \isa {trancl_trans} (theorem), \bold{105} |
569 \item transition systems, 107 |
571 \item transition systems, 109 |
570 \item \isacommand {translations} (command), 26 |
572 \item \isacommand {translations} (command), 55--56 |
571 \item tries, 44--46 |
573 \item tries, 44--46 |
572 \item \isa {True} (constant), 5 |
574 \item \isa {True} (constant), 5 |
573 \item \isa {truncate} (constant), 153 |
575 \item \isa {truncate} (constant), 155 |
574 \item tuples, \see{pairs and tuples}{1} |
576 \item tuples, \see{pairs and tuples}{1} |
575 \item \isacommand {typ} (command), 16 |
577 \item \isacommand {typ} (command), 16 |
576 \item type constraints, \bold{6} |
578 \item type constraints, \bold{6} |
577 \item type constructors, 5 |
579 \item type constructors, 5 |
578 \item type inference, \bold{5} |
580 \item type inference, \bold{5} |
579 \item type synonyms, 25 |
581 \item type synonyms, 25 |
580 \item type variables, 5 |
582 \item type variables, 5 |
581 \item \isacommand {typedecl} (command), 107, 161 |
583 \item \isacommand {typedecl} (command), 109, 163 |
582 \item \isacommand {typedef} (command), 161--164 |
584 \item \isacommand {typedef} (command), 163--166 |
583 \item types, 4--5 |
585 \item types, 4--5 |
584 \subitem declaring, 161 |
586 \subitem declaring, 163 |
585 \subitem defining, 161--164 |
587 \subitem defining, 163--166 |
586 \item \isacommand {types} (command), 25 |
588 \item \isacommand {types} (command), 25 |
587 |
589 |
588 \indexspace |
590 \indexspace |
589 |
591 |
590 \item Ullman, J. D., 135 |
592 \item Ullman, J. D., 137 |
591 \item \texttt {UN}, \bold{199} |
593 \item \texttt {UN}, \bold{201} |
592 \item \texttt {Un}, \bold{199} |
594 \item \texttt {Un}, \bold{201} |
593 \item \isa {UN_E} (theorem), \bold{98} |
595 \item \isa {UN_E} (theorem), \bold{100} |
594 \item \isa {UN_I} (theorem), \bold{98} |
596 \item \isa {UN_I} (theorem), \bold{100} |
595 \item \isa {UN_iff} (theorem), \bold{98} |
597 \item \isa {UN_iff} (theorem), \bold{100} |
596 \item \isa {Un_subset_iff} (theorem), \bold{96} |
598 \item \isa {Un_subset_iff} (theorem), \bold{98} |
597 \item \isacommand {undo} (command), 16 |
599 \item \isacommand {undo} (command), 16 |
598 \item \isa {unfold} (method), \bold{31} |
600 \item \isa {unfold} (method), \bold{31} |
599 \item unification, 66--69 |
601 \item unification, 68--71 |
600 \item \isa {UNION} (constant), 99 |
602 \item \isa {UNION} (constant), 101 |
601 \item \texttt {Union}, \bold{199} |
603 \item \texttt {Union}, \bold{201} |
602 \item union |
604 \item union |
603 \subitem indexed, 98 |
605 \subitem indexed, 100 |
604 \item \isa {Union_iff} (theorem), \bold{98} |
606 \item \isa {Union_iff} (theorem), \bold{100} |
605 \item \isa {unit} (type), 24 |
607 \item \isa {unit} (type), 24 |
606 \item unknowns, 7, \bold{58} |
608 \item unknowns, 7, \bold{60} |
607 \item unsafe rules, \bold{80} |
609 \item unsafe rules, \bold{82} |
608 \item updating a function, \bold{99} |
610 \item update |
|
611 \subitem record, 151 |
|
612 \item updating a function, \bold{101} |
609 |
613 |
610 \indexspace |
614 \indexspace |
611 |
615 |
612 \item variables, 7 |
616 \item variables, 7 |
613 \subitem schematic, 7 |
617 \subitem schematic, 7 |
614 \subitem type, 5 |
618 \subitem type, 5 |
615 \item \isa {vimage_def} (theorem), \bold{101} |
619 \item \isa {vimage_def} (theorem), \bold{103} |
616 |
620 |
617 \indexspace |
621 \indexspace |
618 |
622 |
619 \item Wenzel, Markus, vii |
623 \item Wenzel, Markus, vii |
620 \item \isa {wf_induct} (theorem), \bold{105} |
624 \item \isa {wf_induct} (theorem), \bold{107} |
621 \item \isa {wf_inv_image} (theorem), \bold{105} |
625 \item \isa {wf_inv_image} (theorem), \bold{107} |
622 \item \isa {wf_less_than} (theorem), \bold{104} |
626 \item \isa {wf_less_than} (theorem), \bold{106} |
623 \item \isa {wf_lex_prod} (theorem), \bold{105} |
627 \item \isa {wf_lex_prod} (theorem), \bold{107} |
624 \item \isa {wf_measure} (theorem), \bold{105} |
628 \item \isa {wf_measure} (theorem), \bold{107} |
625 \item \isa {wf_subset} (theorem), 170 |
629 \item \isa {wf_subset} (theorem), 172 |
626 \item \isa {while} (constant), 175 |
630 \item \isa {while} (constant), 177 |
627 \item \isa {While_Combinator} (theory), 175 |
631 \item \isa {While_Combinator} (theory), 177 |
628 \item \isa {while_rule} (theorem), 175 |
632 \item \isa {while_rule} (theorem), 177 |
629 |
633 |
630 \indexspace |
634 \indexspace |
631 |
635 |
632 \item \isa {zadd_ac} (theorems), 143 |
636 \item \isa {zadd_ac} (theorems), 145 |
633 \item \isa {zmult_ac} (theorems), 143 |
637 \item \isa {zmult_ac} (theorems), 145 |
634 |
638 |
635 \end{theindex} |
639 \end{theindex} |