8 \item \verb$~$, \bold{203} |
8 \item \verb$~$, \bold{203} |
9 \item \verb$~=$, \bold{203} |
9 \item \verb$~=$, \bold{203} |
10 \item \ttor, \bold{203} |
10 \item \ttor, \bold{203} |
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}, 203 |
13 \item \texttt{\at}, \bold{10}, \hyperpage{203} |
14 \item \isasymnotin, \bold{203} |
14 \item \isasymnotin, \bold{203} |
15 \item \verb$~:$, \bold{203} |
15 \item \verb$~:$, \bold{203} |
16 \item \isasymInter, \bold{203} |
16 \item \isasymInter, \bold{203} |
17 \item \isasymUnion, \bold{203} |
17 \item \isasymUnion, \bold{203} |
18 \item \isasyminverse, \bold{203} |
18 \item \isasyminverse, \bold{203} |
19 \item \verb$^-1$, \bold{203} |
19 \item \verb$^-1$, \bold{203} |
20 \item \isactrlsup{\isacharasterisk}, \bold{203} |
20 \item \isactrlsup{\isacharasterisk}, \bold{203} |
21 \item \verb$^$\texttt{*}, \bold{203} |
21 \item \verb$^$\texttt{*}, \bold{203} |
22 \item \isasymAnd, \bold{12}, \bold{203} |
22 \item \isasymAnd, \bold{12}, \bold{203} |
23 \item \ttAnd, \bold{203} |
23 \item \ttAnd, \bold{203} |
24 \item \isasymrightleftharpoons, 57 |
24 \item \isasymrightleftharpoons, \hyperpage{57} |
25 \item \isasymrightharpoonup, 57 |
25 \item \isasymrightharpoonup, \hyperpage{57} |
26 \item \isasymleftharpoondown, 57 |
26 \item \isasymleftharpoondown, \hyperpage{57} |
27 \item \emph {$\Rightarrow $}, \bold{5} |
27 \item \emph {$\Rightarrow $}, \bold{5} |
28 \item \ttlbr, \bold{203} |
28 \item \ttlbr, \bold{203} |
29 \item \ttrbr, \bold{203} |
29 \item \ttrbr, \bold{203} |
30 \item \texttt {\%}, \bold{203} |
30 \item \texttt {\%}, \bold{203} |
31 \item \texttt {;}, \bold{7} |
31 \item \texttt {;}, \bold{7} |
32 \item \isa {()} (constant), 24 |
32 \item \isa {()} (constant), \hyperpage{24} |
33 \item \isa {+} (tactical), 93 |
33 \item \isa {+} (tactical), \hyperpage{93} |
34 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
34 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
35 \item \isa {?} (tactical), 93 |
35 \item \isa {?} (tactical), \hyperpage{93} |
36 \item \texttt{|} (tactical), 93 |
36 \item \texttt{|} (tactical), \hyperpage{93} |
37 |
37 |
38 \indexspace |
38 \indexspace |
39 |
39 |
40 \item \isa {0} (constant), 22, 23, 144 |
40 \item \isa {0} (constant), \hyperpage{22, 23}, \hyperpage{144} |
41 \item \isa {1} (constant), 23, 144, 145 |
41 \item \isa {1} (constant), \hyperpage{23}, \hyperpage{144, 145} |
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), 147 |
47 \item \isa {abs} (constant), \hyperpage{147} |
48 \item \texttt {abs}, \bold{203} |
48 \item \texttt {abs}, \bold{203} |
49 \item absolute value, 147 |
49 \item absolute value, \hyperpage{147} |
50 \item \isa {add} (modifier), 29 |
50 \item \isa {add} (modifier), \hyperpage{29} |
51 \item \isa {add_ac} (theorems), 146 |
51 \item \isa {add_ac} (theorems), \hyperpage{146} |
52 \item \isa {add_assoc} (theorem), \bold{146} |
52 \item \isa {add_assoc} (theorem), \bold{146} |
53 \item \isa {add_commute} (theorem), \bold{146} |
53 \item \isa {add_commute} (theorem), \bold{146} |
54 \item \isa {add_mult_distrib} (theorem), \bold{145} |
54 \item \isa {add_mult_distrib} (theorem), \bold{145} |
55 \item \texttt {ALL}, \bold{203} |
55 \item \texttt {ALL}, \bold{203} |
56 \item \isa {All} (constant), 103 |
56 \item \isa {All} (constant), \hyperpage{103} |
57 \item \isa {allE} (theorem), \bold{75} |
57 \item \isa {allE} (theorem), \bold{75} |
58 \item \isa {allI} (theorem), \bold{74} |
58 \item \isa {allI} (theorem), \bold{74} |
59 \item append function, 10--14 |
59 \item append function, \hyperpage{10--14} |
60 \item \isacommand {apply} (command), 15 |
60 \item \isacommand {apply} (command), \hyperpage{15} |
61 \item \isa {arg_cong} (theorem), \bold{90} |
61 \item \isa {arg_cong} (theorem), \bold{90} |
62 \item \isa {arith} (method), 23, 143 |
62 \item \isa {arith} (method), \hyperpage{23}, \hyperpage{143} |
63 \item arithmetic operations |
63 \item arithmetic operations |
64 \subitem for \protect\isa{nat}, 23 |
64 \subitem for \protect\isa{nat}, \hyperpage{23} |
65 \item \textsc {ascii} symbols, \bold{203} |
65 \item \textsc {ascii} symbols, \bold{203} |
66 \item associative-commutative function, 170 |
66 \item Aspinall, David, \hyperpage{viii} |
67 \item \isa {assumption} (method), 63 |
67 \item associative-commutative function, \hyperpage{170} |
|
68 \item \isa {assumption} (method), \hyperpage{63} |
68 \item assumptions |
69 \item assumptions |
69 \subitem of subgoal, 12 |
70 \subitem of subgoal, \hyperpage{12} |
70 \subitem renaming, 76--77 |
71 \subitem renaming, \hyperpage{76--77} |
71 \subitem reusing, 77 |
72 \subitem reusing, \hyperpage{77} |
72 \item \isa {auto} (method), 38, 86 |
73 \item \isa {auto} (method), \hyperpage{38}, \hyperpage{86} |
73 \item \isa {axclass}, 158--164 |
74 \item \isa {axclass}, \hyperpage{158--164} |
74 \item axiom of choice, 80 |
75 \item axiom of choice, \hyperpage{80} |
75 \item axiomatic type classes, 158--164 |
76 \item axiomatic type classes, \hyperpage{158--164} |
76 |
77 |
77 \indexspace |
78 \indexspace |
78 |
79 |
79 \item \isacommand {back} (command), 72 |
80 \item \isacommand {back} (command), \hyperpage{72} |
80 \item \isa {Ball} (constant), 103 |
81 \item \isa {Ball} (constant), \hyperpage{103} |
81 \item \isa {ballI} (theorem), \bold{102} |
82 \item \isa {ballI} (theorem), \bold{102} |
82 \item \isa {best} (method), 86 |
83 \item \isa {best} (method), \hyperpage{86} |
83 \item \isa {Bex} (constant), 103 |
84 \item \isa {Bex} (constant), \hyperpage{103} |
84 \item \isa {bexE} (theorem), \bold{102} |
85 \item \isa {bexE} (theorem), \bold{102} |
85 \item \isa {bexI} (theorem), \bold{102} |
86 \item \isa {bexI} (theorem), \bold{102} |
86 \item \isa {bij_def} (theorem), \bold{104} |
87 \item \isa {bij_def} (theorem), \bold{104} |
87 \item bijections, 104 |
88 \item bijections, \hyperpage{104} |
88 \item binary trees, 18 |
89 \item binary trees, \hyperpage{18} |
89 \item binomial coefficients, 103 |
90 \item binomial coefficients, \hyperpage{103} |
90 \item bisimulations, 110 |
91 \item bisimulations, \hyperpage{110} |
91 \item \isa {blast} (method), 83--84, 86 |
92 \item \isa {blast} (method), \hyperpage{83--84}, \hyperpage{86} |
92 \item \isa {bool} (type), 4, 5 |
93 \item \isa {bool} (type), \hyperpage{4, 5} |
93 \item boolean expressions example, 20--22 |
94 \item boolean expressions example, \hyperpage{20--22} |
94 \item \isa {bspec} (theorem), \bold{102} |
95 \item \isa {bspec} (theorem), \bold{102} |
95 \item \isacommand{by} (command), 67 |
96 \item \isacommand{by} (command), \hyperpage{67} |
96 |
97 |
97 \indexspace |
98 \indexspace |
98 |
99 |
99 \item \isa {card} (constant), 103 |
100 \item \isa {card} (constant), \hyperpage{103} |
100 \item \isa {card_Pow} (theorem), \bold{103} |
101 \item \isa {card_Pow} (theorem), \bold{103} |
101 \item \isa {card_Un_Int} (theorem), \bold{103} |
102 \item \isa {card_Un_Int} (theorem), \bold{103} |
102 \item cardinality, 103 |
103 \item cardinality, \hyperpage{103} |
103 \item \isa {case} (symbol), 32, 33 |
104 \item \isa {case} (symbol), \hyperpage{32, 33} |
104 \item \isa {case} expressions, 5, 6, 18 |
105 \item \isa {case} expressions, \hyperpage{5, 6}, \hyperpage{18} |
105 \item case distinctions, 19 |
106 \item case distinctions, \hyperpage{19} |
106 \item case splits, \bold{31} |
107 \item case splits, \bold{31} |
107 \item \isa {case_tac} (method), 19, 95, 151 |
108 \item \isa {case_tac} (method), \hyperpage{19}, \hyperpage{95}, |
108 \item \isa {cases} (method), 156 |
109 \hyperpage{151} |
109 \item \isa {clarify} (method), 85, 86 |
110 \item \isa {cases} (method), \hyperpage{156} |
110 \item \isa {clarsimp} (method), 85, 86 |
111 \item \isa {clarify} (method), \hyperpage{85, 86} |
|
112 \item \isa {clarsimp} (method), \hyperpage{85, 86} |
111 \item \isa {classical} (theorem), \bold{67} |
113 \item \isa {classical} (theorem), \bold{67} |
112 \item coinduction, \bold{110} |
114 \item coinduction, \bold{110} |
113 \item \isa {Collect} (constant), 103 |
115 \item \isa {Collect} (constant), \hyperpage{103} |
114 \item compiling expressions example, 36--38 |
116 \item compiling expressions example, \hyperpage{36--38} |
115 \item \isa {Compl_iff} (theorem), \bold{100} |
117 \item \isa {Compl_iff} (theorem), \bold{100} |
116 \item complement |
118 \item complement |
117 \subitem of a set, 99 |
119 \subitem of a set, \hyperpage{99} |
118 \item composition |
120 \item composition |
119 \subitem of functions, \bold{104} |
121 \subitem of functions, \bold{104} |
120 \subitem of relations, \bold{106} |
122 \subitem of relations, \bold{106} |
121 \item conclusion |
123 \item conclusion |
122 \subitem of subgoal, 12 |
124 \subitem of subgoal, \hyperpage{12} |
123 \item conditional expressions, \see{\isa{if} expressions}{1} |
125 \item conditional expressions, \see{\isa{if} expressions}{1} |
124 \item conditional simplification rules, 31 |
126 \item conditional simplification rules, \hyperpage{31} |
125 \item \isa {cong} (attribute), 170 |
127 \item \isa {cong} (attribute), \hyperpage{170} |
126 \item congruence rules, \bold{169} |
128 \item congruence rules, \bold{169} |
127 \item \isa {conjE} (theorem), \bold{65} |
129 \item \isa {conjE} (theorem), \bold{65} |
128 \item \isa {conjI} (theorem), \bold{62} |
130 \item \isa {conjI} (theorem), \bold{62} |
129 \item \isa {Cons} (constant), 9 |
131 \item \isa {Cons} (constant), \hyperpage{9} |
130 \item \isacommand {constdefs} (command), 25 |
132 \item \isacommand {constdefs} (command), \hyperpage{25} |
131 \item \isacommand {consts} (command), 10 |
133 \item \isacommand {consts} (command), \hyperpage{10} |
132 \item contrapositives, 67 |
134 \item contrapositives, \hyperpage{67} |
133 \item converse |
135 \item converse |
134 \subitem of a relation, \bold{106} |
136 \subitem of a relation, \bold{106} |
135 \item \isa {converse_iff} (theorem), \bold{106} |
137 \item \isa {converse_iff} (theorem), \bold{106} |
136 \item CTL, 115--120, 185--187 |
138 \item CTL, \hyperpage{115--120}, \hyperpage{185--187} |
137 |
139 |
138 \indexspace |
140 \indexspace |
139 |
141 |
140 \item \isacommand {datatype} (command), 9, 38--43 |
142 \item \isacommand {datatype} (command), \hyperpage{9}, |
141 \item datatypes, 17--22 |
143 \hyperpage{38--43} |
142 \subitem and nested recursion, 40, 44 |
144 \item datatypes, \hyperpage{17--22} |
143 \subitem mutually recursive, 38 |
145 \subitem and nested recursion, \hyperpage{40}, \hyperpage{44} |
144 \subitem nested, 174 |
146 \subitem mutually recursive, \hyperpage{38} |
145 \item \isacommand {defer} (command), 16, 94 |
147 \subitem nested, \hyperpage{174} |
146 \item Definitional Approach, 26 |
148 \item \isacommand {defer} (command), \hyperpage{16}, \hyperpage{94} |
|
149 \item Definitional Approach, \hyperpage{26} |
147 \item definitions, \bold{25} |
150 \item definitions, \bold{25} |
148 \subitem unfolding, \bold{30} |
151 \subitem unfolding, \bold{30} |
149 \item \isacommand {defs} (command), 25 |
152 \item \isacommand {defs} (command), \hyperpage{25} |
150 \item \isa {del} (modifier), 29 |
153 \item \isa {del} (modifier), \hyperpage{29} |
151 \item description operators, 79--81 |
154 \item description operators, \hyperpage{79--81} |
152 \item descriptions |
155 \item descriptions |
153 \subitem definite, 79 |
156 \subitem definite, \hyperpage{79} |
154 \subitem indefinite, 80 |
157 \subitem indefinite, \hyperpage{80} |
155 \item \isa {dest} (attribute), 96 |
158 \item \isa {dest} (attribute), \hyperpage{96} |
156 \item destruction rules, 65 |
159 \item destruction rules, \hyperpage{65} |
157 \item \isa {diff_mult_distrib} (theorem), \bold{145} |
160 \item \isa {diff_mult_distrib} (theorem), \bold{145} |
158 \item difference |
161 \item difference |
159 \subitem of sets, \bold{100} |
162 \subitem of sets, \bold{100} |
160 \item \isa {disjCI} (theorem), \bold{68} |
163 \item \isa {disjCI} (theorem), \bold{68} |
161 \item \isa {disjE} (theorem), \bold{64} |
164 \item \isa {disjE} (theorem), \bold{64} |
162 \item \isa {div} (symbol), 23 |
165 \item \isa {div} (symbol), \hyperpage{23} |
163 \item divides relation, 78, 89, 95--98, 146 |
166 \item divides relation, \hyperpage{78}, \hyperpage{89}, |
|
167 \hyperpage{95--98}, \hyperpage{146} |
164 \item division |
168 \item division |
165 \subitem by negative numbers, 147 |
169 \subitem by negative numbers, \hyperpage{147} |
166 \subitem by zero, 146 |
170 \subitem by zero, \hyperpage{146} |
167 \subitem for type \protect\isa{nat}, 145 |
171 \subitem for type \protect\isa{nat}, \hyperpage{145} |
168 \item domain |
172 \item domain |
169 \subitem of a relation, 106 |
173 \subitem of a relation, \hyperpage{106} |
170 \item \isa {Domain_iff} (theorem), \bold{106} |
174 \item \isa {Domain_iff} (theorem), \bold{106} |
171 \item \isacommand {done} (command), 13 |
175 \item \isacommand {done} (command), \hyperpage{13} |
172 \item \isa {drule_tac} (method), 70, 90 |
176 \item \isa {drule_tac} (method), \hyperpage{70}, \hyperpage{90} |
173 \item \isa {dvd_add} (theorem), \bold{146} |
177 \item \isa {dvd_add} (theorem), \bold{146} |
174 \item \isa {dvd_anti_sym} (theorem), \bold{146} |
178 \item \isa {dvd_anti_sym} (theorem), \bold{146} |
175 \item \isa {dvd_def} (theorem), \bold{146} |
179 \item \isa {dvd_def} (theorem), \bold{146} |
176 |
180 |
177 \indexspace |
181 \indexspace |
178 |
182 |
179 \item \isa {elim!} (attribute), 125 |
183 \item \isa {elim!} (attribute), \hyperpage{125} |
180 \item elimination rules, 63--64 |
184 \item elimination rules, \hyperpage{63--64} |
181 \item \isacommand {end} (command), 14 |
185 \item \isacommand {end} (command), \hyperpage{14} |
182 \item \isa {Eps} (constant), 103 |
186 \item \isa {Eps} (constant), \hyperpage{103} |
183 \item equality, 5 |
187 \item equality, \hyperpage{5} |
184 \subitem of functions, \bold{103} |
188 \subitem of functions, \bold{103} |
185 \subitem of records, 155 |
189 \subitem of records, \hyperpage{155} |
186 \subitem of sets, \bold{100} |
190 \subitem of sets, \bold{100} |
187 \item \isa {equalityE} (theorem), \bold{100} |
191 \item \isa {equalityE} (theorem), \bold{100} |
188 \item \isa {equalityI} (theorem), \bold{100} |
192 \item \isa {equalityI} (theorem), \bold{100} |
189 \item \isa {erule} (method), 64 |
193 \item \isa {erule} (method), \hyperpage{64} |
190 \item \isa {erule_tac} (method), 70 |
194 \item \isa {erule_tac} (method), \hyperpage{70} |
191 \item Euclid's algorithm, 95--98 |
195 \item Euclid's algorithm, \hyperpage{95--98} |
192 \item even numbers |
196 \item even numbers |
193 \subitem defining inductively, 121--125 |
197 \subitem defining inductively, \hyperpage{121--125} |
194 \item \texttt {EX}, \bold{203} |
198 \item \texttt {EX}, \bold{203} |
195 \item \isa {Ex} (constant), 103 |
199 \item \isa {Ex} (constant), \hyperpage{103} |
196 \item \isa {exE} (theorem), \bold{76} |
200 \item \isa {exE} (theorem), \bold{76} |
197 \item \isa {exI} (theorem), \bold{76} |
201 \item \isa {exI} (theorem), \bold{76} |
198 \item \isa {ext} (theorem), \bold{103} |
202 \item \isa {ext} (theorem), \bold{103} |
199 \item \isa {extend} (constant), 157 |
203 \item \isa {extend} (constant), \hyperpage{157} |
200 \item extensionality |
204 \item extensionality |
201 \subitem for functions, \bold{103, 104} |
205 \subitem for functions, \bold{103, 104} |
202 \subitem for records, 155 |
206 \subitem for records, \hyperpage{155} |
203 \subitem for sets, \bold{100} |
207 \subitem for sets, \bold{100} |
204 \item \ttEXU, \bold{203} |
208 \item \ttEXU, \bold{203} |
205 |
209 |
206 \indexspace |
210 \indexspace |
207 |
211 |
208 \item \isa {False} (constant), 5 |
212 \item \isa {False} (constant), \hyperpage{5} |
209 \item \isa {fast} (method), 86, 118 |
213 \item \isa {fast} (method), \hyperpage{86}, \hyperpage{118} |
210 \item Fibonacci function, 47 |
214 \item Fibonacci function, \hyperpage{47} |
211 \item \isa {fields} (constant), 157 |
215 \item \isa {fields} (constant), \hyperpage{157} |
212 \item \isa {finite} (symbol), 103 |
216 \item \isa {finite} (symbol), \hyperpage{103} |
213 \item \isa {Finites} (constant), 103 |
217 \item \isa {Finites} (constant), \hyperpage{103} |
214 \item fixed points, 110 |
218 \item fixed points, \hyperpage{110} |
215 \item flags, 5, 6, 33 |
219 \item flags, \hyperpage{5, 6}, \hyperpage{33} |
216 \subitem setting and resetting, 5 |
220 \subitem setting and resetting, \hyperpage{5} |
217 \item \isa {force} (method), 85, 86 |
221 \item \isa {force} (method), \hyperpage{85, 86} |
218 \item formulae, 5--6 |
222 \item formulae, \hyperpage{5--6} |
219 \item forward proof, 86--92 |
223 \item forward proof, \hyperpage{86--92} |
220 \item \isa {frule} (method), 77 |
224 \item \isa {frule} (method), \hyperpage{77} |
221 \item \isa {frule_tac} (method), 70 |
225 \item \isa {frule_tac} (method), \hyperpage{70} |
222 \item \isa {fst} (constant), 24 |
226 \item \isa {fst} (constant), \hyperpage{24} |
223 \item function types, 5 |
227 \item function types, \hyperpage{5} |
224 \item functions, 103--105 |
228 \item functions, \hyperpage{103--105} |
225 \subitem partial, 176 |
229 \subitem partial, \hyperpage{176} |
226 \subitem total, 11, 46--52 |
230 \subitem total, \hyperpage{11}, \hyperpage{46--52} |
227 \subitem underdefined, 177 |
231 \subitem underdefined, \hyperpage{177} |
228 |
232 |
229 \indexspace |
233 \indexspace |
230 |
234 |
231 \item \isa {gcd} (constant), 87--88, 95--98 |
235 \item \isa {gcd} (constant), \hyperpage{87--88}, \hyperpage{95--98} |
232 \item generalizing for induction, 123 |
236 \item generalizing for induction, \hyperpage{123} |
233 \item generalizing induction formulae, 35 |
237 \item generalizing induction formulae, \hyperpage{35} |
234 \item Girard, Jean-Yves, \fnote{65} |
238 \item Girard, Jean-Yves, \fnote{65} |
235 \item Gordon, Mike, 3 |
239 \item Gordon, Mike, \hyperpage{3} |
236 \item grammars |
240 \item grammars |
237 \subitem defining inductively, 134--139 |
241 \subitem defining inductively, \hyperpage{134--139} |
238 \item ground terms example, 129--134 |
242 \item ground terms example, \hyperpage{129--134} |
239 |
243 |
240 \indexspace |
244 \indexspace |
241 |
245 |
242 \item \isa {hd} (constant), 17, 37 |
246 \item \isa {hd} (constant), \hyperpage{17}, \hyperpage{37} |
243 \item Hilbert's $\varepsilon$-operator, 80 |
247 \item Hilbert's $\varepsilon$-operator, \hyperpage{80} |
244 \item HOLCF, 43 |
248 \item HOLCF, \hyperpage{43} |
245 \item Hopcroft, J. E., 139 |
249 \item Hopcroft, J. E., \hyperpage{139} |
246 \item \isa {hypreal} (type), 149 |
250 \item \isa {hypreal} (type), \hyperpage{149} |
247 |
251 |
248 \indexspace |
252 \indexspace |
249 |
253 |
250 \item \isa {Id_def} (theorem), \bold{106} |
254 \item \isa {Id_def} (theorem), \bold{106} |
251 \item \isa {id_def} (theorem), \bold{104} |
255 \item \isa {id_def} (theorem), \bold{104} |
252 \item identifiers, \bold{6} |
256 \item identifiers, \bold{6} |
253 \subitem qualified, \bold{4} |
257 \subitem qualified, \bold{4} |
254 \item identity function, \bold{104} |
258 \item identity function, \bold{104} |
255 \item identity relation, \bold{106} |
259 \item identity relation, \bold{106} |
256 \item \isa {if} expressions, 5, 6 |
260 \item \isa {if} expressions, \hyperpage{5, 6} |
257 \subitem simplification of, 33 |
261 \subitem simplification of, \hyperpage{33} |
258 \subitem splitting of, 31, 49 |
262 \subitem splitting of, \hyperpage{31}, \hyperpage{49} |
259 \item if-and-only-if, 6 |
263 \item if-and-only-if, \hyperpage{6} |
260 \item \isa {iff} (attribute), 84, 96, 124 |
264 \item \isa {iff} (attribute), \hyperpage{84}, \hyperpage{96}, |
|
265 \hyperpage{124} |
261 \item \isa {iffD1} (theorem), \bold{88} |
266 \item \isa {iffD1} (theorem), \bold{88} |
262 \item \isa {iffD2} (theorem), \bold{88} |
267 \item \isa {iffD2} (theorem), \bold{88} |
263 \item image |
268 \item image |
264 \subitem under a function, \bold{105} |
269 \subitem under a function, \bold{105} |
265 \subitem under a relation, \bold{106} |
270 \subitem under a relation, \bold{106} |
266 \item \isa {image_def} (theorem), \bold{105} |
271 \item \isa {image_def} (theorem), \bold{105} |
267 \item \isa {Image_iff} (theorem), \bold{106} |
272 \item \isa {Image_iff} (theorem), \bold{106} |
268 \item \isa {impI} (theorem), \bold{66} |
273 \item \isa {impI} (theorem), \bold{66} |
269 \item implication, 66--67 |
274 \item implication, \hyperpage{66--67} |
270 \item \isa {ind_cases} (method), 125 |
275 \item \isa {ind_cases} (method), \hyperpage{125} |
271 \item \isa {induct_tac} (method), 12, 19, 52, 184 |
276 \item \isa {induct_tac} (method), \hyperpage{12}, \hyperpage{19}, |
272 \item induction, 180--187 |
277 \hyperpage{52}, \hyperpage{184} |
273 \subitem complete, 182 |
278 \item induction, \hyperpage{180--187} |
274 \subitem deriving new schemas, 184 |
279 \subitem complete, \hyperpage{182} |
275 \subitem on a term, 181 |
280 \subitem deriving new schemas, \hyperpage{184} |
276 \subitem recursion, 51--52 |
281 \subitem on a term, \hyperpage{181} |
277 \subitem structural, 19 |
282 \subitem recursion, \hyperpage{51--52} |
278 \subitem well-founded, 109 |
283 \subitem structural, \hyperpage{19} |
279 \item induction heuristics, 34--36 |
284 \subitem well-founded, \hyperpage{109} |
280 \item \isacommand {inductive} (command), 121 |
285 \item induction heuristics, \hyperpage{34--36} |
|
286 \item \isacommand {inductive} (command), \hyperpage{121} |
281 \item inductive definition |
287 \item inductive definition |
282 \subitem simultaneous, 135 |
288 \subitem simultaneous, \hyperpage{135} |
283 \item inductive definitions, 121--139 |
289 \item inductive definitions, \hyperpage{121--139} |
284 \item \isacommand {inductive\_cases} (command), 125, 133 |
290 \item \isacommand {inductive\_cases} (command), \hyperpage{125}, |
285 \item infinitely branching trees, 43 |
291 \hyperpage{133} |
|
292 \item infinitely branching trees, \hyperpage{43} |
286 \item infix annotations, \bold{54} |
293 \item infix annotations, \bold{54} |
287 \item \isacommand{infixr} (annotation), 10 |
294 \item \isacommand{infixr} (annotation), \hyperpage{10} |
288 \item \isa {inj_on_def} (theorem), \bold{104} |
295 \item \isa {inj_on_def} (theorem), \bold{104} |
289 \item injections, 104 |
296 \item injections, \hyperpage{104} |
290 \item \isa {insert} (constant), 101 |
297 \item \isa {insert} (constant), \hyperpage{101} |
291 \item \isa {insert} (method), 91--92 |
298 \item \isa {insert} (method), \hyperpage{91--92} |
292 \item instance, \bold{160} |
299 \item instance, \bold{160} |
293 \item \texttt {INT}, \bold{203} |
300 \item \texttt {INT}, \bold{203} |
294 \item \texttt {Int}, \bold{203} |
301 \item \texttt {Int}, \bold{203} |
295 \item \isa {int} (type), 147--148 |
302 \item \isa {int} (type), \hyperpage{147--148} |
296 \item \isa {INT_iff} (theorem), \bold{102} |
303 \item \isa {INT_iff} (theorem), \bold{102} |
297 \item \isa {IntD1} (theorem), \bold{99} |
304 \item \isa {IntD1} (theorem), \bold{99} |
298 \item \isa {IntD2} (theorem), \bold{99} |
305 \item \isa {IntD2} (theorem), \bold{99} |
299 \item integers, 147--148 |
306 \item integers, \hyperpage{147--148} |
300 \item \isa {INTER} (constant), 103 |
307 \item \isa {INTER} (constant), \hyperpage{103} |
301 \item \texttt {Inter}, \bold{203} |
308 \item \texttt {Inter}, \bold{203} |
302 \item \isa {Inter_iff} (theorem), \bold{102} |
309 \item \isa {Inter_iff} (theorem), \bold{102} |
303 \item intersection, 99 |
310 \item intersection, \hyperpage{99} |
304 \subitem indexed, 102 |
311 \subitem indexed, \hyperpage{102} |
305 \item \isa {IntI} (theorem), \bold{99} |
312 \item \isa {IntI} (theorem), \bold{99} |
306 \item \isa {intro} (method), 68 |
313 \item \isa {intro} (method), \hyperpage{68} |
307 \item \isa {intro!} (attribute), 122 |
314 \item \isa {intro!} (attribute), \hyperpage{122} |
308 \item \isa {intro_classes} (method), 160 |
315 \item \isa {intro_classes} (method), \hyperpage{160} |
309 \item introduction rules, 62--63 |
316 \item introduction rules, \hyperpage{62--63} |
310 \item \isa {inv} (constant), 80 |
317 \item \isa {inv} (constant), \hyperpage{80} |
311 \item \isa {inv_image_def} (theorem), \bold{109} |
318 \item \isa {inv_image_def} (theorem), \bold{109} |
312 \item inverse |
319 \item inverse |
313 \subitem of a function, \bold{104} |
320 \subitem of a function, \bold{104} |
314 \subitem of a relation, \bold{106} |
321 \subitem of a relation, \bold{106} |
315 \item inverse image |
322 \item inverse image |
316 \subitem of a function, 105 |
323 \subitem of a function, \hyperpage{105} |
317 \subitem of a relation, 108 |
324 \subitem of a relation, \hyperpage{108} |
318 \item \isa {itrev} (constant), 34 |
325 \item \isa {itrev} (constant), \hyperpage{34} |
319 |
326 |
320 \indexspace |
327 \indexspace |
321 |
328 |
322 \item \isacommand {kill} (command), 16 |
329 \item \isacommand {kill} (command), \hyperpage{16} |
323 |
330 |
324 \indexspace |
331 \indexspace |
325 |
332 |
326 \item $\lambda$ expressions, 5 |
333 \item $\lambda$ expressions, \hyperpage{5} |
327 \item LCF, 43 |
334 \item LCF, \hyperpage{43} |
328 \item \isa {LEAST} (symbol), 23, 79 |
335 \item \isa {LEAST} (symbol), \hyperpage{23}, \hyperpage{79} |
329 \item least number operator, \see{\protect\isa{LEAST}}{79} |
336 \item least number operator, \see{\protect\isa{LEAST}}{79} |
330 \item Leibniz, Gottfried Wilhelm, 53 |
337 \item Leibniz, Gottfried Wilhelm, \hyperpage{53} |
331 \item \isacommand {lemma} (command), 13 |
338 \item \isacommand {lemma} (command), \hyperpage{13} |
332 \item \isacommand {lemmas} (command), 87, 96 |
339 \item \isacommand {lemmas} (command), \hyperpage{87}, \hyperpage{96} |
333 \item \isa {length} (symbol), 18 |
340 \item \isa {length} (symbol), \hyperpage{18} |
334 \item \isa {length_induct}, \bold{184} |
341 \item \isa {length_induct}, \bold{184} |
335 \item \isa {less_than} (constant), 108 |
342 \item \isa {less_than} (constant), \hyperpage{108} |
336 \item \isa {less_than_iff} (theorem), \bold{108} |
343 \item \isa {less_than_iff} (theorem), \bold{108} |
337 \item \isa {let} expressions, 5, 6, 31 |
344 \item \isa {let} expressions, \hyperpage{5, 6}, \hyperpage{31} |
338 \item \isa {Let_def} (theorem), 31 |
345 \item \isa {Let_def} (theorem), \hyperpage{31} |
339 \item \isa {lex_prod_def} (theorem), \bold{109} |
346 \item \isa {lex_prod_def} (theorem), \bold{109} |
340 \item lexicographic product, \bold{109}, 172 |
347 \item lexicographic product, \bold{109}, \hyperpage{172} |
341 \item {\texttt{lfp}} |
348 \item {\texttt{lfp}} |
342 \subitem applications of, \see{CTL}{110} |
349 \subitem applications of, \see{CTL}{110} |
343 \item Library, 4 |
350 \item Library, \hyperpage{4} |
344 \item linear arithmetic, 22--24, 143 |
351 \item linear arithmetic, \hyperpage{22--24}, \hyperpage{143} |
345 \item \isa {List} (theory), 17 |
352 \item \isa {List} (theory), \hyperpage{17} |
346 \item \isa {list} (type), 5, 9, 17 |
353 \item \isa {list} (type), \hyperpage{5}, \hyperpage{9}, |
347 \item \isa {list.split} (theorem), 32 |
354 \hyperpage{17} |
|
355 \item \isa {list.split} (theorem), \hyperpage{32} |
348 \item \isa {lists_mono} (theorem), \bold{131} |
356 \item \isa {lists_mono} (theorem), \bold{131} |
349 \item Lowe, Gavin, 190--191 |
357 \item Lowe, Gavin, \hyperpage{190--191} |
350 |
358 |
351 \indexspace |
359 \indexspace |
352 |
360 |
353 \item \isa {Main} (theory), 4 |
361 \item \isa {Main} (theory), \hyperpage{4} |
354 \item major premise, \bold{69} |
362 \item major premise, \bold{69} |
355 \item \isa {make} (constant), 157 |
363 \item \isa {make} (constant), \hyperpage{157} |
356 \item \isa {max} (constant), 23, 24 |
364 \item \isa {max} (constant), \hyperpage{23, 24} |
357 \item measure functions, 47, 108 |
365 \item measure functions, \hyperpage{47}, \hyperpage{108} |
358 \item \isa {measure_def} (theorem), \bold{109} |
366 \item \isa {measure_def} (theorem), \bold{109} |
359 \item meta-logic, \bold{74} |
367 \item meta-logic, \bold{74} |
360 \item methods, \bold{16} |
368 \item methods, \bold{16} |
361 \item \isa {min} (constant), 23, 24 |
369 \item \isa {min} (constant), \hyperpage{23, 24} |
362 \item mixfix annotations, \bold{53} |
370 \item mixfix annotations, \bold{53} |
363 \item \isa {mod} (symbol), 23 |
371 \item \isa {mod} (symbol), \hyperpage{23} |
364 \item \isa {mod_div_equality} (theorem), \bold{145} |
372 \item \isa {mod_div_equality} (theorem), \bold{145} |
365 \item \isa {mod_mult_distrib} (theorem), \bold{145} |
373 \item \isa {mod_mult_distrib} (theorem), \bold{145} |
366 \item model checking example, 110--120 |
374 \item model checking example, \hyperpage{110--120} |
367 \item \emph{modus ponens}, 61, 66 |
375 \item \emph{modus ponens}, \hyperpage{61}, \hyperpage{66} |
368 \item \isa {mono_def} (theorem), \bold{110} |
376 \item \isa {mono_def} (theorem), \bold{110} |
369 \item monotone functions, \bold{110}, 133 |
377 \item monotone functions, \bold{110}, \hyperpage{133} |
370 \subitem and inductive definitions, 131--132 |
378 \subitem and inductive definitions, \hyperpage{131--132} |
371 \item \isa {more} (constant), 152, 154 |
379 \item \isa {more} (constant), \hyperpage{152}, \hyperpage{154} |
372 \item \isa {mp} (theorem), \bold{66} |
380 \item \isa {mp} (theorem), \bold{66} |
373 \item \isa {mult_ac} (theorems), 146 |
381 \item \isa {mult_ac} (theorems), \hyperpage{146} |
374 \item multiple inheritance, \bold{163} |
382 \item multiple inheritance, \bold{163} |
375 \item multiset ordering, \bold{109} |
383 \item multiset ordering, \bold{109} |
376 |
384 |
377 \indexspace |
385 \indexspace |
378 |
386 |
379 \item \isa {nat} (type), 4, 22, 145--147 |
387 \item \isa {nat} (type), \hyperpage{4}, \hyperpage{22}, |
380 \item \isa {nat_less_induct} (theorem), 182 |
388 \hyperpage{145--147} |
381 \item natural deduction, 61--62 |
389 \item \isa {nat_less_induct} (theorem), \hyperpage{182} |
382 \item natural numbers, 22, 145--147 |
390 \item natural deduction, \hyperpage{61--62} |
383 \item Needham-Schroeder protocol, 189--191 |
391 \item natural numbers, \hyperpage{22}, \hyperpage{145--147} |
384 \item negation, 67--69 |
392 \item Needham-Schroeder protocol, \hyperpage{189--191} |
385 \item \isa {Nil} (constant), 9 |
393 \item negation, \hyperpage{67--69} |
386 \item \isa {no_asm} (modifier), 29 |
394 \item \isa {Nil} (constant), \hyperpage{9} |
387 \item \isa {no_asm_simp} (modifier), 30 |
395 \item \isa {no_asm} (modifier), \hyperpage{29} |
388 \item \isa {no_asm_use} (modifier), 30 |
396 \item \isa {no_asm_simp} (modifier), \hyperpage{30} |
389 \item non-standard reals, 149 |
397 \item \isa {no_asm_use} (modifier), \hyperpage{30} |
|
398 \item non-standard reals, \hyperpage{149} |
390 \item \isa {None} (constant), \bold{24} |
399 \item \isa {None} (constant), \bold{24} |
391 \item \isa {notE} (theorem), \bold{67} |
400 \item \isa {notE} (theorem), \bold{67} |
392 \item \isa {notI} (theorem), \bold{67} |
401 \item \isa {notI} (theorem), \bold{67} |
393 \item numbers, 143--149 |
402 \item numbers, \hyperpage{143--149} |
394 \item numeric literals, 144 |
403 \item numeric literals, \hyperpage{144} |
395 \subitem for type \protect\isa{nat}, 145 |
404 \subitem for type \protect\isa{nat}, \hyperpage{145} |
396 \subitem for type \protect\isa{real}, 149 |
405 \subitem for type \protect\isa{real}, \hyperpage{149} |
397 |
406 |
398 \indexspace |
407 \indexspace |
399 |
408 |
400 \item \isa {O} (symbol), 106 |
409 \item \isa {O} (symbol), \hyperpage{106} |
401 \item \texttt {o}, \bold{203} |
410 \item \texttt {o}, \bold{203} |
402 \item \isa {o_def} (theorem), \bold{104} |
411 \item \isa {o_def} (theorem), \bold{104} |
403 \item \isa {OF} (attribute), 89--90 |
412 \item \isa {OF} (attribute), \hyperpage{89--90} |
404 \item \isa {of} (attribute), 87, 90 |
413 \item \isa {of} (attribute), \hyperpage{87}, \hyperpage{90} |
405 \item \isa {only} (modifier), 29 |
414 \item \isa {only} (modifier), \hyperpage{29} |
406 \item \isacommand {oops} (command), 13 |
415 \item \isacommand {oops} (command), \hyperpage{13} |
407 \item \isa {option} (type), \bold{24} |
416 \item \isa {option} (type), \bold{24} |
408 \item ordered rewriting, \bold{170} |
417 \item ordered rewriting, \bold{170} |
409 \item overloading, 23, 159--161 |
418 \item overloading, \hyperpage{23}, \hyperpage{159--161} |
410 \subitem and arithmetic, 144 |
419 \subitem and arithmetic, \hyperpage{144} |
411 |
420 |
412 \indexspace |
421 \indexspace |
413 |
422 |
414 \item pairs and tuples, 24, 149--152 |
423 \item pairs and tuples, \hyperpage{24}, \hyperpage{149--152} |
415 \item parent theories, \bold{4} |
424 \item parent theories, \bold{4} |
416 \item pattern matching |
425 \item pattern matching |
417 \subitem and \isacommand{recdef}, 47 |
426 \subitem and \isacommand{recdef}, \hyperpage{47} |
418 \item patterns |
427 \item patterns |
419 \subitem higher-order, \bold{171} |
428 \subitem higher-order, \bold{171} |
420 \item PDL, 112--114 |
429 \item PDL, \hyperpage{112--114} |
421 \item \isacommand {pr} (command), 16, 94 |
430 \item \isacommand {pr} (command), \hyperpage{16}, \hyperpage{94} |
422 \item \isacommand {prefer} (command), 16, 94 |
431 \item \isacommand {prefer} (command), \hyperpage{16}, \hyperpage{94} |
423 \item prefix annotation, \bold{56} |
432 \item prefix annotation, \bold{56} |
424 \item primitive recursion, \see{recursion, primitive}{1} |
433 \item primitive recursion, \see{recursion, primitive}{1} |
425 \item \isacommand {primrec} (command), 10, 18, 38--43 |
434 \item \isacommand {primrec} (command), \hyperpage{10}, \hyperpage{18}, |
426 \item print mode, 55 |
435 \hyperpage{38--43} |
427 \item \isacommand {print\_syntax} (command), 54 |
436 \item print mode, \hyperpage{55} |
|
437 \item \isacommand {print\_syntax} (command), \hyperpage{54} |
428 \item product type, \see{pairs and tuples}{1} |
438 \item product type, \see{pairs and tuples}{1} |
429 \item Proof General, \bold{7} |
439 \item Proof General, \bold{7} |
430 \item proof state, 12 |
440 \item proof state, \hyperpage{12} |
431 \item proofs |
441 \item proofs |
432 \subitem abandoning, \bold{13} |
442 \subitem abandoning, \bold{13} |
433 \subitem examples of failing, 81--83 |
443 \subitem examples of failing, \hyperpage{81--83} |
434 \item protocols |
444 \item protocols |
435 \subitem security, 189--199 |
445 \subitem security, \hyperpage{189--199} |
436 |
446 |
437 \indexspace |
447 \indexspace |
438 |
448 |
439 \item quantifiers, 6 |
449 \item quantifiers, \hyperpage{6} |
440 \subitem and inductive definitions, 129--131 |
450 \subitem and inductive definitions, \hyperpage{129--131} |
441 \subitem existential, 76 |
451 \subitem existential, \hyperpage{76} |
442 \subitem for sets, 102 |
452 \subitem for sets, \hyperpage{102} |
443 \subitem instantiating, 78 |
453 \subitem instantiating, \hyperpage{78} |
444 \subitem universal, 73--76 |
454 \subitem universal, \hyperpage{73--76} |
445 |
455 |
446 \indexspace |
456 \indexspace |
447 |
457 |
448 \item \isa {r_into_rtrancl} (theorem), \bold{106} |
458 \item \isa {r_into_rtrancl} (theorem), \bold{106} |
449 \item \isa {r_into_trancl} (theorem), \bold{107} |
459 \item \isa {r_into_trancl} (theorem), \bold{107} |
450 \item range |
460 \item range |
451 \subitem of a function, 105 |
461 \subitem of a function, \hyperpage{105} |
452 \subitem of a relation, 106 |
462 \subitem of a relation, \hyperpage{106} |
453 \item \isa {range} (symbol), 105 |
463 \item \isa {range} (symbol), \hyperpage{105} |
454 \item \isa {Range_iff} (theorem), \bold{106} |
464 \item \isa {Range_iff} (theorem), \bold{106} |
455 \item \isa {Real} (theory), 149 |
465 \item \isa {Real} (theory), \hyperpage{149} |
456 \item \isa {real} (type), 148--149 |
466 \item \isa {real} (type), \hyperpage{148--149} |
457 \item real numbers, 148--149 |
467 \item real numbers, \hyperpage{148--149} |
458 \item \isacommand {recdef} (command), 46--52, 108, 172--180 |
468 \item \isacommand {recdef} (command), \hyperpage{46--52}, |
459 \subitem and numeric literals, 144 |
469 \hyperpage{108}, \hyperpage{172--180} |
460 \item \isa {recdef_cong} (attribute), 176 |
470 \subitem and numeric literals, \hyperpage{144} |
461 \item \isa {recdef_simp} (attribute), 49 |
471 \item \isa {recdef_cong} (attribute), \hyperpage{176} |
462 \item \isa {recdef_wf} (attribute), 174 |
472 \item \isa {recdef_simp} (attribute), \hyperpage{49} |
463 \item \isacommand {record} (command), 153 |
473 \item \isa {recdef_wf} (attribute), \hyperpage{174} |
464 \item records, 152--158 |
474 \item \isacommand {record} (command), \hyperpage{153} |
465 \subitem extensible, 154--155 |
475 \item records, \hyperpage{152--158} |
|
476 \subitem extensible, \hyperpage{154--155} |
466 \item recursion |
477 \item recursion |
467 \subitem guarded, 177 |
478 \subitem guarded, \hyperpage{177} |
468 \subitem primitive, 18 |
479 \subitem primitive, \hyperpage{18} |
469 \subitem well-founded, \bold{173} |
480 \subitem well-founded, \bold{173} |
470 \item recursion induction, 51--52 |
481 \item recursion induction, \hyperpage{51--52} |
471 \item \isacommand {redo} (command), 16 |
482 \item \isacommand {redo} (command), \hyperpage{16} |
472 \item reflexive and transitive closure, 106--108 |
483 \item reflexive and transitive closure, \hyperpage{106--108} |
473 \item reflexive transitive closure |
484 \item reflexive transitive closure |
474 \subitem defining inductively, 126--129 |
485 \subitem defining inductively, \hyperpage{126--129} |
475 \item \isa {rel_comp_def} (theorem), \bold{106} |
486 \item \isa {rel_comp_def} (theorem), \bold{106} |
476 \item relations, 105--108 |
487 \item relations, \hyperpage{105--108} |
477 \subitem well-founded, 108--109 |
488 \subitem well-founded, \hyperpage{108--109} |
478 \item \isa {rename_tac} (method), 76--77 |
489 \item \isa {rename_tac} (method), \hyperpage{76--77} |
479 \item \isa {rev} (constant), 10--14, 34 |
490 \item \isa {rev} (constant), \hyperpage{10--14}, \hyperpage{34} |
480 \item rewrite rules, \bold{27} |
491 \item rewrite rules, \bold{27} |
481 \subitem permutative, \bold{170} |
492 \subitem permutative, \bold{170} |
482 \item rewriting, \bold{27} |
493 \item rewriting, \bold{27} |
483 \item \isa {rotate_tac} (method), 30 |
494 \item \isa {rotate_tac} (method), \hyperpage{30} |
484 \item \isa {rtrancl_refl} (theorem), \bold{106} |
495 \item \isa {rtrancl_refl} (theorem), \bold{106} |
485 \item \isa {rtrancl_trans} (theorem), \bold{106} |
496 \item \isa {rtrancl_trans} (theorem), \bold{106} |
486 \item rule induction, 122--124 |
497 \item rule induction, \hyperpage{122--124} |
487 \item rule inversion, 124--125, 133--134 |
498 \item rule inversion, \hyperpage{124--125}, \hyperpage{133--134} |
488 \item \isa {rule_format} (attribute), 181 |
499 \item \isa {rule_format} (attribute), \hyperpage{181} |
489 \item \isa {rule_tac} (method), 70 |
500 \item \isa {rule_tac} (method), \hyperpage{70} |
490 \subitem and renaming, 77 |
501 \subitem and renaming, \hyperpage{77} |
491 |
502 |
492 \indexspace |
503 \indexspace |
493 |
504 |
494 \item \isa {safe} (method), 85, 86 |
505 \item \isa {safe} (method), \hyperpage{85, 86} |
495 \item safe rules, \bold{84} |
506 \item safe rules, \bold{84} |
496 \item selector |
507 \item selector |
497 \subitem record, 153 |
508 \subitem record, \hyperpage{153} |
498 \item \isa {set} (type), 5, 99 |
509 \item \isa {set} (type), \hyperpage{5}, \hyperpage{99} |
499 \item set comprehensions, 101--102 |
510 \item set comprehensions, \hyperpage{101--102} |
500 \item \isa {set_ext} (theorem), \bold{100} |
511 \item \isa {set_ext} (theorem), \bold{100} |
501 \item sets, 99--103 |
512 \item sets, \hyperpage{99--103} |
502 \subitem finite, 103 |
513 \subitem finite, \hyperpage{103} |
503 \subitem notation for finite, \bold{101} |
514 \subitem notation for finite, \bold{101} |
504 \item settings, \see{flags}{1} |
515 \item settings, \see{flags}{1} |
505 \item \isa {show_brackets} (flag), 6 |
516 \item \isa {show_brackets} (flag), \hyperpage{6} |
506 \item \isa {show_types} (flag), 5, 16 |
517 \item \isa {show_types} (flag), \hyperpage{5}, \hyperpage{16} |
507 \item \isa {simp} (attribute), 11, 28 |
518 \item \isa {simp} (attribute), \hyperpage{11}, \hyperpage{28} |
508 \item \isa {simp} (method), \bold{28} |
519 \item \isa {simp} (method), \bold{28} |
509 \item \isa {simp} del (attribute), 28 |
520 \item \isa {simp} del (attribute), \hyperpage{28} |
510 \item \isa {simp_all} (method), 29, 38 |
521 \item \isa {simp_all} (method), \hyperpage{29}, \hyperpage{38} |
511 \item simplification, 27--33, 169--172 |
522 \item simplification, \hyperpage{27--33}, \hyperpage{169--172} |
512 \subitem of \isa{let}-expressions, 31 |
523 \subitem of \isa{let}-expressions, \hyperpage{31} |
513 \subitem with definitions, 30 |
524 \subitem with definitions, \hyperpage{30} |
514 \subitem with/of assumptions, 29 |
525 \subitem with/of assumptions, \hyperpage{29} |
515 \item simplification rule, 171--172 |
526 \item simplification rule, \hyperpage{171--172} |
516 \item simplification rules, 28 |
527 \item simplification rules, \hyperpage{28} |
517 \subitem adding and deleting, 29 |
528 \subitem adding and deleting, \hyperpage{29} |
518 \item \isa {simplified} (attribute), 87, 90 |
529 \item \isa {simplified} (attribute), \hyperpage{87}, \hyperpage{90} |
519 \item \isa {size} (constant), 17 |
530 \item \isa {size} (constant), \hyperpage{17} |
520 \item \isa {snd} (constant), 24 |
531 \item \isa {snd} (constant), \hyperpage{24} |
521 \item \isa {SOME} (symbol), 80 |
532 \item \isa {SOME} (symbol), \hyperpage{80} |
522 \item \texttt {SOME}, \bold{203} |
533 \item \texttt {SOME}, \bold{203} |
523 \item \isa {Some} (constant), \bold{24} |
534 \item \isa {Some} (constant), \bold{24} |
524 \item \isa {some_equality} (theorem), \bold{80} |
535 \item \isa {some_equality} (theorem), \bold{80} |
525 \item \isa {someI} (theorem), \bold{80} |
536 \item \isa {someI} (theorem), \bold{80} |
526 \item \isa {someI2} (theorem), \bold{80} |
537 \item \isa {someI2} (theorem), \bold{80} |
527 \item \isa {someI_ex} (theorem), \bold{81} |
538 \item \isa {someI_ex} (theorem), \bold{81} |
528 \item sorts, 164 |
539 \item sorts, \hyperpage{164} |
529 \item \isa {spec} (theorem), \bold{74} |
540 \item \isa {spec} (theorem), \bold{74} |
530 \item \isa {split} (attribute), 32 |
541 \item \isa {split} (attribute), \hyperpage{32} |
531 \item \isa {split} (constant), 150 |
542 \item \isa {split} (constant), \hyperpage{150} |
532 \item \isa {split} (method), 31, 150 |
543 \item \isa {split} (method), \hyperpage{31}, \hyperpage{150} |
533 \item \isa {split} (modifier), 32 |
544 \item \isa {split} (modifier), \hyperpage{32} |
534 \item split rule, \bold{32} |
545 \item split rule, \bold{32} |
535 \item \isa {split_if} (theorem), 32 |
546 \item \isa {split_if} (theorem), \hyperpage{32} |
536 \item \isa {split_if_asm} (theorem), 32 |
547 \item \isa {split_if_asm} (theorem), \hyperpage{32} |
537 \item \isa {ssubst} (theorem), \bold{71} |
548 \item \isa {ssubst} (theorem), \bold{71} |
538 \item structural induction, \see{induction, structural}{1} |
549 \item structural induction, \see{induction, structural}{1} |
539 \item subclasses, 158, 163 |
550 \item subclasses, \hyperpage{158}, \hyperpage{163} |
540 \item subgoal numbering, 46 |
551 \item subgoal numbering, \hyperpage{46} |
541 \item \isa {subgoal_tac} (method), 92 |
552 \item \isa {subgoal_tac} (method), \hyperpage{92} |
542 \item subgoals, 12 |
553 \item subgoals, \hyperpage{12} |
543 \item subset relation, \bold{100} |
554 \item subset relation, \bold{100} |
544 \item \isa {subsetD} (theorem), \bold{100} |
555 \item \isa {subsetD} (theorem), \bold{100} |
545 \item \isa {subsetI} (theorem), \bold{100} |
556 \item \isa {subsetI} (theorem), \bold{100} |
546 \item \isa {subst} (method), 71 |
557 \item \isa {subst} (method), \hyperpage{71} |
547 \item substitution, 71--73 |
558 \item substitution, \hyperpage{71--73} |
548 \item \isa {Suc} (constant), 22 |
559 \item \isa {Suc} (constant), \hyperpage{22} |
549 \item \isa {surj_def} (theorem), \bold{104} |
560 \item \isa {surj_def} (theorem), \bold{104} |
550 \item surjections, 104 |
561 \item surjections, \hyperpage{104} |
551 \item \isa {sym} (theorem), \bold{88} |
562 \item \isa {sym} (theorem), \bold{88} |
552 \item symbols, \bold{55} |
563 \item symbols, \bold{55} |
553 \item syntax, 6, 11 |
564 \item syntax, \hyperpage{6}, \hyperpage{11} |
554 \item \isacommand {syntax} (command), 56 |
565 \item \isacommand {syntax} (command), \hyperpage{56} |
555 \item syntax translations, 57 |
566 \item syntax translations, \hyperpage{57} |
556 |
567 |
557 \indexspace |
568 \indexspace |
558 |
569 |
559 \item tacticals, 93 |
570 \item tacticals, \hyperpage{93} |
560 \item tactics, 12 |
571 \item tactics, \hyperpage{12} |
561 \item \isacommand {term} (command), 16 |
572 \item \isacommand {term} (command), \hyperpage{16} |
562 \item term rewriting, \bold{27} |
573 \item term rewriting, \bold{27} |
563 \item termination, \see{functions, total}{1} |
574 \item termination, \see{functions, total}{1} |
564 \item terms, 5 |
575 \item terms, \hyperpage{5} |
565 \item \isa {THE} (symbol), 79 |
576 \item \isa {THE} (symbol), \hyperpage{79} |
566 \item \isa {the_equality} (theorem), \bold{79} |
577 \item \isa {the_equality} (theorem), \bold{79} |
567 \item \isa {THEN} (attribute), \bold{88}, 90, 96 |
578 \item \isa {THEN} (attribute), \bold{88}, \hyperpage{90}, |
568 \item \isacommand {theorem} (command), \bold{11}, 13 |
579 \hyperpage{96} |
569 \item theories, 4 |
580 \item \isacommand {theorem} (command), \bold{11}, \hyperpage{13} |
|
581 \item theories, \hyperpage{4} |
570 \subitem abandoning, \bold{16} |
582 \subitem abandoning, \bold{16} |
571 \item \isacommand {theory} (command), 16 |
583 \item \isacommand {theory} (command), \hyperpage{16} |
572 \item theory files, 4 |
584 \item theory files, \hyperpage{4} |
573 \item \isacommand {thm} (command), 16 |
585 \item \isacommand {thm} (command), \hyperpage{16} |
574 \item \isa {tl} (constant), 17 |
586 \item \isa {tl} (constant), \hyperpage{17} |
575 \item \isa {ToyList} example, 9--14 |
587 \item \isa {ToyList} example, \hyperpage{9--14} |
576 \item \isa {trace_simp} (flag), 33 |
588 \item \isa {trace_simp} (flag), \hyperpage{33} |
577 \item tracing the simplifier, \bold{33} |
589 \item tracing the simplifier, \bold{33} |
578 \item \isa {trancl_trans} (theorem), \bold{107} |
590 \item \isa {trancl_trans} (theorem), \bold{107} |
579 \item transition systems, 111 |
591 \item transition systems, \hyperpage{111} |
580 \item \isacommand {translations} (command), 57 |
592 \item \isacommand {translations} (command), \hyperpage{57} |
581 \item tries, 44--46 |
593 \item tries, \hyperpage{44--46} |
582 \item \isa {True} (constant), 5 |
594 \item \isa {True} (constant), \hyperpage{5} |
583 \item \isa {truncate} (constant), 157 |
595 \item \isa {truncate} (constant), \hyperpage{157} |
584 \item tuples, \see{pairs and tuples}{1} |
596 \item tuples, \see{pairs and tuples}{1} |
585 \item \isacommand {typ} (command), 16 |
597 \item \isacommand {typ} (command), \hyperpage{16} |
586 \item type constraints, \bold{6} |
598 \item type constraints, \bold{6} |
587 \item type constructors, 5 |
599 \item type constructors, \hyperpage{5} |
588 \item type inference, \bold{5} |
600 \item type inference, \bold{5} |
589 \item type synonyms, 25 |
601 \item type synonyms, \hyperpage{25} |
590 \item type variables, 5 |
602 \item type variables, \hyperpage{5} |
591 \item \isacommand {typedecl} (command), 111, 165 |
603 \item \isacommand {typedecl} (command), \hyperpage{111}, |
592 \item \isacommand {typedef} (command), 165--168 |
604 \hyperpage{165} |
593 \item types, 4--5 |
605 \item \isacommand {typedef} (command), \hyperpage{165--168} |
594 \subitem declaring, 165 |
606 \item types, \hyperpage{4--5} |
595 \subitem defining, 165--168 |
607 \subitem declaring, \hyperpage{165} |
596 \item \isacommand {types} (command), 25 |
608 \subitem defining, \hyperpage{165--168} |
597 |
609 \item \isacommand {types} (command), \hyperpage{25} |
598 \indexspace |
610 |
599 |
611 \indexspace |
600 \item Ullman, J. D., 139 |
612 |
|
613 \item Ullman, J. D., \hyperpage{139} |
601 \item \texttt {UN}, \bold{203} |
614 \item \texttt {UN}, \bold{203} |
602 \item \texttt {Un}, \bold{203} |
615 \item \texttt {Un}, \bold{203} |
603 \item \isa {UN_E} (theorem), \bold{102} |
616 \item \isa {UN_E} (theorem), \bold{102} |
604 \item \isa {UN_I} (theorem), \bold{102} |
617 \item \isa {UN_I} (theorem), \bold{102} |
605 \item \isa {UN_iff} (theorem), \bold{102} |
618 \item \isa {UN_iff} (theorem), \bold{102} |
606 \item \isa {Un_subset_iff} (theorem), \bold{100} |
619 \item \isa {Un_subset_iff} (theorem), \bold{100} |
607 \item \isacommand {undo} (command), 16 |
620 \item \isacommand {undo} (command), \hyperpage{16} |
608 \item \isa {unfold} (method), \bold{31} |
621 \item \isa {unfold} (method), \bold{31} |
609 \item Unicode, 55 |
622 \item Unicode, \hyperpage{55} |
610 \item unification, 70--73 |
623 \item unification, \hyperpage{70--73} |
611 \item \isa {UNION} (constant), 103 |
624 \item \isa {UNION} (constant), \hyperpage{103} |
612 \item \texttt {Union}, \bold{203} |
625 \item \texttt {Union}, \bold{203} |
613 \item union |
626 \item union |
614 \subitem indexed, 102 |
627 \subitem indexed, \hyperpage{102} |
615 \item \isa {Union_iff} (theorem), \bold{102} |
628 \item \isa {Union_iff} (theorem), \bold{102} |
616 \item \isa {unit} (type), 24 |
629 \item \isa {unit} (type), \hyperpage{24} |
617 \item unknowns, 7, \bold{62} |
630 \item unknowns, \hyperpage{7}, \bold{62} |
618 \item unsafe rules, \bold{84} |
631 \item unsafe rules, \bold{84} |
619 \item update |
632 \item update |
620 \subitem record, 153 |
633 \subitem record, \hyperpage{153} |
621 \item updating a function, \bold{103} |
634 \item updating a function, \bold{103} |
622 |
635 |
623 \indexspace |
636 \indexspace |
624 |
637 |
625 \item variables, 7 |
638 \item variables, \hyperpage{7} |
626 \subitem schematic, 7 |
639 \subitem schematic, \hyperpage{7} |
627 \subitem type, 5 |
640 \subitem type, \hyperpage{5} |
628 \item \isa {vimage_def} (theorem), \bold{105} |
641 \item \isa {vimage_def} (theorem), \bold{105} |
629 |
642 |
630 \indexspace |
643 \indexspace |
631 |
644 |
632 \item Wenzel, Markus, vii |
645 \item Wenzel, Markus, \hyperpage{vii} |
633 \item \isa {wf_induct} (theorem), \bold{109} |
646 \item \isa {wf_induct} (theorem), \bold{109} |
634 \item \isa {wf_inv_image} (theorem), \bold{109} |
647 \item \isa {wf_inv_image} (theorem), \bold{109} |
635 \item \isa {wf_less_than} (theorem), \bold{108} |
648 \item \isa {wf_less_than} (theorem), \bold{108} |
636 \item \isa {wf_lex_prod} (theorem), \bold{109} |
649 \item \isa {wf_lex_prod} (theorem), \bold{109} |
637 \item \isa {wf_measure} (theorem), \bold{109} |
650 \item \isa {wf_measure} (theorem), \bold{109} |
638 \item \isa {wf_subset} (theorem), 174 |
651 \item \isa {wf_subset} (theorem), \hyperpage{174} |
639 \item \isa {while} (constant), 179 |
652 \item \isa {while} (constant), \hyperpage{179} |
640 \item \isa {While_Combinator} (theory), 179 |
653 \item \isa {While_Combinator} (theory), \hyperpage{179} |
641 \item \isa {while_rule} (theorem), 179 |
654 \item \isa {while_rule} (theorem), \hyperpage{179} |
642 |
655 |
643 \indexspace |
656 \indexspace |
644 |
657 |
645 \item \isa {zadd_ac} (theorems), 147 |
658 \item \isa {zadd_ac} (theorems), \hyperpage{147} |
646 \item \isa {zmult_ac} (theorems), 147 |
659 \item \isa {zmult_ac} (theorems), \hyperpage{147} |
647 |
660 |
648 \end{theindex} |
661 \end{theindex} |