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