Isabelle: a generic theorem prover
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Lecture notes in computer science
828 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 321 S. |
| ISBN: | 3540582444 0387582444 |
Staff View
MARC
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| 100 | 1 | |a Paulson, Lawrence C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Isabelle |b a generic theorem prover |c Lawrence C. Paulson. With contributions by Tobias Nipkow |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a XVII, 321 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in computer science |v 828 | |
| 630 | 0 | 4 | |a Isabelle (Computer file) |
| 650 | 7 | |a Automatische bewijsvoering |2 gtt | |
| 650 | 4 | |a Théorèmes - Démonstration automatique | |
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| 650 | 7 | |a logique mathématique |2 inriac | |
| 650 | 7 | |a logique |2 inriac | |
| 650 | 7 | |a métalogique |2 inriac | |
| 650 | 7 | |a théorie démonstration |2 inriac | |
| 650 | 7 | |a vérification logiciel |2 inriac | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 0 | 7 | |a Isabelle |g Programm |0 (DE-588)4353452-1 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1820874843687485440 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
I
INTRODUCTION
TO
ISABELLE
1
1
FOUNDATIONS
.
3
1.1
FORMALIZING
LOGICAL
SYNTAX
IN
ISABELLE
.
3
1.2
FORMALIZING
LOGICAL
RULES
IN
ISABELLE
.
7
1.3
PROOF
CONSTRUCTION
IN
ISABELLE
.
11
1.4
LIFTING
A
RULE
INTO
A
CONTEXT
.
15
1.5
BACKWARD
PROOF
BY
RESOLUTION
.
17
1.6
VARIATIONS
ON
RESOLUTION
.
21
2
GETTING
STARTED
WITH
ISABELLE
.
25
2.1
FORWARD
PROOF
.
25
2.2
BACKWARD
PROOF
.
30
2.3
QUANTIFIER
REASONING
.
34
3
ADVANCED
METHODS
.
41
3.1
DERIVING
RULES
IN
ISABELLE
.
41
3.2
DEFINING
THEORIES
.
46
3.3
THEORY
EXAMPLE:
THE
NATURAL
NUMBERS
.
52
3.4
REFINEMENT
WITH
EXPLICIT
INSTANTIATION
.
55
3.5
A
PROLOG
INTERPRETER
.
58
II
THE
ISABELLE
REFERENCE
MANUAL
63
4
BASIC
USE
OF
ISABELLE
.
65
4.1
BASIC
INTERACTION
WITH
ISABELLE
.
65
4.2
ENDING
A
SESSION
.
66
4.3
READING
ML
FILES
.
66
4.4
PRINTING
OF
TERMS
AND
THEOREMS
.
66
4.5
DISPLAYING
EXCEPTIONS
AS
ERROR
MESSAGES
.
68
4.6
SHELL
SCRIPTS
.
68
XII
TABLE
OF
CONTENTS
5
PROOF
MANAGEMENT:
THE
SUBGOAL
MODULE
.
71
5.1
BASIC
COMMANDS
.
71
5.2
SHORTCUTS
FOR
APPLYING
TACTICS
.
74
5.3
EXECUTING
BATCH
PROOFS
.
76
5.4
MANAGING
MULTIPLE
PROOFS
.
77
5.5
DEBUGGING
AND
INSPECTING
.
78
6
TACTICS
.
81
6.1
RESOLUTION
AND
ASSUMPTION
TACTICS
.
81
6.2
OTHER
BASIC
TACTICS
.
83
6.3
OBSCURE
TACTICS
.
85
6.4
MANAGING
LOTS
OF
RULES
.
87
6.5
PROGRAMMING
TOOLS
FOR
PROOF
STRATEGIES
.
89
6.6
SEQUENCES
.
90
7
TACTICALS
.
93
7.1
THE
BASIC
TACTICALS
.
93
7.2
CONTROL
AND
SEARCH
TACTICALS
.
95
7.3
TACTICALS
FOR
SUBGOAL
NUMBERING
.
98
8
THEOREMS
AND
FORWARD
PROOF
.
101
8.1
BASIC
OPERATIONS
ON
THEOREMS
.
101
8.2
PRIMITIVE
META-LEVEL
INFERENCE
RULES
.
105
8.3
DERIVED
RULES
FOR
GOAL-DIRECTED
PROOF
.
109
9
THEORIES,
TERMS
AND
TYPES
.
113
9.1
DEFINING
THEORIES
.
113
9.2
LOADING
A
NEW
THEORY
.
115
9.3
RELOADING
MODIFIED
THEORIES
.
116
9.4
BASIC
OPERATIONS
ON
THEORIES
.
118
9.5
TERMS
.
119
9.6
VARIABLE
BINDING
.
120
9.7
CERTIFIED
TERMS
.
121
9.8
TYPES
.
122
9.9
CERTIFIED
TYPES
.
122
10
DEFINING
LOGICS
.
125
10.1
PRIORITY
GRAMMARS
.
125
10.2
THE
PURE
SYNTAX
.
126
10.3
MIXFIX
DECLARATIONS
.
131
10.4
EXAMPLE:
SOME
MINIMAL
LOGICS
.
136
11
SYNTAX
TRANSFORMATIONS
.
139
11.1
ABSTRACT
SYNTAX
TREES
.
139
11.2
TRANSFORMING
PARSE
TREES
TO
ASTS
.
140
11.3
TRANSFORMING
ASTS
TO
TERMS
.
142
TABLE
OF
CONTENTS
XIII
11.4
PRINTING
OF
TERMS
.
142
11.5
MACROS:
SYNTACTIC
REWRITING
.
144
11.6
TRANSLATION
FUNCTIONS
.
150
12
SUBSTITUTION
TACTICS
.
153
12.1
SUBSTITUTION
RULES
.
153
12.2
SUBSTITUTION
IN
THE
HYPOTHESES
.
154
12.3
SETTING
UP
HYP_SUBST_TAC
.
155
13
SIMPLIFICATION
.
157
13.1
SIMPLIFICATION
SETS
.
157
13.2
THE
SIMPLIFICATION
TACTICS
.
160
13.3
EXAMPLES
USING
THE
SIMPLIFIER
.
161
13.4
PERMUTATIVE
REWRITE
RULES
.
164
13.5
*SETTING
UP
THE
SIMPLIFIER
.
166
14
THE
CLASSICAL
REASONER
.
171
14.1
THE
SEQUENT
CALCULUS
.
171
14.2
SIMULATING
SEQUENTS
BY
NATURAL
DEDUCTION
.
172
14.3
EXTRA
RULES
FOR
THE
SEQUENT
CALCULUS
.
173
14.4
CLASSICAL
RULE
SETS
.
174
14.5
THE
CLASSICAL
TACTICS
.
176
14.6
SETTING
UP
THE
CLASSICAL
REASONER
.
178
III
ISABELLE
'
S
OBJECT-LOGICS
179
15
BASIC
CONCEPTS
.
181
15.1
SYNTAX
DEFINITIONS
.
182
15.2
PROOF
PROCEDURES
.
183
16
FIRST-ORDER
LOGIC
.
185
16.1
SYNTAX
AND
RULES
OF
INFERENCE
.
185
16.2
GENERIC
PACKAGES
.
186
16.3
INTUITIONISTIC
PROOF
PROCEDURES
.
186
16.4
CLASSICAL
PROOF
PROCEDURES
.
191
16.5
AN
INTUITIONISTIC
EXAMPLE
.
192
16.6
AN
EXAMPLE
OF
INTUITIONISTIC
NEGATION
.
193
16.7
A
CLASSICAL
EXAMPLE
.
195
16.8
DERIVED
RULES
AND
THE
CLASSICAL
TACTICS
.
196
17
ZERMELO-FRAENKEL
SET
THEORY
.
203
17.1
WHICH
VERSION
OF AXIOMATIC
SET
THEORY?
.
203
17.2
THE
SYNTAX
OF
SET
THEORY
.
204
17.3
BINDING
OPERATORS
.
206
17.4
THE
ZERMELO-FRAENKEL
AXIOMS
.
208
XIV
TABLE
OF
CONTENTS
17.5
FROM
BASIC
LEMMAS
TO
FUNCTION
SPACES
.
211
17.6
FURTHER
DEVELOPMENTS
.
219
17.7
SIMPLIFICATION
RULES
.
228
17.8
THE
EXAMPLES
DIRECTORY
.
229
17.9
A
PROOF
ABOUT
POWERSETS
.
230
17.10
MONOTONICITY
OF
THE
UNION
OPERATOR
.
232
17.11
LOW-LEVEL
REASONING
ABOUT
FUNCTIONS
.
233
18
HIGHER-ORDER
LOGIC
.
235
18.1
SYNTAX
.
235
18.2
RULES
OF
INFERENCE
.
240
18.3
A
FORMULATION
OF
SET
THEORY
.
245
18.4
GENERIC
PACKAGES
AND
CLASSICAL
REASONING
.
251
18.5
TYPES
.
253
18.6
THE
EXAMPLES
DIRECTORIES
.
259
18.7
EXAMPLE:
CANTOR
'
S
THEOREM
.
260
19
FIRST-ORDER
SEQUENT
CALCULUS
.
263
19.1
UNIFICATION
FOR
LISTS
.
263
19.2
SYNTAX
AND
RULES
OF
INFERENCE
.
265
19.3
TACTICS
FOR
THE
CUT
RULE
.
267
19.4
TACTICS
FOR
SEQUENTS
.
268
19.5
PACKAGING
SEQUENT
RULES
.
269
19.6
PROOF
PROCEDURES
.
270
19.7
A
SIMPLE
EXAMPLE
OF
CLASSICAL
REASONING
.
271
19.8
A
MORE
COMPLEX
PROOF
.
272
20
CONSTRUCTIVE
TYPE
THEORY
.
275
20.1
SYNTAX
.
277
20.2
RULES
OF
INFERENCE
.
277
20.3
RULE
LISTS
.
281
20.4
TACTICS
FOR
SUBGOAL
REORDERING
.
284
20.5
REWRITING
TACTICS
.
284
20.6
TACTICS
FOR
LOGICAL
REASONING
.
285
20.7
A
THEORY
OF
ARITHMETIC
.
286
20.8
THE
EXAMPLES
DIRECTORY
.
286
20.9
EXAMPLE:
TYPE
INFERENCE
.
288
20.10
AN
EXAMPLE
OF
LOGICAL
REASONING
.
289
20.11
EXAMPLE:
DERIVING
A
CURRYING
FUNCTIONAL
.
292
20.12
EXAMPLE:
PROVING
THE
AXIOM
OF
CHOICE
.
293
A
SYNTAX
OF
ISABELLE
THEORIES
.
297
REFERENCES
.
301
INDEX
.
305 |
| any_adam_object | 1 |
| author | Paulson, Lawrence C. |
| author_facet | Paulson, Lawrence C. |
| author_role | aut |
| author_sort | Paulson, Lawrence C. |
| author_variant | l c p lc lcp |
| building | Verbundindex |
| bvnumber | BV009676056 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.9.A96P38 1994 |
| callnumber-search | QA76.9.A96P38 1994 |
| callnumber-sort | QA 276.9 A96 P38 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 240 |
| classification_tum | DAT 706f |
| ctrlnum | (OCoLC)246321016 (DE-599)BVBBV009676056 |
| dewey-full | 511.3/0285/5320 511.3/0285/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/0285/53 20 511.3/0285/53 |
| dewey-search | 511.3/0285/53 20 511.3/0285/53 |
| dewey-sort | 3511.3 3285 253 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV009676056 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T15:06:11Z |
| institution | BVB |
| isbn | 3540582444 0387582444 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006399684 |
| oclc_num | 246321016 |
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| physical | XVII, 321 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Paulson, Lawrence C. Verfasser aut Isabelle a generic theorem prover Lawrence C. Paulson. With contributions by Tobias Nipkow Berlin [u.a.] Springer 1994 XVII, 321 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 828 Isabelle (Computer file) Automatische bewijsvoering gtt Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction inriac langage formel inriac logique mathématique inriac logique inriac métalogique inriac théorie démonstration inriac vérification logiciel inriac Automatic theorem proving Isabelle Programm (DE-588)4353452-1 gnd rswk-swf Isabelle Programm (DE-588)4353452-1 s DE-604 Lecture notes in computer science 828 (DE-604)BV000000607 828 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006399684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Paulson, Lawrence C. Isabelle a generic theorem prover Lecture notes in computer science Isabelle (Computer file) Automatische bewijsvoering gtt Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction inriac langage formel inriac logique mathématique inriac logique inriac métalogique inriac théorie démonstration inriac vérification logiciel inriac Automatic theorem proving Isabelle Programm (DE-588)4353452-1 gnd |
| subject_GND | (DE-588)4353452-1 |
| title | Isabelle a generic theorem prover |
| title_auth | Isabelle a generic theorem prover |
| title_exact_search | Isabelle a generic theorem prover |
| title_full | Isabelle a generic theorem prover Lawrence C. Paulson. With contributions by Tobias Nipkow |
| title_fullStr | Isabelle a generic theorem prover Lawrence C. Paulson. With contributions by Tobias Nipkow |
| title_full_unstemmed | Isabelle a generic theorem prover Lawrence C. Paulson. With contributions by Tobias Nipkow |
| title_short | Isabelle |
| title_sort | isabelle a generic theorem prover |
| title_sub | a generic theorem prover |
| topic | Isabelle (Computer file) Automatische bewijsvoering gtt Théorèmes - Démonstration automatique Théorèmes - Démonstration automatique ram déduction inriac langage formel inriac logique mathématique inriac logique inriac métalogique inriac théorie démonstration inriac vérification logiciel inriac Automatic theorem proving Isabelle Programm (DE-588)4353452-1 gnd |
| topic_facet | Isabelle (Computer file) Automatische bewijsvoering Théorèmes - Démonstration automatique déduction langage formel logique mathématique logique métalogique théorie démonstration vérification logiciel Automatic theorem proving Isabelle Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006399684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000607 |
| work_keys_str_mv | AT paulsonlawrencec isabelleagenerictheoremprover |