Interactive theorem proving and program development: Coq'Art, the calculus of inductive constructions
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
2004
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| Series: | Texts in theoretical computer science : an EATCS series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 469 S. |
| ISBN: | 3540208542 |
Staff View
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| 245 | 1 | 0 | |a Interactive theorem proving and program development |b Coq'Art, the calculus of inductive constructions |c Yves Bertot ; Pierre Castéran |
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| adam_text | YVES BERTOT * PIERRE CASTER AN INTERACTIVE THEOREM PROVING AND PROGRAM
DEVELOPMENT COQ ART:THE CALCULUS OF INDUCTIVE CONSTRUCTIONS FOREWORD BY
GERARD HUET AND CHRISTINE PAULIN-MOHRING SPRINGER CONTENTS A BRIEF
OVERVIEW 1 1.1 EXPRESSIONS, TYPES, AND FUNCTIONS 2 1.2 PROPOSITIONS AND
PROOFS 3 1.3 PROPOSITIONS AND TYPES 4 1.4 SPECIFICATIONS AND CERTIFIED
PROGRAMS 5 1.5 A SORTING EXAMPLE 5 1.5.1 INDUCTIVE DEFINITIONS 6 1.5.2
THE RELATION TO HAVE THE SAME ELEMENTS 6 1.5.3 A SPECIFICATION FOR A
SORTING PROGRAM 7 1.5.4 AN AUXILIARY FUNCTION 7 1.5.5 THE MAIN SORTING
FUNCTION 8 1.6 LEARNING COQ 9 1.7 CONTENTS OF THIS BOOK 9 1.8 LEXICAL
CONVENTIONS 11 TYPES AND EXPRESSIONS 13 2.1 FIRST STEPS 13 2.1.1 TERMS,
EXPRESSIONS, TYPES 14 2.1.2 INTERPRETATION SCOPES 14 2.1.3 TYPE CHECKING
15 2.2 THE RULES OF THE GAME 17 2.2.1 SIMPLE TYPES 17 2.2.2 IDENTIFIERS,
ENVIRONMENTS, CONTEXTS 18 2.2.3 EXPRESSIONS AND THEIR TYPES 20 2.2.4
FREE AND BOUND VARIABLES; A-CONVERSION 27 2.3 DECLARATIONS AND
DEFINITIONS 29 2.3.1 GLOBAL DECLARATIONS AND DEFINITIONS 29 2.3.2
SECTIONS AND LOCAL VARIABLES 30 2.4 COMPUTING 33 2.4.1 SUBSTITUTION 34
2.4.2 REDUCTION RULES 34 XVIII CONTENTS 2.4.3 REDUCTION SEQUENCES 36
2.4.4 CONVERTIBILITY 37 2.5 TYPES, SORTS, AND UNIVERSES 37 2.5.1 THE SET
SORT 37 2.5.2 UNIVERSES 38 2.5.3 DEFINITIONS AND DECLARATIONS OF
SPECIFICATIONS 39 2.6 REALIZING SPECIFICATIONS 41 3 PROPOSITIONS AND
PROOFS 43 3.1 MINIMAL PREPOSITIONAL LOGIC 45 3.1.1 THE WORLD OF
PROPOSITIONS AND PROOFS 45 3.1.2 GOALS AND TACTICS 46 3.1.3 A FIRST
GOAL-DIRECTED PROOF 47 3.2 RELATING TYPING RULES AND TACTICS 51 3.2.1
PROPOSITION BUILDING RULES 51 3.2.2 INFERENCE RULES AND TACTICS 52 3.3
STRUCTURE OF AN INTERACTIVE PROOF 56 3.3.1 ACTIVATING THE GOAL HANDLING
SYSTEM 57 3.3.2 CURRENT STAGE OF AN INTERACTIVE PROOF 57 3.3.3 UNDOING
57 3.3.4 REGULAR END OF A PROOF 58 3.4 PROOF IRRELEVANCE 58 3.4.1
THEOREM VERSUS DEFINITION 59 3.4.2 ARE TACTICS HELPFUL FOR BUILDING
PROGRAMS? 59 3.5 SECTIONS AND PROOFS 60 3.6 COMPOSING TACTICS 61 3.6.1
TACTICALS 61 3.6.2 MAINTENANCE ISSUES 65 3.7 ON COMPLETENESS FOR
PROPOSITIONAL LOGIC 67 3.7.1 A COMPLETE SET OF TACTICS 67 3.7.2
UNPROVABLE PROPOSITIONS 68 3.8 SOME MORE TACTICS 68 3.8.1 THE CUT AND
ASSERT TACTICS 68 3.8.2 AN INTRODUCTION TO AUTOMATIC TACTICS 70 3.9 A
NEW KIND OF ABSTRACTION 71 4 DEPENDENT PRODUCTS, OR PANDORA S BOX 73 4.1
IN PRAISE OF DEPENDENCE 74 4.1.1 EXTENDING THE SCOPE OF ARROWS 74 4.1.2
ON BINDING 78 4.1.3 A NEW CONSTRUCT 79 4.2 TYPING RULES AND DEPENDENT
PRODUCTS 81 4.2.1 THE APPLICATION TYPING RULE 81 4.2.2 THE ABSTRACTION
TYPING RULE 84 4.2.3 TYPE INFERENCE 86 CONTENTS XIX 4.2.4 THE CONVERSION
RULE 90 4.2.5 DEPENDENT PRODUCTS AND THE CONVERTIBILITY ORDER 90 4.3 *
EXPRESSIVE POWER OF THE DEPENDENT PRODUCT 91 4.3.1 FORMATION RULE FOR
PRODUCTS 91 4.3.2 DEPENDENT TYPES 92 4.3.3 POLYMORPHISM 94 4.3.4
EQUALITY IN THE COQ SYSTEM 98 4.3.5 HIGHER-ORDER TYPES 99 EVERYDAY LOGIC
105 5.1 PRACTICAL ASPECTS OF DEPENDENT PRODUCTS 105 5.1.1 EXACT AND
ASSUMPTION 105 5.1.2 THE INTRO TACTIC 106 5.1.3 THE APPLY TACTIC 108
5.1.4 THE UNFOLD TACTIC 115 5.2 LOGICAL CONNECTIVES 116 5.2.1
INTRODUCTION AND ELIMINATION RULES 116 5.2.2 USING CONTRADICTIONS 118
5.2.3 NEGATION 119 5.2.4 CONJUNCTION AND DISJUNCTION 121 5.2.5 ABOUT THE
REPEAT TACTICAL 123 5.2.6 EXISTENTIAL QUANTIFICATION 123 5.3 EQUALITY
AND REWRITING 124 5.3.1 PROVING EQUALITIES 124 5.3.2 USING EQUALITY:
REWRITING TACTICS 125 5.3.3 * THE PATTERN TACTIC 127 5.3.4 * CONDITIONAL
REWRITING 128 5.3.5 SEARCHING THEOREMS FOR REWRITING 129 5.3.6 OTHER
TACTICS ON EQUALITY 129 5.4 TACTIC SUMMARY TABLE 130 5.5 ***
IMPREDICATIVE DEFINITIONS 130 5.5.1 WARNING 130 5.5.2 TRUE AND FALSE 130
5.5.3 LEIBNIZ EQUALITY 131 5.5.4 SOME OTHER CONNECTIVES AND QUANTIFIERS
133 5.5.5 A GUIDELINE FOR IMPREDICATIVE DEFINITIONS 135 INDUCTIVE DATA
TYPES 137 6.1 TYPES WITHOUT RECURSION 137 6.1.1 ENUMERATED TYPES 137
6.1.2 SIMPLE REASONING AND COMPUTING 139 6.1.3 THE ELIM TACTIC 141 6.1.4
PATTERN MATCHING 142 6.1.5 RECORD TYPES 145 6.1.6 RECORDS WITH VARIANTS
146 XX CONTENTS 6.2 CASE-BASED REASONING 148 6.2.1 THE CASE TACTIC 148
6.2.2 CONTRADICTORY EQUALITIES 151 6.2.3 INJECTIVE CONSTRUCTORS 153
6.2.4 INDUCTIVE TYPES AND EQUALITY 156 6.2.5 * GUIDELINES FOR THE CASE
TACTIC 156 6.3 RECURSIVE TYPES 160 6.3.1 NATURAL NUMBERS AS AN INDUCTIVE
TYPE 161 6.3.2 PROOF BY INDUCTION ON NATURAL NUMBERS 162 6.3.3 RECURSIVE
PROGRAMMING 164 6.3.4 VARIATIONS IN THE FORM OF CONSTRUCTORS 167 6.3.5
** TYPES WITH FUNCTIONAL FIELDS 170 6.3.6 PROOFS ON RECURSIVE FUNCTIONS
172 6.3.7 ANONYMOUS RECURSIVE FUNCTIONS (FIX) 174 6.4 POLYMORPHIC TYPES
175 6.4.1 POLYMORPHIC LISTS 175 6.4.2 THE OPTION TYPE 177 6.4.3 THE TYPE
OF PAIRS 179 6.4.4 THE TYPE OF DISJOINT SUMS 180 6.5 * DEPENDENT
INDUCTIVE TYPES 180 6.5.1 FIRST-ORDER DATA AS PARAMETERS 180 6.5.2
VARIABLY DEPENDENT INDUCTIVE TYPES 181 6.6 * EMPTY TYPES 184 6.6.1
NON-DEPENDENT EMPTY TYPES 184 6.6.2 DEPENDENCE AND EMPTY TYPES 185 7
TACTICS AND AUTOMATION 187 7.1 TACTICS FOR INDUCTIVE TYPES 187 7.1.1
CASE-BY-CASE ANALYSIS AND RECURSION 187 7.1.2 CONVERSIONS 188 7.2
TACTICS AUTO AND EAUTO 190 7.2.1 TACTIC DATABASE HANDLING: HINT 191
7.2.2 * THE EAUTO TACTIC 194 7.3 AUTOMATIC TACTICS FOR REWRITING 194
7.3.1 THE AUTOREWRITE TACTIC 194 7.3.2 THE SUBST TACTIC 195 7.4
NUMERICAL TACTICS 196 7.4.1 THE RING TACTIC 196 7.4.2 THE OMEGA TACTIC
198 7.4.3 THE FIELD TACTIC 199 7.4.4 THE F OURIER TACTIC 200 7.5 OTHER
DECISION PROCEDURES 200 7.6 ** THE TACTIC DEFINITION LANGUAGE 201 7.6.1
ARGUMENTS IN TACTICS 202 7.6.2 PATTERN MATCHING 203 CONTENTS XXI 7.6.3
USING REDUCTION IN DEFINED TACTICS 210 INDUCTIVE PREDICATES 211 8.1
INDUCTIVE PROPERTIES 211 8.1.1 A FEW EXAMPLES 211 8.1.2 INDUCTIVE
PREDICATES AND LOGIC PROGRAMMING 213 8.1.3 ADVICE FOR INDUCTIVE
DEFINITIONS 214 8.1.4 THE EXAMPLE OF SORTED LISTS 215 8.2 INDUCTIVE
PROPERTIES AND LOGICAL CONNECTIVES 217 8.2.1 REPRESENTING TRUTH 218
8.2.2 REPRESENTING CONTRADICTION 218 8.2.3 REPRESENTING CONJUNCTION 219
8.2.4 REPRESENTING DISJUNCTION 219 8.2.5 REPRESENTING EXISTENTIAL
QUANTIFICATION 219 8.2.6 REPRESENTING EQUALITY 220 8.2.7 ***
HETEROGENEOUS EQUALITY 220 8.2.8 AN EXOTIC INDUCTION PRINCIPLE? 225 8.3
REASONING ABOUT INDUCTIVE PROPERTIES 226 8.3.1 STRUCTURED INTROS 226
8.3.2 THE CONSTRUCTOR TACTICS 227 8.3.3 * INDUCTION ON INDUCTIVE
PREDICATES 227 8.3.4 * INDUCTION ON LE 229 8.4 * INDUCTIVE RELATIONS AND
FUNCTIONS . 233 8.4.1 REPRESENTING THE FACTORIAL FUNCTION 234 8.4.2 **
REPRESENTING THE SEMANTICS OF A LANGUAGE 239 8.4.3 ** PROVING SEMANTIC
PROPERTIES 240 8.5 * ELABORATE BEHAVIOR OF ELIM 244 8.5.1 INSTANTIATING
THE ARGUMENT 244 8.5.2 INVERSION 246 * FUNCTIONS AND THEIR
SPECIFICATIONS 251 9.1 INDUCTIVE TYPES FOR SPECIFICATIONS 252 9.1.1 THE
SUBSET TYPE 252 9.1.2 NESTED SUBSET TYPES 254 9.1.3 CERTIFIED DISJOINT
SUM 254 9.1.4 HYBRID DISJOINT SUM 256 9.2 STRONG SPECIFICATIONS 256
9.2.1 WELL-SPECIFIED FUNCTIONS 257 9.2.2 BUILDING FUNCTIONS AS PROOFS
257 9.2.3 PRECONDITIONS FOR PARTIAL FUNCTIONS 258 9.2.4 ** PROVING
PRECONDITIONS 259 9.2.5 ** REINFORCING SPECIFICATIONS 260 9.2.6 ***
MINIMAL SPECIFICATION STRENGTHENING 261 9.2.7 THE REFINE TACTIC 265 9.3
VARIATIONS ON STRUCTURAL RECURSION 267 XXII CONTENTS 9.3.1 STRUCTURAL
RECURSION WITH MULTIPLE STEPS 267 9.3.2 SIMPLIFYING THE STEP 271 9.3.3
RECURSIVE FUNCTIONS WITH SEVERAL ARGUMENTS 271 9.4 ** BINARY DIVISION
276 9.4.1 WEAKLY SPECIFIED DIVISION 276 9.4.2 WELL-SPECIFIED BINARY
DIVISION 281 10 * EXTRACTION AND IMPERATIVE PROGRAMMING 285 10.1
EXTRACTING TOWARD FUNCTIONAL LANGUAGES 285 10.1.1 THE EXTRACTION COMMAND
286 10.1.2 THE EXTRACTION MECHANISM 287 10.1.3 PROP, SET, AND EXTRACTION
295 10.2 DESCRIBING IMPERATIVE PROGRAMS 297 10.2.1 THE WHY TOOL 297
10.2.2 *** THE INNER WORKINGS OF WHY 300 11 * A CASE STUDY 309 11.1
BINARY SEARCH TREES 309 11.1.1 THE DATA STRUCTURE 309 11.1.2 A NAI VE
APPROACH TO DECIDING OCCURRENCE 311 11.1.3 DESCRIBING SEARCH TREES 311
11.2 SPECIFYING PROGRAMS 313 11.2.1 FINDING AN OCCURRENCE 313 11.2.2
INSERTING A NUMBER 313 11.2.3 ** REMOVING A NUMBER 314 11.3 AUXILIARY
LEMMAS 315 11.4 REALIZING SPECIFICATIONS 315 11.4.1 REALIZING THE
OCCURRENCE TEST 315 11.4.2 INSERTION 318 11.4.3 REMOVING ELEMENTS 322
11.5 POSSIBLE IMPROVEMENTS 323 11.6 ANOTHER EXAMPLE 324 12 * THE MODULE
SYSTEM 325 12.1 SIGNATURES 326 12.2 MODULES 328 12.2.1 BUILDING A MODULE
328 12.2.2 AN EXAMPLE: KEYS 329 12.2.3 PARAMETRIC MODULES (FUNCTORS) 332
12.3 A THEORY OF DECIDABLE ORDER RELATIONS 335 12.3.1 ENRICHING A THEORY
WITH A FUNCTOR 335 12.3.2 LEXICOGRAPHIC ORDER AS A FUNCTOR 337 12.4 A
DICTIONARY MODULE 339 12.4.1 ENRICHED IMPLEMENTATIONS 340 12.4.2
CONSTRUCTING A DICTIONARY WITH A FUNCTOR 340 CONTENTS XXIII 12.4.3 A
TRIVIAL IMPLEMENTATION 340 12.4.4 AN EFFICIENT IMPLEMENTATION 342 12.5
CONCLUSION 345 13 ** INFINITE OBJECTS AND PROOFS 347 13.1 CO-INDUCTIVE
TYPES 347 13.1.1 THE COLNDUCTIVE COMMAND 347 13.1.2 SPECIFIC FEATURES OF
CO-INDUCTIVE TYPES 348 13.1.3 INFINITE LISTS (STREAMS) 348 13.1.4 LAZY
LISTS 349 13.1.5 LAZY BINARY TREES 349 13.2 TECHNIQUES FOR CO-INDUCTIVE
TYPES 350 13.2.1 BUILDING FINITE OBJECTS 350 13.2.2 PATTERN MATCHING 350
13.3 BUILDING INFINITE OBJECTS 351 13.3.1 A FAILED ATTEMPT 352 13.3.2
THE COFIXPOINT COMMAND 352 13.3.3 A FEW CO-RECURSIVE FUNCTIONS 354
13.3.4 BADLY FORMED DEFINITIONS 356 13.4 UNFOLDING TECHNIQUES 357 13.4.1
SYSTEMATIC DECOMPOSITION 358 13.4.2 APPLYING THE DECOMPOSITION LEMMA 358
13.4.3 SIMPLIFYING A CALL TO A CO-RECURSIVE FUNCTION 359 13.5 INDUCTIVE
PREDICATES OVER CO-INDUCTIVE TYPES 361 13.6 CO-INDUCTIVE PREDICATES 362
13.6.1 A PREDICATE FOR INFINITE SEQUENCES 363 13.6.2 BUILDING INFINITE
PROOFS 363 13.6.3 GUARD CONDITION VIOLATION 365 13.6.4 ELIMINATION
TECHNIQUES 366 13.7 BISIMILARITY 368 13.7.1 THE BISIMILAR PREDICATE 368
13.7.2 USING BISIMILARITY 370 13.8 THE PARK PRINCIPLE 371 13.9 LTL 372
13.10A CASE STUDY: TRANSITION SYSTEMS 375 13.10.1AUTOMATA AND TRACES 375
13.11CONCLUSION 376 14 ** FOUNDATIONS OF INDUCTIVE TYPES 377 14.1
FORMATION RULES 377 14.1.1 THE INDUCTIVE TYPE 377 14.1.2 THE
CONSTRUCTORS 379 14.1.3 BUILDING THE INDUCTION PRINCIPLE 382 14.1.4
TYPING RECURSORS 385 14.1.5 INDUCTION PRINCIPLES FOR PREDICATES 392 XXIV
CONTENTS 14.1.6 THE SCHEME COMMAND 394 14.2 *** PATTERN MATCHING AND
RECURSION ON PROOFS 394 14.2.1 RESTRICTIONS ON PATTERN MATCHING 395
14.2.2 RELAXING THE RESTRICTIONS 396 14.2.3 RECURSION 398 14.3 MUTUALLY
INDUCTIVE TYPES 400 14.3.1 TREES AND FORESTS 400 14.3.2 PROOFS BY MUTUAL
INDUCTION 402 14.3.3 *** TREES AND TREE LISTS 404 15 * GENERAL RECURSION
407 15.1 BOUNDED RECURSION 408 15.2 ** WELL-FOUNDED RECURSIVE FUNCTIONS
411 15.2.1 WELL-FOUNDED RELATIONS 411 15.2.2 ACCESSIBILITY PROOFS 411
15.2.3 ASSEMBLING WELL-FOUNDED RELATIONS 413 15.2.4 WELL-FOUNDED
RECURSION 414 15.2.5 THE RECURSOR WELL_F OUNDED_INDUCTION 414 15.2.6
WELL-FOUNDED EUCLIDEAN DIVISION 415 15.2.7 NESTED RECURSION 419 15.3 **
GENERAL RECURSION BY ITERATION 420 15.3.1 THE FUNCTIONAL RELATED TO A
RECURSIVE FUNCTION 421 15.3.2 TERMINATION PROOF 421 15.3.3 BUILDING THE
ACTUAL FUNCTION 424 15.3.4 PROVING THE FIXPOINT EQUATION 424 15.3.5
USING THE FIXPOINT EQUATION 426 15.3.6 DISCUSSION 427 15.4 *** RECURSION
ON AN AD HOC PREDICATE 427 15.4.1 DEFINING AN AD HOC PREDICATE 428
15.4.2 INVERSION THEOREMS 428 15.4.3 DEFINING THE FUNCTION 429 15.4.4
PROVING PROPERTIES OF THE FUNCTION 430 16 * PROOF BY REFLECTION 433 16.1
GENERAL PRESENTATION 433 16.2 DIRECT COMPUTATION PROOFS 435 16.3 **
PROOF BY ALGEBRAIC COMPUTATION 438 16.3.1 PROOFS MODULO ASSOCIATIVITY
438 16.3.2 MAKING THE TYPE AND THE OPERATOR MORE GENERIC 442 16.3.3 ***
COMMUTATIVITY: SORTING VARIABLES 445 16.4 CONCLUSION 447 APPENDIX 449
INSERTION SORT 449 CONTENTS XXV REFERENCES 453 INDEX 459 COQ AND ITS
LIBRARIES 460 EXAMPLES FROM THE BOOK 464
|
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| author | Bertot, Yves Castéran, Pierre |
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| ctrlnum | (OCoLC)249648441 (DE-599)BVBBV019325517 |
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| dewey-ones | 004 - Computer science |
| dewey-raw | 004.015113 |
| dewey-search | 004.015113 |
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| id | DE-604.BV019325517 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:57:42Z |
| institution | BVB |
| isbn | 3540208542 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012792619 |
| oclc_num | 249648441 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-29T |
| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-29T |
| physical | XXV, 469 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts in theoretical computer science : an EATCS series |
| spelling | Bertot, Yves Verfasser aut Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions Yves Bertot ; Pierre Castéran Berlin [u.a.] Springer 2004 XXV, 469 S. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science : an EATCS series Automatisches Beweisverfahren Programmverifikation - Automatisches Beweisverfahren Automatic theorem proving Computer programming Programmverifikation (DE-588)4135576-3 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Programmverifikation (DE-588)4135576-3 s Castéran, Pierre Verfasser aut HEBIS Datenaustausch Mainz application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012792619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertot, Yves Castéran, Pierre Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions Automatisches Beweisverfahren Programmverifikation - Automatisches Beweisverfahren Automatic theorem proving Computer programming Programmverifikation (DE-588)4135576-3 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| subject_GND | (DE-588)4135576-3 (DE-588)4069034-9 |
| title | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions |
| title_auth | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions |
| title_exact_search | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions |
| title_full | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions Yves Bertot ; Pierre Castéran |
| title_fullStr | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions Yves Bertot ; Pierre Castéran |
| title_full_unstemmed | Interactive theorem proving and program development Coq'Art, the calculus of inductive constructions Yves Bertot ; Pierre Castéran |
| title_short | Interactive theorem proving and program development |
| title_sort | interactive theorem proving and program development coq art the calculus of inductive constructions |
| title_sub | Coq'Art, the calculus of inductive constructions |
| topic | Automatisches Beweisverfahren Programmverifikation - Automatisches Beweisverfahren Automatic theorem proving Computer programming Programmverifikation (DE-588)4135576-3 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| topic_facet | Automatisches Beweisverfahren Programmverifikation - Automatisches Beweisverfahren Automatic theorem proving Computer programming Programmverifikation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012792619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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