Algorithmic Logic

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Springer Science & Business Media, Nov 30, 1987 - Computers - 372 pages
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Contents

INTRODUCTION
1
2 AN INFORMAL INTRODUCTION TO FORMALIZED LANGUAGES
5
3 ASSIGNING MEANINGS TO PROGRAMS
11
4 SEMANTIC PROPERTIES OF PROGRAMS
16
5 EXPRESSIVITY AN INTRODUCTION TO THE LANGUAGE OF ALGORITHMIC LOGIC
18
6 ON APPLICATIONS
20
LOGIC OF DETERMINISTIC ITERATIVE PROGRAMS
23
1 LANGUAGE
24
21 RATIONAL NUMBERS
194
22 COMPLEX NUMBERS
195
23 REAL NUMBERS
200
24 CONCLUDING REMARKS
202
BIBLIOGRAPHIC REMARKS
204
PR0P0S1TI0NAL ALGORITHMIC LOGIC
206
1 SYNTAX AND SEMANTICS
208
2 SEMANTIC PROPERTIES OF PROGRAM SCHEMES
212

2 SEMANTICS
30
3 EXPRESSIVENESS
38
4 PROPERTIES OF THE SEMANTIC CONSEQUENCE OPERATION
51
5 AXIOMATIZATION
56
6 MODELS AND CONSISTENCY
65
7 USEFUL TAUTOLOGIES AND INFERENCE RULES
69
8 AN EXAMPLE OF A CORRECTNESS PROOF
75
BIBLIOGRAPHIC REMARKS
77
METAMATHEMATICAL INVESTIGATIONS OF ALGORITHMIC LOGIC
79
2 THE COMPLETENESS THEOREM
89
3 TWO COROLLARIES OF THE COMPLETENESS THEOREM
95
4 THE STANDARD EXECUTION METHOD IS IMPLICITLY DEFINED BY THE AXIOMATIZATION OF ALGORITHMIC LOGIC
97
5 GENTZEN TYPE AXIOMATIZATION
103
6 THE NORMAL FORM OF PROGRAMS
109
7 EQUALITY
115
8 GENERALIZED TERMS
119
9 PARTIAL FUNCTIONS
122
10 MANY SORTED STRUCTURES
127
11 DEFINABILITY AND PROGRAMMABILITY
131
12 INESSENTIALrTY OF DEFINITIONS
135
BIBLIOGRAPHIC REMARKS
137
ALGORITHMIC PROPERTIES OF DATA STRUCTURES
138
2 DICTIONARIES
141
3 THEORY OF DICTIONARIES
142
4 REPRESENTATION THEOREM FOR MODELS OF ATD
149
5 ON COMPLEXITY OF ATD
151
6 THE THEORY OF PRIORITY QUEUES
154
7 THE THEORY OF NATURAL NUMBERS
155
8 STACKS
159
9 THE THEORY OF STACKS
160
10 THE REPRESENTATION THEOREM FOR STACKS
164
11 IMPLEMENTATIONS OF ARITHMETIC AND DICTIONARIES
166
12 THEORY OF LINKS AND STACKSATSL
167
LANGUAGE
173
14 QUEUES
176
15 BINARY TREES
179
16 BINARY SEARCH TREES
181
17 AN INTERPRETATION OF THE THEORY OF PRIORITY QUEUES
184
18 AN IMPLEMENTATION OF PRIORITY QUEUES
187
19 ARRAYS
190
20 HASHTABLES
193
3 PROPERTIES OF SEMANTIC STRUCTURES
221
4 THE SEMANTIC CONSEQUENCE OPERATION IS NOT COMPACT
228
5 THE SYNTACTIC CONSEQUENCE OPERATION
229
6 EXAMPLES OF PROPOSITIONAL THEORIES
233
7 LINDENBAUM ALGEBRA
237
PROGRAMS
239
9 PARTIAL FUNCTIONAL INTERPRETATIONS
243
THE COMPLETENESS THEOREM
248
VARIABLES
257
12 YANOV SCHEMES
261
13 APPLICATION OF PAL IN MICROPROGRAMMING
263
BIBLIOGRAPHIC REMARKS
268
NONDETERMINISM IN ALGORITHMIC LOGIC
269
1 NONDETERMINISTIC whilePROGRAMS AND THEIR SEMANTICS
270
2 PROPERTIES OF NONDETERMINISTIC PROGRAMS
273
3 THE SUBSTITUTION THEOREM
277
4 NONDETERMINISTIC ALGORITHMIC LOGIC
282
5 CERTAIN METAMATHEMATICAL RESULTS
286
6 ON ISOMORPHISM OF DATA STRUCTURES
289
7 ON THE EQUIVALENCE OF NONDETERMINISTIC PROGRAMS
291
BIBLIOGRAPHIC REMARKS
297
PROBLEMS AND THEORIES INSPIRED BY THE LOGLAN PROJECT
298
1 CONCURRENT PROGRAMS
299
2 MAX SEMANTICS
300
3 COMPARISON WITH SOME OTHER CONCEPTS OF CONCURRENCY
303
4 A COMPARISON OF MAX AND ARB SEMANTICS IN THE CASE OF PETRI NETS
311
5 CRITICAL REMARKS CONCERNING MAX SEMANTICS
315
6 LIBERAL SEMANTICS
318
7 AN ALGORITHMIC THEORY OF REFERENCES
328
8 REPRESENTATION THEOREM FOR ATR THEORY
332
9 SPECIFICATION OF UNIVOCAL REFERENCES
338
10 VIRTUAL MEMORY
339
11 CONCATENABLE TYPE DECLARATIONS
341
12 AN IMPLEMENTATION OF RATIONAL NUMBERS
344
BIBLIOGRAPHIC REMARKS
346
BOOLEAN ALGEBRAS
348
THE PROOF OF LEMMA 22 FROM CHAPTER III
352
BIBLIOGRAPHY
356
INDEX
369
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