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| Greibach S.A. — Theory of Program Structures: Schemes, Semantics, Verification |
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| Предметный указатель |
Acceptable construction 4-48
Address 2-10
Address, transfer address 2-10
Ancestor 4-11
Array 7-51
Array, program scheme augmented by arrays 7-52
assignment statement 2-1 2-10
Assignment statement, extended assignment statement 4-44
Atomic formula A-1
Axiom of assignment 5-29
Back dominate 4-35
Block 4-14ff
Block, block composition 4-14
Block, block iteration 4-15
Block, block replacement lemma 4-15—4-16
Block, block structure theorem 4-18—4-19
Block, block structured program 4-15
Block, division into major blocks 4-20 4-23 4-24
Block, equivalence to tree-like graph 4-16 4-17
Block, subblock 4-15
Boolean expression 4-45
Boolean expression in recursion schemes 7-11
Boolean expression, arbitrary Boolean expressions in WHILE constructions 4-46—4-48
Boolean expression, type of wff A-1
CALL 7-34
Call, first level call 7-42
Call, recursive call 7-42
Canonical form 4-1
Canonical transformation 4-1
Chain dominate 4-36ff
Closed graph 4-30
Computation 2-6ff 2-11ff
Computation Record 4-2
Computation record, equivalent computation records 4-3
Computation record, test added computation record 4-3
Computation state 2-6
Computation, complete terminated computation 2-7
Computation, computation halts 2-8
Computationally equivalent 4-3
Computationally equivalent, strongly computationally equivalent 4-3
Computationally isomorphic 4-3
Computationally isomorphic, strongly computationally isomorphic 4-3
Conjunct; conjunction A-5
Consistent path 3-7
Consistent path set 3-7
Constants 2-1 2-4
correctness see "Partial correctness" "Total
Counter, augmentation by one counter 8-4
Counter, augmentation by two counters 8-6
Critical point 4-53—4-54
Cycle dominate 4-36ff
Decidable 6-2
Decidable, partially decidable 6-2
Disjunct; disjunction A-5
diverge 2-8
Dominate 4-11 4-35
Entry node 4-6
Execution sequence 3-2ff
Exhaustive simplification procedure 6-20ff
Exit node 4-7
Finite equivalence 2-17 6-14ff
Finite state acceptor, two-tape one-way deterministic finite state acceptor 6-3ff
Flow diagram 2-2
Flowchartable recursion scheme 7-17ff
Free program scheme 3-18
Free recursion scheme 7-10
Free tree program scheme 3-20
Graph, closed graph 4-30
Graph, graph homomorphic image 4-5
Graph, graph isomorphic 4-5
Graph, graph isomorphism 4-5
Graph, line-like graph 4-37
Graph, single entry single exit graph 4-30
Graph, single entry subgraph 4-6
Graph, tree-like graph 4-11
Graph, zero entry graph 4-30
Graph, zero exit graph 4-30
Halt everywhere; always halting 2-16
Herbrand universe 3-1
Homomorphic image 4-4
Homomorphic image, strong homomorphic image 4-5
Ianov scheme 6-29ff
IF-THEN construction 4-33
IF-THEN construction, extended IF-THEN construction 4-45
IF-THEN construction, simply extended IF-THEN construction 4-44
Incomparable classes of schemes 7-11
Inconsistent sentence A-6
Induction points 5-10
Inductive assertions 5-10
Infinity lemma 3-10
Interpretation 2-5
Interpretation of a wff A-3ff
Interpretation, compatible interpretations 2-22
Interpretation, finite interpretation 2-6
Interpretation, free interpretation 3-1ff
Interpretation, Herbrand interpretation 3-1ff
Interpretation, minimal interpretation 2-22
Interpretation, recursive interpretation 2-6
Intertranslatable 7-10
Konig's lemma 3-10
Label 7-52
Label, program scheme augmented by labels 7-52
Leaftest 7-62
Leaftest, Eleaftest 7-66
Liberal scheme 3-32ff
Line-like 4-37
Locator scheme 7-56 7-57 7-61
Logically equivalent A-6
Logically implies A-6
Loop program 4-49
Macroexpansion 7-42
Macroexpansion, complete first level macroexpansion 7-42
Minimization 4-51
| Model A-6
Monadic program scheme 3-21
Monadic recursion scheme 7-13 8-1ff
Monadic recursion scheme, free monadic recursion scheme 8-13ff
Parameters, actual parameters 7-34
Parameters, formal parameters 7-35
Partial correctness 2-26
Partial correctness and verification formula 5-9ff
Partial correctness of a path 5-4
Partial correctness of a scheme A-7
Post Correspondence Problem 3-24
Primitive recursion 4-49
Primitive recursive functions 4-50
Procedure body 7-35
Procedure definition 7-35
PROGRAM 2-6
Program scheme 2-2ff
Program scheme, always halting program scheme 3-13
Program scheme, free program scheme 3-18
Program scheme, free tree program scheme 3-20
Program scheme, linear form of a program scheme 2-10ff
Program scheme, monadic program scheme 3-21
Program scheme, tree program scheme 3-13
Pushdown store 7-51
Pushdown store, program scheme augmented by one pushdown store 7-51
Pushdown store, simple pushdown store 8-1
Q-sets 3-3ff 3-18
Quantifier A-1ff
Reasonable equivalence 2-20 6-20ff
Recursion augmented program scheme 7-35
Recursion equation 7-1
Recursion equation, linear recursion equation 7-13
Recursion scheme 7-4ff
Recursion scheme, computation in a recursion scheme 7-4ff
Recursion scheme, flowchartable recursion scheme 7-17
Recursion scheme, linear recursion scheme 7-13 7-26ff
Recursion scheme, monadic recursion scheme 7-13 8-1ff
Recursion scheme, monadic recursion scheme, left linear monadic recursion scheme 8-12
Recursion scheme, monadic recursion scheme, linear monadic recursion scheme 8-12
Recursion scheme, monadic recursion scheme, right linear monadic recursion scheme 8-12
Recursion scheme, right linear recursion scheme 7-33
Recursion scheme, simple recursion scheme 7-12
RECURSIVE 6-2
Recursive equivalence 2-17
Recursively enumerable 6-1
Rule of composition 5-29
Rule of conditional statements 5-30
Rule of consequence 5-30
Rule of iteration 5-30
Satisfiable A-6
Sentence A-6
Sentence, pretty sentence A-2
Single entry single exit subgraph 1-30
Single entry subgraph 1-6
STEP construction 1-19
STEP program 4-49
Strong equivalence 2-17
Strong equivalence of recursion schemes 7-10
Strong equivalence, relative to I 1-6
Structurally similar 4-4
Structurally similar, strongly structurally similar 4-4
Term 2-1 7-3
Term, extended functional term 1-11 7-3 A-1
Term, extended predicate term 1-11
Term, functional term 2-1
Term, linear term 7-12
Term, nonterminal term 7-3
Term, predicate term 2-1
Term, simple term 7-3
Term, terminal term 7-3
Term, very simple term 7-3
terminate 2-8
Termination problem 2-16
Test statement 2-2 2-10
Total correctness 2-26 5-8ff 5-14ff 6-26ff A-7
Total equivalence 2-19
Translatable 7-2 7-10
Translatable, effectively intertranslatable 7-10
Translatable, effectively translatable 7-10
Translatable, intertranslatable 7-10
Translatable, weakly translatable 8-25
Translation of scheme 7-2
Tree program scheme 3-13
Tree with reinitializations 4-20
Tree-like 4-11
Ultimately periodic tape 6-3
Valid sentence A-6
Value language of monadic program scheme 3-21 8-7
Value language of monadic recursion scheme 8-6
Value language, interpreted value language of monadic recursion scheme 8-7
Variables 2-1
Variables, bound variables A-2
Variables, free variables A-2
variables, global variables 7-35
Variables, local variables 7-35
Verification condition 5-2
Verification formula 5-8—5-9ff
Verification procedure 5-16ff
Weak equivalence 2-20
Well-formed formula, wff A-1
Well-formed formula, wff, pretty wff A-2
Well-formed formula, wff, quantifier-free wff A-1
Well-structured subscheme 1-31—1-32
WHILE composition 4-34
WHILE construction 4-34
WHILE construction, partially extended WHILE construction 4-45
WHILE construction, simply extended WHILE construction 4-44
WHILE program 4-49
WHILE program, simple WHILE program 4-35
WHILE scheme 4-49
WHILE scheme, simple WHILE scheme 4-35
Zero entry 4-30
Zero exit 4-30
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