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Greibach S.A. — Theory of Program Structures: Schemes, Semantics, Verification
Greibach S.A. — Theory of Program Structures: Schemes, Semantics, Verification

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Название: Theory of Program Structures: Schemes, Semantics, Verification

Автор: Greibach S.A.


The material in these lecture notes offers an exposition - aijned at graduate students rather than researchers in the field - of a topic often called "program schemata" or "schematology". The subject matter represents one approach to formalizing the elusive notion of the "semantics of programming languages". The idea is to model an "abstract flowchart" and study the interrelation between the syntax of programs (what can be said about their behavior from their format) and the semantics (what they actually "do", depending on the interpretation, the programming language, and perhaps even the implementation) and examine the application of formal proof systems to verify properties of programs.

Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 375

Добавлена в каталог: 05.12.2010

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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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