3. Описание этапа синтаксического анализа.
3.1 Построение кс-грамматики входного языка.
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S → Decl void main() { SOp }
SOp → Op SOp SOp → ε
Op → Lab: NOp; Op → NOp; Op → DecT;
DecT → typedef Typ ID DecT → typedef vector [Dim] ID
NOp → { SOp } NOp → COpG NOp → COp NOp → CycOp NOp → TrOp NOp → InOp NOp → OutOp NOp → Exp
COpG → (Exp)? Exp : Exp
COp → if (Exp) Op else Op COp → if (Exp) Op
CycOp → for (NEx;NEx;NEx) Op
NEx → Exp NEx → ε
TrOp → goto Lab
OutOp → printf ( Pr NPr )
NPr → , Pr NPr NPr → ε Pr → Var Pr → Num Pr → Str
InOp → scanf Var
Exp → Exp || Dis Exp → Dis Exp → Exp UnOp Exp → Exp GOp Exp Dis → Dis && Con Dis → Con |
Con → Con AddOp Rel Con → Rel
Rel → Rel RelOp Sm Rel → Sm
Sm → Sm MOp Ml Sm → Ml
Ml → Num Ml → Var Ml → (Exp) Ml → UnOp Ml Ml → ! Ml
Decl → Decl1; Decl Decl → ε
Decl1 → Typ ID Decl1’ Decl1 → const Typ ID Decl1’ Decl1 → vector ID Dim Decl1’’
Decl1’ → = Num Decl1’ → ε Decl1’’ → = VecVal Decl1’’ → ε
VecVal → [ELV LNum]
LNum → , ELV LNum LNum → ε
Var → ID Var → VecVal Var → ElV
ElV → ID [ Ind ] ElV → Num
Typ → Type Typ → ID Lab → ID Dim → CN Ind → CN Num → CF Num → CN |
3.2 Определение класса кс-грамматики входного языка.
Построенная грамматика входного языка должна входить в класс LL(1) – грамматик. Для этого необходимо устранить левую рекурсию и провести левую факторизацию. Получим LL(1) – грамматику:
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1
2 3
4 5 6
7 8 9
10 11 12 13 14 15 16 17
18
19 20 21
22
23 24
25
26
27 28 29 30 31
32
33 34 35 36 37 38 39 |
S → Decl void main() { SOp }
SOp → Op SOp SOp → ε
Op → Lab: NOp; Op → NOp; Op → DecT;
DecT → typedef DecT’ DecT’ → Typ ID DecT’ → vector [Dim] ID
NOp → { SOp } NOp → COpG NOp → COp NOp → CycOp NOp → TrOp NOp → InOp NOp → OutOp NOp → Exp
COpG → (Exp)? Exp : Exp
COp → if (Exp) Op COp’ COp’ → else Op COp’ → ε
CycOp → for (NEx;NEx;NEx) Op
NEx → Exp NEx → ε
TrOp → goto Lab
OutOp → printf ( Pr NPr )
NPr → , Pr NPr NPr → ε Pr → Var Pr → Num Pr → Str
InOp → scanf Var
Exp → Dis Exp’ Exp’ → || Dis Exp’ Exp’ → GOp Dis Exp’ Exp’ → UnOp Exp’ Exp’ → ε Dis → Con Dis’ Dis’→ && Con Dis’ |
40
41 42 43
44 45 46
47 48 49
50 51 52 53 54
55 56
57 58 59
60 61 62 63
64 65 66
67 68 69 70
71 72 73 74 75 76 77 78
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Dis’ → ε
Con → Rel Con’ Con’ → AddOp Rel Con’ Con’ → ε
Rel → Sm Rel’ Rel’ → RelOp Sm Rel’ Rel’ → ε
Sm → Ml Sm’ Sm’ → MOp Ml Sm’ Sm’ → ε
Ml → Num Ml → Var Ml → (Exp) Ml → UnOp Ml Ml → ! Ml
Decl → Decl1; Decl Decl → ε
Decl1 → Typ ID Decl1’ Decl1 → const Typ ID Decl1’ Decl1 → vector ID Dim Decl1’’
Decl1’ → = Num Decl1’ → ε Decl1’’ → = VecVal Decl1’’ → ε
VecVal → [ELV LNum] LNum → , ELV LNum LNum → ε
Var → ID Var’ Var → VecVal Var’ → [ Ind ] Var’ → ε
ElV → ID ElV → Num Typ → Type Typ → ID Dim → CN Ind → CN Num → CF Num → CN |
Разбор для LL(1)-грамматики можно осуществить с помощью 1-предсказывающего алгоритма разбора, который использует входную ленту, магазин и выходную ленту.
Vp
– алфавит
магазинных символов, Σ – алфавит
терминальных символов. Работой алгоритма
управляет управляющая таблица М, задающая
отображение множества
в множество, состоящее из следующих
элементов:
(β, i), где
-
правая часть вывода с номеромiВЫБРОС
ДОПУСК
ОШИБКА
Алгоритм анализирует входную цепочку, выполняя последовательность тактов. Пусть FIRST (x) = {a}, тогда работа алгоритма в зависимости от элемента управляющей таблицы М(Х, а) определяется следующим образом:
М(Х, а)= (β, i) -
М(a, а)=ВЫБРОС -
М
=ДОПУСК -
-
завершение работы, выходная цепочка π
– левый разбор входной цепочкиМ(Х, а)=ОШИБКА – разбор прекращается, выдается сообщение об ошибке.
В нижеприведенной таблице управления столбцы – терминальные символы (токены), строки – магазинные символы. Для компактности вместо пары (β, i) приводится только номер правила вывода i, цепочка β – правая часть этого правила. Выброс обозначен буквой «в», пустые ячейки – ошибка.
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ID |
Lab |
CN |
CF |
Str |
I F |
EL SE |
MA IN |
VO ID |
FOR |
GO TO |
PRIN TF |
SCANF |
TYPEDE |
CONST |
VECTOR |
Type |
GOp |
= |
Add Op |
M Op |
Rel Op |
Un Op |
! |
|| |
&& |
( |
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{ |
} |
[ |
] |
, |
; |
Sep |
ε |
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S |
1 |
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1 |
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1 |
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1 |
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1 |
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Decl |
55 |
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56 |
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55 |
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55 |
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SOp |
2 |
2 |
2 |
2 |
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2 |
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2 |
2 |
2 |
2 |
2 |
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2 |
2 |
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2 |
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2 |
3 |
2 |
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Op |
5 |
4 |
5 |
5 |
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5 |
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5 |
5 |
5 |
5 |
6 |
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5 |
5 |
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5 |
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5 |
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5 |
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Nop |
17 |
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17 |
17 |
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12 |
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13 |
14 |
16 |
15 |
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17 |
17 |
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11 |
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10 |
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17 |
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DecT |
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7 |
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DecT’ |
8 |
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9 |
8 |
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CopG |
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18 |
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Cop |
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19 |
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Cop' |
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20 |
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CycOp |
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TrOp |
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InOp |
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26 |
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OutOp |
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31 |
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NPr |
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26 |
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25 |
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Pr |
29 |
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30 |
30 |
31 |
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29 |
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Exp |
33 |
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33 |
33 |
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33 |
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33 |
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33 |
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Exp' |
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35 |
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36 |
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35 |
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37 |
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37 |
37 |
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Dis |
38 |
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38 |
38 |
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38 |
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38 |
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38 |
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Dis' |
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40 |
40 |
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40 |
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40 |
39 |
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40 |
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40 |
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40 |
40 |
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Con |
41 |
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41 |
41 |
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41 |
41 |
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41 |
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41 |
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Con' |
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43 |
43 |
42 |
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43 |
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43 |
43 |
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43 |
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43 |
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43 |
43 |
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Rel |
44 |
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44 |
44 |
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44 |
44 |
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44 |
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Rel' |
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46 |
46 |
46 |
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45 |
46 |
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46 |
46 |
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46 |
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46 |
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46 |
46 |
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Sm |
47 |
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47 |
47 |
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47 |
47 |
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47 |
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Sm' |
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49 |
49 |
49 |
48 |
49 |
49 |
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49 |
49 |
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49 |
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49 |
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49 |
49 |
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Ml |
51 |
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50 |
50 |
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53 |
54 |
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52 |
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51 |
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Decl1 |
57 |
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58 |
59 |
57 |
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Decl1’ |
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60 |
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61 |
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Decl1’’ |
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62 |
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63 |
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Typ |
74 |
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73 |
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Dim |
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75 |
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Var |
67 |
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68 |
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Var’ |
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70 |
70 |
70 |
70 |
70 |
70 |
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70 |
70 |
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70 |
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70 |
69 |
70 |
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70 |
70 |
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VecVal |
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64 |
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Num |
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78 |
77 |
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LNum |
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66 |
65 |
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ElV |
71 |
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72 |
72 |
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Ind |
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76 |
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ID |
в |
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Lab |
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в |
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CN |
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в |
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CF |
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в |
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в |
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IF |
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в |
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ELSE |
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MAIN |
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в |
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VOID |
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FOR |
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GOTO |
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PRINTF |
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SCANF |
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допуск |