Translation Program

Use the push-pull parsing algorithm to parse each input string w; then construct its parse tree if it exists:

1) w = id - (id + id).

2) w = (id + id) / id.

3) w = (id + id)- (id.

4) w = id + * (id - id) / id.

5) w = (id + id) / (id + id).

6) w = id * id - id) + id.

7) w = id * (id + id)/(id - id).

3.46. Given a grammar with the following production rules:

1. E  E+T ;

2. E  T ; 3.T  T*F ; 4.T  F ;

5. F  (E) ;

6. F  id.

With the parse table being:

Status

Action						Goto
id	+	*	(	)	$	E	T	F
0	s 5			s 4			1	2	3
1		s 6				account
2		r 2	s 7		r 2	r 2
3		r 4	r 4		r 4	r 4
4	s 5			s 4			8	2	3
5		r 6	r 6		r 6	r 6
6	s 5			s 4				9	3
7	s 5			s 4					10
8		s 6			s 11
9		r 1	s 7		r 1	r 1
10		r 3	r 3		r 3	r 3
11		r 5	r 5		r 5	r 5

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BT 3.464.6 SLR Parsing Table

Use the LR parsing algorithm to parse the input string:

1) w = id * (id + id).

2) w = id + id + id).

3) w = id + * id + id.

4) w = id + (id + id).

5) w = (id + (id + id))* id.

6) w = (id + id) * (id + id).

7) w = id * ((id + id)* id).

3.47. Given a grammar that generates mathematical expressions with the generation rules: E → E * T | T;

T → T + F | F ;

F → F / G | G ; G → G - B | B;

B → ( E ) | id .

1) Construct the LR(0) item set family of the grammar.

2) Build action and goto functions for the SLR parser of the grammar.

3) Build an SLR parser table for the grammar.

4) Use the parsing algorithm to parse the input string:

1) w = id - (id + id).

2) w = (id + id) / id.

3) w = (id + id) - (id.

4) w = id + * (id - id) / id.

5) w = (id + id) / (id + id).

6) w = id * id - id) + id.

7) w = id * (id + id)/(id - id).

SUMMARY SOLUTION OR GUIDE

CHAPTER 1

1.9. Summary solution

1. digit  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Then: + digit is a token;

+ 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 is the vocabulary pattern of the digit card;

+ Each digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is a lexeme of the digit card.

2. digits  digit(digit) *

Then: + digits is a token;

+ The regular expression digit(digit) * is the pattern of the digits tag;

+ Each number: 0, 1, 20, 135, ... is a lexeme of the digits tag.

3. optional_fraction  . digits | ε

Then: + optional_fraction is a token;

+ The regular expression . digits | ε is the lexical pattern of the optional_fraction tag;

+ Each: ε, .0, .5, .21, .135, ... is a lexeme of the optional_fraction tag.

4. optional_exponent  ( E ( + | - | ε ) digits) | ε Then: + optional_exponent is a token;

+ Regular expression ( E ( + | - | ε ) digits) | ε is the lexical pattern of the optional_exponent tag;

+ Each: ε, E-1, E5, E+2, E135, ... is a lexeme of the optional_exponent tag.

5. nums  digits optional_fraction optional_exponent Then: + nums is a token;

+ Regular expression: digits optional_fraction optional_exponent is the lexical pattern of the num tag;

+ Each: 1, 126, 572E-1, 329.22 E5, 143.0 E+2, ... is a lexeme of the nums tag.

1.10. Summary solution

a) With the high-level programming language Pascal

1. Data type

- Integer

digit  0 | 1 |...| 9 ; sign  + | - | ε ;

digits  (sign)(digit)(digit)

- Short integer (sortint)

- Long integer (longint)

- Real number

+ Fixed floating point real number optional_fraction  . digits | ε ;

number  (sign)(digits)(optional_fraction)

+ Floating point numbers

optional_exponent  ( E ( + | - | ε ) digits) | ε;

nums  digits optional_fraction optional_exponent.

- Character (Char) – alphabet

Char  A | B | ...| Z | a | b |...| z | 0 | 1|...| 9| ( | ) | [ | ] | { | }| ?| < | -| +| ...

- String

String  (char)(char)

- logical (boolean)

Boolean  true | false

...

2. Relational operation (Relop) relop  < | <= | > | >= | <>

3. Arithmetic operation (operator)

Operator  +  -  *  /  **

4. Assignment Assign  :=

5. Name (Identifer)

letter  A | B | ...| Z | a | b |...| z ; digit  0 | 1 | ...| 9 ;

id  (letter| _ ) (letter | digit | _ ) *

6. Standard identifier

Integer  Integer; Shortint  Shortint; longint  longint; real  real;

Char  Char; String  String; Boolean  Boolean; pi  3.141...;

There are also many other standard names such as: sqr, sqrt, copy, val, max, min, ...

7. Keyword

If  if;

then  then; else  else; while  while; due to  due to;

to  to; for  for;

repeat  repeat; until  until; program  program; label  label;

const  const; var  var;

function  function; procedure  procedure; begin  begin

end  end

8. Signs ,

- semi  ;

- comma  ,

- Dot  .

- twodot  :

...

9. Space, tab, newline delim  blank | tab | newline ;

ws  delim .

10. othersign  (, ), …

…

b) With high-level programming language C: Similar

CHAPTER 2

2.10. Summary solution

Status

Token	Lexeme
1	function	function
2	begin	begin
3	if	if
4	then	then
5	else	else
6	end	end
7	id	max2, i , j

integer	Integer
9	Assign	: =
10	twocham	:
11	relop	>
12	semi	;

Table BT 2.10.

2.11. Summary solution

Status

Token	Lexeme
1	PROGRAM	PROGRAM
2	VAR	VAR
3	FUNCTION	FUNCTION
4	Begin	Begin
5	End	End
6	PROCEDURE	PROCEDURE
7	REPEAT	REPEAT
8	UNTIL	UNTIL
9	If	If
10	Then	Then
11	Id	GPTB2, a, b, c, x1, x2, Delta, Ptb2, r
12	Semi	;
13	Comma	,
14	Twocham	:
15	Real	real
16	Assign	:=
17	Sqr	Sqr
18	Sqrt	Sqrt
19	Write	Write
20	WriteIn	WriteIn
21	readln	readln

Operator	-, +, *, /,
23	othersign	(, )
24	Litral	„a=‟, „b=‟, „c=‟, „inexplicable equation‟, „double-solved equation x1 = x2 =‟, „x2 =‟, The equation has two solutions: x1=
25	relop	<>, <, >, =,
26	digits	0, 1, 2
27	dot	.