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NOTE: The midterm exam is on Thursday, March 29.
The exam will cover Chapters 1 - 8 (except for Chapter 4) from the textbook and the following material on expression grammars and recursive descent parsers.
- Problem 1:
- Do the following Exercises from the textbook.
- From the end of Chapter 2, do Exercises 1a,c,f,h,i,j,l, 2a,c,f,h,i,j,l (pages 24-25).
- From the end of Chapter 3, do Exercises 1, 3, 4 (pages 41-42).
- From the end of Chapter 6, do Exercises 2 and 4 (page 102).
- From the end of Chapter 8, do Exercises 1 - 5 (pages 130-131).
- Problem 2:
- For each of the following expressions, rewrite the expression in both prefix and postfix notation, and draw an abstract syntax tree (i.e., an expression tree) for the expression.
(a) a * b + c
(b) a * (b + c)
(c) a * b + c * d
(d) a * (b + c) * d
- Problem 3:
- Describe in English the language defined by the following grammar. (Note: Do not use English to describe the grammar, describe the language defined by the grammar.)
<S> -> <A> <B> <C>
<A> -> 'a' <A> | 'a'
<B> -> 'b' <B> | 'b'
<C> -> 'c' <C> | 'c'
- Problem 4:
- Consider the following grammar.
<S> -> <A> 'a' <B> 'b'
<A> -> <A> 'b' | 'b'
<B> -> 'a' <B> | 'a'
Which of the following words are in the language generated by this grammar?
(a) baab
(b) bbbab
(c) bbaaaaa
(d) bbaab
- Problem 5:
- Consider the following grammar.
<S> -> 'a' <S> 'c' <B> | <A> | 'b'
<A> -> 'c' <A> | 'c'
<B> -> <A> | 'd'
Which of the following words are in the language generated by this grammar?
(a) abcd
(b) acccbd
(c) acccbcc
(d) acd
(e) accc
- Problem 6:
- For each of the following parts, define a grammar for the words, over the alphabet containing just 0 and 1, that are described.
(a) All words ending with a 1.
(b) All words of length exactly 8.
(c) All words that contain the string 0101.
(d) All words with odd length. Show how to parse the word 00100 using your grammar.
- Problem 7:
- The following grammar is motivated by declarations in C.
Declaration ::= Type Declarator ';'
Type ::= 'int' | 'char'
Declarator ::= '*' Declarator
| Declarator '[' Digit ']'
| Declarator '(' Type ')'
| '(' Declarator ')'
| Letter
Letter ::= 'a' | 'b' | ... | 'y' | 'z'
Digit ::= '1' | '2' | ... | '8' | '9'
(a) Give 5 examples of strings generated by this grammar.
(b) Show that this grammar is ambiguous.
- Problem 8:
- The following C function computes the number of decimal digits in a positive integer.
int numdigits(int x)
{ int t = x, n = 1;
while (t >= 10)
{ n++;
t = t/10;
}
return n;
}
(a) Implement this function in ML.
(b) Modify your function from part (a) so that it works with negative integers.
- Problem 9:
- Explain in detail exactly what the C, C++, Java expression
i + j / k
means and what its type is when the variables have the following types. Be sure to specify any
implicit type conversions.
- (a)
int i, j, k;
- (b)
int i, j; double k;
- (c)
double i; int j, k;
- Problem 10:
- Part (a) In C (or C++) explain the difference in meaning between the following two lines.
enum x { a, b };
enum { c, d } x;
In particular, what does each x represent? (Enumerations are described in our textbook on pages 89-90.)
- Part (b) The following code will compile in C but not in C++. Explain why. (Hint: Look up the two kinds of type equivalence. Type equivalence is described in our textbook on pages 100-101.)
int main()
{
enum { a, b } x;
enum { c, d } y;
y = c;
x = y;
return 0;
}
- Problem 11:
- Consider the following grammar for postfix expressions.
Postfix -> Postfix Postfix BinOp
| Postfix UnOp
| Number
BinOp -> '+' | '-' | '*' | '/'
UnOp -> 'neg' | 'sqrt'
Number -> any valid Java double
- Part (a) Draw the parse tree (not the expression tree) for the expression
4 5 + sqrt 3 *
- Part (b) Explain why you cannot write a recursive descent parser for this grammar.
- Part (c) Draw the abstract syntax tree for the expression
4 5 + sqrt 3 *
- Problem 12:
- Consider the following grammar for postfix expressions. (The symbol EMPTY in the grammar means that we produce an empty string. See page 15 of the textbook.)
Postfix -> Number Postfix2
Postfix2 -> Postfix BinOp Postfix2
| UnOp Postfix2
| EMPTY
BinOp -> '+' | '-' | '*' | '/'
UnOp -> 'neg' | 'sqrt'
Number -> any valid Java double
- Part (a) Draw the parse tree (not the expression tree) for the expression
4 5 + sqrt 3 *
- Part (b) Explain why the abstract syntax tree for the expression
4 5 + sqrt 3 *
is the same as it was for Problem 11, even though the grammar has changed.
- Part (c) Explain why you can write a recursive descent parser for this grammar.
- Part (d) Write the Java code for the
getPostfix() and getPostfix2() methods that would implement a recognizing parser (assume the usual interface to the Tokenizer).
private static void getPostfix(Tokenizer tokens)
{
}//getPostfix()
private static void getPostfix2(Tokenizer tokens)
{
}//getPostfix2()
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