CS321 – Solved

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Total Points: 50 Time: 3 hours

Question: 1 2 3 Total
Points: 10 10 30 50
Banking system
An interest calculator performs simple operations on funds that are deposited in banks.
It is also able to combine various interest calculation operations in a natural way.
Suppose x is the fund deposited for k years. The available operations are:
• regular: this is written x+k in our expressions, though our C function that computes it is called regular(··· ). The resulting value of this operation is x+(x∗2.01)/100∗k. For example, x = 100
k = 3
x + k = 106.03
• simple: this is written x ∗ k, and is computed by the C function simple(··· ). The resulting value of this function is x +(x ∗ 5.5 ∗ k)/100.
• compound: this is written compound(x, k) and is computed by the C function compound(··· ).
The resulting value of this function is x(1 + 5.7/k)k.
Let CALC be the language of banking system that can be generated by the following grammar
S → E E → e
E → regular(E,E)
E → simple(E,E)
E → compound(E,E)
NUM → 0 | 1 | 2 | 3 ··· | 9
In this grammar, the non-terminals are S, E and NUM. Treat regular,simple and compound as just single tokens. For simple and compound, we allow any nonempty prefix of the function name as well as the full name; e.g., s, si, sim, …, simple are all acceptable lexemes for the token simple.
1. Construct a lex file Prob1 to build a lexical analyser for CALC.
Sample output:
$ ./a.out regular(s(co(500,2)))
Token: regular; Lexeme: regular
Token and Lexeme: (
Token: simple; Lexeme: s
Token and Lexeme: (
Token: compound; Lexeme: co
Token and Lexeme: (
Token: NUM; Lexeme: 500
Token and Lexeme: ,
Token: NUM; Lexeme: 2
Token and Lexeme: <newline> Control − D [10]
2. Make a copy of prob1.l, call it prob2.l, then modify it so that it can be used with yacc. Then construct a yacc file prob2.y. Then use these lex and yacc files to build a parser for CALC.
The core of your task is to write the grammar rules in the Rules section, in yacc format, with associated actions (using the examples in chain.y as a guide).
Sample output:
$ ./a.out regular(s(co(500,2),2),2)
8557.1922975 Control − D [10]
3. In a hypothetical programming language STUD, the type huh[2][3] can be read as ”two sighs of 3 huhs”. The corresponding type expression is sigh(2,sigh(3,huh)). The expression sigh takes two parameters, a number and huh. Write a SDD for the type huh. Implement your SDD with an LL(1) parser and identify whether each attribute used is synthesized or inherited. You can use your LL(1) parser from previous labs. [30]


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