# CSE340 Project 2 Solution

1 Introduction
In this project, you will write a C or C++ program that reads a description of a context free grammar, then, depending on the command line argument passed to the program, performs one of the following tasks: 1) print the list of terminal followed by the non-terminals in the order in which they appear in the grammar rules, 2) find useless symbols in the grammar and remove rules with useless symbols, 3) calculate FIRST sets, 4) calculate FOLLOW sets and 5) determine if the grammar has a predictive parser.

2 Input Format
The following context-free grammar specifies the input format:
Rule-list → Rule Rule-list | Rule
Id-list → ID Id-list | ID
Rule → ID ARROW Right-hand-side HASH
Right-hand-side → Id-list | 
The tokens used in the above grammar description are defined by the following regular expressions:
ID = letter (letter + digit)*
HASH = #
DOUBLEHASH = ##
ARROW = -
Where digit is the digits from 0 through 9 and letter is the upper and lower case letters a through z and A through Z. Tokens are case-sensitive. Tokens are space separated and there is at least one whitespace character between any two successive tokens.

3 Semantics
Each grammar rule starts with a non-terminal symbol (the left-hand side of the rule) followed by ARROW, then followed by a sequence of zero or more terminals and non-terminals, which represent the right-hand side of the rule. If the sequence of terminals and non-terminals in the right-hand 1 side is empty, then the right hand side represents  and the rule has the form A →  (if A is the
left hand side).
The set of non-terminals for the grammar is the set of symbols that appear to the left of an arrow. Grammar symbols that do not appear to the left of an arrow are terminal symbols. The start symbol of the grammar is the left hand side of the first rule of the grammar.
Note that the convention of using upper-case letters for non-terminals and lower-case letters for terminals is not used here.

3.1 Example
Here is an example input:
decl - idList colon ID #
idList - ID idList1 #
idList1 - #
idList1 - COMMA ID idList1 #
##
The list of non-terminal symbols in the order in which they appear in the grammar is:
Non-Terminals = {decl, idList, idList1}
The list of terminal symbols in the order in which they appear in the grammar is:
Terminals = {colon,ID, COMMA}
The list of grammar rules in the order in which they appear is:
decl → idList colon ID
idList → ID idList1
idList1 → 
idList1 → COMMA ID idList1
Note that even though the example shows that each rule is on a line by itself, a rule can be split into multiple lines, or even multiple rules can be on the same line, according to the formal specification. The following input describes the same grammar as the above example:
decl - idList colon ID # idList - ID idList1 #
idList1 - # idList1
- COMMA ID idList1 # ##
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4 Output Specifications
Your program should read the input grammar from standard input, and read the requested task number from the first command line argument (we provide code to read the task number). Then, your program should calculate the requested output based on the task number and print the results in the specified format for each task to standard output (stdout). The following specifies the exact requirements for each task number.

Task one simply outputs the list of terminals followed by the list of non-terminals in the order in which they appear in the grammar rules.
Example: For the input grammar
decl - idList colon ID #
idList - ID idList1 #
idList1 - #
idList1 - COMMA ID idList1 #
##
the expected output for task 1 is:
colon ID COMMA decl idList idList1
Example: Given the input grammar:
decl - idList colon ID #
idList1 - #
idList1 - COMMA ID idList1 #
idList - ID idList1 #
##
the expected output for task 1 is:
colon ID COMMA decl idList idList1
Note that in this example, even though the rule for idList1 is before the rule for idList, idList appears before idList1 in the grammar rules.

4.2 Task 2: Find useless symbols
Determine useless symbols in the grammar and remove rules that contain useless symbols. Then output each rule of the remaining rules on a single line in the following format:
<LHS - <RHS
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Where <LHS should be replaced by the left-hand side of the grammar rule and <RHS should be replaced by the right-hand side of the grammar rule. If the grammar rule is of form A → , use # to represent the epsilon. Note that this is different from the input format.
The grammar rules should be printed in the same relative order that they originally had. So, if Rule1 and Rule2 are not removed after the elimination of useless symbols, and Rule1 appears before Rule2 in the original grammar, then Rule1 should be printed before Rule2 in the output.
Definition: Symbol A is not useless if there is a derivation starting from S (the start symbol) in which A appears and the derivation leads to a string of terminals w or the empty string (w ∈ T

):
S
∗⇒ ...A... ∗⇒ w
Example 1: Given the following input grammar :
decl - idList colon ID #
idList - ID idList1 #
idList1 - #
idList1 - COMMA ID idList1 #
##
the expected output for task 2 is:
decl - idList colon ID
idList - ID idList1
idList1 - #
idList1 - COMMA ID idList1
Note that none of the symbols of this grammar are useless.
Example 2: Given the following input grammar:
S - A B #
S - C #
C - c #
S - a #
A - a A #
B - b #
##
the expected output for task 2 is:
S - C
C - c
S - a
Note that A and B are useless symbols and the modified grammar has only three rules. Also note that the relative order of the rules is preserved.
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4.3 Task 3: Calculate FIRST Sets
Compute the FIRST sets of all non-terminals. Then, for each of the non-terminals of the input grammar, in the order that it appears in the grammar, output one line in the following format:
FIRST(<symbol) = { <set_items }
Where <symbol should be replaced by the non-terminal and <set_items should be replaced by a comma-separated list of elements of the set ordered in the following manner:
• If  belongs to the set, represent it as #
• If  belongs to the set, it should be listed before any other elements
• All other elements of the set should be sorted in the order in which they appear in the grammar
Example: Given the input grammar:
decl - idList colon ID #
idList - ID idList1 #
idList1 - #
idList1 - COMMA ID idList1 #
##
the expected output for task 3 is:
FIRST(decl) = { ID }
FIRST(idList) = { ID }
FIRST(idList1) = { #, COMMA }
For each of the non-terminals of the input grammar, in the order that they appear in the nonterminals section of the input, compute the FOLLOW set for that non-terminal and output one line in the following format:
FOLLOW(<symbol) = { <set_items }
Where <symbol should be replaced by the non-terminal and <set_items should be replaced by the comma-separated list of elements of the set ordered in the following manner:
• If EOF belongs in the set, represent it as \$
• If EOF belongs in the set, it should be listed before any other elements
• All other elements of the set should be sorted in the order in which they appear in the grammar
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Example: Given the input grammar:
decl - idList colon ID #
idList - ID idList1 #
idList1 - #
idList1 - COMMA ID idList1 #
##
the expected output for task 4 is:
FOLLOW(decl) = { \$ }
FOLLOW(idList) = { colon }
FOLLOW(idList1) = { colon }
4.5 Task 5: Determine if the grammar has a predictive parser
Determine if the grammar has a predictive parser and output either YES or NO accordingly.
Example: The expected output for the example input grammar given in section 3.1 for task 5 is:
YES
5 Implementation
5.1 Lexer
A lexer that can recognize ID, ARROW, HASH and DOUBLEHASH tokens is provided for this project.
You are free to use it if you like.
As mentioned in the introduction, your program must read the grammar from stdin and the task number from command line arguments. The following piece of code shows how to read the first
command line argument and perform a task based on the value of that argument. Use this code as a starting point for your main function.
/* NOTE: You should get the full version of this code as part of the project
material, do not copy/paste from this document. */
#include <stdio.h
#include <stdlib.h
int main (int argc, char* argv[])
{
if (argc < 2) {
printf("Error: missing argument\n");
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return 1;
}
case 1:
break;
// ...
default: