CS374: Principles of Programming Languages - Parsing (100 Points)

Assignment Goals

The goals of this assignment are:
  1. To implement a recursive descent parser for a grammar
  2. To use tools like lex to create a scanner for a given set of identifiers from a grammar
  3. To use tools like yacc to create a parse table and parser for a grammar

Background Reading and References

Please refer to the following readings and examples offering templates to help get you started:

The Assignment

The purpose of this labs is to implement a recursive descent parser for a simple LL(1) parser, and then to define a lex and yacc parser to create and parse according to a parse table.

Part 1: Recursive Descent Parser

Consider our recursive descent parser for the following grammar:

expr: term addsub expr
    | term
term: factor muldiv term
    | factor
factor: num
      | "(" expr ")"
addsub: "+" | "-"
muldiv: "*" | "/"
num: [0-9]+

Which we implemented as follows [1] [2]:


#include <stdio.h>
#include <ctype.h>
#include <stdlib.h>
#include <string.h>

int expr(void);
char token;

// remove the next character from the stream
char pop() {
    char ch = getchar();
    printf("Popped %c\n", ch);
    return ch;

// check the next character, but don't remove it from the stream
char peek() {
    char ch = pop();
    ungetc(ch, stdin);
    printf("Pushed %c\n", ch);
    return ch;

int readint() {
    int numchars = 0;
    char* val = (char*) malloc(1); // for the trailing \0
    token = peek();
    while(isdigit(token)) {
        numchars = numchars + 1;
        val = (char*) realloc(val, numchars + 1); // for the trailing \0
        val[numchars-1] = token;
        token = peek();
    val[numchars] = '\0'; // null terminate
    int result = atoi(val);
    printf("Read int from string %s (length %d): %d\n", val, strlen(val), result);
    return result;

int factor(void) {
    printf("In factor\n");
    int value;
    token = peek();

    if (token == '(') { // resolve parens as a whole new expression, resolving to a value, regardless of where they occur in the input (since they are highest precedence)
        pop(); // (
        value = expr();
        token = pop(); // )

        if(token != ')') {
            printf("Error parsing factor, imbalanced parenthesis\n");
    } else if (isdigit(token)) {
        value = readint();
    } else {
        printf("Error parsing factor\n");
    printf("Factor value: %d\n", value);

    return value;

int term(void) {
    printf("In term\n");
    // get the mandatory first factor
    int value = factor();
    token = peek();

    // now handle the optional second term
    // there is still a common left prefix that we can try to simplify with left factoring
    if(token == '*') {
        pop(); // *
        value *= term();       
    } else if(token == '/') {
        pop(); // /
        value /= term();
    } // these are optional in the grammar, so no error if this is not found    

    printf("Term value: %d\n", value);
    return value;

int expr() {
    printf("In expr\n");
    // get the mandatory first term
    int value = term();
    token = peek();

    // now handle the optional second expr
    if(token == '+') {
        pop(); // +
        value += expr();        
    } else if(token == '-') {
        pop(); // -
        value -= expr();
    } // these are optional in the grammar, so no error if this is not found
    printf("Expression value: %d\n", value);
    return value;

int main(void) {
    token = peek();
    int result = expr();
    printf("Result: %d\n", result);

    return 0;

Notice the term and expression nonterminals require left factoring in order to properly implement repeating expressions. Revise the grammar to factor these common productions, and include your revised grammar with your submission. Then, modify the example recursive descent parser to call your new nonterminals.

Part 2: A Calculator Parser with Variable Assignments

Consider our flex and bison scanner and parser definitions for a calculator grammar:


%option noyywrap       

#include <stdio.h>

#define YY_DECL int yylex()

#include "calc.tab.h"



[ \t]	                ; // ignore all whitespace
[0-9]+		            {yylval.ival = atoi(yytext); return T_INT;}
"+"		                {return T_PLUS;}
"-"		                {return T_MINUS;}
"*"		                {return T_MULTIPLY;}
"/"		                {return T_DIVIDE;}
"("		                {return T_LEFT;}
")"		                {return T_RIGHT;}
\n                      {return T_NEWLINE;}




#include <stdio.h>
#include <stdlib.h>
#include <string.h>

extern int yylex();
extern int yyparse();
extern FILE* yyin;

void yyerror(const char* s);


%union {
	int ival;

%token<ival> T_INT

%type<ival> expr term factor
%start calc


    | calc line                     

line: T_NEWLINE  
    | expr T_NEWLINE                { printf("%d\n", $1); } // no return value needed, no type 

expr: term T_PLUS expr              { $$ = $1 + $3; }
    | term T_MINUS expr             { $$ = $1 - $3; }
    | term                          { $$ = $1; }
term: factor T_MULTIPLY term        { $$ = $1 * $3; }
    | factor T_DIVIDE term          { $$ = $1 / $3; }
    | factor                        { $$ = $1; }
factor: T_INT                       { $$ = $1; }            // just resolve the value!
      | T_LEFT expr T_RIGHT         { $$ = $2; }            // expr will resolve to a value!

int main() {
    yyin = stdin;
    do {
    } while(!feof(yyin));

void yyerror(const char* s) {
	fprintf(stderr, "Parse error: %s\n", s);

First, modify this scanner and parser to support floating point values instead of integer values. You will modify your numeric token type to include an optional decimal point, and use the atof function to convert it to a floating point value. You will also modify your types union in the parser to be a float type instead of an int. Run your calculator with some test inputs to verify that it is working.

Now, we will modify the grammar to support variable assignments. To do this, we will support new grammar productions that allow storing an expression into a variable defined by an identifier that you can retrieve like a numeric value. We will also add a type to our types union whose type is a char* (the name of the identifier variable). Create a new token called T_ID (the name is arbitrary!) whose lexeme is one or more alphabetical characters, and a new token called T_ASSIGN that is the lexeme :=. You’ll have two new productions: a new line of the form T_ID T_ASSIGN expr line, and a new factor production that resolves to T_ID. The type of the T_ID token will be text, so you can set the token type of whichever union element you associated with the char*.

Symbol Table

Let’s add a symbol table linked list to the header definitions section of your parser file. This will be a linked list of structures that contain a name, a type, and a value:

struct symbol {
    char* name;
    int type;
    union {
        int ival;
    } value;
    struct symbol* next;

If you encounter the assignment production, print the expression result like before, but now, also assign the value to the symbol table:

struct symbol* sym = putsymbol($1, TYPE_IVAL); 
sym->value.ival = $3;

Your T_ID factor production can retrieve this value from the linked list, and resolve to the value that it finds. Since our example adds items to the list from the front, the most recent value is always bound to the symbol name. So, you can return the first instance of the symbol.

The code to manipulate the linked list (insert and search) is provided for you, and can also be included in the header definitions of your parser file.

const int TYPE_IVAL = 0;
struct symbol* symboltable = NULL;

struct symbol* putsymbol(char* name, int type) {
    struct symbol* sym = (struct symbol *) malloc(sizeof(struct symbol));
    sym->type = type;
    sym->name = malloc(strlen(name)+1);
    strncpy(sym->name, name, strlen(name)+1);

    if(type == TYPE_IVAL) {
        sym->value.ival = 0;
    sym->next = symboltable;
    symboltable = sym;
    return sym;

struct symbol* getsymbol(char* name) {
    struct symbol* p = symboltable;
    struct symbol* result = NULL;
    while(p != NULL) {
        if(strcmp(p->name, name) == 0) {
            // only catch the first instance, since newer items are placed in the front of the list
            if(result == NULL) {
                result = p;
        p = p->next;
    return result;


  1. https://gist.github.com/mlabbe/81d667bac36aa60787fee60e3647a0a8 

  2. https://github.com/meyerd/flex-bison-example 


In your submission, please include answers to any questions asked on the assignment page in your README file. If you wrote code as part of this assignment, please describe your design, approach, and implementation in your README file as well. Finally, include answers to the following questions:
  • Describe what you did, how you did it, what challenges you encountered, and how you solved them.
  • Please answer any questions found throughout the narrative of this assignment.
  • If collaboration with a buddy was permitted, did you work with a buddy on this assignment? If so, who? If not, do you certify that this submission represents your own original work?
  • Please identify any and all portions of your submission that were not originally written by you (for example, code originally written by your buddy, or anything taken or adapted from a non-classroom resource). It is always OK to use your textbook and instructor notes; however, you are certifying that any portions not designated as coming from an outside person or source are your own original work.
  • Approximately how many hours it took you to finish this assignment (I will not judge you for this at all...I am simply using it to gauge if the assignments are too easy or hard)?
  • Your overall impression of the assignment. Did you love it, hate it, or were you neutral? One word answers are fine, but if you have any suggestions for the future let me know.
  • Using the grading specifications on this page, discuss briefly the grade you would give yourself and why. Discuss each item in the grading specification.
  • Any other concerns that you have. For instance, if you have a bug that you were unable to solve but you made progress, write that here. The more you articulate the problem the more partial credit you will receive (it is fine to leave this blank).

Assignment Rubric

Description Pre-Emerging (< 50%) Beginning (50%) Progressing (85%) Proficient (100%)
Algorithm Implementation (60%) The algorithm fails on the test inputs due to major issues, or the program fails to compile and/or run The algorithm fails on the test inputs due to one or more minor issues The algorithm is implemented to solve the problem correctly according to given test inputs, but would fail if executed in a general case due to a minor issue or omission in the algorithm design or implementation A reasonable algorithm is implemented to solve the problem which correctly solves the problem according to the given test inputs, and would be reasonably expected to solve the problem in the general case
Code Quality and Documentation (30%) Code commenting and structure are absent, or code structure departs significantly from best practice, and/or the code departs significantly from the style guide Code commenting and structure is limited in ways that reduce the readability of the program, and/or there are minor departures from the style guide Code documentation is present that re-states the explicit code definitions, and/or code is written that mostly adheres to the style guide Code is documented at non-trivial points in a manner that enhances the readability of the program, and code is written according to the style guide
Writeup and Submission (10%) An incomplete submission is provided The program is submitted, but not according to the directions in one or more ways (for example, because it is lacking a readme writeup) The program is submitted according to the directions with a minor omission or correction needed, and with at least superficial responses to the bolded questions throughout The program is submitted according to the directions, including a readme writeup describing the solution, and thoughtful answers to the bolded questions throughout

Please refer to the Style Guide for code quality examples and guidelines.