CS 360
Winter 2018
Programming Language Concepts
CS 360-001 Tuesday/Thursday 15:30-16:50 (Rush 209)
CS 360-002 Tuesday/Thursday 14:00-15:20 (Rush 209)
CS 360-003 Tuesday 18:30-21:20 (UCross 151)

Geoffrey Mainland
Office: University Crossings 106
Office hours: Mondays 4pm–7pm; Thursdays 5pm–6pm.
Teaching Assistant:
Xiao Han
CLC office hours: Tuesday 12pm–2pm; Thursday 6pm–8pm
Allen Yang
CLC office hours: Wednesday 6pm–8pm

Homework 7: Finite Automata and Regular Expressions

Due Friday, March 16, 11:59:59PM EST.

Accept this assignment on GitHub Classroom here. The standard homework instructions apply.

In this assignment, you will implement several function we saw in lecture using Haskell and build a compiler from regular expressions to C.

You must implement the functions as specified. You may write other helper functions and define test data in your file, but you may not change the functions’ names or the number or order of arguments.

Your changes should be made to the files we have provided as described in each problem below. We have included a non-functional version of every function you must write, so you can also grep the source we have provided to find the function we have asked you to implement.

Note that source files are located in the src subdirectory.

This assignment is worth 50 points. There are 71 possible points.


  1. Read about list comprehensions in LYAH.
  2. You can escape characters (like '"') in string constants with a backslash, just as in C.

Working with the fsm program

When you type make, your code will be compile to a binary named fsm in the bin directory. This binary will take a regular expression and perform one or more operations on it:

  1. Dump a graphical representation of the NFA to a file using the --nfa-dot option.
  2. Compile the NFA to C using the --to-c option.
  3. Match the regular expression against a string using the --match option.

When running the fsm program, you may encounter an error like this:

fsm: epsilon.dot: commitBuffer: invalid argument (invalid character)

If this happens, you need to set your LANG environment variable to a language that supports unicode. To do this, we suggest that you type the following at the shell prompt:

export LANG=en_US.UTF-8

You should not encounter this error when using the virtual machine.

Problem 1: Implement NFA Matching (10 points)

Implement the nfaMatch function in the file NfaMatch.hs.

Start by figuring out what the base case is and handling it properly. In the base case, how can you tell if a match occurred?

Be sure to use the function epsilonClosure to calculate the $\epsilon$ closure of the initial state when you calculate the initial set of states for your NFA simulator. You will want to use one of the function we saw in lecture to handle transitions on a literal. I used a recursive helper function that takes the current set of states and a string to match. My helper function is two lines long, not counting the type signature.

You can test your nfaMatch function like this:

$ ./fsm "(ab)*" --match "ab"
(ab)* matched "ab" using the naive matcher
(ab)* matched "ab" using the nfa matcher
(ab)* matched "ab" using the dfa matcher
$ ./fsm "(ab)*" --match "a" 
(ab)* did not match "a" using the naive matcher
(ab)* did not match "a" using the nfa matcher
(ab)* did not match "a" using the dfa matcher

With the --match argument, the fsm program will attempt to match the regular expression using:

  1. The naive backtracking matcher we saw in lecture.
  2. Your nfaMatch with the NFA you built from the regular expression.
  3. Your nfaMatch with the minimized DFA we built from your NFA.

You can test your NFA simulator by running make test.

Note that until you complete Problem 2, you won’t be able to match regular expressions that contain literals or concatenation. However, the first two tests run by make test in the “Non-regexp NFA” test category should exercise your nfaMatch sufficiently. These tests use a raw NFA built by hand, not one compiled from a regular expression.

Problem 2: Translating Regular Expressions to NFAs (20 points total)

We have partially implement the translation from regular expressions to NFAs that we saw in lecture in the file RegExpToNfa.hs. For this problem, you must complete the implementation. All your changes should appear in the file RegExpToNfa.hs

Refer to the lecture notes if you do not understand how to construct an NFA from a regular expression.


  1. Be careful to renumber the states of the second NFA in the sequence. This can be done with the function numberNfaFrom.
  2. When constructing the moves of the combined NFA, you will need to add one extra move from the accepting state of the first NFA to the starting state of the second NFA. You can use the acceptState function to get the single accepting state of an NFA.

Problem 2.1: Literals (10 points)

Implement the NFA construction for literals. It is almost exactly like the $\epsilon$ construction, which we have given you, but instead of creating an NFA with a single $\epsilon$ transition (represented by the Emove data constructor), you must create a transition on a literal character (represented by the Move data constructor).

Problem 2.2: Concatenation (10 points)

Implement the NFA construction for the concatenation of two regular expressions, i.e., one regular expression followed in sequence by another.

We have given you the implementation of alternation, i.e., one regular expression or another, as well as Kleene star. Unlike alternation, you do not have to create any new states.

Problem 3: Translating an NFA to a dot file (20 points)

For this problem, you will implement the conversion of an NFA into a graphical form by completing the toDot function in the file NfaToDot.hs. This function takes an NFA and outputs a description of the graphical representation of the NFA in the dot language. The dot language is a plain text graph description language. A command-line program called dot converts this plain text graph representation into a picture in one of many formats (pdf, svg, png, etc.). If you are curious, you can read about the dot language here, but the example below should tell you all you need to know.

You will need to implement the stateToDot and moveToDot functions.

The stateToDot function should generate a string in the dot language that describes a single NFA state using the dot language. Remember, this state could be an accepting state.

The moveToDot function should generate a string in the dot language that describes a single NFA transition using the dot language. This transition could be an $\epsilon$ transition.

Remember, there are two types of NFA nodes (accepting states and non-accepting states) and two types of edges ($\epsilon$ transitions and symbol transitions). It would make sense to write two helper functions: one for generating dot syntax for nodes, and one for generating dot syntax for edges. You could parametrize these functions by, e.g., shape and/or label. We have given you a string constant epsilon that you can use to label $\epsilon$ transitions.

Here is an example session:

$ ./fsm --nfa-dot=ab.dot ab
$ cat ab.dot 
digraph fsm {
start [shape="plaintext",label="start"];
$ dot -Tpdf -o ab.pdf ab.dot

The following command converts the ab.dot file into a PDF named ab.pdf.

dot -Tpdf -o ab.pdf ab.dot

If you are using one of the lab workstations, you can view this PDF using evince.

If you type make figs, a number of examples will be built to test your dot translator.

Problem 4: Compiling a DFA to C (20 points)

For this problem you will create a regular expression to C compiler by completing the implementation of the dfaToC function in the file DfaToC.hs. There are two local functions used by dfaToC that you must complete: genCharCase and genTransitionCase.

The genCharCase function generates a string containing the C code for handling a single character in the input (inside the switch (*(cs++)) block). For example, in the code below, genCharCase is called twice, once to generate the case statement that handles 'a', and again to generate the case statement that handles 'b'. The genCharCase function should call genTransitionCase for all transitions involving the character genCharCase was given as an argument. You will probably want to use map to do this.

The genTransitionCase function generates C code to handle the state transitions on a character. In the code below, it generates the inner case statements (inside the switch (state) blocks).

Both functions should generate a string. This string will contain several lines of code. You may find it useful to use the stack function to combine multiple lines of code as we have done elsewhere in this file.

The --to-c argument to fsm will use the dfaToC function to generate code to match the specified regular expression. We have included a simple driver as main.c. You can use it as follows:

$ ./bin/fsm --to-c=match.c "(ab)*" 
$ make match
gcc -o match main.c match.c
$ ./match "" ab a             
"" matched
"ab" matched
"a" did not match

This is the contents of my match.c when compiling “(ab)*”

int match(const char* cs)
  int state = 0;
  int accept = 1;
  while (1) {
    switch (*(cs++)) {
      case 'a':
        switch (state) {
          case 0:
            state = 1;
            accept = 0;
          default: return 0;
      case 'b':
        switch (state) {
          case 1:
            state = 0;
            accept = 1;
          default: return 0;
      case '\0': return accept;
      default: return 0;

Problem 5: Homework Statistics (1 point)

How long did spend on each problem? Please tell us in your README.md. You may enter time using any format described here.