HaLeX
HaLeX: A Haskell Library to Model,
Manipulate and
Visualize Regular Languages
http://www.di.uminho.pt/~jas/Research/HaLeX
Copyright João Saraiva
Department of Computer Science,
University of Minho,
Braga, Portugal
saraiva@di.uminho.pt
Version: 1.2.6 (January, 2017)
1 What is HaleX
HaLeX is a library of datatypes and functions implemented in Haskell
that allows us to model, manipulate and animate regular languages.
This library was developed in the context of a programming methodology
course for undergraduate students, and as a consequence, it was
defined mainly for educational purposes.
2 Features of the Library
The library provides the following features:

The definition of deterministic finite automata, nondeterministic
finite automata, and regular expressions directly and
straightforwardly in Haskell.

The definition of the acceptance functions for all those models.

The transformation from regular expressions into nondeterministic
finite automata (NDFA) and from NDFA into deterministic finite
automata (DFA).

The transformation from NDFA and DFA into regular expressions

The minimization of the number of states of deterministic finite
automata.

The equivalence of regular expressions and finite automata.

The graphical representation of finite automata.

The definition of reactive finite automata.

The automatic animation of the acceptance function of finite automata.
The animations are produced in an external tool: the
highquality graph visualization system GraphViz. Thus, to be
able to visualize and animate regular languages, you have to
install GraphViz tool.
The GraphViz system is public domain and it is available at:
http://www.research.att.com/sw/tools/graphviz/
3 The HaLeX Library
The library consists of the following modules:

RegExp.hs > Regular Expressions

Dfa.hs > Deterministic Finite Automata (DFA)

Ndfa.hs > Non Deterministic Finite Automata (NDFA)

RegExp2Fa.hs > Converts Regular expressions into Finite Automata

RegExpAsDiGraph.hs > Graphic Representation of Regular Expressions

FaAsDiGraph.hs > Graphic Representation of Finite Automata
(using GraphViz language/tools)

FaOperations.hs > Operations on Finite Automata
(ndfa2dfa , dfa2ndfa, unions , concats, etc)

FaClasses.hs > Type Classes to overload operations

Minimize.hs > Minimization of the number of states

Equivalence.hs > Equivalence of Regular Expressions/Automata

ReactiveDfa.hs > Reactive Finite Automata

Dfa2MDfa.hs > Produces a Reactive Dfa from a DFA

RegExpParser.hs > Simple Parser for Concrete Regular Expressions
(Unix like notation)

Parser.hs > Basic Parser Combinators

Main.hs > The Main Module of halex Tool (see next section)

MainAnim.hs > The Main Fomule to run Animations

faAnin.lefty > A script written in lefty (one of GraphViz tools)
that animates the acceptance function
The HaLeX library includes a useful tool to manipulate and vizualize
regular languages: the halex tool. This is a batch tool that can be
used in Unix pipes. It accepts as input a regular expression and it
produces Haskell or graphic representations (graphviz) based on finite
automata.
To install the halex tool, just compile the library modules using a
Haskell compiler (see file INSTALL).
4.1 The synopsis of halex is:
Usage: halex options [file] ...
List of options:
N, n NDFA generate NonDeterministic Finite Automaton
D, d DFA generate Deterministic Finite Automaton
M, m MinDfa generate Minimized Deterministic Finite Automaton
E, e Dfa with Effects generate Reactive Deterministic Finite Automaton
G, g graph generate GraphViz input file
S, s Sync State include a Synk State In the Graph Representation
R string, r string regular expression=string specify regular expression
o file output=file specify output file
h, ? help output a brief help message
4.2 Running halex: some Examples

Generating a Haskellbased NDFA
halex N R"('+''')?d*('.')?d+"

Producing the postscript of the graphic representation of a NDFA
halex N G R"('+''')?d*('.')?d+"  dot Tps

DFA with minimal number of states, visualized with dotty (one of
GraphViz tools)
halex D M G R"('+''')?d*('.')?d+"  dotty 

Proving one law of the algebra of regular expressions
halex R"a*" R"(a+)?"
4.2.1 Running one Animation
 First, we have to configure the path in the makefile
Make_Animation (subdirectory scripts) that produces the executable
for the animation. Update the variable HaLeX_DIR with the location
of the HaLeX library oin your machine.
 The above makefile, uses the Haskell main module MainAnim.hs
(subdirectory src) which calls the GraphViz tool lefty with the
script that animates the finite automata (file faAnim.lefty in
subdirectory scripts). Edit that module and update the path of
lefty_tool constant function.
 After that we are able to produce and run the animations. For
example, we can produce the reactive finite automata as
follows
halex E M R"('+''')?d*('.')?d+"
which generates the automaton (in this case, the minimized
automaton, due to the use of the M option) in the file
GenMDfa.hs.
 The Haskell module MainAnim is the main module to run the animations.
It imports the previouly generated GenMDfa and it produces the
animations.
Its main function accepts as argument the sentence to be
accepted/animated by the acceptance function and calls the lefty
tool.
 The lefty tool interprets the lefty script (faAnim.lefty), which
produces the animations. Lefty provides the text view of the
script. To start running the animation we have to call the
functions provided in the lefty script:
 fa.init()
 fa.main()
which initialize the lefty tool and the animation. Write these
functions in the top frame followed by return. At this moment, a
new window will be displayed that contains the graphic
representation of the input. The right button of the mouse
provides a set of operations to run the animation
(forwards/backwards, adjusting the speed, tracking the path,
etc)
6 Lecture/Exercise Notes
I have started developing the HaLeX library in 2000 in the context of
a third year course on programming methodology. This course has a
working load of 24 hours of theoretical classes and another 24 hours
of laboratory classes, running for 12 weeks (\ie, a semester). The
theoretical classes introduce the basic concepts of regular
expressions, finite automata and contextfree languages. HaLeX is
used to support such classes. In the laboratory (a two hour class per
week) the students have to solve exercises using a computer.
I have defined eleven exercise sets (one per week), using literate
Haskell, that the students have to complete. Each set of exercises
defines a module of the \HaLeX\ library. Thus, at the end of the
course the students have a complete documentation of all the exercises
and topics covered in the course, and, also, of the HaLeX library.
The Exercise Notes are (still in Portuguese...) avaliable at the HaLeX
homepage.