Automata Visualiser

Automata Visualiser is a Haskell eDSL for creating images of various types of automata. There is built in support for (D/N)FAs, PDAs, and Turing Machines, with easy extensibililty available to add your own automata types via the TransitionLabel type class.

Automata can be output to both an image format (SVG) and a LaTeX format (TikZ). Alternate output formats can be implemented by writing a function f :: AutomatonConfig -> AutomatonLayout s t -> AutomatonRender.

Automata Visualiser is available to use in an online playground at https://automata.codingcactus.codes

Local Installation

The package isn't available on Hackage currently, but you can install it using the GitHub link in the cabal.project file:

packages: .

source-repository-package
    type: git
    location: https://github.com/Coding-Cactus/automata-visualiser

allow-newer: latex-svg-image:*

And can then be included as a dependency in your .cabal file as automata-visualiser.

Syntax Documentation

Automata are defined with the AutomatonBuilder monad. You need to also specify the types used for the state and transition labels. State labels must implement the Label type class, and transition labels must implement the TransitionLabel type class. These have been implemented for most common types. For example, for an automaton with String state labels and Int transition labels, use AutomatonBuilder String Int

To create new states, simply use the state function, passing the desired label as the only parameter. To declare states as the initial state or as final states, use the initial and final functions respectively.

To create transitions between states, an arrow syntax is used of the form state >--[transition label]--> state. Multiple labels can be placed within the square brackets separated by commas to attach multiple labels to a single transition arrow in the produced diagram.

automaton :: AutomatonBuilder String Int
automaton = do
  a <- state "a"
  b <- state "b"

  initial a
  final b

  a >--[0]--> b
  b >--[0,1]--> b

Extra Transition Types

• PDA transition labels can be created with the (~~) operator. For example: 0 ~~ ('a', 'b') represents the transition of seeing a 0 and popping 'a' off the stack and pushing 'b' onto the stack. The type of this transition label is StackTransition Int Char.
• Turing Machine labels can be created with the TmT constructor. For example TmT 0 1 R represents the transition of seeing a 0 on the tape, writing a 1 and then moving the head to the right. The type of this transition label is TuringMachineTransition Int.

Examples of these can be seen on https://automata.codingcactus.codes

Manual Positioning

Automata Visualiser attempts to automatically position the states in an aesthetically pleasing way. However, if you wish to alter the layout manually, you can do so with the following functions:

• state1 `above` state2 positions state1 directly above state2.
• Using the same syntax, the functions leftOf, rightOf, and below can also be used
• For complete control over state positioning, the position function can be used. This function takes: two states, an angle (in degrees), and a distance at which the states should be positioned. For example position state1 state2 45 2 will position state2 at and angle of 45 degress from state1, at a distance of 2 units.

Transition Shorthand

The tr and tr' functions can be used as shorter altnertives to the arrow transition syntax. Recreating the above example using these functions looks can be done as follows:

automaton :: AutomatonBuilder String Int
automaton = do
  a <- state "a"
  b <- state "b"

  initial a
  final b

  tr' a b 0
  tr a b [0,1]

Configuration

There are a few configuration options available to tweak the appearance of the diagrams. These can be set with the AutomatonConfig type. A default configuration is available as defaultConfig.

config :: AutomatonConfig
config = setConfig {
  acceptanceStyle = ..., -- DoubleCircle or Arrow
  svgStateRadius  = ..., -- Alter the state radius in SVG outputs by a multiplicative constant
  svgLoopRadius   = ..., -- Alter the self loop radius in SVG output by a multiplicative constant
  svgLoopSepAngle = ..., -- Alter the endpoint separation angle of self loop in SVG output by a multiplicative constant
  tikzLoopWidth   = ...  -- Alter the width of self loops in TikZ output by a multiplicative constant
}

Generating Images

To finally generate the visual representation of your automata, the render function can be used.

main :: IO ()
main = do
  render config fileName tikz automaton -- output to TikZ format
  render config fileName svg  automaton -- output to SVG format

LaTex Support

Automata Visualiser supports LaTeX maths mode syntax in both state and transition labels. For SVG output, your local LaTeX installation is used if available, and for TikZ output: LaTeX syntax is trivially available.

If you don't have LaTeX installed locally, the online playground can be used.