Step by Step solution about How to resolve the algorithm Langton's ant step by step in the Haskell programming language

Source Code Explanation

1. Importing Libraries

import Data.Set (member,insert,delete,Set)

This imports the Data.Set module for working with sets.

2. Functional Utilities

(>>>) = flip (.)
p ?>> (f, g) = \x -> if p x then f x else g x

These are two helper functions:

• (>>>) is function composition with flipped order.
• p ?>> (f, g) is a conditional selector function that applies f if p is True and g otherwise.

3. State Data Type

data State = State { antPosition :: Point
                  , antDirection :: Point
                  , getCells :: Set Point }

The State data type represents the state of the Langton's Ant simulation, including the ant's position, direction, and the set of visited cells.

• Point is defined as a tuple of two floating-point numbers.

4. Simulation Step

step :: State -> State
step = isBlack ?>> (setWhite >>> turnRight,
                   setBlack >>> turnLeft) >>> move

The step function takes a State and applies the following operations, depending on whether the current cell is black or white:

• If the cell is black, setWhite sets the cell to white and turnRight turns the ant right.
• If the cell is white, setBlack sets the cell to black and turnLeft turns the ant left.
• Finally, move moves the ant one step in the current direction.

5. task Function

task :: State -> State
task = iterate step 
  >>> dropWhile ((< 50) . distance . antPosition) 
  >>> getCells . head

• iterate step continuously applies the step function to the state.
• dropWhile ((< 50) . distance . antPosition) drops states where the ant is within a 50-unit radius of the origin.
• getCells . head extracts the set of visited cells from the first state that meets the distance criterion.

6. main Function (Image Rendering)

main = display w white (draw (task initial))

• This version of main creates a graphical window using the Gloss library to display the simulation.
• w is the window configuration.
• initial is the initial state of the ant.
• draw is a function that converts the final set of visited cells into a graphical representation.

7. Alternative main Function (Interactive Simulation)

main = simulate w white 500 initial draw (\_ _ -> step)

• This alternative version of main creates an interactive simulation.
• w is the window configuration.
• initial is the initial state of the ant.
• draw is a function that converts the current state into a graphical representation.
• (\_ _ -> step) is a function that applies the step function to the current state.

import Data.Set (member,insert,delete,Set)


-- functional sequence 
(>>>) = flip (.)

-- functional choice
p ?>> (f, g) = \x -> if p x then f x else g x


data State = State { antPosition :: Point
                   , antDirection :: Point
                   , getCells :: Set Point }

type Point = (Float, Float)


step :: State -> State
step = isBlack ?>> (setWhite >>> turnRight,
                    setBlack >>> turnLeft) >>> move
  where
    isBlack   (State p _     m) = member p m
    setBlack  (State p d     m) = State p d (insert p m)
    setWhite  (State p d     m) = State p d (delete p m)
    turnRight (State p (x,y) m) = State p (y,-x) m
    turnLeft  (State p (x,y) m) = State p (-y,x) m
    move (State (x,y) (dx,dy) m) = State (x+dx, y+dy) (dx, dy) m


task :: State -> State
task = iterate step 
   >>> dropWhile ((< 50) . distance . antPosition) 
   >>> getCells . head
  where distance (x,y) = max (abs x) (abs y)


import Graphics.Gloss

main = display w white (draw (task initial))
  where
    w = InWindow "Langton's Ant" (400,400) (0,0)
    initial = State (0,0) (1,0) mempty
    draw = foldMap drawCell
    drawCell (x,y) = Translate (10*x) (10*y) $ rectangleSolid 10 10


main = simulate w white 500 initial draw (\_ _ -> step)
  where
    w = InWindow "Langton's Ant" (400,400) (0,0)
    initial = State (0,0) (1,0) mempty
    draw (State p _ s) = pictures [foldMap drawCell s, color red $ drawCell p]
    drawCell (x,y) = Translate (10*x) (10*y) $ rectangleSolid 10 10