Learning Haskell with Chess

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olodom This page is about learning Haskell using the board game Chess as a running example. The complete code can be found at http://www.steffen-mazanek.de/dateien/projekte/hsChess.zip.

@German Haskellers: You may also have a look at the tex-files used for our student exercises, http://www.steffen-mazanek.de/dateien/projekte/hsChess-teaching-german.zip.

1 Exercise 1 - data types

1.1 Learning targets

• recapitulate Haskell types (keywords
  type
  and
  data
  , product and sum types)
  • Helium: equality and show functions (pattern matching)
  • Haskell: type classes (
    Show
    ,
    Eq
    ,
    deriving
    )
• list handling (boards will be represented by lists of lists)
• special character
  '\n'
  ,
  putStr::String->IO ()

1.2 Tasks

• Define data types that represent boards (
  Board
  ), squares (
  Square
  ), positions (
  Pos
  ), pieces (
  Piece
  , supported by
  PieceColor
  and
  PieceType
  ) and game states (
  State
  ).
  • Helium: Implement suited eq and show functions.
  • Haskell: Define/derive instances of
    Show
    and
    Eq
• Implement a function
  prettyBoard::Board->String
  , that transforms a board into a clearly arranged string representation (human readable :-)). Support this function with auxiliary functions that pretty print pieces, squares, ...
• Define the initial board (
  initialBoard::Board
  ), test
  prettyBoard
  with
  initialBoard
  .
• Implement a simple evaluation function
  evalBoard::Board->Int
  as the difference of material on board, for this purpose define a function
  valuePiece
  that maps pieces to their values (pawn->1, knight and bishop->3, queen->9, rook->5, king->"infinity"=1000).

2 Exercise 2 - move generator

2.1 Learning targets

• list comprehension
• stepwise refinement

2.2 Tasks

• Define a function
  movePos::Pos->Pos->Board->Board
  such that
  movePos p1 p2 b
  moves the piece at p1 to p2 (overwrite the square at p2 with the square at p1 and delete p1). Do not check whether the move is valid at this stage. Hint: Define a function
  updateBoard
  first. On top of this further define a function
  deleteSquare
  . Its much simpler to have these functions at hand.
• Implement a function
  colorPos::PieceColor->Board->[Pos]
  whose result is the list of the positions of the pieces of a certain color.
• Define
  moves::PieceType->[(Int,Int)]
  that returns the base moving vectors for a particular piece (return empty list for pawns here, because their vector depends on the color).
• Implement
  genMoves::Board->Pos->[Board]
  , it takes a board b and a position p and results in the list of all boards that may follow if you move the piece at p on board b.
• Combine
  colorPos
  and
  genMoves
  to a function
  nextStates::State->[State]
  that returns all possible successor states.

3 Exercise 3 - gametree generation and minimax algorithm

3.1 Learning targets

• break code in modules
• complexity
• recursive data structures -> recursive algorithms

3.2 Tasks

• Define a data type that represents a game tree (
  GameTree
  ).
• Roughly estimate the number of nodes of the gametree with depth 4.
• Define a function
  play::Gametree->Int
  , that computes the value of a given game tree using the minimax Algorithm.
• Implement the function
  doMove::State->State
  , that choses the (best) next state.

Category: Education