# Learning Haskell with Chess

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− | This page is about learning Haskell using the board game Chess as a running example. The | + | olodom |

+ | [[Category:Education]] | ||

+ | 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. | |

− | + | ==Exercise 1 - data types== | |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | < | + | ===Learning targets=== |

− | < | + | *recapitulate Haskell types (keywords <hask>type</hask> and <hask>data</hask>, product and sum types) |

− | < | + | **Helium: equality and show functions (pattern matching) |

− | < | + | **Haskell: type classes (<hask>Show</hask>, <hask>Eq</hask>, <hask>deriving</hask>) |

− | < | + | *list handling (boards will be represented by lists of lists) |

− | + | *special character <hask>'\n'</hask>, <hask>putStr::String->IO ()</hask> | |

− | < | + | |

− | </ | + | |

− | < | + | ===Tasks=== |

− | < | + | *Define data types that represent boards (<hask>Board</hask>), squares (<hask>Square</hask>), positions (<hask>Pos</hask>), pieces (<hask>Piece</hask>, supported by <hask>PieceColor</hask> and <hask>PieceType</hask>) and game states (<hask>State</hask>). |

− | < | + | **Helium: Implement suited eq and show functions. |

+ | **Haskell: Define/derive instances of <hask>Show</hask> and <hask>Eq</hask> | ||

+ | *Implement a function <hask>prettyBoard::Board->String</hask>, 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 (<hask>initialBoard::Board</hask>), test <hask>prettyBoard</hask> with <hask>initialBoard</hask>. | ||

+ | *Implement a simple evaluation function <hask>evalBoard::Board->Int</hask> as the difference of material on board, for this purpose define a function <hask>valuePiece</hask> that maps pieces to their values (pawn->1, knight and bishop->3, queen->9, rook->5, king->"infinity"=1000). | ||

− | < | + | ==Exercise 2 - move generator== |

− | < | + | ===Learning targets=== |

− | < | + | *list comprehension |

− | < | + | *stepwise refinement |

− | < | + | ===Tasks=== |

− | < | + | *Define a function <hask>movePos::Pos->Pos->Board->Board</hask> such that <hask>movePos p1 p2 b</hask> 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 <hask>updateBoard</hask> first. On top of this further define a function <hask>deleteSquare</hask>. Its much simpler to have these functions at hand. |

− | </ | + | *Implement a function <hask>colorPos::PieceColor->Board->[Pos]</hask> whose result is the list of the positions of the pieces of a certain color. |

− | < | + | *Define <hask>moves::PieceType->[(Int,Int)]</hask> that returns the base moving vectors for a particular piece (return empty list for pawns here, because their vector depends on the color). |

− | < | + | *Implement <hask>genMoves::Board->Pos->[Board]</hask>, 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 <hask>colorPos</hask> and <hask>genMoves</hask> to a function <hask>nextStates::State->[State]</hask> that returns all possible successor states. |

− | + | ||

− | + | ==Exercise 3 - gametree generation and minimax algorithm== | |

− | + | ===Learning targets=== | |

− | + | *break code in modules | |

+ | *complexity | ||

+ | *recursive data structures -> recursive algorithms | ||

+ | |||

+ | ===Tasks=== | ||

+ | *Define a data type that represents a game tree (<hask>GameTree</hask>). | ||

+ | *Roughly estimate the number of nodes of the gametree with depth 4. | ||

+ | *Define a function <hask>play::Gametree->Int</hask>, that computes the value of a given game tree using the minimax Algorithm. | ||

+ | *Implement the function <hask>doMove::State->State</hask>, that choses the (best) next state. |

## Latest revision as of 22:54, 5 October 2008

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.

## Contents |

## [edit] 1 Exercise 1 - data types

### [edit] 1.1 Learning targets

- recapitulate Haskell types (keywords andtype, product and sum types)data
- 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 ()

### [edit] 1.2 Tasks

- Define data types that represent boards (), squares (Board), positions (Square), pieces (Pos, supported byPieceandPieceColor) and game states (PieceType).State
- Helium: Implement suited eq and show functions.
- Haskell: Define/derive instances of andShowEq

- Implement a function , that transforms a board into a clearly arranged string representation (human readable :-)). Support this function with auxiliary functions that pretty print pieces, squares, ...prettyBoard::Board->String
- Define the initial board (), testinitialBoard::BoardwithprettyBoard.initialBoard
- Implement a simple evaluation function as the difference of material on board, for this purpose define a functionevalBoard::Board->Intthat maps pieces to their values (pawn->1, knight and bishop->3, queen->9, rook->5, king->"infinity"=1000).valuePiece

## [edit] 2 Exercise 2 - move generator

### [edit] 2.1 Learning targets

- list comprehension
- stepwise refinement

### [edit] 2.2 Tasks

- Define a function such thatmovePos::Pos->Pos->Board->Boardmoves 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 functionmovePos p1 p2 bfirst. On top of this further define a functionupdateBoard. Its much simpler to have these functions at hand.deleteSquare
- Implement a function whose result is the list of the positions of the pieces of a certain color.colorPos::PieceColor->Board->[Pos]
- Define that returns the base moving vectors for a particular piece (return empty list for pawns here, because their vector depends on the color).moves::PieceType->[(Int,Int)]
- Implement , 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.genMoves::Board->Pos->[Board]
- Combine andcolorPosto a functiongenMovesthat returns all possible successor states.nextStates::State->[State]

## [edit] 3 Exercise 3 - gametree generation and minimax algorithm

### [edit] 3.1 Learning targets

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

### [edit] 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 , that computes the value of a given game tree using the minimax Algorithm.play::Gametree->Int
- Implement the function , that choses the (best) next state.doMove::State->State