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.
Exercise 1 - data types
Learning targets
- recapitulate Haskell types (keywords
type
anddata
, 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 ()
Tasks
- Define data types that represent boards (
Board
), squares (Square
), positions (Pos
), pieces (Piece
, supported byPieceColor
andPieceType
) and game states (State
).- Helium: Implement suited eq and show functions.
- Haskell: Define/derive instances of
Show
andEq
- 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
), testprettyBoard
withinitialBoard
. - Implement a simple evaluation function
evalBoard::Board->Int
as the difference of material on board, for this purpose define a functionvaluePiece
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
movePos::Pos->Pos->Board->Board
such thatmovePos 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 functionupdateBoard
first. On top of this further define a functiondeleteSquare
. 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
andgenMoves
to a functionnextStates::State->[State]
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 (
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.