sbv-5.14: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Copyright | (c) Levent Erkok
License | BSD3
Maintainer | erkokl@gmail.com
Stability | experimental
Safe Haskell | None
Language | Haskell2010

Data.SBV.Examples.Puzzles.Sudoku

Contents

- Modeling Sudoku
- Solving Sudoku puzzles
- Example boards

Description

The Sudoku solver, quintessential SMT solver example!

Synopsis

- type Row = [SWord8]
- type Board = [Row]
- check :: [SWord8] -> SBool
- valid :: Board -> SBool
- type Puzzle = (Int, [SWord8] -> Board)
- sudoku :: Puzzle -> IO ()
- dispSolution :: Puzzle -> (Bool, [Word8]) -> IO ()
- solveAll :: Puzzle -> IO ()
- puzzle0 :: Puzzle
- puzzle1 :: Puzzle
- puzzle2 :: Puzzle
- puzzle3 :: Puzzle
- puzzle4 :: Puzzle
- puzzle5 :: Puzzle
- puzzle6 :: Puzzle
- allPuzzles :: IO ()

# Modeling Sudoku

type Row = [SWord8] Source #

A row is a sequence of 8-bit words, too large indeed for representing 1-9, but does not harm

type Board = [Row] Source #

A Sudoku board is a sequence of 9 rows

check :: [SWord8] -> SBool Source #

Given a series of elements, make sure they are all different and they all are numbers between 1 and 9

valid :: Board -> SBool Source #

Given a full Sudoku board, check that it is valid

type Puzzle = (Int, [SWord8] -> Board) Source #

A puzzle is a pair: First is the number of missing elements, second is a function that given that many elements returns the final board.

# Solving Sudoku puzzles

sudoku :: Puzzle -> IO () Source #

Solve a given puzzle and print the results

dispSolution :: Puzzle -> (Bool, [Word8]) -> IO () Source #

Helper function to display results nicely, not really needed, but helps presentation

solveAll :: Puzzle -> IO () Source #

Find all solutions to a puzzle

# Example boards

puzzle0 :: Puzzle Source #

Find an arbitrary good board

puzzle1 :: Puzzle Source #

A random puzzle, found on the internet..

puzzle2 :: Puzzle Source #

Another random puzzle, found on the internet..

puzzle3 :: Puzzle Source #

Another random puzzle, found on the internet..

puzzle4 :: Puzzle Source #

According to the web, this is the toughest sudoku puzzle ever.. It even has a name: Al Escargot: http://zonkedyak.blogspot.com/2006/11/worlds-hardest-sudoku-puzzle-al.html

puzzle5 :: Puzzle Source #

This one has been called diabolical, apparently

puzzle6 :: Puzzle Source #

The following is nefarious according to http://haskell.org/haskellwiki/Sudoku

allPuzzles :: IO () Source #

Solve them all, this takes a fraction of a second to run for each case