Data.SBV.Examples.Puzzles.U2Bridge

The famous U2 bridge crossing puzzle: http://www.brainj.net/puzzle.php?id=u2

Modeling the puzzle

data U2Member

U2 band members. We want to translate this to SMT-Lib as a data-type, and hence the deriving mechanism.

Constructors

Bono

Edge

Adam

Larry

Instances

Eq U2Member

Data U2Member

Ord U2Member

Read U2Member

Show U2Member

HasKind U2Member

SymWord U2Member

SatModel U2Member

type SU2Member = SBV U2Member

Symbolic shorthand for a U2Member

bono :: SU2Member

Shorthands for symbolic versions of the members

edge :: SU2Member

Shorthands for symbolic versions of the members

adam :: SU2Member

Shorthands for symbolic versions of the members

larry :: SU2Member

Shorthands for symbolic versions of the members

type Time = Word32

Model time using 32 bits

type STime = SBV Time

Symbolic variant for time

crossTime :: U2Member -> Time

Crossing times for each member of the band

sCrossTime :: SU2Member -> STime

The symbolic variant.. The duplication is unfortunate.

data Location

Location of the flash

Constructors

Here

There

Instances

Eq Location

Data Location

Ord Location

Read Location

Show Location

HasKind Location

SymWord Location

SatModel Location

type SLocation = SBV Location

Symbolic variant of Location

here :: SLocation

Shorthands for symbolic versions of locations

there :: SLocation

Shorthands for symbolic versions of locations

data Status

The status of the puzzle after each move

Constructors

Status

Fields

time :: STime

elapsed time

flash :: SLocation

location of the flash

lBono :: SLocation

location of Bono

lEdge :: SLocation

location of Edge

lAdam :: SLocation

location of Adam

lLarry :: SLocation

location of Larry

Instances

Mergeable Status

Mergeable instance for Status simply walks down the structure fields and merges them.

Mergeable a => Mergeable (Move a)

Mergeable instance for Move simply pushes the merging the data after run of each branch starting from the same state.

start :: Status

Start configuration, time elapsed is 0 and everybody is here

type Move a = State Status a

A puzzle move is modeled as a state-transformer

peek :: (Status -> a) -> Move a

Read the state via an accessor function

whereIs :: SU2Member -> Move SLocation

Given an arbitrary member, return his location

xferFlash :: Move ()

Transferring the flash to the other side

xferPerson :: SU2Member -> Move ()

Transferring a person to the other side

bumpTime1 :: SU2Member -> Move ()

Increment the time, when only one person crosses

bumpTime2 :: SU2Member -> SU2Member -> Move ()

Increment the time, when two people cross together

whenS :: SBool -> Move () -> Move ()

Symbolic version of when

move1 :: SU2Member -> Move ()

Move one member, remembering to take the flash

move2 :: SU2Member -> SU2Member -> Move ()

Move two members, again with the flash

Actions

type Actions = [(SBool, SU2Member, SU2Member)]

A move action is a sequence of triples. The first component is symbolically True if only one member crosses. (In this case the third element of the triple is irrelevant.) If the first component is (symbolically) False, then both members move together

run :: Actions -> Move [Status]

Run a sequence of given actions.

Recognizing valid solutions

isValid :: Actions -> SBool

Check if a given sequence of actions is valid, i.e., they must all cross the bridge according to the rules and in less than 17 seconds

Solving the puzzle

solveN :: Int -> IO Bool

See if there is a solution that has precisely n steps

solveU2 :: IO ()

Solve the U2-bridge crossing puzzle, starting by testing solutions with increasing number of steps, until we find one. We have:

>>> solveU2
Checking for solutions with 1 move.
Checking for solutions with 2 moves.
Checking for solutions with 3 moves.
Checking for solutions with 4 moves.
Checking for solutions with 5 moves.
Solution #1: 
 0 --> Edge, Bono
 2 <-- Bono
 3 --> Larry, Adam
13 <-- Edge
15 --> Edge, Bono
Total time: 17
Solution #2: 
 0 --> Edge, Bono
 2 <-- Edge
 4 --> Larry, Adam
14 <-- Bono
15 --> Edge, Bono
Total time: 17
Found: 2 solutions with 5 moves.

Finding all possible solutions to the puzzle.