sbv-5.11: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Copyright(c) Levent Erkok
LicenseBSD3
Maintainererkokl@gmail.com
Stabilityexperimental
Safe HaskellNone
LanguageHaskell2010

Data.SBV.Examples.Puzzles.U2Bridge

Contents

Description

The famous U2 bridge crossing puzzle: http://www.braingle.com/brainteasers/515/u2.html

Synopsis

Modeling the puzzle

data U2Member Source

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

type SU2Member = SBV U2Member Source

Symbolic shorthand for a U2Member

bono :: SU2Member Source

Shorthands for symbolic versions of the members

edge :: SU2Member Source

Shorthands for symbolic versions of the members

adam :: SU2Member Source

Shorthands for symbolic versions of the members

larry :: SU2Member Source

Shorthands for symbolic versions of the members

type Time = Word32 Source

Model time using 32 bits

type STime = SBV Time Source

Symbolic variant for time

crossTime :: U2Member -> Time Source

Crossing times for each member of the band

sCrossTime :: SU2Member -> STime Source

The symbolic variant.. The duplication is unfortunate.

data Location Source

Location of the flash

Constructors

Here 
There 

Instances

type SLocation = SBV Location Source

Symbolic variant of Location

here :: SLocation Source

Shorthands for symbolic versions of locations

there :: SLocation Source

Shorthands for symbolic versions of locations

data Status Source

The status of the puzzle after each move

This type is equipped with an automatically derived Mergeable instance because each field is Mergeable. A Generic instance must also be derived for this to work, and the DeriveAnyClass language extension must be enabled. The derived Mergeable instance simply walks down the structure field by field and merges each one. An equivalent hand-written Mergeable instance is provided in a comment below.

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

Generic Status Source 
Mergeable Status Source 
Mergeable a => Mergeable (Move a) Source

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

type Rep Status Source 

start :: Status Source

Start configuration, time elapsed is 0 and everybody is here

type Move a = State Status a Source

A puzzle move is modeled as a state-transformer

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

Read the state via an accessor function

whereIs :: SU2Member -> Move SLocation Source

Given an arbitrary member, return his location

xferFlash :: Move () Source

Transferring the flash to the other side

xferPerson :: SU2Member -> Move () Source

Transferring a person to the other side

bumpTime1 :: SU2Member -> Move () Source

Increment the time, when only one person crosses

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

Increment the time, when two people cross together

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

Symbolic version of when

move1 :: SU2Member -> Move () Source

Move one member, remembering to take the flash

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

Move two members, again with the flash

Actions

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

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] Source

Run a sequence of given actions.

Recognizing valid solutions

isValid :: Actions -> SBool Source

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 Source

See if there is a solution that has precisely n steps

solveU2 :: IO () Source

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.