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

Documentation.SBV.Examples.Puzzles.Birthday

Contents

Types and values
The puzzle

Description

This is a formalization of the Cheryl's birthday problem, which went viral in April 2015. (See http://www.nytimes.com/2015/04/15/science/a-math-problem-from-singapore-goes-viral-when-is-cheryls-birthday.html.)

Here's the puzzle:

Albert and Bernard just met Cheryl. "When’s your birthday?" Albert asked Cheryl.

Cheryl thought a second and said, "I’m not going to tell you, but I’ll give you some clues." She wrote down a list of 10 dates:

  May 15, May 16, May 19
  June 17, June 18
  July 14, July 16
  August 14, August 15, August 17

"My birthday is one of these," she said.

Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day. 
“Can you figure it out now?” she asked Albert.

Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!

When is Cheryl’s birthday?

NB. Thanks to Amit Goel for suggesting the formalization strategy used in here.

Synopsis

data Month
- = May
- | Jun
- | Jul
- | Aug
data Day
- = D14
- | D15
- | D16
- | D17
- | D18
- | D19
type SMonth = SBV Month
sMay :: SBV Month
sJun :: SBV Month
sJul :: SBV Month
sAug :: SBV Month
type SDay = SBV Day
sD14 :: SBV Day
sD15 :: SBV Day
sD16 :: SBV Day
sD17 :: SBV Day
sD18 :: SBV Day
sD19 :: SBV Day
data Birthday = BD SMonth SDay
mkBirthday :: Symbolic Birthday
valid :: Birthday -> SBool
puzzle :: ConstraintSet
cheryl :: IO ()

Types and values

data Month Source #

Months. We only put in the months involved in the puzzle for simplicity

Constructors

May
Jun
Jul
Aug

Instances

Instances details

Data Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Month -> c Month # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Month # toConstr :: Month -> Constr # dataTypeOf :: Month -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Month) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Month) # gmapT :: (forall b. Data b => b -> b) -> Month -> Month # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Month -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Month -> r # gmapQ :: (forall d. Data d => d -> u) -> Month -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Month -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Month -> m Month # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Month -> m Month # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Month -> m Month #
Read Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods readsPrec :: Int -> ReadS Month # readList :: ReadS [Month] # readPrec :: ReadPrec Month # readListPrec :: ReadPrec [Month] #
Show Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods showsPrec :: Int -> Month -> ShowS # show :: Month -> String # showList :: [Month] -> ShowS #
Eq Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods (==) :: Month -> Month -> Bool # (/=) :: Month -> Month -> Bool #
Ord Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods compare :: Month -> Month -> Ordering # (<) :: Month -> Month -> Bool # (<=) :: Month -> Month -> Bool # (>) :: Month -> Month -> Bool # (>=) :: Month -> Month -> Bool # max :: Month -> Month -> Month # min :: Month -> Month -> Month #
SymVal Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods mkSymVal :: MonadSymbolic m => VarContext -> Maybe String -> m (SBV Month) Source # literal :: Month -> SBV Month Source # fromCV :: CV -> Month Source # isConcretely :: SBV Month -> (Month -> Bool) -> Bool Source # free :: MonadSymbolic m => String -> m (SBV Month) Source # free_ :: MonadSymbolic m => m (SBV Month) Source # mkFreeVars :: MonadSymbolic m => Int -> m [SBV Month] Source # symbolic :: MonadSymbolic m => String -> m (SBV Month) Source # symbolics :: MonadSymbolic m => [String] -> m [SBV Month] Source # unliteral :: SBV Month -> Maybe Month Source # isConcrete :: SBV Month -> Bool Source # isSymbolic :: SBV Month -> Bool Source #
HasKind Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods kindOf :: Month -> Kind Source # hasSign :: Month -> Bool Source # intSizeOf :: Month -> Int Source # isBoolean :: Month -> Bool Source # isBounded :: Month -> Bool Source # isReal :: Month -> Bool Source # isFloat :: Month -> Bool Source # isDouble :: Month -> Bool Source # isRational :: Month -> Bool Source # isFP :: Month -> Bool Source # isUnbounded :: Month -> Bool Source # isUserSort :: Month -> Bool Source # isChar :: Month -> Bool Source # isString :: Month -> Bool Source # isList :: Month -> Bool Source # isSet :: Month -> Bool Source # isTuple :: Month -> Bool Source # isMaybe :: Month -> Bool Source # isEither :: Month -> Bool Source # showType :: Month -> String Source #
SatModel Month Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods parseCVs :: [CV] -> Maybe (Month, [CV]) Source # cvtModel :: (Month -> Maybe b) -> Maybe (Month, [CV]) -> Maybe (b, [CV]) Source #

data Day Source #

Days. Again, only the ones mentioned in the puzzle.

Constructors

D14
D15
D16
D17
D18
D19

Instances

Instances details

Data Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Day -> c Day # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Day # toConstr :: Day -> Constr # dataTypeOf :: Day -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Day) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Day) # gmapT :: (forall b. Data b => b -> b) -> Day -> Day # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Day -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Day -> r # gmapQ :: (forall d. Data d => d -> u) -> Day -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Day -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Day -> m Day # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Day -> m Day # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Day -> m Day #
Read Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods readsPrec :: Int -> ReadS Day # readList :: ReadS [Day] # readPrec :: ReadPrec Day # readListPrec :: ReadPrec [Day] #
Show Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods showsPrec :: Int -> Day -> ShowS # show :: Day -> String # showList :: [Day] -> ShowS #
Eq Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods (==) :: Day -> Day -> Bool # (/=) :: Day -> Day -> Bool #
Ord Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods compare :: Day -> Day -> Ordering # (<) :: Day -> Day -> Bool # (<=) :: Day -> Day -> Bool # (>) :: Day -> Day -> Bool # (>=) :: Day -> Day -> Bool # max :: Day -> Day -> Day # min :: Day -> Day -> Day #
SymVal Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods mkSymVal :: MonadSymbolic m => VarContext -> Maybe String -> m (SBV Day) Source # literal :: Day -> SBV Day Source # fromCV :: CV -> Day Source # isConcretely :: SBV Day -> (Day -> Bool) -> Bool Source # free :: MonadSymbolic m => String -> m (SBV Day) Source # free_ :: MonadSymbolic m => m (SBV Day) Source # mkFreeVars :: MonadSymbolic m => Int -> m [SBV Day] Source # symbolic :: MonadSymbolic m => String -> m (SBV Day) Source # symbolics :: MonadSymbolic m => [String] -> m [SBV Day] Source # unliteral :: SBV Day -> Maybe Day Source # isConcrete :: SBV Day -> Bool Source # isSymbolic :: SBV Day -> Bool Source #
HasKind Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods kindOf :: Day -> Kind Source # hasSign :: Day -> Bool Source # intSizeOf :: Day -> Int Source # isBoolean :: Day -> Bool Source # isBounded :: Day -> Bool Source # isReal :: Day -> Bool Source # isFloat :: Day -> Bool Source # isDouble :: Day -> Bool Source # isRational :: Day -> Bool Source # isFP :: Day -> Bool Source # isUnbounded :: Day -> Bool Source # isUserSort :: Day -> Bool Source # isChar :: Day -> Bool Source # isString :: Day -> Bool Source # isList :: Day -> Bool Source # isSet :: Day -> Bool Source # isTuple :: Day -> Bool Source # isMaybe :: Day -> Bool Source # isEither :: Day -> Bool Source # showType :: Day -> String Source #
SatModel Day Source #
Instance details Defined in Documentation.SBV.Examples.Puzzles.Birthday Methods parseCVs :: [CV] -> Maybe (Day, [CV]) Source # cvtModel :: (Day -> Maybe b) -> Maybe (Day, [CV]) -> Maybe (b, [CV]) Source #

type SMonth = SBV Month Source #

Symbolic version of the type Month.

sMay :: SBV Month Source #

Symbolic version of the constructor May.

sJun :: SBV Month Source #

Symbolic version of the constructor Jun.

sJul :: SBV Month Source #

Symbolic version of the constructor Jul.

sAug :: SBV Month Source #

Symbolic version of the constructor Aug.

type SDay = SBV Day Source #

Symbolic version of the type Day.

sD14 :: SBV Day Source #

Symbolic version of the constructor D14.

sD15 :: SBV Day Source #

Symbolic version of the constructor D15.

sD16 :: SBV Day Source #

Symbolic version of the constructor D16.

sD17 :: SBV Day Source #

Symbolic version of the constructor D17.

sD18 :: SBV Day Source #

Symbolic version of the constructor D18.

sD19 :: SBV Day Source #

Symbolic version of the constructor D19.

data Birthday Source #

Represent the birthday as a record

Constructors

BD SMonth SDay

mkBirthday :: Symbolic Birthday Source #

Make a valid symbolic birthday

valid :: Birthday -> SBool Source #

Is this a valid birthday? i.e., one that was declared by Cheryl to be a possibility.

The puzzle

puzzle :: ConstraintSet Source #

Encode the conversation as given in the puzzle.

NB. Lee Pike pointed out that not all the constraints are actually necessary! (Private communication.) The puzzle still has a unique solution if the statements a1 and b1 (i.e., Albert and Bernard saying they themselves do not know the answer) are removed. To experiment you can simply comment out those statements and observe that there still is a unique solution. Thanks to Lee for pointing this out! In fact, it is instructive to assert the conversation line-by-line, and see how the search-space gets reduced in each step.

cheryl :: IO () Source #

Find all solutions to the birthday problem. We have:

>>> cheryl
Solution #1:
  birthMonth = Jul :: Month
  birthDay   = D16 :: Day
This is the only solution.