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module Y2016.M11.D15.Exercise where
import Data.Monoid
-- below import available from 1HaskellADay repository
import Y2016.M11.D14.Exercise
It's a question of unification.
Yesterday, we had a 'simple' logic puzzle. A conundrum arose, however, when
the value AMY also happened to be the same person as (Person DaughterInLaw).
How can we show these two things are equal?
Well, structurally, they are not, so to equate them would be a major twist
on the Eq-instance and then have possibly major consequences.
So, ick!
But SCIENCE to the rescue.
There is a thing in logical programming called unification. That does not
solve our problem at all, but if we look through the problem through a logic
lens we can see that we can use unification with a different structure
If we redeclare Person to be
Person (Maybe Name) Role
then we take a definition of unification to be 'Nothing unifies with a Just-
value and is promoted to that Just-value,' then we no longer strain at
redefining equality.
So, let's look at some simple rules for a simply unifier.
1. Just x unifies with Just y if x == y
2. Nothing unifies with Just x IN THE UNIFICATION MONAD (monad? applicative?)
3. Nothing unifies with Nothing
1. and 3. are simple enough. What about that 2.?
Today's Haskell problem: define simple (not occurs-checking) unification for
the Maybe-type.
data Unity x = U x
instance Functor Unity where
fmap f u = undefined
instance Applicative Unity where
pure = undefined
(<*>) = undefined
instance Monad Unity where
return x = undefined
u >>= f = undefined
instance Monoid x => Monoid (Unity x) where
mempty = undefined
u1 `mappend` u2 = undefined
-- does requiring x to be monoidal simplify the monoidal definition?
-- does requiring x to be monoidal complicate the monoidal Unity-use?
unify :: Monad m => Maybe a -> Maybe a -> m (Maybe a)
unify x y = undefined
-- hint: does it 'work' when unification fails because Just 3 /= Just 4?
-- Exercises: unify (or don't unify) the following. How would you go about it?
type Name = String
data Human = Pers (Maybe Name) Role
deriving (Eq, Show)
toUnify :: [(Human, Human)]
toUnify = [(Pers x y, Pers a b) | x <- [Nothing, Just "Amy"],
a <- [Nothing, Just "Amy"],
y <- [Husband, Mother, DaughterInLaw, Sister],
b <- [Husband, Mother, DaughterInLaw, Sister]]
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