# Using existential types

Mike Gunter m at ryangunter.com
Wed Oct 8 10:40:35 EDT 2003

```Jan-Willem Maessen <jmaessen at MIT.EDU> writes:

> Tomasz Zielonka <t.zielonka at zodiac.mimuw.edu.pl> wrote:
> [...]
> > data Stat i o = -- aggregate function taking i's on input and producing o
> >     forall s. Stat
> > 	s		-- init
> > 	(s -> i -> s)	-- update
> > 	(s -> o)	-- result
> [...]
> * But it bugs me that an awful lot of examples of existential typing
>   could be obtained simply by currying / lazy evaluation.  In this
>   case, however, the "update" function lets us absorb additional input
>   as in the subsequent message (which I've now accidentally deleted):

I'm not convinced that existentials are needed here.

mike

import Prelude hiding ( sum )

data Stat i o = Stat { update :: i -> Stat i o
, result :: o }

runStat :: Stat i o -> [i] -> o
runStat stat = result . foldl update stat

stateStat       :: (s -> i -> s) -> (s -> o) -> s -> Stat i o
stateStat updateF resultF initState = Stat
{ update = \i -> stateStat updateF resultF (updateF initState i)
, result = resultF initState }

instance Functor (Stat a) where
fmap f st = Stat { update = fmap f . update st, result = f (result st) }

avg :: Fractional n => Stat n n
avg = fmap (\(s,c) -> if c /= 0 then s/c else 0) (pair sum count)

fold :: (a -> b -> a) -> a -> Stat b a
fold f = stateStat f id

count :: Num n => Stat a n
count = fold (\s _ -> s+1) 0

sum :: Num n => Stat n n
sum = fold (+) 0

pair :: Stat a b -> Stat a c -> Stat a (b,c)
pair (Stat upd1 res1) (Stat upd2 res2) = Stat (\i -> pair (upd1 i) (upd2 i)) (res1, res2)

main = error "no main"
```