[Haskell-cafe] Short circuiting and the Maybe monad

[David Menendez]

On Sat, May 17, 2008 at 1:24 AM, Kim-Ee Yeoh <a.biurvOir4 at asuhan.com> wrote:
>
>
> Dan Piponi-2 wrote:
>>
>> In fact, you can use the Reader monad as a fixed size container monad.
>>
>
> Interesting that you say that. Reader seems to me more as an anti-container
> monad.

You just have to think of the environment as an address into an
implicit structure. For example, Bool -> a is isomorphic to (a,a).
Thus,

data Diag a = D { p1 :: a, p2 :: a }

to :: Diag a -> (Bool -> a)
to (D a b) p = if p then a else b

from :: (Bool -> a) -> Diag a
from f = D (f True) (f False)

Some transformations applied to the monad instance for ((->) Bool) gets you:

instance Monad Diag where
    return x       = D x x
    D a b >>= f = D (p1 (f a), p2 (f b))

This works for any enumeration.

Here's a more complex example,

data Stream a = a :< Stream a
type Nat = Integer
   -- we'll pretend this can't ever be negative

to :: Stream a -> (Nat -> a)
to (a :< as) 0 = a
to (a :< as) n = to as n

from :: (Nat -> a) -> Stream a
from f = go 0 where go n = f n :< go (n + 1)

shead (a :< as) = a
stail (a :< as) = as

instance Monad Stream where
    return x = x :< return x
    (a :< as) >>= f = shead (f a) :< (as >>= stail . f)

Assuming I haven't mistyped anything,

   to (m >>= f) n = to (f (to m n)) n

-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>