Nested "Maybe"

[Ben Bacarisse]

This group is looking quiet, but you never know...

Recently I wanted a type that adds another alternative to Maybe,
specifically an approximate result, so I wrote (somewhat without
thinking)

data Approximate a = Roughly a | Maybe a

Haskell does not complain about the type (after all, it just looks like
I'm defining a constructor called Maybe) but, equally obviously, I can't
write a function like this

f a | a < 0 = Nothing
| a > 10000 = Roughly (sqrt a)
| otherwise = Just (a / 2)

without type errors. I can nest the Maybe in a new type:

data Approximate a = Roughly a | Exactly (Maybe a)

f a | a < 0 = Exactly Nothing
| a > 10000 = Roughly (sqrt a)
| otherwise = Exactly (Just (a / 2))

but I can't help wondering if I'm missing a neater way to do this.

--
Ben.

[Paul Rubin]

Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> data Approximate a = Roughly a | Exactly (Maybe a)
>
> f a | a < 0 = Exactly Nothing
> | a > 10000 = Roughly (sqrt a)
> | otherwise = Exactly (Just (a / 2))
>
> but I can't help wondering if I'm missing a neater way to do this.

That looks inside out? I.e. the Maybe should be on the outside.

data Precision a = Roughly a | Exactly a
data Approximate a = Maybe (Precision a)

f a | a < 0 = Nothing
| a > 10000 = Just (Roughly (sqrt a))
| otherwise = Just (Exactly (a/2))

[Paul Rubin]

Paul Rubin <no.e...@nospam.invalid> writes:
> data Precision a = Roughly a | Exactly a
> data Approximate a = Maybe (Precision a)

Alternatively maybe you want an actual 3-way Maybe, e.g.

data Approximate a = Invalid | Roughly a | Exactly a

and then you could write typeclass instances (monad, monoid, etc.)
analogously with Maybe.

[Mark Carroll]

On 405 Mar 2020, Ben Bacarisse wrote:

> Recently I wanted a type that adds another alternative to Maybe,
> specifically an approximate result, so I wrote (somewhat without
> thinking)
>
> data Approximate a = Roughly a | Maybe a
>
> Haskell does not complain about the type (after all, it just looks like
> I'm defining a constructor called Maybe)

Yes, I think that's exactly what you're doing, unconnected with the type
Maybe.

(snip)

> I can nest the Maybe in a new type:
>
> data Approximate a = Roughly a | Exactly (Maybe a)
>
> f a | a < 0 = Exactly Nothing
> | a > 10000 = Roughly (sqrt a)
> | otherwise = Exactly (Just (a / 2))

That's what I would have done, depending on why I wanted to use Maybe at
all. E.g., if you don't need much of what Maybe does, you could ignore
it and define your own three-option type and reimplement the Maybe-like
stuff you do need. Or you may find you get much of what you need if you
wrap the other way, e.g., leave it as a,

data Approximate a = Roughly a | Exactly a

and use Maybe (Approximate a).

> but I can't help wondering if I'm missing a neater way to do this.

I'm not aware of one but I know only "pedestrian" Haskell so somebody,
perhaps more familiar with esoteric extensions, may be able to show us
some magic.

-- Mark