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Nested "Maybe"

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  Nested "Maybe" Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-04-09 22:13 +0100
    Re: Nested "Maybe" Paul Rubin <no.email@nospam.invalid> - 2021-04-09 14:24 -0700
      Re: Nested "Maybe" Paul Rubin <no.email@nospam.invalid> - 2021-04-09 14:27 -0700
    Re: Nested "Maybe" Mark Carroll <mtbc@bcs.org> - 2021-04-09 17:33 -0400

#564 — Nested "Maybe"

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.

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#565

Ben Bacarisse <ben.usenet@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))

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#566

Paul Rubin <no.email@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.

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#567

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

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