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Alternative instance for Const

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chessai .

22 Mar 2020 22 Mar '20

12:14 a.m.

We already have instance Monoid m => Applicative (Const m) we could easily add instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>) which trivially satisfies left/right identity and associativity. I propose we add this instance to base.

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Zemyla

22 Mar 22 Mar

1:52 a.m.

No, the Alternative instance should be based on semirings instead. The one you propose isn't distributive. Lacking general semirings, the best we can do at the moment is newtypes for each semiring we have. For instance: newtype NumConst a b = NumConst { getNumConst :: a } deriving (Functor) instance Num a => Applicative (NumConst a) where pure = const (NumConst 1) (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst a u -> NumConst a v) (*) instance Num a => Alternative (NumConst a) where empty = NumConst 0 (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b -> NumConst a b) (+) On Sat, Mar 21, 2020, 13:44 chessai . wrote:

We already have

instance Monoid m => Applicative (Const m)

we could easily add

instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>)

which trivially satisfies left/right identity and associativity.

I propose we add this instance to base. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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Simon Jakobi

3:16 a.m.

Hi Zemyla, Could you clarify where the requirement for distributivity comes from? The haddocks for Alternative don't mention it: http://downloads.haskell.org/~ghc/8.10.1-rc1/docs/html/libraries/base-4.14.0... Thanks, Simon Am Sa., 21. März 2020 um 21:23 Uhr schrieb Zemyla :

No, the Alternative instance should be based on semirings instead. The one you propose isn't distributive.

Lacking general semirings, the best we can do at the moment is newtypes for each semiring we have. For instance:

newtype NumConst a b = NumConst { getNumConst :: a } deriving (Functor)

instance Num a => Applicative (NumConst a) where pure = const (NumConst 1) (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst a u -> NumConst a v) (*)

instance Num a => Alternative (NumConst a) where empty = NumConst 0 (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b -> NumConst a b) (+)

On Sat, Mar 21, 2020, 13:44 chessai . wrote:

...
We already have

instance Monoid m => Applicative (Const m)

we could easily add

instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>)

which trivially satisfies left/right identity and associativity.

I propose we add this instance to base. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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Oleg Grenrus

4:24 a.m.

https://wiki.haskell.org/Typeclassopedia#Laws_6 On 21.3.2020 23.46, Simon Jakobi via Libraries wrote:

Hi Zemyla,

Could you clarify where the requirement for distributivity comes from?

The haddocks for Alternative don't mention it: http://downloads.haskell.org/~ghc/8.10.1-rc1/docs/html/libraries/base-4.14.0...

Thanks, Simon

Am Sa., 21. März 2020 um 21:23 Uhr schrieb Zemyla :

...
No, the Alternative instance should be based on semirings instead. The one you propose isn't distributive.

Lacking general semirings, the best we can do at the moment is newtypes for each semiring we have. For instance:

newtype NumConst a b = NumConst { getNumConst :: a } deriving (Functor)

instance Num a => Applicative (NumConst a) where pure = const (NumConst 1) (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst a u -> NumConst a v) (*)

instance Num a => Alternative (NumConst a) where empty = NumConst 0 (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b -> NumConst a b) (+)

On Sat, Mar 21, 2020, 13:44 chessai . wrote:

...
We already have

instance Monoid m => Applicative (Const m)

we could easily add

instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>)

which trivially satisfies left/right identity and associativity.

I propose we add this instance to base. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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chessai .

4:53 a.m.

As far as I'm aware, distributivity is neither required nor adhered to by many types in core libraries and beyond. Only left and right identity, and associativity. This instance would also play well with the existing Applicative instance. On Sat, Mar 21, 2020, 3:54 PM Oleg Grenrus wrote:

https://wiki.haskell.org/Typeclassopedia#Laws_6

On 21.3.2020 23.46, Simon Jakobi via Libraries wrote:

...
Hi Zemyla,

Could you clarify where the requirement for distributivity comes from?

The haddocks for Alternative don't mention it:

http://downloads.haskell.org/~ghc/8.10.1-rc1/docs/html/libraries/base-4.14.0...

...
Thanks, Simon

Am Sa., 21. März 2020 um 21:23 Uhr schrieb Zemyla :

...
No, the Alternative instance should be based on semirings instead. The

one you propose isn't distributive.

...
...
Lacking general semirings, the best we can do at the moment is newtypes

for each semiring we have. For instance:

...
newtype NumConst a b = NumConst { getNumConst :: a } deriving (Functor)

instance Num a => Applicative (NumConst a) where pure = const (NumConst 1) (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst

a u -> NumConst a v) (*)

...
instance Num a => Alternative (NumConst a) where empty = NumConst 0 (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b ->

NumConst a b) (+)

...
On Sat, Mar 21, 2020, 13:44 chessai . wrote:

...
We already have

instance Monoid m => Applicative (Const m)

we could easily add

instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>)

which trivially satisfies left/right identity and associativity.

I propose we add this instance to base. _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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Andreas Abel

2:57 p.m.

No, the Alternative instance should be based on semirings instead. The one you propose isn't distributive.

+1. -1 on non-distributive default instances. On 2020-03-21 21:22, Zemyla wrote:

No, the Alternative instance should be based on semirings instead. The one you propose isn't distributive.

Lacking general semirings, the best we can do at the moment is newtypes for each semiring we have. For instance:

newtype NumConst a b = NumConst { getNumConst :: a } deriving (Functor)

instance Num a => Applicative (NumConst a) where pure = const (NumConst 1) (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst a u -> NumConst a v) (*)

instance Num a => Alternative (NumConst a) where empty = NumConst 0 (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b -> NumConst a b) (+)

On Sat, Mar 21, 2020, 13:44 chessai . mailto:chessai1996@gmail.com> wrote:

We already have

instance Monoid m => Applicative (Const m)

we could easily add

instance Monoid m => Alternative (Const m) where empty = coerce mempty (<|>) = coerce (<>)

which trivially satisfies left/right identity and associativity.

I propose we add this instance to base. _______________________________________________ Libraries mailing list Libraries@haskell.org mailto:Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

_______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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participants (5)

Andreas Abel
chessai .
Oleg Grenrus
Simon Jakobi
Zemyla