Generalize indexing function

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Dannyu NDos

10 Apr 2021 10 Apr '21

10:48 p.m.

I noticed that the list indexing function, (!!), is generalizable. I'm showing some instances: {-# LANGUAGE MultiParamTypeClasses #-} import Data.Complex import Data.Functor.Compose import Data.Functor.Product import Data.Functor.Sum import Data.List.NonEmpty import Data.Maybe infix 9 !? infixl 9 ! class Indexable i a where (!?) :: i b -> a -> Maybe b (!) :: Indexable i a => i b -> a -> b x ! n = fromJust (x !? n) instance Indexable [] Int where [] !? _ = Nothing (x:_) !? 0 = Just x (_:xs) !? n | n < 0 = Nothing | otherwise = xs !? (n-1) instance Indexable ((->) a) (Identity a) where f !? Identity n = Just (f n) instance Indexable ((,) a) () where (_,x) !? _ = Just x instance Indexable Complex Bool where (x :+ _) !? False = Just x (_ :+ y) !? True = Just y instance (Indexable f a, Indexable g b) => Indexable (Compose f g) (a,b) where Compose z !? (m,n) = do y <- z !? m y !? n instance (Indexable f a, Indexable g b) => Indexable (Product f g) (Either a b) where Pair x _ !? Left m = x !? m Pair _ y !? Right n = y !? n instance (Indexable f a, Indexable g a) => Indexable (Sum f g) (Identity a) where InL x !? Identity n = x !? n InR y !? Identity n = y !? n instance Indexable NonEmpty Int where (x :| xs) !? n = (x : xs) !? n

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Keith

10 Apr 10 Apr

10:57 p.m.

Might be more convenient to use an associated type family. And in practice, using types like '()' and 'Bool' as indexes is not super useful when you've already committed to using 'Int' as the (partial) index type of '[]'. - Keith Sent from my phone with K-9 Mail. On April 10, 2021 10:48:42 PM UTC, Dannyu NDos wrote:

...

I noticed that the list indexing function, (!!), is generalizable. I'm showing some instances:

{-# LANGUAGE MultiParamTypeClasses #-}

import Data.Complex import Data.Functor.Compose import Data.Functor.Product import Data.Functor.Sum import Data.List.NonEmpty import Data.Maybe

infix 9 !? infixl 9 !

class Indexable i a where (!?) :: i b -> a -> Maybe b

(!) :: Indexable i a => i b -> a -> b x ! n = fromJust (x !? n)

instance Indexable [] Int where [] !? _ = Nothing (x:_) !? 0 = Just x (_:xs) !? n | n < 0 = Nothing | otherwise = xs !? (n-1)

instance Indexable ((->) a) (Identity a) where f !? Identity n = Just (f n)

instance Indexable ((,) a) () where (_,x) !? _ = Just x

instance Indexable Complex Bool where (x :+ _) !? False = Just x (_ :+ y) !? True = Just y

instance (Indexable f a, Indexable g b) => Indexable (Compose f g) (a,b) where Compose z !? (m,n) = do y <- z !? m y !? n

instance (Indexable f a, Indexable g b) => Indexable (Product f g) (Either a b) where Pair x _ !? Left m = x !? m Pair _ y !? Right n = y !? n

instance (Indexable f a, Indexable g a) => Indexable (Sum f g) (Identity a) where InL x !? Identity n = x !? n InR y !? Identity n = y !? n

instance Indexable NonEmpty Int where (x :| xs) !? n = (x : xs) !? n

Henning Thielemann

11 Apr 11 Apr

12:14 a.m.

On Sat, 10 Apr 2021, Keith wrote:

...

Might be more convenient to use an associated type family.

I have done something similar here: http://hackage.haskell.org/package/comfort-array

Carter Schonwald

3:18 a.m.

I really like the landscape of indexinbg flavores you've included henning! i've def thought about similar stuff, and its nice to see it fleshed out :) On Sat, Apr 10, 2021 at 8:15 PM Henning Thielemann < lemming@henning-thielemann.de> wrote:

...

On Sat, 10 Apr 2021, Keith wrote:

...
Might be more convenient to use an associated type family.

I have done something similar here: http://hackage.haskell.org/package/comfort-array _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

George Wilson

6:32 a.m.

Does this class have any laws? From what I can tell, this is useful only as an overloading of some identifiers - I don't see what useful functions I could write in terms of this as an abstraction. Cheers, George On Sun, 11 Apr 2021, 08:49 Dannyu NDos, wrote:

...

I noticed that the list indexing function, (!!), is generalizable. I'm showing some instances:

{-# LANGUAGE MultiParamTypeClasses #-}

import Data.Complex import Data.Functor.Compose import Data.Functor.Product import Data.Functor.Sum import Data.List.NonEmpty import Data.Maybe

infix 9 !? infixl 9 !

class Indexable i a where (!?) :: i b -> a -> Maybe b

(!) :: Indexable i a => i b -> a -> b x ! n = fromJust (x !? n)

instance Indexable [] Int where [] !? _ = Nothing (x:_) !? 0 = Just x (_:xs) !? n | n < 0 = Nothing | otherwise = xs !? (n-1)

instance Indexable ((->) a) (Identity a) where f !? Identity n = Just (f n)

instance Indexable ((,) a) () where (_,x) !? _ = Just x

instance Indexable Complex Bool where (x :+ _) !? False = Just x (_ :+ y) !? True = Just y

instance (Indexable f a, Indexable g b) => Indexable (Compose f g) (a,b) where Compose z !? (m,n) = do y <- z !? m y !? n

instance (Indexable f a, Indexable g b) => Indexable (Product f g) (Either a b) where Pair x _ !? Left m = x !? m Pair _ y !? Right n = y !? n

instance (Indexable f a, Indexable g a) => Indexable (Sum f g) (Identity a) where InL x !? Identity n = x !? n InR y !? Identity n = y !? n

instance Indexable NonEmpty Int where (x :| xs) !? n = (x : xs) !? n

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

Akhra Gannon

7:01 a.m.

It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n On Sat, Apr 10, 2021, 11:33 PM George Wilson wrote:

...

Does this class have any laws? From what I can tell, this is useful only as an overloading of some identifiers - I don't see what useful functions I could write in terms of this as an abstraction.

Cheers, George

On Sun, 11 Apr 2021, 08:49 Dannyu NDos, wrote:

...
I noticed that the list indexing function, (!!), is generalizable. I'm showing some instances:

{-# LANGUAGE MultiParamTypeClasses #-}

import Data.Complex import Data.Functor.Compose import Data.Functor.Product import Data.Functor.Sum import Data.List.NonEmpty import Data.Maybe

infix 9 !? infixl 9 !

class Indexable i a where (!?) :: i b -> a -> Maybe b

(!) :: Indexable i a => i b -> a -> b x ! n = fromJust (x !? n)

instance Indexable [] Int where [] !? _ = Nothing (x:_) !? 0 = Just x (_:xs) !? n | n < 0 = Nothing | otherwise = xs !? (n-1)

instance Indexable ((->) a) (Identity a) where f !? Identity n = Just (f n)

instance Indexable ((,) a) () where (_,x) !? _ = Just x

instance Indexable Complex Bool where (x :+ _) !? False = Just x (_ :+ y) !? True = Just y

instance (Indexable f a, Indexable g b) => Indexable (Compose f g) (a,b) where Compose z !? (m,n) = do y <- z !? m y !? n

instance (Indexable f a, Indexable g b) => Indexable (Product f g) (Either a b) where Pair x _ !? Left m = x !? m Pair _ y !? Right n = y !? n

instance (Indexable f a, Indexable g a) => Indexable (Sum f g) (Identity a) where InL x !? Identity n = x !? n InR y !? Identity n = y !? n

instance Indexable NonEmpty Int where (x :| xs) !? n = (x : xs) !? n

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

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Henning Thielemann

10:03 a.m.

On Sun, 11 Apr 2021, Akhra Gannon wrote:

...

It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ? I think, xs!!n is a single element.

Akhra Gannon

10:11 a.m.

Yeah, I mis-composed that. Pretty sure there's a formulation around take/head that works but I'm clearly not in a headspace to find it! On Sun, Apr 11, 2021, 3:03 AM Henning Thielemann < lemming@henning-thielemann.de> wrote:

...

On Sun, 11 Apr 2021, Akhra Gannon wrote:

...
It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ?

I think, xs!!n is a single element.

Tom Ellis

10:35 a.m.

On Sun, Apr 11, 2021 at 12:03:04PM +0200, Henning Thielemann wrote:

...

On Sun, 11 Apr 2021, Akhra Gannon wrote:

...
It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ?

I think, xs!!n is a single element.

Presumably `xs !! n == fromList xs !! n`

Keith

3:28 p.m.

`xs !! () == fromList xs !! ()` seems to be a type error? -- Keith Sent from my phone with K-9 Mail. On April 11, 2021 10:35:53 AM UTC, Tom Ellis wrote:

...

On Sun, Apr 11, 2021 at 12:03:04PM +0200, Henning Thielemann wrote:

...
On Sun, 11 Apr 2021, Akhra Gannon wrote:

...
It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ?

I think, xs!!n is a single element.

Presumably `xs !! n == fromList xs !! n` _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Keith

3:33 p.m.

Maybe `xs !! n == fromList xs !! fromEnum n`? -- Keith Sent from my phone with K-9 Mail. On April 11, 2021 10:35:53 AM UTC, Tom Ellis wrote:

...

On Sun, Apr 11, 2021 at 12:03:04PM +0200, Henning Thielemann wrote:

...
On Sun, 11 Apr 2021, Akhra Gannon wrote:

...
It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ?

I think, xs!!n is a single element.

Presumably `xs !! n == fromList xs !! n` _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

Keith

3:41 p.m.

Sorry to spam, just realized that destroys the Map and (->) instances. -- Keith Sent from my phone with K-9 Mail. On April 11, 2021 10:35:53 AM UTC, Tom Ellis wrote:

...

On Sun, Apr 11, 2021 at 12:03:04PM +0200, Henning Thielemann wrote:

...
On Sun, 11 Apr 2021, Akhra Gannon wrote:

...
It's distributive under IsList. fromList (xs !! n) == (fromList xs) !! n

fromList (xs !! n) ?

I think, xs!!n is a single element.

Presumably `xs !! n == fromList xs !! n` _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries

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participants (7)

Akhra Gannon
Carter Schonwald
Dannyu NDos
George Wilson
Henning Thielemann
Keith
Tom Ellis