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List: haskell-cafe
Subject: Re: [Haskell-cafe] Size-indexed monoids
From: Hiromi ISHII <konn.jinro () gmail ! com>
Date: 2017-02-23 3:46:37
Message-ID: 526A4BC4-156E-492D-A5AF-F5F2351F3090 () gmail ! com
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Oops, I sent this directly to Kosyrev... I resent this to cafe for the sake of knowledge sharing.
(Sorry Kosyrev for recieving the same message twice...)
---
Hi,
I once write `sized` package, which wraps ListLike functors instead of Monoids:
http://hackage.haskell.org/package/sized
This can be indexed both with peano numeral and GHC.TypeLits.Nat.
To get the latter working, I use several GHC Plugins.
> On 2017/02/23 0:34, Kosyrev Serge <skosyrev@ptsecurity.com> wrote:
>
> Good day!
>
> What is the proper type class for stronger-typed (size-indexed) monoids:
> - that is, monoids carrying their "size" in the type
> - preferably as GHC.TypeLits.Nat
> - preferably on Hackage
> ?
>
> I'm quite prepared to the idea that a monoid is an entirely wrong abstraction,
> from a category-theoretic standpoint, so I would gladly learn of a better one : -)
>
> Use case:
>
>> {-# LANGUAGE DataKinds, GADTs, KindSignatures, TypeOperators, UnicodeSyntax, StandaloneDeriving #-}
>>
>> module Understanding.Types where
>>
>> import GHC.TypeLits
>>
>> data T (depth ∷ Nat) p where
>> TZ ∷ T 0 p
>> TS ∷ (Show p, CmpNat (m + 1) n ~ EQ) ⇒
>> { payload ∷ p
>> , next ∷ T m a } → T n a
>> deriving instance Show p ⇒ Show (T d p)
>>
>> instance Monoid (T d p) where
>> mempty = TZ
>> mappend TZ TZ = TZ
>> mappend TZ t@(TS _ _) = t
>> mappend t@(TS _ _) TZ = t
>> mappend tl@(TS pl nl) tr = TS pl $ mappend nl tr
>
> As it is, even the mempty case rejects such a blatant violation of
> polymorphism, since `T 0 p` cannot unify with `T n p`.
>
> So, ideally (I think), I would like something like this:
>
>> class TypedMonoid a where
>> tmempty ∷ a 0
>> tmappend ∷ a n → a m → a (n + m)
>
> --
> с уважениeм / respectfully,
> Косырев Сергей
> --
> "Most deadly errors arise from obsolete assumptions."
> -- Frank Herbert, Children of Dune
> _______________________________________________
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> Only members subscribed via the mailman list are allowed to post.
----- 石井 大海 ---------------------------
konn.jinro@gmail.com
筑波大学数理物質科学 究科
数学専攻 博士後期課程一年
----------------------------------------------
> 2017/02/23 0:34、Kosyrev Serge <skosyrev@ptsecurity.com> のメール:
>
> Good day!
>
> What is the proper type class for stronger-typed (size-indexed) monoids:
> - that is, monoids carrying their "size" in the type
> - preferably as GHC.TypeLits.Nat
> - preferably on Hackage
> ?
>
> I'm quite prepared to the idea that a monoid is an entirely wrong abstraction,
> from a category-theoretic standpoint, so I would gladly learn of a better one : -)
>
> Use case:
>
>> {-# LANGUAGE DataKinds, GADTs, KindSignatures, TypeOperators, UnicodeSyntax, StandaloneDeriving #-}
>>
>> module Understanding.Types where
>>
>> import GHC.TypeLits
>>
>> data T (depth ∷ Nat) p where
>> TZ ∷ T 0 p
>> TS ∷ (Show p, CmpNat (m + 1) n ~ EQ) ⇒
>> { payload ∷ p
>> , next ∷ T m a } → T n a
>> deriving instance Show p ⇒ Show (T d p)
>>
>> instance Monoid (T d p) where
>> mempty = TZ
>> mappend TZ TZ = TZ
>> mappend TZ t@(TS _ _) = t
>> mappend t@(TS _ _) TZ = t
>> mappend tl@(TS pl nl) tr = TS pl $ mappend nl tr
>
> As it is, even the mempty case rejects such a blatant violation of
> polymorphism, since `T 0 p` cannot unify with `T n p`.
>
> So, ideally (I think), I would like something like this:
>
>> class TypedMonoid a where
>> tmempty ∷ a 0
>> tmappend ∷ a n → a m → a (n + m)
>
> --
> с уважениeм / respectfully,
> Косырев Сергей
> --
> "Most deadly errors arise from obsolete assumptions."
> -- Frank Herbert, Children of Dune
> _______________________________________________
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> Only members subscribed via the mailman list are allowed to post.
----- 石井 大海 ---------------------------
konn.jinro@gmail.com
筑波大学数理物質科学 究科
数学専攻 博士後期課程一年
----------------------------------------------
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