[Agda] stdlib for practical programming
Dmytro Starosud
d.starosud at gmail.com
Thu Sep 26 17:29:20 CEST 2013
I didn't mean full support of "classes" in Agda.
I wanted just some library, implemented in Agda using
instance/implicit arguments, allowing functions overloading.
Also I looked into
http://www2.tcs.ifi.lmu.de/~abel/repos/AgdaPrelude/, which would be
exactly what I need.
But I see it hasn't been supported for a long time.
Have you seen anything else?
Best regards,
Dima
2013/9/26 Sergei Meshveliani <mechvel at botik.ru>:
> On Wed, 2013-09-25 at 19:36 +0300, Dmytro Starosud wrote:
>> By "implicit parameters" do you mean {{instance}} parameters?
>>
>> Thanks,
>> Dima
>>
>> 2013/9/24 Sergei Meshveliani <mechvel at botik.ru>:
>> > On Tue, 2013-09-24 at 19:00 +0300, Dmytro Starosud wrote:
>> >> Hello everybody!
>> >>
>> >> I would like to use Agda for practical programming rather just proof checker.
>> >> For this purpose I need library with type classes and stuff for IO
>> >> operations which would make easier fast prototyping.
>> >> [..]
>> >
>> > After 1 year experience with writing a computer algebra library in Agda
>> > I start to think that classes are not needed, that
>> > dependent records + implicit parameters of Agda is better.
>
>
>
> Please, withdraw my previous respond. Here is the improved one.
>
> --------------------------------------------
> Yes, {{instance}} parameters also.
> For example:
>
> nat+group = ... -- : Group
> natPair+group = ... -- : Group
>
> f : ℕ → ℕ × ℕ → ℕ
> f m (n1 , n2) = m + sum2 ((n1 , n2) + (0, 1))
> where
> sum2 (k , l) = k + l
> open Group {{...}}
>
> Here nat+group is the instance of the additive Group for ℕ,
> _+_ is the operation of such a group,
> natPairGroup is the instance of the additive Group for ℕ × ℕ
> (suppose that these two instances are built earlier),
>
> the implementation of f uses _+_ as both of ℕ and of ℕ × ℕ.
>
> Here is a concrete example, which is type-checked:
>
> ------------------------------------------------------------------------
> open import Function using (case_of_)
> open import Relation.Binary using (DecSetoid; module DecSetoid;
> DecTotalOrder; module DecTotalOrder)
> open import Relation.Nullary.Core using (yes; no)
> open import Data.Nat as Nat using (ℕ; decTotalOrder)
> open import Data.List using (List; []; _∷_)
> open import Relation.Binary.List.Pointwise as LP using (decSetoid)
>
> f : ℕ → List ℕ → List ℕ
> f _ [] = []
> f x (y ∷ ys) = case x ≟ y of \
> { (yes _) → case ys ≟ zs of \ { (yes _) → []
> ; (no _) → x ∷ ys }
> ; (no _) → ys
> }
> where
> natDecSetoid = DecTotalOrder.Eq.decSetoid Nat.decTotalOrder
> lDecSetoid = LP.decSetoid natDecSetoid
> open DecSetoid {{...}}
>
> zs = 0 ∷ 1 ∷ []
> ------------------------------------------------------------------------
>
> It uses the same symbol _≟_ to decide equality on ℕ and on List ℕ
> in the same scope in the `case' expression.
>
> _≟_ is an operation of the `class' DecSetoid.
>
> The instance natDecSetoid of DecSetoid is extracted from the
> library instance of DecTotalOrder for ℕ.
> The instance of lDecSetoid of DecSetoid is for List ℕ,
> it is built by applying a library function LP.decSetoid to
> natDecSetoid.
>
> I do not know of whether open Foo {{...}} will serve so nicely in a
> more complex environment, but at least this sets a question:
>
> why do we need classes, if this example done by implicit instance
> arguments?
>
> Can people provide a simple example showing that classes are desirable?
>
> Another point on classes it that classes will be (if implemented) given
> not in full but somewhat in 2/3. This is due to the
> language/implementation problem of _overlapping instances_.
> For example, in advanced algebra, overlapping instances do appear.
>
> Regards,
>
> ------
> Sergei
>
>
More information about the Agda
mailing list