[Agda] stdlib for practical programming
Sergei Meshveliani
mechvel at botik.ru
Thu Sep 26 14:17:50 CEST 2013
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
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