[Haskell-cafe] [ANN]: fin & vec

[Oleg Grenrus]

I'm happy to announce two packages:

- http://hackage.haskell.org/package/fin
- http://hackage.haskell.org/package/vec

In short they provide following types:

    data Nat where Z | S Nat

    data Fin (n :: Nat) where
        Z ::          Fin ('S n)
        S :: Fin n -> Fin ('S n)

    data Vec (n :: Nat) a where
        VNil  :: Vec 'Z a
        (:::) :: a -> Vec n a -> Vec ('S n) a

Main motivation for creating these packages is that I didn't found anything
similar on Hackage. Before comparison with the alternatives, let me
mention few
highlights:

- `fin` and `vec` support GHC-7.8.4 .. GHC-8.2.1; and I plan to keep support
  window as wide as possible.

- `fin` package provides `Data.Fin.Enum` module to work generically with
  enumerations. It's (subjectively) more ergonomic than working with
  `All ((:~:) a) xs => NS I xs` from `generics-sop` [1]

- `fin` package defines `InlineInduction` class,
  letting us trick GHC to unfold recursion. One general example is

        unfoldedFix :: forall n a proxy. InlineInduction n
                    => proxy n -> (a -> a) -> a
        unfoldedFix _ = getFix (inlineInduction1 start step :: Fix n a)
where
            start :: Fix 'Z a
            start = Fix fix

            step :: Fix m a -> Fix ('S m) a
            step (Fix go) = Fix $ \f -> f (go f)

        newtype Fix (n :: Nat) a = Fix { getFix :: (a -> a) -> a }

   So, for statically known @n@, GHC's inliner will "simplify":

       unfoldedFix (Proxy :: Proxy Nat3) f = f (f (f (fix f)))

- `fin` has very light dependency footprint:
  `base`, `deepseq`, `hashable` (and transitively `text`) on GHC>=8.0

- `vec` has a little more dependencies, essentially `lens`. See dependency
  diagram in the readme. [2]

- `vec` comes in three flavours:

    * __naive__: with explicit recursion. It's simple, constraint-less,
yet slow.

    * __pull__: using `Fin n -> a` representation, which fuses well,
      but makes some programs hard to write. And

    * __inline__: which uses `InlineInduction`, unrolling
      recursion if the size of 'Vec' is known statically.

Differences with other packages
-------------------------------

### fin

- [type-natural](http://hackage.haskell.org/package/type-natural) depends
  on @singletons@ package. `fin` will try to stay light on the dependencies,
  and support as many GHC versions as practical.

- [peano](http://hackage.haskell.org/package/peano) is very incomplete

- [nat](http://hackage.haskell.org/package/nat) as well.

- [PeanoWitnesses](https://hackage.haskell.org/package/PeanoWitnesses)
  doesn't use @DataKinds at .

- [type-combinators](http://hackage.haskell.org/package/type-combinators)
  is a big package.

### vec

- [linear](http://hackage.haskell.org/package/linear) has 'V' type,
  which uses 'Vector' from @vector@ package as backing store.
  `Vec` is a real GADT, but tries to provide as many useful instances (upto
  @lens@).

- [sized-vector](http://hackage.haskell.org/package/sized-vector) depends
  on 'singletons' package. `vec` isn't light on dependencies either,
  but try to provide wide GHC support.

- [sized](https://hackage.haskell.org/package/sized) also depends
  on a 'singletons' package. The 'Sized f n a' type is generalisation of
  linears 'V' for any 'ListLike'.

- [clash-prelude](https://hackage.haskell.org/package/clash-prelude)
  is a kitchen sink package, which has 'CLaSH.Sized.Vector' module.
  Also depends on 'singletons'.

Disclaimer
----------

These are the "first released versions", i.e. `fin-0` and `vec-0`.
Don't be fooled by 0, we use them in production.

We don't have (yet?) a use-case where proper full inlining would matter, it
seems to work with simple examples. The `vec` package includes simple dot
product benchmark, it gives sensible results:

- *list* version sets the baseline, built-in fusion seems to kick in.
- using `vector` is 3x slower (?)
- naive `Vec` is even slower, not surprisingly
- `Data.Vec.Pull` approach is slower, *except*
- that without conversions it's up to speed with `vector`
- `InlineInduction` is *fastest*.

Acknowledgements
----------------

- *APLicative Programming with Naperian Functors* [3] has the very similar
  `Nat`, `Fin` and `Vec` (sections 2--4). I spotted few missing functions in
  `vec` by re-reading the paper (`vgroup` is `chunks` and `viota` is
`universe`).
  I don't claim that my library is novel in any kind :)
- I learned *Pull array* idea from Josef Svenningsson talk at SmallFP
2017 [4].
  See the video [5] if interested.
- Herbert Valerio Riedel for the idea to split `fin` out of `vec`. It turned
  out to be very light package.
- Andres Löh for discussions about `generics-sop` [1], and about the static
  inlining idea.
- Joachim Breitner for creating `inspection-testing` [6], which really helps
  validating optimisations working.

Cheers,
Oleg


- [1] http://hackage.haskell.org/package/generics-sop
- [2] https://github.com/phadej/vec#dependencies
- [3]
https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/aplicative.pdf
- [4] http://clojutre.org/2017/
- [5]
https://www.youtube.com/watch?v=5PZh0BcjIbY&list=PLetHPRQvX4a9uUK2JUZrgjtC_x4CeNLtN&index=5
- [6] http://hackage.haskell.org/package/inspection-testing


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