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@. - [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