Generics using @(,)@ and @Either@, with algebraic operations and typed conversions.

shapely-data is a library for working with algebraic datatypes in a simple generic form made up of haskell's primitive product, sum and unit types: (,), Either, and (), providing something like light-weight Structural Typing.

The library was not designed to facilitate generic traversals or abstraction over different recursion schemes, but rather to (from most to least important)

• Provide a good story for (,)Either as a lingua franca/ generic representation that other library writers can use without dependencies, encouraging abstractions in terms of products and sums

• Support algebraic operations on ADTs, making types composable

• Support powerful, typed conversions between Shapely types

Influences

I've taken lots of inspiration, code, names, ideas, and type-level programming techniques from, in particular

• Oleg Kiselyov's HList work

• Edward Kmett's "categories" package

• Chris Taylor's "Algebra of Algebraic Datatypes" series at http://chris-taylor.github.io/blog/2013/02/10/the-algebra-of-algebraic-data-types/

Issues and Limitations:

• massage does not support mutually-recursive types and other more complicated recursion schemes, nor type application.

• While all classes except Shapely are considered closed, we don't do any tricks to enforce that in the API yet.

• In fancier functions that use type equality (e.g. coerce), types need to be unambiguous so type signatures are sometimes required.

• type errors, especially in massage and coerce, can be cryptic

• TH deriving hasn't been considered for fancier types like GADTs, existential types, etc. some of which may have sensible Shapely instances

• Performance hasn't been tested at all yet.

shapely-data is a haskell library up here on hackage for working with algebraic datatypes in a simple generic form made up of haskell's primitive product, sum and unit types: (,), Either, and ().

You can install it with

cabal install shapely-data

Motivation and examples

In order from most to least important to me, here are the concerns that motivated the library:

• Provide a good story for (,)/Either as a /lingua franca/ generic representation that other library writers can use without dependencies, encouraging abstractions in terms of products and sums (motivated specifically by my work on simple-actors.

• Support algebraic operations on ADTs, making types composable

  -- multiplication: let a = (X,(X,(X,()))) b = Left (Y,(Y,())) :: Either (Y,(Y,())) (Z,()) ab = a >*< b in ab == ( Left (X,(X,(X,(Y,(Y,()))))) :: Either (X,(X,(X,(Y,(Y,()))))) (X,(X,(X,(Z,())))) )

  -- exponentiation: fanout (head,(tail,(Prelude.length,()))) [1..3] == (1,([2,3],(3,()))) (unfanin (_4 ary (shiftl . Sh.reverse)) 1 2 3 4) == (3,(2,(1,(4,()))))

• Support powerful, typed conversions between Shapely types

  data F1 = F1 (Maybe F1) (Maybe [Int]) deriving Eq data F2 = F2 (Maybe F2) (Maybe [Int]) deriving Eq f2 :: F2 f2 = coerce (F1 Nothing $ Just [1..3])

  data Tsil a = Snoc (Tsil a) a | Lin deriving Eq truth = massage "123" == Snoc (Snoc (Snoc Lin '3') '2') '1'

Lowest on the list is supporting abstracting over different recursion schemes or supporting generic traversals and folds, though some basic support is planned.

Finally, in at least some cases this can completely replace GHC.Generics and may be a bit simpler. See examples/Generics.hs for an example of the GHC.Generics wiki example ported to shapely-data. And for a nice view on the changes that were required, do:

git show 3a65e95 | perl /usr/share/doc/git/contrib/diff-highlight/diff-highlight

Why not GHC.Generics?

The GHC.Generics representation has a lot of metadata and a complex structure that can be useful in deriving default instances; more important to us is to have a simple, canonical representation such that two types that differ only in constructor names can be expected to have identical generic representations.

This supports APIs that are type-agnostic (e.g. a database library that returns a generic Product, convertible later with to), and allows us to define algebraic operations and composition & conversion functions.