Generic Programming using True Sums of Products

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BSD-3-Clause licensed by Edsko de Vries, Andres Löh
Maintained by [email protected]
This version can be pinned in stack with:generics-sop-,4312

A library to support the definition of generic functions. Datatypes are viewed in a uniform, structured way: the choice between constructors is represented using an n-ary sum, and the arguments of each constructor are represented using an n-ary product.

The module Generics.SOP is the main module of this library and contains more detailed documentation.

Examples of using this library are provided by the following packages:

A detailed description of the ideas behind this library is provided by the paper:

Changes (2017-04-21)

  • GHC 8.2 compatibility.

  • Make :.: an instance of Applicative, Foldable and Traversable.

  • Add functions apInjs'_NP and apInjs'_POP. These are variants of apInjs_NP and apInjs'_POP that return their result as an n-ary product, rather than collapsing it into a list.

  • Add hexpand (and expand_NS and expand_SOP). These functions expand sums into products, given a default value to fill the other slots.

  • Add utility functions such as mapII or mapIK that lift functions into different combinations of identity and constant functors.

  • Add NFData (and lifted variants) instances for basic functors, products and sums. (2017-02-02)

  • Add hindex (and index_NS and index_SOP).

  • Add hapInjs as a generalization of apInjs_NP and apInjs_POP.

  • Make basic functors instances of lifted classes (such as Eq1 etc). (2016-12-04)

  • Add various metadata getters

  • Add hdicts.

  • Add catamorphisms and anamorphisms for NP and NS.

  • TH compatibility changes for GHC 8.1 (master). (2016-07-10)

  • Introduced unZ to destruct a unary sum.

  • Add Haddock @since annotations for various functions. (2016-02-08)

  • Now includes a CHANGELOG.

  • Should now work with ghc-8.0.1-rc1 and -rc2 (thanks to Oleg Grenrus).

  • Introduced hd and tl to project out of a product, and Projection and projections as duals of Injection and injections. (2015-10-23)

  • Now tested with ghc-7.10

  • Introduced names hmap, hcmap, hzipWith, hczipWith for hliftA, hcliftA, hliftA2, hcliftA2, respectively. Similarly for the specialized versions of these functions.

  • The constraint transformers All and All2 are now defined as type classes, not type families. As a consequence, the partial applications All c and All2 c are now possible.

  • Because of the redefinition of All and All2, some special cases are no longer necessary. For example, cpure_POP can now be implemented as a nested application of pure_NP.

  • Because of the redefinition of All and All2, the functions hcliftA' and variants (with prime!) are now deprecated. One can easily use the normal versions instead. For example, the definition of hcliftA' is now simply

    hcliftA' p = hcliftA (allP p)
        allP :: proxy c -> Proxy (All c)
        allP _ = Proxy
  • Because All and All2 are now type classes, they now have superclass constraints implying that the type-level lists they are ranging over must have singletons.

    class (SListI xs,  ...) => All c xs
    class (SListI xss, ...) => All2 c xss

    Some type signatures can be simplified due to this.

  • The SingI typeclass and Sing datatypes are now deprecated. The replacements are called SListI and SList. The sing method is now called sList. The difference is that the new versions reveal only the spine of the list, and contain no singleton representation for the elements anymore.

    For one-dimensional type-level lists, replace

    SingI xs => ... 


    SListI xs => ...

    For two-dimensional type-level lists, replace

    SingI xss => ...


    All SListI xss => ...

    Because All itself implies SListI xss (see above), this constraint is equivalent to the old Sing xss.

    The old names are provided for (limited) backward compatibility. They map to the new constructs. This will work in some, but not all scenarios.

    The function lengthSing has also been renamed to lengthSList for consistency, and the old name is deprecated.

  • All Proxy c arguments have been replaced by proxy c flexible arguments, so that other type constructors can be used as proxies.

  • Class-level composition (Compose), pairing (And), and a trivial constraint (Top) have been added. Type-level map (Map) has been removed. Occurrences such as

    All c (Map f xs)

    should now be replaced with

    All (c `Compose` f) xs
  • There is a new module called Generics.SOP.Dict that contains functions for manipulating dictionaries explicitly. These can be used to prove theorems about non-trivial class constraints such as the ones that get built using All and All2. Some such theorems are provided.

  • There is a new TH function deriveGenericFunctions that derives the code of a datatype and conversion functions, but does not create a class instance. (Contributed by Oleg Grenrus.)

  • There is a new TH function deriveMetadataValue that derives a DatatypeInfo value for a datatype, but does not create an instance of HasDatatypeInfo. (Contributed by Oleg Grenrus.)

  • There is a very simple example file. (Contributed by Oleg Grenrus.)

  • The function hcollapse for NS now results in an a rather than an I a, matching the specialized version collapse_NS. (Suggested by Roman Cheplyaka.) (2015-03-27)

  • Updated version bounds for ghc-prim (for ghc-7.10). (2015-03-20)

  • Preparations for ghc-7.10.

  • Documentation fix. (Contributed by Roman Cheplyaka.)

0.1.1 (2015-01-06)

  • Documentation fixes.

  • Add superclass constraint (TODO).

  • Now derive tuple instance for tuples up to 30 components. (Contributed by Michael Orlitzky.)