Generics.SOP.Universe

The (generic) representation of a datatype.

A datatype is isomorphic to the sum-of-products of its code. The isomorphism is witnessed by from and to from the Generic class.

The class of representable datatypes.

The SOP approach to generic programming is based on viewing datatypes as a representation (Rep) built from the sum of products of its components. The components of a datatype are specified using the Code type family.

The isomorphism between the original Haskell datatype and its representation is witnessed by the methods of this class, from and to. So for instances of this class, the following laws should (in general) hold:

to . from === id :: a -> a
from . to === id :: Rep a -> Rep a

You typically don't define instances of this class by hand, but rather derive the class instance automatically.

Option 1: Derive via the built-in GHC-generics. For this, you need to use the DeriveGeneric extension to first derive an instance of the Generic class from module GHC.Generics. With this, you can then give an empty instance for Generic, and the default definitions will just work. The pattern looks as follows:

import qualified GHC.Generics as GHC
import Generics.SOP

...

data T = ... deriving (GHC.Generic, ...)

instance Generic T -- empty
instance HasDatatypeInfo T -- empty, if you want/need metadata

Option 2: Derive via Template Haskell. For this, you need to enable the TemplateHaskell extension. You can then use deriveGeneric from module Generics.SOP.TH to have the instance generated for you. The pattern looks as follows:

import Generics.SOP
import Generics.SOP.TH

...

data T = ...

deriveGeneric ''T -- derives HasDatatypeInfo as well

Tradeoffs: Whether to use Option 1 or 2 is mainly a matter of personal taste. The version based on Template Haskell probably has less run-time overhead.

Non-standard instances: It is possible to give Generic instances manually that deviate from the standard scheme, as long as at least

to . from === id :: a -> a

still holds.

A class of datatypes that have associated metadata.

It is possible to use the sum-of-products approach to generic programming without metadata. If you need metadata in a function, an additional constraint on this class is in order.

You typically don't define instances of this class by hand, but rather derive the class instance automatically. See the documentation of Generic for the options.

Constraint that captures that a datatype is a product type, i.e., a type with a single constructor.

It also gives access to the code for the arguments of that constructor.

Direct access to the part of the code that is relevant for a product type.

Convert from a product type to its product representation.

Convert a product representation to the original type.

Constraint that captures that a datatype is an enumeration type, i.e., none of the constructors have any arguments.

Convert from an enum type to its sum representation.

Convert a sum representation to ihe original type.

Constraint that captures that a datatype is a single-constructor, single-field datatype. This always holds for newtype-defined types, but it can also be true for data-defined types.

The constraint also gives access to the type that is wrapped.

Direct access to the part of the code that is relevant for wrapped types and newtypes.

Convert from a wrapped type to its inner type.

Convert a type to a wrapped type.

Constraint that captures that a datatype is a newtype. This makes use of the fact that newtypes are always coercible to the type they wrap, whereas datatypes are not.

Convert a newtype to its inner type.

This is a specialised synonym for coerce.

Convert a type to a newtype.

This is a specialised synonym for coerce.