Generics.Deriving.Base

generic-deriving-1.14.5: Generic programming library for generalised deriving.

Safe Haskell | Safe
Language | Haskell2010

Generics.Deriving.Base

Contents

- Introduction
  - Representing datatypes
  - Derived and fundamental representation types
    - Individual fields of constructors: `K1`
    - Meta information: `M1`
    - Additional generic representation type constructors
      - Empty datatypes: `V1`
      - Constructors without fields: `U1`
    - Representation of types with many constructors or many fields
  - Defining datatype-generic functions
    - Definition of the generic representation types
    - Generic instances
    - The wrapper and generic default
    - Omitting generic instances
  - Generic constructor classes
    - The `Generic1` class
    - Representation of `* -> *` types
    - Representation of unlifted types

Synopsis

# Introduction

Datatype-generic functions are are based on the idea of converting values of a datatype `T` into corresponding values of a (nearly) isomorphic type ``Rep` T`. The type ``Rep` T` is built from a limited set of type constructors, all provided by this module. A datatype-generic function is then an overloaded function with instances for most of these type constructors, together with a wrapper that performs the mapping between `T` and ``Rep` T`. By using this technique, we merely need a few generic instances in order to implement functionality that works for any representable type.

Representable types are collected in the `Generic` class, which defines the associated type `Rep` as well as conversion functions `from` and `to`. Typically, you will not define `Generic` instances by hand, but have the compiler derive them for you.

## Representing datatypes

The key to defining your own datatype-generic functions is to understand how to represent datatypes using the given set of type constructors.

Let us look at an example first:

    data Tree a = Leaf a | Node (Tree a) (Tree a)
      deriving Generic

The above declaration (which requires the language pragma `DeriveGeneric`) causes the following representation to be generated:

    class Generic (Tree a) where
      type Rep (Tree a) =
        D1 D1Tree
          (C1 C1_0Tree
             (S1 NoSelector (Par0 a))
           :+:
           C1 C1_1Tree
             (S1 NoSelector (Rec0 (Tree a))
              :*:
              S1 NoSelector (Rec0 (Tree a))))
      ...

Hint: You can obtain information about the code being generated from GHC by passing the `-ddump-deriv` flag. In GHCi, you can expand a type family such as `Rep` using the `:kind!` command.

## Derived and fundamental representation types

There are many datatype-generic functions that do not distinguish between positions that are parameters or positions that are recursive calls. There are also many datatype-generic functions that do not care about the names of datatypes and constructors at all. To keep the number of cases to consider in generic functions in such a situation to a minimum, it turns out that many of the type constructors introduced above are actually synonyms, defining them to be variants of a smaller set of constructors.

### Individual fields of constructors: `K1`

The type constructors `Par0` and `Rec0` are variants of `K1`:

    type Par0 = K1 P
    type Rec0 = K1 R

Here, `P` and `R` are type-level proxies again that do not have any associated values.

### Meta information: `M1`

The type constructors `S1`, `C1` and `D1` are all variants of `M1`:

    type S1 = M1 S
    type C1 = M1 C
    type D1 = M1 D

The types `S`, `C` and `R` are once again type-level proxies, just used to create several variants of `M1`.

### Additional generic representation type constructors

Next to `K1`, `M1`, `:+:` and `:*:` there are a few more type constructors that occur in the representations of other datatypes.

#### Empty datatypes: `V1`

For empty datatypes, `V1` is used as a representation. For example,

    data Empty deriving Generic

yields

    instance Generic Empty where
      type Rep Empty = D1 D1Empty V1

#### Constructors without fields: `U1`

If a constructor has no arguments, then `U1` is used as its representation. For example the representation of `Bool` is

    instance Generic Bool where
      type Rep Bool =
        D1 D1Bool
          (C1 C1_0Bool U1 :+: C1 C1_1Bool U1)

### Representation of types with many constructors or many fields

As `:+:` and `:*:` are just binary operators, one might ask what happens if the datatype has more than two constructors, or a constructor with more than two fields. The answer is simple: the operators are used several times, to combine all the constructors and fields as needed. However, users /should not rely on a specific nesting strategy/ for `:+:` and `:*:` being used. The compiler is free to choose any nesting it prefers. (In practice, the current implementation tries to produce a more or less balanced nesting, so that the traversal of the structure of the datatype from the root to a particular component can be performed in logarithmic rather than linear time.)

## Defining datatype-generic functions

A datatype-generic function comprises two parts:

1. Generic instances for the function, implementing it for most of the representation type constructors introduced above.
2. A wrapper that for any datatype that is in `Generic`, performs the conversion between the original value and its `Rep`-based representation and then invokes the generic instances.

As an example, let us look at a function `encode` that produces a naive, but lossless bit encoding of values of various datatypes. So we are aiming to define a function

    encode :: Generic a => a -> [Bool]

where we use `Bool` as our datatype for bits.

For part 1, we define a class `Encode'`. Perhaps surprisingly, this class is parameterized over a type constructor `f` of kind `* -> *`. This is a technicality: all the representation type constructors operate with kind `* -> *` as base kind. But the type argument is never being used. This may be changed at some point in the future. The class has a single method, and we use the type we want our final function to have, but we replace the occurrences of the generic type argument `a` with `f p` (where the `p` is any argument; it will not be used).

    class Encode' f where
      encode' :: f p -> [Bool]

With the goal in mind to make `encode` work on `Tree` and other datatypes, we now define instances for the representation type constructors `V1`, `U1`, `:+:`, `:*:`, `K1`, and `M1`.

### Definition of the generic representation types

In order to be able to do this, we need to know the actual definitions of these types:

    data    V1        p                       -- lifted version of Empty
    data    U1        p = U1                  -- lifted version of ()
    data    (:+:) f g p = L1 (f p) | R1 (g p) -- lifted version of Either
    data    (:*:) f g p = (f p) :*: (g p)     -- lifted version of (,)
    newtype K1    i c p = K1 { unK1 :: c }    -- a container for a c
    newtype M1  i t f p = M1 { unM1 :: f p }  -- a wrapper

So, `U1` is just the unit type, `:+:` is just a binary choice like `Either`, `:*:` is a binary pair like the pair constructor `(,)`, and `K1` is a value of a specific type `c`, and `M1` wraps a value of the generic type argument, which in the lifted world is an `f p` (where we do not care about `p`).

### Generic instances

The instance for `V1` is slightly awkward (but also rarely used):

    instance Encode' V1 where
      encode' x = undefined

There are no values of type `V1 p` to pass (except undefined), so this is actually impossible. One can ask why it is useful to define an instance for `V1` at all in this case? Well, an empty type can be used as an argument to a non-empty type, and you might still want to encode the resulting type. As a somewhat contrived example, consider `[Empty]`, which is not an empty type, but contains just the empty list. The `V1` instance ensures that we can call the generic function on such types.

There is exactly one value of type `U1`, so encoding it requires no knowledge, and we can use zero bits:

    instance Encode' U1 where
      encode' U1 = []

In the case for `:+:`, we produce `False` or `True` depending on whether the constructor of the value provided is located on the left or on the right:

    instance (Encode' f, Encode' g) => Encode' (f :+: g) where
      encode' (L1 x) = False : encode' x
      encode' (R1 x) = True  : encode' x

In the case for `:*:`, we append the encodings of the two subcomponents:

    instance (Encode' f, Encode' g) => Encode' (f :*: g) where
      encode' (x :*: y) = encode' x ++ encode' y

The case for `K1` is rather interesting. Here, we call the final function `encode` that we yet have to define, recursively. We will use another type class `Encode` for that function:

    instance (Encode c) => Encode' (K1 i c) where
      encode' (K1 x) = encode x

Note how `Par0` and `Rec0` both being mapped to `K1` allows us to define a uniform instance here.

Similarly, we can define a uniform instance for `M1`, because we completely disregard all meta-information:

    instance (Encode' f) => Encode' (M1 i t f) where
      encode' (M1 x) = encode' x

Unlike in `K1`, the instance for `M1` refers to `encode'`, not `encode`.

### The wrapper and generic default

We now define class `Encode` for the actual `encode` function:

    class Encode a where
      encode :: a -> [Bool]
      default encode :: (Generic a) => a -> [Bool]
      encode x = encode' (from x)

The incoming `x` is converted using `from`, then we dispatch to the generic instances using `encode'`. We use this as a default definition for `encode`. We need the 'default encode' signature because ordinary Haskell default methods must not introduce additional class constraints, but our generic default does.

Defining a particular instance is now as simple as saying

    instance (Encode a) => Encode (Tree a)

### Omitting generic instances

It is not always required to provide instances for all the generic representation types, but omitting instances restricts the set of datatypes the functions will work for:

- If no `:+:` instance is given, the function may still work for empty datatypes or datatypes that have a single constructor, but will fail on datatypes with more than one constructor.
- If no `:*:` instance is given, the function may still work for datatypes where each constructor has just zero or one field, in particular for enumeration types.
- If no `K1` instance is given, the function may still work for enumeration types, where no constructor has any fields.
- If no `V1` instance is given, the function may still work for any datatype that is not empty.
- If no `U1` instance is given, the function may still work for any datatype where each constructor has at least one field.

An `M1` instance is always required (but it can just ignore the meta-information, as is the case for `encode` above).

## Generic constructor classes

Datatype-generic functions as defined above work for a large class of datatypes, including parameterized datatypes. (We have used `Tree` as our example above, which is of kind `* -> *`.) However, the `Generic` class ranges over types of kind `*`, and therefore, the resulting generic functions (such as `encode`) must be parameterized by a generic type argument of kind `*`.

What if we want to define generic classes that range over type constructors (such as `Functor`, `Traversable`, or `Foldable`)?

### The `Generic1` class

Like `Generic`, there is a class `Generic1` that defines a representation `Rep1` and conversion functions `from1` and `to1`, only that `Generic1` ranges over types of kind `* -> *`. The `Generic1` class is also derivable.

The representation `Rep1` is ever so slightly different from `Rep`. Let us look at `Tree` as an example again:

    data Tree a = Leaf a | Node (Tree a) (Tree a)
      deriving Generic1

The above declaration causes the following representation to be generated:

class `Generic1` Tree where type `Rep1` Tree = `D1` D1Tree (`C1` C1_0Tree (`S1` `NoSelector` `Par1`) `:+:` `C1` C1_1Tree (`S1` `NoSelector` (`Rec1` Tree) `:*:` `S1` `NoSelector` (`Rec1` Tree))) ...

The representation reuses `D1`, `C1`, `S1` (and thereby `M1`) as well as `:+:` and `:*:` from `Rep`. (This reusability is the reason that we carry around the dummy type argument for kind-`*`-types, but there are already enough different names involved without duplicating each of these.)

What's different is that we now use `Par1` to refer to the parameter (and that parameter, which used to be `a`), is not mentioned explicitly by name anywhere; and we use `Rec1` to refer to a recursive use of `Tree a`.

### Representation of `* -> *` types

Unlike `Par0` and `Rec0`, the `Par1` and `Rec1` type constructors do not map to `K1`. They are defined directly, as follows:

    newtype Par1   p = Par1 { unPar1 ::   p } -- gives access to parameter p
    newtype Rec1 f p = Rec1 { unRec1 :: f p } -- a wrapper

In `Par1`, the parameter `p` is used for the first time, whereas `Rec1` simply wraps an application of `f` to `p`.

Note that `K1` (in the guise of `Rec0`) can still occur in a `Rep1` representation, namely when the datatype has a field that does not mention the parameter.

The declaration

    data WithInt a = WithInt Int a
      deriving Generic1

yields

    class Rep1 WithInt where
      type Rep1 WithInt =
        D1 D1WithInt
          (C1 C1_0WithInt
            (S1 NoSelector (Rec0 Int)
             :*:
             S1 NoSelector Par1))

If the parameter `a` appears underneath a composition of other type constructors, then the representation involves composition, too:

    data Rose a = Fork a [Rose a]

yields

    class Rep1 Rose where
      type Rep1 Rose =
        D1 D1Rose
          (C1 C1_0Rose
            (S1 NoSelector Par1
             :*:
             S1 NoSelector ([] :.: Rec1 Rose)

where

    newtype (:.:) f g p = Comp1 { unComp1 :: f (g p) }

### Representation of unlifted types

If one were to attempt to derive a Generic instance for a datatype with an unlifted argument (for example, `Int#`), one might expect the occurrence of the `Int#` argument to be marked with ``Rec0` `Int#``. This won't work, though, since `Int#` is of kind `#` and `Rec0` expects a type of kind `*`. In fact, polymorphism over unlifted types is disallowed completely.

One solution would be to represent an occurrence of `Int#` with 'Rec0 Int' instead. With this approach, however, the programmer has no way of knowing whether the `Int` is actually an `Int#` in disguise.

Instead of reusing `Rec0`, a separate data family `URec` is used to mark occurrences of common unlifted types:

    data family URec a p

    data instance URec (Ptr ()) p = UAddr   { uAddr#   :: Addr#   }
    data instance URec Char     p = UChar   { uChar#   :: Char#   }
    data instance URec Double   p = UDouble { uDouble# :: Double# }
    data instance URec Int      p = UFloat  { uFloat#  :: Float#  }
    data instance URec Float    p = UInt    { uInt#    :: Int#    }
    data instance URec Word     p = UWord   { uWord#   :: Word#   }

Several type synonyms are provided for convenience:

    type UAddr   = URec (Ptr ())
    type UChar   = URec Char
    type UDouble = URec Double
    type UFloat  = URec Float
    type UInt    = URec Int
    type UWord   = URec Word

The declaration

    data IntHash = IntHash Int#
      deriving Generic

yields

    instance Generic IntHash where
      type Rep IntHash =
        D1 D1IntHash
          (C1 C1_0IntHash
            (S1 NoSelector UInt))

Currently, only the six unlifted types listed above are generated, but this may be extended to encompass more unlifted types in the future.