Generics.MultiRec.Base

This module is the base of the multirec library. It defines the view of a family of datatypes: All the datatypes of the family are represented as indexed functors that are built up from the structure types defined in this module. Furthermore, in order to use the library for a family, conversion functions have to be defined between the original datatypes and their representation. The type class that holds these conversion functions are also defined here.

Structure types

data I xi r ix

Represents recursive positions. The first argument indicates which type to recurse on.

Constructors

I

Fields

unI :: r xi

Instances

El phi xi => HFunctor phi (I xi)

El phi xi => HEq phi (I xi)

El phi xi => HShow phi (I xi)

El phi xi => HReadPrec phi (I xi)

(Constructor c, HReadPrec phi (I xi)) => HReadPrec phi (C c (I xi))

ConNames (I a)

Fold (I xi)

Fold (I xi)

CountAtoms (I xi)

Functor f => Fold ((:.:) f (I xi))

Fold g => Fold ((:*:) (I xi) g)

Fold g => Fold ((:*:) (I xi) g)

type Alg (I xi) r = r -> r

For an identity, we turn the recursive result into a final result. Note that the index can change.

type Comp (I xi) r ix = r xi

type Alg (I xi) r ix = r xi -> r ix

For an identity, we turn the recursive result into a final result. Note that the index can change.

type Alg ((:*:) (I xi) g) r = r -> Alg g r

For a product where the left hand side is an identity, we take the recursive result as an additional argument.

type Alg ((:.:) f (I xi)) r ix = f (r xi) -> r ix

data K a r ix

Represents constant types that do not belong to the family.

Constructors

K

Fields

unK :: a

Instances

HFunctor phi (K x)

Eq a => HEq phi (K a)

For constant types, we make use of the standard equality function.

Show a => HShow phi (K a)

For constant types, we make use of the standard show function.

Read a => HReadPrec phi (K a)

(Constructor c, HReadPrec phi (K a)) => HReadPrec phi (C c (K a))

ConNames (K x)

Fold (K a)

Fold (K a)

CountAtoms (K a)

Fold g => Fold ((:*:) (K a) g)

Fold g => Fold ((:*:) (K a) g)

type Alg (K a) r = a -> r

For a constant, we take the constant value to a result.

type Comp (K a) r ix = a

type Alg (K a) r ix = a -> r ix

For a constant, we take the constant value to a result.

type Alg ((:*:) (K a) g) r = a -> Alg g r

For a product where the left hand side is a constant, we take the value as an additional argument.

data U r ix

Represents constructors without fields.

Constructors

U

Instances

ConNames U

Fold U

Fold U

HFunctor phi U

HEq phi U

HShow phi U

HReadPrec phi U

Constructor c => HReadPrec phi (C c U)

type Alg U r = r

For a unit, no arguments are available.

type Alg U r ix = r ix

For a unit, no arguments are available.

data (f :+: g) r ix infixr 5

Represents sums (choices between constructors).

Constructors

L (f r ix)

R (g r ix)

Instances

(HFunctor phi f, HFunctor phi g) => HFunctor phi ((:+:) f g)

(HEq phi f, HEq phi g) => HEq phi ((:+:) f g)

(HShow phi f, HShow phi g) => HShow phi ((:+:) f g)

(HReadPrec phi f, HReadPrec phi g) => HReadPrec phi ((:+:) f g)

(ConNames f, ConNames g) => ConNames ((:+:) f g)

(Fold f, Fold g) => Fold ((:+:) f g)

(Fold f, Fold g) => Fold ((:+:) f g)

type Alg ((:+:) f g) r = (Alg f r, Alg g r)

For a sum, the algebra is a pair of two algebras.

type Alg ((:+:) f g) r ix = (Alg f r ix, Alg g r ix)

For a sum, the algebra is a pair of two algebras.

data (f :*: g) r ix infixr 7

Represents products (sequences of fields of a constructor).

Constructors

(f r ix) :*: (g r ix) infixr 7

Instances

(HFunctor phi f, HFunctor phi g) => HFunctor phi ((:*:) f g)

(HEq phi f, HEq phi g) => HEq phi ((:*:) f g)

(HShow phi f, HShow phi g) => HShow phi ((:*:) f g)

(Constructor c, CountAtoms ((:*:) f g), HReadPrec phi f, HReadPrec phi g) => HReadPrec phi (C c ((:*:) f g))

(HReadPrec phi f, HReadPrec phi g) => HReadPrec phi ((:*:) f g)

ConNames ((:*:) f g)

Fold g => Fold ((:*:) (K a) g)

Fold g => Fold ((:*:) (I xi) g)

Fold g => Fold ((:*:) (K a) g)

Fold g => Fold ((:*:) (I xi) g)

(CountAtoms f, CountAtoms g) => CountAtoms ((:*:) f g)

type Alg ((:*:) (K a) g) r = a -> Alg g r

For a product where the left hand side is a constant, we take the value as an additional argument.

type Alg ((:*:) (I xi) g) r = r -> Alg g r

For a product where the left hand side is an identity, we take the recursive result as an additional argument.

type Alg ((:*:) f g) r ix = Comp f r ix -> Alg g r ix

For a product where the left hand side is a constant, we take the value as an additional argument.

data (f :>: ix) r ix' where infix 6

Is used to indicate the type that a particular constructor injects to.

Constructors

Tag :: f r ix -> (f :>: ix) r ix

Instances

HFunctor phi f => HFunctor phi ((:>:) f ix)

HEq phi f => HEq phi ((:>:) f ix)

HShow phi f => HShow phi ((:>:) f ix)

(HReadPrec phi f, EqS phi, El phi ix) => HReadPrec phi ((:>:) f ix)

ConNames f => ConNames ((:>:) f ix)

Fold f => Fold ((:>:) f xi)

Fold f => Fold ((:>:) f xi)

type Alg ((:>:) f xi) r = Alg f r

Tags are ignored.

type Alg ((:>:) f xi) r ix = Alg f r xi

A tag changes the index of the final result.

unTag :: (f :>: ix) r ix -> f r ix

Destructor for '(:>:)'.

data (f :.: g) r ix

Represents composition with functors of kind * -> *.

Constructors

D

Fields

unD :: f (g r ix)

Instances

(Traversable f, HFunctor phi g) => HFunctor phi ((:.:) f g)

(Eq1 f, HEq phi g) => HEq phi ((:.:) f g)

(Show1 f, Traversable f, HShow phi g) => HShow phi ((:.:) f g)

(Constructor c, HReadPrec phi ((:.:) f g)) => HReadPrec phi (C c ((:.:) f g))

(Read1 f, HReadPrec phi g) => HReadPrec phi ((:.:) f g)

ConNames ((:.:) f g)

Functor f => Fold ((:.:) f (I xi))

type Comp ((:.:) f g) r ix = f (Comp g r ix)

type Alg ((:.:) f (I xi)) r ix = f (r xi) -> r ix

data C c f r ix where

Represents constructors.

Constructors

C :: f r ix -> C c f r ix

Instances

(Constructor c, HFunctor phi f) => HFunctor phi (C c f)

(Constructor c, HEq phi f) => HEq phi (C c f)

(Constructor c, HShow phi f) => HShow phi (C c f)

(Constructor c, CountAtoms ((:*:) f g), HReadPrec phi f, HReadPrec phi g) => HReadPrec phi (C c ((:*:) f g))

(Constructor c, HReadPrec phi ((:.:) f g)) => HReadPrec phi (C c ((:.:) f g))

(Constructor c, HReadPrec phi (K a)) => HReadPrec phi (C c (K a))

(Constructor c, HReadPrec phi (I xi)) => HReadPrec phi (C c (I xi))

Constructor c => HReadPrec phi (C c U)

Constructor c => ConNames (C c f)

Fold f => Fold (C c f)

Fold f => Fold (C c f)

type Alg (C c f) r = Alg f r

Constructors are ignored.

type Alg (C c f) r ix = Alg f r ix

Constructors are ignored.

unC :: C c f r ix -> f r ix

Destructor for C.

Constructor information

module Generics.MultiRec.Constructor

Unlifted variants

newtype I0 a

Unlifted version of I.

Constructors

I0

Fields

unI0 :: a

Instances

Functor I0

Applicative I0

newtype K0 a b

Unlifted version of K.

Constructors

K0

Fields

unK0 :: a

Instances

Functor (K0 a)

Indexed families

type family PF phi :: (* -> *) -> * -> *

Type family describing the pattern functor of a family.

class El phi ix where

Class for the members of a family.

Methods

proof :: phi ix

class Fam phi where

Class that contains the shallow conversion functions for a family.

Methods

from :: phi ix -> ix -> PF phi I0 ix

to :: phi ix -> PF phi I0 ix -> ix

index :: El phi ix => phi ix

For backwards-compatibility: a synonym for proof.

Equality for indexed families

module Generics.MultiRec.TEq

class EqS phi where

Semi-decidable equality for types of a family.

Methods

eqS :: phi ix -> phi ix' -> Maybe (ix :=: ix')