Copyright	(c) 2008--2010 Universiteit Utrecht
License	BSD3
Maintainer	generics@haskell.org
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell2010

Generics.MultiRec.Base

Contents

Structure types
- Constructor information
- Unlifted variants
Indexed families
- Equality for indexed families

Description

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.

Synopsis

Structure types

data I xi r ix Source

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) Source
El phi xi => HEq phi (I xi) Source
El phi xi => HShow phi (I xi) Source
El phi xi => HReadPrec phi (I xi) Source
(Constructor c, HReadPrec phi (I xi)) => HReadPrec phi (C c (I xi)) Source
ConNames (I a) Source
Fold (I xi) Source
Fold (I xi) Source
CountAtoms (I xi) Source
Functor f => Fold ((:.:) f (I xi)) Source
Fold g => Fold ((:*:) (I xi) g) Source
Fold g => Fold ((:*:) (I xi) g) Source
type Alg (I xi) r = r -> r Source	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 Source
type Alg (I xi) r ix = r xi -> r ix Source	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 Source	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 Source

data K a r ix Source

Represents constant types that do not belong to the family.

Constructors

K
Fields unK :: a

Instances

HFunctor phi (K x) Source
Eq a => HEq phi (K a) Source	For constant types, we make use of the standard equality function.
Show a => HShow phi (K a) Source	For constant types, we make use of the standard show function.
Read a => HReadPrec phi (K a) Source
(Constructor c, HReadPrec phi (K a)) => HReadPrec phi (C c (K a)) Source
ConNames (K x) Source
Fold (K a) Source
Fold (K a) Source
CountAtoms (K a) Source
Fold g => Fold ((:*:) (K a) g) Source
Fold g => Fold ((:*:) (K a) g) Source
type Alg (K a) r = a -> r Source	For a constant, we take the constant value to a result.
type Comp (K a) r ix = a Source
type Alg (K a) r ix = a -> r ix Source	For a constant, we take the constant value to a result.
type Alg ((:*:) (K a) g) r = a -> Alg g r Source	For a product where the left hand side is a constant, we take the value as an additional argument.

data U r ix Source

Represents constructors without fields.

Constructors

U

Instances

ConNames U Source
Fold U Source
Fold U Source
HFunctor phi U Source
HEq phi U Source
HShow phi U Source
HReadPrec phi U Source
Constructor c => HReadPrec phi (C c U) Source
type Alg U r = r Source	For a unit, no arguments are available.
type Alg U r ix = r ix Source	For a unit, no arguments are available.

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

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) Source
(HEq phi f, HEq phi g) => HEq phi ((:+:) f g) Source
(HShow phi f, HShow phi g) => HShow phi ((:+:) f g) Source
(HReadPrec phi f, HReadPrec phi g) => HReadPrec phi ((:+:) f g) Source
(ConNames f, ConNames g) => ConNames ((:+:) f g) Source
(Fold f, Fold g) => Fold ((:+:) f g) Source
(Fold f, Fold g) => Fold ((:+:) f g) Source
type Alg ((:+:) f g) r = (Alg f r, Alg g r) Source	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) Source	For a sum, the algebra is a pair of two algebras.

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

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) Source
(HEq phi f, HEq phi g) => HEq phi ((:*:) f g) Source
(HShow phi f, HShow phi g) => HShow phi ((:*:) f g) Source
(Constructor c, CountAtoms ((::) f g), HReadPrec phi f, HReadPrec phi g) => HReadPrec phi (C c ((::) f g)) Source
(HReadPrec phi f, HReadPrec phi g) => HReadPrec phi ((:*:) f g) Source
ConNames ((:*:) f g) Source
Fold g => Fold ((:*:) (K a) g) Source
Fold g => Fold ((:*:) (I xi) g) Source
Fold g => Fold ((:*:) (K a) g) Source
Fold g => Fold ((:*:) (I xi) g) Source
(CountAtoms f, CountAtoms g) => CountAtoms ((:*:) f g) Source
type Alg ((:*:) (K a) g) r = a -> Alg g r Source	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 Source	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 Source	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 Source

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) Source
HEq phi f => HEq phi ((:>:) f ix) Source
HShow phi f => HShow phi ((:>:) f ix) Source
(HReadPrec phi f, EqS phi, El phi ix) => HReadPrec phi ((:>:) f ix) Source
ConNames f => ConNames ((:>:) f ix) Source
Fold f => Fold ((:>:) f xi) Source
Fold f => Fold ((:>:) f xi) Source
type Alg ((:>:) f xi) r = Alg f r Source	Tags are ignored.
type Alg ((:>:) f xi) r ix = Alg f r xi Source	A tag changes the index of the final result.

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

Destructor for '(:>:)'.

data (f :.: g) r ix Source

Represents composition with functors of kind * -> *.

Constructors

D
Fields unD :: f (g r ix)

Instances

(Traversable f, HFunctor phi g) => HFunctor phi ((:.:) f g) Source
(Eq1 f, HEq phi g) => HEq phi ((:.:) f g) Source
(Show1 f, Traversable f, HShow phi g) => HShow phi ((:.:) f g) Source
(Constructor c, HReadPrec phi ((:.:) f g)) => HReadPrec phi (C c ((:.:) f g)) Source
(Read1 f, HReadPrec phi g) => HReadPrec phi ((:.:) f g) Source
ConNames ((:.:) f g) Source
Functor f => Fold ((:.:) f (I xi)) Source
type Comp ((:.:) f g) r ix = f (Comp g r ix) Source
type Alg ((:.:) f (I xi)) r ix = f (r xi) -> r ix Source

data C c f r ix where Source

Represents constructors.

Constructors

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

Instances

(Constructor c, HFunctor phi f) => HFunctor phi (C c f) Source
(Constructor c, HEq phi f) => HEq phi (C c f) Source
(Constructor c, HShow phi f) => HShow phi (C c f) Source
(Constructor c, CountAtoms ((::) f g), HReadPrec phi f, HReadPrec phi g) => HReadPrec phi (C c ((::) f g)) Source
(Constructor c, HReadPrec phi ((:.:) f g)) => HReadPrec phi (C c ((:.:) f g)) Source
(Constructor c, HReadPrec phi (K a)) => HReadPrec phi (C c (K a)) Source
(Constructor c, HReadPrec phi (I xi)) => HReadPrec phi (C c (I xi)) Source
Constructor c => HReadPrec phi (C c U) Source
Constructor c => ConNames (C c f) Source
Fold f => Fold (C c f) Source
Fold f => Fold (C c f) Source
type Alg (C c f) r = Alg f r Source	Constructors are ignored.
type Alg (C c f) r ix = Alg f r ix Source	Constructors are ignored.

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

Destructor for C.

Constructor information

module Generics.MultiRec.Constructor

Unlifted variants

newtype I0 a Source

Unlifted version of I.

Constructors

I0
Fields unI0 :: a

Instances

Functor I0 Source
Applicative I0 Source

newtype K0 a b Source

Unlifted version of K.

Constructors

K0
Fields unK0 :: a

Instances

Functor (K0 a) Source

Indexed families

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

Type family describing the pattern functor of a family.

class El phi ix where Source

Class for the members of a family.

Methods

proof :: phi ix Source

class Fam phi where Source

Class that contains the shallow conversion functions for a family.

Methods

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

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

index :: El phi ix => phi ix Source

For backwards-compatibility: a synonym for proof.

Equality for indexed families

module Generics.MultiRec.TEq

class EqS phi where Source

Semi-decidable equality for types of a family.

Methods

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