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 => HReadPrec phi (I xi)

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (I xi I0 ix)

El phi xi => HFunctor phi (I xi)

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> I xi r ix -> a (I xi r' ix)

El phi xi => HShow phi (I xi)

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (I xi) [Int -> ShowS]

El phi xi => HEq phi (I xi)

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> I xi r ix -> I xi r ix -> Bool

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (I xi) I0 ix)

CountAtoms (I xi)

Defined in Generics.MultiRec.Read

Methods

countatoms :: I xi r ix -> Int

Fold (I xi)

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (I xi) r -> I xi (K0 r) ix -> r

Fold (I xi)

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (I xi) r ix -> I xi r ix -> r ix

ConNames (I a)

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: I a r ix -> [String]

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (I xi :*: g) r -> (I xi :*: g) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlg

Methods

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

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (I xi :*: g) r ix -> (I xi :*: g) r ix -> r ix

type Alg (I xi) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Comp (I xi) r ix

Defined in Generics.MultiRec.FoldAlg

type Comp (I xi) r ix = r xi

type Alg (I xi) r ix

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

Defined in Generics.MultiRec.FoldAlg

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

type Alg (I xi :*: g) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (f :.: I xi) r ix

Defined in Generics.MultiRec.FoldAlg

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

Read a => HReadPrec phi (K a)

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (K a I0 ix)

HFunctor phi (K x)

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> K x r ix -> a (K x r' ix)

Show a => HShow phi (K a)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (K a) [Int -> ShowS]

Eq a => HEq phi (K a)

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> K a r ix -> K a r ix -> Bool

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (K a) I0 ix)

CountAtoms (K a)

Defined in Generics.MultiRec.Read

Methods

countatoms :: K a r ix -> Int

Fold (K a)

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (K a) r -> K a (K0 r) ix -> r

Fold (K a)

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (K a) r ix -> K a r ix -> r ix

ConNames (K x)

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: K x r ix -> [String]

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (K a :*: g) r -> (K a :*: g) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (K a :*: g) r ix -> (K a :*: g) r ix -> r ix

type Alg (K a) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Comp (K a) r ix

Defined in Generics.MultiRec.FoldAlg

type Comp (K a) r ix = a

type Alg (K a) r ix

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

Defined in Generics.MultiRec.FoldAlg

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

type Alg (K a :*: g) r

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

Defined in Generics.MultiRec.FoldAlgK

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

data U (r :: * -> *) ix

Represents constructors without fields.

Constructors

U

Instances

Fold U

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg U r -> U (K0 r) ix -> r

Fold U

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg U r ix -> U r ix -> r ix

ConNames U

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: U r ix -> [String]

HReadPrec phi U

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (U I0 ix)

HFunctor phi U

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> U r ix -> a (U r' ix)

HShow phi U

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi U [Int -> ShowS]

HEq phi U

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> U r ix -> U r ix -> Bool

Constructor c => HReadPrec phi (C c U)

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c U I0 ix)

type Alg U r

For a unit, no arguments are available.

Defined in Generics.MultiRec.FoldAlgK

type Alg U r = r

type Alg U r ix

For a unit, no arguments are available.

Defined in Generics.MultiRec.FoldAlg

type Alg U r ix = r ix

data (f :+: g) (r :: * -> *) ix infixr 5

Represents sums (choices between constructors).

Constructors

L (f r ix)

R (g r ix)

Instances

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec ((f :+: g) I0 ix)

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

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> (f :+: g) r ix -> a ((f :+: g) r' ix)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (f :+: g) [Int -> ShowS]

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> (f :+: g) r ix -> (f :+: g) r ix -> Bool

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (f :+: g) r -> (f :+: g) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (f :+: g) r ix -> (f :+: g) r ix -> r ix

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

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: (f :+: g) r ix -> [String]

type Alg (f :+: g) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (f :+: g) r ix

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

Defined in Generics.MultiRec.FoldAlg

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

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

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (f :*: g) I0 ix)

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec ((f :*: g) I0 ix)

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

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> (f :*: g) r ix -> a ((f :*: g) r' ix)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (f :*: g) [Int -> ShowS]

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> (f :*: g) r ix -> (f :*: g) r ix -> Bool

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

Defined in Generics.MultiRec.Read

Methods

countatoms :: (f :*: g) r ix -> Int

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (K a :*: g) r -> (K a :*: g) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (I xi :*: g) r -> (I xi :*: g) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (K a :*: g) r ix -> (K a :*: g) r ix -> r ix

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (I xi :*: g) r ix -> (I xi :*: g) r ix -> r ix

ConNames (f :*: g)

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: (f :*: g) r ix -> [String]

type Alg (K a :*: g) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (I xi :*: g) r

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

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (f :*: g) r ix

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

Defined in Generics.MultiRec.FoldAlg

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

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

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix0 -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec ((f :>: ix) I0 ix0)

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

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix0. phi ix0 -> r ix0 -> a (r' ix0)) -> phi ix1 -> (f :>: ix) r ix1 -> a ((f :>: ix) r' ix1)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (f :>: ix) [Int -> ShowS]

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix0. phi ix0 -> r ix0 -> r ix0 -> Bool) -> phi ix1 -> (f :>: ix) r ix1 -> (f :>: ix) r ix1 -> Bool

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

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (f :>: xi) r -> (f :>: xi) (K0 r) ix -> r

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

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (f :>: xi) r ix -> (f :>: xi) r ix -> r ix

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

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: (f :>: ix) r ix0 -> [String]

type Alg (f :>: xi) r

Tags are ignored.

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (f :>: xi) r ix

A tag changes the index of the final result.

Defined in Generics.MultiRec.FoldAlg

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

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

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (f :.: g) I0 ix)

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec ((f :.: g) I0 ix)

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

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> (f :.: g) r ix -> a ((f :.: g) r' ix)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (f :.: g) [Int -> ShowS]

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> (f :.: g) r ix -> (f :.: g) r ix -> Bool

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

Defined in Generics.MultiRec.FoldAlg

Methods

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

ConNames (f :.: g)

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: (f :.: g) r ix -> [String]

type Comp (f :.: g) r ix

Defined in Generics.MultiRec.FoldAlg

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

type Alg (f :.: I xi) r ix

Defined in Generics.MultiRec.FoldAlg

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (f :*: g) I0 ix)

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (f :.: g) I0 ix)

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (K a) I0 ix)

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

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c (I xi) I0 ix)

Constructor c => HReadPrec phi (C c U)

Defined in Generics.MultiRec.Read

Methods

hreader :: phi ix -> (forall ix1. phi ix1 -> ReadPrec (I0 ix1)) -> ReadPrec (C c U I0 ix)

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

Defined in Generics.MultiRec.HFunctor

Methods

hmapA :: Applicative a => (forall ix. phi ix -> r ix -> a (r' ix)) -> phi ix -> C c f r ix -> a (C c f r' ix)

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

Defined in Generics.MultiRec.Show

Methods

hShowsPrecAlg :: Algebra' phi (C c f) [Int -> ShowS]

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

Defined in Generics.MultiRec.Eq

Methods

heq :: (forall ix. phi ix -> r ix -> r ix -> Bool) -> phi ix -> C c f r ix -> C c f r ix -> Bool

Fold f => Fold (C c f)

Defined in Generics.MultiRec.FoldAlgK

Methods

alg :: Alg (C c f) r -> C c f (K0 r) ix -> r

Fold f => Fold (C c f)

Defined in Generics.MultiRec.FoldAlg

Methods

alg :: Alg (C c f) r ix -> C c f r ix -> r ix

Constructor c => ConNames (C c f)

Defined in Generics.MultiRec.ConNames

Methods

hconNames :: C c f r ix -> [String]

type Alg (C c f) r

Constructors are ignored.

Defined in Generics.MultiRec.FoldAlgK

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

type Alg (C c f) r ix

Constructors are ignored.

Defined in Generics.MultiRec.FoldAlg

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

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

Defined in Generics.MultiRec.Base

Methods

fmap :: (a -> b) -> I0 a -> I0 b

(<$) :: a -> I0 b -> I0 a

Applicative I0

Defined in Generics.MultiRec.Base

Methods

pure :: a -> I0 a

(<*>) :: I0 (a -> b) -> I0 a -> I0 b

liftA2 :: (a -> b -> c) -> I0 a -> I0 b -> I0 c

(*>) :: I0 a -> I0 b -> I0 b

(<*) :: I0 a -> I0 b -> I0 a

newtype K0 a b

Unlifted version of K.

Constructors

K0

Fields

• unK0 :: a

Instances

Functor (K0 a)

Defined in Generics.MultiRec.Base

Methods

fmap :: (a0 -> b) -> K0 a a0 -> K0 a b

(<$) :: a0 -> K0 a b -> K0 a a0

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')