Symantic.Classes

Comibnators in this module conflict with usual ones from the Prelude hence they are meant to be imported either explicitely or qualified.

Type ReprKind

type ReprKind = Type -> Type

The kind of repr(esentations) throughout this library.

Class Abstractable

class Abstractable repr where

Minimal complete definition

Nothing

Methods

lam :: (repr a -> repr b) -> repr (a -> b)

Lambda term abstraction, in HOAS (Higher-Order Abstract Syntax) style.

default lam :: FromDerived Abstractable repr => Derivable repr => (repr a -> repr b) -> repr (a -> b)

lam1 :: (repr a -> repr b) -> repr (a -> b)

Like lam but whose argument must be used only once, hence safe to beta-reduce (inline) without duplicating work.

default lam1 :: FromDerived Abstractable repr => Derivable repr => (repr a -> repr b) -> repr (a -> b)

var :: repr a -> repr a

default var :: FromDerived1 Abstractable repr => repr a -> repr a

(.@) :: repr (a -> b) -> repr a -> repr b infixl 9

Application, aka. unabstract.

default (.@) :: FromDerived2 Abstractable repr => repr (a -> b) -> repr a -> repr b

Instances

Abstractable Viewer

Defined in Symantic.Viewer

Methods

lam :: (Viewer a -> Viewer b) -> Viewer (a -> b)

lam1 :: (Viewer a -> Viewer b) -> Viewer (a -> b)

var :: Viewer a -> Viewer a

(.@) :: Viewer (a -> b) -> Viewer a -> Viewer b

Abstractable repr => Abstractable (SomeData repr)

Defined in Symantic.Data

Methods

lam :: (SomeData repr a -> SomeData repr b) -> SomeData repr (a -> b)

lam1 :: (SomeData repr a -> SomeData repr b) -> SomeData repr (a -> b)

var :: SomeData repr a -> SomeData repr a

(.@) :: SomeData repr (a -> b) -> SomeData repr a -> SomeData repr b

Abstractable repr => Derivable (Data Abstractable repr)

Defined in Symantic.Data

Methods

derive :: Data Abstractable repr a -> Derived (Data Abstractable repr) a

data Data Abstractable repr a

Defined in Symantic.Data

data Data Abstractable repr a where

• (:@) :: forall (repr :: ReprKind) a b. SomeData repr (a -> b) -> SomeData repr a -> Data Abstractable repr b
• Lam :: forall (repr :: ReprKind) a b. (SomeData repr a -> SomeData repr b) -> Data Abstractable repr (a -> b)
• Lam1 :: forall (repr :: ReprKind) a b. (SomeData repr a -> SomeData repr b) -> Data Abstractable repr (a -> b)
• Var :: forall (repr :: Type -> Type) a. repr a -> Data Abstractable repr a

Class Functionable

class Functionable repr where

Minimal complete definition

Nothing

Methods

const :: repr (a -> b -> a)

default const :: FromDerived Functionable repr => repr (a -> b -> a)

flip :: repr ((a -> b -> c) -> b -> a -> c)

default flip :: FromDerived Functionable repr => repr ((a -> b -> c) -> b -> a -> c)

id :: repr (a -> a)

default id :: FromDerived Functionable repr => repr (a -> a)

(.) :: repr ((b -> c) -> (a -> b) -> a -> c) infixr 9

default (.) :: FromDerived Functionable repr => repr ((b -> c) -> (a -> b) -> a -> c)

($) :: repr ((a -> b) -> a -> b) infixr 0

default ($) :: FromDerived Functionable repr => repr ((a -> b) -> a -> b)

Instances

Abstractable repr => Functionable (SomeData repr)

Defined in Symantic.Data

Methods

const :: SomeData repr (a -> b -> a)

flip :: SomeData repr ((a -> b -> c) -> b -> a -> c)

id :: SomeData repr (a -> a)

(.) :: SomeData repr ((b -> c) -> (a -> b) -> a -> c)

($) :: SomeData repr ((a -> b) -> a -> b)

Class Anythingable

class Anythingable repr where

Minimal complete definition

Nothing

Methods

anything :: repr a -> repr a

Instances

Anythingable Viewer

Defined in Symantic.Viewer

Methods

anything :: Viewer a -> Viewer a

Anythingable (SomeData repr)

Defined in Symantic.Data

Methods

anything :: SomeData repr a -> SomeData repr a

Anythingable repr => Derivable (Data Anythingable repr)

Defined in Symantic.Data

Methods

derive :: Data Anythingable repr a -> Derived (Data Anythingable repr) a

Anythingable (Data Anythingable repr)

Defined in Symantic.Data

Methods

anything :: Data Anythingable repr a -> Data Anythingable repr a

data Data Anythingable repr a

Defined in Symantic.Data

data Data Anythingable repr a where

• Anything :: forall (repr :: Type -> Type) a. repr a -> Data Anythingable repr a

Class Bottomable

class Bottomable repr where

Methods

bottom :: repr a

Instances

Bottomable Viewer

Defined in Symantic.Viewer

Methods

bottom :: Viewer a

Bottomable repr => Derivable (Data Bottomable repr)

Defined in Symantic.Data

Methods

derive :: Data Bottomable repr a -> Derived (Data Bottomable repr) a

data Data Bottomable repr a

Defined in Symantic.Data

data Data Bottomable repr a where

• Bottom :: forall (repr :: ReprKind) a. Data Bottomable repr a

Class Constantable

class Constantable c repr where

Minimal complete definition

Nothing

Methods

constant :: c -> repr c

default constant :: FromDerived (Constantable c) repr => c -> repr c

Instances

Show c => Constantable c Viewer

Defined in Symantic.Viewer

Methods

constant :: c -> Viewer c

(Constantable c repr, Typeable c) => Constantable c (SomeData repr)

Defined in Symantic.Data

Methods

constant :: c -> SomeData repr c

Constantable c (Data (Constantable c) repr)

Defined in Symantic.Data

Methods

constant :: c -> Data (Constantable c) repr c

Constantable c repr => Derivable (Data (Constantable c) repr)

Defined in Symantic.Data

Methods

derive :: Data (Constantable c) repr a -> Derived (Data (Constantable c) repr) a

data Data (Constantable c) repr a

Defined in Symantic.Data

data Data (Constantable c) repr a where

• Constant :: forall c (repr :: ReprKind). c -> Data (Constantable c) repr c

Class Eitherable

class Eitherable repr where

Minimal complete definition

Nothing

Methods

left :: repr (l -> Either l r)

default left :: FromDerived Eitherable repr => repr (l -> Either l r)

right :: repr (r -> Either l r)

default right :: FromDerived Eitherable repr => repr (r -> Either l r)

Instances

Eitherable Viewer

Defined in Symantic.Viewer

Methods

left :: Viewer (l -> Either l r)

right :: Viewer (r -> Either l r)

Eitherable repr => Eitherable (SomeData repr)

Defined in Symantic.Data

Methods

left :: SomeData repr (l -> Either l r)

right :: SomeData repr (r -> Either l r)

Eitherable repr => Derivable (Data Eitherable repr)

Defined in Symantic.Data

Methods

derive :: Data Eitherable repr a -> Derived (Data Eitherable repr) a

Eitherable (Data Eitherable repr)

Defined in Symantic.Data

Methods

left :: Data Eitherable repr (l -> Either l r)

right :: Data Eitherable repr (r -> Either l r)

data Data Eitherable repr a

Defined in Symantic.Data

data Data Eitherable repr a where

• Left :: forall (repr :: ReprKind) l r. Data Eitherable repr (l -> Either l r)
• Right :: forall (repr :: ReprKind) r l. Data Eitherable repr (r -> Either l r)

Class Equalable

class Equalable repr where

Minimal complete definition

Nothing

Methods

equal :: Eq a => repr (a -> a -> Bool) infix 4

default equal :: FromDerived Equalable repr => Eq a => repr (a -> a -> Bool)

Instances

Equalable Viewer

Defined in Symantic.Viewer

Methods

equal :: Eq a => Viewer (a -> a -> Bool)

Equalable repr => Equalable (SomeData repr)

Defined in Symantic.Data

Methods

equal :: Eq a => SomeData repr (a -> a -> Bool)

Equalable repr => Derivable (Data Equalable repr)

Defined in Symantic.Data

Methods

derive :: Data Equalable repr a -> Derived (Data Equalable repr) a

Equalable (Data Equalable repr)

Defined in Symantic.Data

Methods

equal :: Eq a => Data Equalable repr (a -> a -> Bool)

data Data Equalable repr a

Defined in Symantic.Data

data Data Equalable repr a where

• Equal :: forall a (repr :: ReprKind). Eq a => Data Equalable repr (a -> a -> Bool)

(==) :: Abstractable repr => Equalable repr => Eq a => repr a -> repr a -> repr Bool infix 4

Class IfThenElseable

class IfThenElseable repr where

Minimal complete definition

Nothing

Methods

ifThenElse :: repr Bool -> repr a -> repr a -> repr a

default ifThenElse :: FromDerived3 IfThenElseable repr => repr Bool -> repr a -> repr a -> repr a

Instances

IfThenElseable repr => IfThenElseable (SomeData repr)

Defined in Symantic.Data

Methods

ifThenElse :: SomeData repr Bool -> SomeData repr a -> SomeData repr a -> SomeData repr a

IfThenElseable repr => Derivable (Data IfThenElseable repr)

Defined in Symantic.Data

Methods

derive :: Data IfThenElseable repr a -> Derived (Data IfThenElseable repr) a

IfThenElseable repr => IfThenElseable (Data IfThenElseable repr)

Defined in Symantic.Data

Methods

ifThenElse :: Data IfThenElseable repr Bool -> Data IfThenElseable repr a -> Data IfThenElseable repr a -> Data IfThenElseable repr a

data Data IfThenElseable repr a

Defined in Symantic.Data

data Data IfThenElseable repr a where

• IfThenElse :: forall (repr :: ReprKind) a. SomeData repr Bool -> SomeData repr a -> SomeData repr a -> Data IfThenElseable repr a

Class Inferable

class Inferable a repr where

Minimal complete definition

Nothing

Methods

infer :: repr a

default infer :: FromDerived (Inferable a) repr => repr a

unit :: Inferable () repr => repr ()

bool :: Inferable Bool repr => repr Bool

char :: Inferable Char repr => repr Char

int :: Inferable Int repr => repr Int

natural :: Inferable Natural repr => repr Natural

string :: Inferable String repr => repr String

Class Listable

class Listable repr where

Minimal complete definition

Nothing

Methods

cons :: repr (a -> [a] -> [a])

default cons :: FromDerived Listable repr => repr (a -> [a] -> [a])

nil :: repr [a]

default nil :: FromDerived Listable repr => repr [a]

Instances

Listable Viewer

Defined in Symantic.Viewer

Methods

cons :: Viewer (a -> [a] -> [a])

nil :: Viewer [a]

Listable repr => Listable (SomeData repr)

Defined in Symantic.Data

Methods

cons :: SomeData repr (a -> [a] -> [a])

nil :: SomeData repr [a]

Listable repr => Derivable (Data Listable repr)

Defined in Symantic.Data

Methods

derive :: Data Listable repr a -> Derived (Data Listable repr) a

Listable (Data Listable repr)

Defined in Symantic.Data

Methods

cons :: Data Listable repr (a -> [a] -> [a])

nil :: Data Listable repr [a]

data Data Listable repr a

Defined in Symantic.Data

data Data Listable repr a where

• Cons :: forall (repr :: ReprKind) a. Data Listable repr (a -> [a] -> [a])
• Nil :: forall (repr :: ReprKind) a. Data Listable repr [a]

Class Maybeable

class Maybeable repr where

Minimal complete definition

Nothing

Methods

nothing :: repr (Maybe a)

default nothing :: FromDerived Maybeable repr => repr (Maybe a)

just :: repr (a -> Maybe a)

default just :: FromDerived Maybeable repr => repr (a -> Maybe a)

Instances

Maybeable Viewer

Defined in Symantic.Viewer

Methods

nothing :: Viewer (Maybe a)

just :: Viewer (a -> Maybe a)

Maybeable repr => Maybeable (SomeData repr)

Defined in Symantic.Data

Methods

nothing :: SomeData repr (Maybe a)

just :: SomeData repr (a -> Maybe a)

Maybeable repr => Derivable (Data Maybeable repr)

Defined in Symantic.Data

Methods

derive :: Data Maybeable repr a -> Derived (Data Maybeable repr) a

Maybeable (Data Maybeable repr)

Defined in Symantic.Data

Methods

nothing :: Data Maybeable repr (Maybe a)

just :: Data Maybeable repr (a -> Maybe a)

data Data Maybeable repr a

Defined in Symantic.Data

data Data Maybeable repr a where

• Nothing :: forall (repr :: ReprKind) a. Data Maybeable repr (Maybe a)
• Just :: forall (repr :: ReprKind) a. Data Maybeable repr (a -> Maybe a)

Class IsoFunctor

class IsoFunctor repr where

Minimal complete definition

Nothing

Methods

(<%>) :: Iso a b -> repr a -> repr b infixl 4

default (<%>) :: FromDerived1 IsoFunctor repr => Iso a b -> repr a -> repr b

Type Iso

data Iso a b

Constructors

Iso

Fields

• a2b :: a -> b
• b2a :: b -> a

Instances

Category Iso

Defined in Symantic.Classes

Methods

id :: forall (a :: k). Iso a a

(.) :: forall (b :: k) (c :: k) (a :: k). Iso b c -> Iso a b -> Iso a c

Class ProductFunctor

class ProductFunctor repr where

Beware that this is an infixr, not infixl like <*>; this is to follow what is expected by ADT.

Minimal complete definition

Nothing

Methods

(<.>) :: repr a -> repr b -> repr (a, b) infixr 4

default (<.>) :: FromDerived2 ProductFunctor repr => repr a -> repr b -> repr (a, b)

(<.) :: repr a -> repr () -> repr a infixr 4

default (<.) :: IsoFunctor repr => repr a -> repr () -> repr a

(.>) :: repr () -> repr a -> repr a infixr 4

default (.>) :: IsoFunctor repr => repr () -> repr a -> repr a

Class SumFunctor

class SumFunctor repr where

Beware that this is an infixr, not infixl like <|>; this is to follow what is expected by ADT.

Minimal complete definition

Nothing

Methods

(<+>) :: repr a -> repr b -> repr (Either a b) infixr 3

default (<+>) :: FromDerived2 SumFunctor repr => repr a -> repr b -> repr (Either a b)

Class AlternativeFunctor

class AlternativeFunctor repr where

Beware that this is an infixr, not infixl like <|>; this is to follow what is expected by ADT.

Minimal complete definition

Nothing

Methods

(<|>) :: repr a -> repr a -> repr a infixr 3

default (<|>) :: FromDerived2 AlternativeFunctor repr => repr a -> repr a -> repr a

Class Dicurryable

class Dicurryable repr where

Minimal complete definition

Nothing

Methods

dicurry :: CurryN args => proxy args -> (args -..-> a) -> (a -> Tuples args) -> repr (Tuples args) -> repr a

default dicurry :: FromDerived1 Dicurryable repr => CurryN args => proxy args -> (args -..-> a) -> (a -> Tuples args) -> repr (Tuples args) -> repr a

construct :: forall args a repr. Dicurryable repr => Generic a => EoTOfRep a => CurryN args => Tuples args ~ EoT (ADT a) => args ~ Args (args -..-> a) => (args -..-> a) -> repr (Tuples args) -> repr a

adt :: forall adt repr. IsoFunctor repr => Generic adt => RepOfEoT adt => EoTOfRep adt => repr (EoT (ADT adt)) -> repr adt

Class Monoidable

class (Emptyable repr, Semigroupable repr) => Monoidable repr

Instances

(Emptyable repr, Semigroupable repr) => Monoidable repr

Defined in Symantic.Classes

Class Emptyable

class Emptyable repr where

Minimal complete definition

Nothing

Methods

empty :: repr a

default empty :: FromDerived Emptyable repr => repr a

Instances

Emptyable repr => Emptyable (SomeData repr)

Defined in Symantic.Data

Methods

empty :: SomeData repr a

Emptyable repr => Derivable (Data Emptyable repr)

Defined in Symantic.Data

Methods

derive :: Data Emptyable repr a -> Derived (Data Emptyable repr) a

Emptyable (Data Emptyable repr)

Defined in Symantic.Data

Methods

empty :: Data Emptyable repr a

data Data Emptyable repr a

Defined in Symantic.Data

data Data Emptyable repr a where

• Empty :: forall (repr :: ReprKind) a. Data Emptyable repr a

Class Semigroupable

class Semigroupable repr where

Minimal complete definition

Nothing

Methods

concat :: Semigroup a => repr (a -> a -> a) infixr 6

default concat :: FromDerived Semigroupable repr => Semigroup a => repr (a -> a -> a)

Instances

Semigroupable repr => Semigroupable (SomeData repr)

Defined in Symantic.Data

Methods

concat :: Semigroup a => SomeData repr (a -> a -> a)

Semigroupable repr => Derivable (Data Semigroupable repr)

Defined in Symantic.Data

Methods

derive :: Data Semigroupable repr a -> Derived (Data Semigroupable repr) a

Semigroupable (Data Semigroupable repr)

Defined in Symantic.Data

Methods

concat :: Semigroup a => Data Semigroupable repr (a -> a -> a)

data Data Semigroupable repr a

Defined in Symantic.Data

data Data Semigroupable repr a where

• Concat :: forall a (repr :: ReprKind). Semigroup a => Data Semigroupable repr (a -> a -> a)

(<>) :: Abstractable repr => Semigroupable repr => Semigroup a => repr a -> repr a -> repr a infixr 6

Class Optionable

class Optionable repr where

Minimal complete definition

Nothing

Methods

option :: repr a -> repr a

default option :: FromDerived1 Optionable repr => repr a -> repr a

optional :: repr a -> repr (Maybe a)

default optional :: FromDerived1 Optionable repr => repr a -> repr (Maybe a)

Class Repeatable

class Repeatable repr where

Minimal complete definition

Nothing

Methods

many0 :: repr a -> repr [a]

default many0 :: FromDerived1 Repeatable repr => repr a -> repr [a]

many1 :: repr a -> repr [a]

default many1 :: FromDerived1 Repeatable repr => repr a -> repr [a]

many :: Repeatable repr => repr a -> repr [a]

Alias to many0.

some :: Repeatable repr => repr a -> repr [a]

Alias to many1.

Class Permutable

class Permutable repr where

Minimal complete definition

permutable, perm, noPerm, permWithDefault

Associated Types

type Permutation (repr :: ReprKind) = (r :: ReprKind) | r -> repr

type Permutation repr = Permutation (Derived repr)

Methods

permutable :: Permutation repr a -> repr a

perm :: repr a -> Permutation repr a

noPerm :: Permutation repr ()

permWithDefault :: a -> repr a -> Permutation repr a

optionalPerm :: Eitherable repr => IsoFunctor repr => Permutable repr => repr a -> Permutation repr (Maybe a)

(<&>) :: Permutable repr => ProductFunctor (Permutation repr) => repr a -> Permutation repr b -> Permutation repr (a, b) infixr 4

(<?&>) :: Eitherable repr => IsoFunctor repr => Permutable repr => ProductFunctor (Permutation repr) => repr a -> Permutation repr b -> Permutation repr (Maybe a, b) infixr 4

(<*&>) :: Eitherable repr => Repeatable repr => IsoFunctor repr => Permutable repr => ProductFunctor (Permutation repr) => repr a -> Permutation repr b -> Permutation repr ([a], b) infixr 4

(<+&>) :: Eitherable repr => Repeatable repr => IsoFunctor repr => Permutable repr => ProductFunctor (Permutation repr) => repr a -> Permutation repr b -> Permutation repr ([a], b) infixr 4

Class Routable

class Routable repr where

Minimal complete definition

Nothing

Methods

(<!>) :: repr a -> repr b -> repr (a, b) infixr 4

default (<!>) :: FromDerived2 Routable repr => repr a -> repr b -> repr (a, b)

pattern (:!:) :: a -> b -> (a, b) infixr 4

Like (,) but infixr. Mostly useful for clarity when using Routable.

Class Voidable

class Voidable repr where

Minimal complete definition

Nothing

Methods

void :: a -> repr a -> repr ()

Useful to supply (a) to a (repr) consuming (a), for example in the format of a printing interpreter.

default void :: FromDerived1 Voidable repr => a -> repr a -> repr ()

Class Substractable

class Substractable repr where

Minimal complete definition

Nothing

Methods

(<->) :: repr a -> repr b -> repr a infixr 3

default (<->) :: FromDerived2 Substractable repr => repr a -> repr b -> repr a