Safe Haskell	None
Language	Haskell2010

UVMHS.Core.Classes.Morphism

Documentation

type (→⁻) (m :: Type -> Type) (n :: Type -> Type) = forall a. m a -> n a infixr 1 Source #

type (→⁼) (t :: (Type -> Type) -> Type -> Type) (u :: (Type -> Type) -> Type -> Type) = forall (m :: Type -> Type). t m →⁻ u m infixr 1 Source #

class a ⇄ b | a -> b where infixr 1 Source #

Methods

isoto :: a -> b Source #

isofr :: b -> a Source #

Instances

Instances details

𝕊 ⇄ (𝐼 ℂ) Source #
Instance details Defined in UVMHS.Core.Data.Iter Methods isoto :: 𝕊 -> 𝐼 ℂ Source # isofr :: 𝐼 ℂ -> 𝕊 Source #
(𝑂 a) ⇄ (() ∨ a) Source #
Instance details Defined in UVMHS.Core.Data.Option Methods isoto :: 𝑂 a -> () ∨ a Source # isofr :: (() ∨ a) -> 𝑂 a Source #

data Iso a b Source #

Constructors

Iso
Fields ito :: a -> b ifr :: b -> a

Instances

Instances details

Category Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Reflexive Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: Iso a a Source #
Symmetric Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: Iso a b -> Iso b a Source #
Transitive Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: Iso b c -> Iso a b -> Iso a c Source #

toiso :: a ⇄ b => Iso a b Source #

friso :: a ⇄ b => Iso b a Source #

class (t :: Type -> Type) ⇄⁻ (u :: Type -> Type) | t -> u where infixr 1 Source #

Methods

isoto2 :: t →⁻ u Source #

isofr2 :: u →⁻ t Source #

data Iso2 (t :: Type -> Type) (u :: Type -> Type) Source #

Constructors

Iso2
Fields ito2 :: t →⁻ u ifr2 :: u →⁻ t

Instances

Instances details

Category Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Reflexive Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: forall (a :: Type -> Type). Iso2 a a Source #
Symmetric Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: forall (a :: Type -> Type) (b :: Type -> Type). Iso2 a b -> Iso2 b a Source #
Transitive Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: forall (b :: Type -> Type) (c :: Type -> Type) (a :: Type -> Type). Iso2 b c -> Iso2 a b -> Iso2 a c Source #

toiso2 :: forall (t :: Type -> Type) (u :: Type -> Type). t ⇄⁻ u => Iso2 t u Source #

friso2 :: forall (t :: Type -> Type) (u :: Type -> Type). t ⇄⁻ u => Iso2 u t Source #

class (v :: (Type -> Type) -> Type -> Type) ⇄⁼ (w :: (Type -> Type) -> Type -> Type) | v -> w where infixr 1 Source #

Methods

isoto3 :: v →⁼ w Source #

isofr3 :: w →⁼ v Source #

Instances

Instances details

(RWST r o s) ⇄⁼ (((ReaderT r :: (Type -> Type) -> Type -> Type) ⊡ WriterT o) ⊡ StateT s) Source #
Instance details Defined in UVMHS.Core.Monads Methods isoto3 :: RWST r o s →⁼ (((ReaderT r :: (Type -> Type) -> Type -> Type) ⊡ WriterT o) ⊡ StateT s) Source # isofr3 :: (((ReaderT r :: (Type -> Type) -> Type -> Type) ⊡ WriterT o) ⊡ StateT s) →⁼ RWST r o s Source #

data Iso3 (v :: (Type -> Type) -> Type -> Type) (w :: (Type -> Type) -> Type -> Type) Source #

Constructors

Iso3
Fields ito3 :: v →⁼ w ifr3 :: w →⁼ v

Instances

Instances details

Category Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Reflexive Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: forall (a :: (Type -> Type) -> Type -> Type). Iso3 a a Source #
Symmetric Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: forall (a :: (Type -> Type) -> Type -> Type) (b :: (Type -> Type) -> Type -> Type). Iso3 a b -> Iso3 b a Source #
Transitive Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: forall (b :: (Type -> Type) -> Type -> Type) (c :: (Type -> Type) -> Type -> Type) (a :: (Type -> Type) -> Type -> Type). Iso3 b c -> Iso3 a b -> Iso3 a c Source #

toiso3 :: forall (v :: (Type -> Type) -> Type -> Type) (w :: (Type -> Type) -> Type -> Type). v ⇄⁼ w => Iso3 v w Source #

friso3 :: forall (v :: (Type -> Type) -> Type -> Type) (w :: (Type -> Type) -> Type -> Type). v ⇄⁼ w => Iso3 w v Source #

class Reflexive (t :: k -> k -> Type) where Source #

Methods

refl :: forall (a :: k). t a a Source #

Instances

Instances details

Reflexive (≤) Source #
Instance details Defined in UVMHS.Core.Static Methods refl :: forall (a :: 𝐍). a ≤ a Source #
Reflexive Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: Iso a a Source #
Reflexive (⌲) Source #
Instance details Defined in UVMHS.Core.Data.Lens Methods refl :: a ⌲ a Source #
Reflexive (⟢) Source #
Instance details Defined in UVMHS.Core.Data.Lens Methods refl :: a ⟢ a Source #
Reflexive (->) Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: a -> a Source #
Reflexive Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: forall (a :: (Type -> Type) -> Type -> Type). Iso3 a a Source #
Reflexive Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods refl :: forall (a :: Type -> Type). Iso2 a a Source #

class Transitive (t :: k -> k -> Type) where Source #

Methods

(⊚) :: forall (b :: k) (c :: k) (a :: k). t b c -> t a b -> t a c infixl 7 Source #

Instances

Instances details

Transitive (<) Source #
Instance details Defined in UVMHS.Core.Static Methods (⊚) :: forall (b :: 𝐍) (c :: 𝐍) (a :: 𝐍). (b < c) -> (a < b) -> a < c Source #
Transitive (≤) Source #
Instance details Defined in UVMHS.Core.Static Methods (⊚) :: forall (b :: 𝐍) (c :: 𝐍) (a :: 𝐍). (b ≤ c) -> (a ≤ b) -> a ≤ c Source #
Transitive Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: Iso b c -> Iso a b -> Iso a c Source #
Transitive (⌲) Source #
Instance details Defined in UVMHS.Core.Data.Lens Methods (⊚) :: (b ⌲ c) -> (a ⌲ b) -> a ⌲ c Source #
Transitive (⟢) Source #
Instance details Defined in UVMHS.Core.Data.Lens Methods (⊚) :: (b ⟢ c) -> (a ⟢ b) -> a ⟢ c Source #
Transitive (->) Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: (b -> c) -> (a -> b) -> a -> c Source #
Transitive Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: forall (b :: (Type -> Type) -> Type -> Type) (c :: (Type -> Type) -> Type -> Type) (a :: (Type -> Type) -> Type -> Type). Iso3 b c -> Iso3 a b -> Iso3 a c Source #
Transitive Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods (⊚) :: forall (b :: Type -> Type) (c :: Type -> Type) (a :: Type -> Type). Iso2 b c -> Iso2 a b -> Iso2 a c Source #

class (Reflexive t, Transitive t) => Category (t :: k -> k -> Type) Source #

Instances

Instances details

Category (≤) Source #
Instance details Defined in UVMHS.Core.Static
Category Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Category (⌲) Source #
Instance details Defined in UVMHS.Core.Data.Lens
Category (⟢) Source #
Instance details Defined in UVMHS.Core.Data.Lens
Category (->) Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Category Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism
Category Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism

class Symmetric (t :: k -> k -> Type) where Source #

Methods

sym :: forall (a :: k) (b :: k). t a b -> t b a Source #

Instances

Instances details

Symmetric Iso Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: Iso a b -> Iso b a Source #
Symmetric Iso3 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: forall (a :: (Type -> Type) -> Type -> Type) (b :: (Type -> Type) -> Type -> Type). Iso3 a b -> Iso3 b a Source #
Symmetric Iso2 Source #
Instance details Defined in UVMHS.Core.Classes.Morphism Methods sym :: forall (a :: Type -> Type) (b :: Type -> Type). Iso2 a b -> Iso2 b a Source #