Copyright	(c) 2016 Justus Sagemüller
License	GPL v3 (see COPYING)
Maintainer	(@) jsag $ hvl.no
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Category.Constrained.Reified

Contents

Reified versions of the category classes

Description

GADTs that mirror the class hierarchy from Category to (at the moment) Cartesian, reifying all the available “free” composition operations.

These can be used as a “trivial base case“ for all kinds of categories: it turns out these basic operations are often not so trivial to implement, or only possible with stronger constraints than you'd like. For instance, the category of affine mappings can only be implemented directly as a category on vector spaces, because the identity mapping has zero constant offset.

By leaving the free compositions reified to runtime syntax trees, this problem can be avoided. In other applications, you may not need these cases, but can still benefit from them for optimisation (composition with id is always trivial, and so on).

Synopsis

data ReCategory (k :: Type -> Type -> Type) α β where
- ReCategory :: forall (k :: Type -> Type -> Type) α β. k α β -> ReCategory k α β
- CategoryId :: forall (k :: Type -> Type -> Type) α. Object k α => ReCategory k α α
- CategoryCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReCategory k α β1 -> ReCategory k β1 β -> ReCategory k α β
data ReCartesian (k :: Type -> Type -> Type) α β where
- ReCartesian :: forall (k :: Type -> Type -> Type) α β. k α β -> ReCartesian k α β
- CartesianId :: forall (k :: Type -> Type -> Type) α. Object k α => ReCartesian k α α
- CartesianCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReCartesian k α β1 -> ReCartesian k β1 β -> ReCartesian k α β
- CartesianSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReCartesian k (α1, β1) (β1, α1)
- CartesianAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReCartesian k α (α, u)
- CartesianDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReCartesian k (β, u) β
- CartesianRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReCartesian k (α1, (β1, γ)) ((α1, β1), γ)
- CartesianRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReCartesian k ((α1, β1), γ) (α1, (β1, γ))
data ReMorphism (k :: Type -> Type -> Type) α β where
- ReMorphism :: forall (k :: Type -> Type -> Type) α β. k α β -> ReMorphism k α β
- MorphismId :: forall (k :: Type -> Type -> Type) α. Object k α => ReMorphism k α α
- MorphismCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReMorphism k α β1 -> ReMorphism k β1 β -> ReMorphism k α β
- MorphismSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReMorphism k (α1, β1) (β1, α1)
- MorphismAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReMorphism k α (α, u)
- MorphismDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReMorphism k (β, u) β
- MorphismRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReMorphism k (α1, (β1, γ)) ((α1, β1), γ)
- MorphismRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReMorphism k ((α1, β1), γ) (α1, (β1, γ))
- MorphismPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => ReMorphism k α1 β1 -> ReMorphism k γ δ -> ReMorphism k (α1, γ) (β1, δ)
data RePreArrow (k :: Type -> Type -> Type) α β where
- RePreArrow :: forall (k :: Type -> Type -> Type) α β. k α β -> RePreArrow k α β
- PreArrowId :: forall (k :: Type -> Type -> Type) α. Object k α => RePreArrow k α α
- PreArrowCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => RePreArrow k α β1 -> RePreArrow k β1 β -> RePreArrow k α β
- PreArrowSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => RePreArrow k (α1, β1) (β1, α1)
- PreArrowAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => RePreArrow k α (α, u)
- PreArrowDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => RePreArrow k (β, u) β
- PreArrowRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => RePreArrow k (α1, (β1, γ)) ((α1, β1), γ)
- PreArrowRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => RePreArrow k ((α1, β1), γ) (α1, (β1, γ))
- PreArrowPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => RePreArrow k α1 β1 -> RePreArrow k γ δ -> RePreArrow k (α1, γ) (β1, δ)
- PreArrowFanout :: forall (k :: Type -> Type -> Type) α β1 γ. (Object k α, ObjectPair k β1 γ) => RePreArrow k α β1 -> RePreArrow k α γ -> RePreArrow k α (β1, γ)
- PreArrowTerminal :: forall (k :: Type -> Type -> Type) α. Object k α => RePreArrow k α (UnitObject k)
- PreArrowFst :: forall (k :: Type -> Type -> Type) β β1. ObjectPair k β β1 => RePreArrow k (β, β1) β
- PreArrowSnd :: forall (k :: Type -> Type -> Type) α1 β. ObjectPair k α1 β => RePreArrow k (α1, β) β
data ReWellPointed (k :: Type -> Type -> Type) α β where
- ReWellPointed :: forall (k :: Type -> Type -> Type) α β. k α β -> ReWellPointed k α β
- WellPointedId :: forall (k :: Type -> Type -> Type) α. Object k α => ReWellPointed k α α
- WellPointedCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReWellPointed k α β1 -> ReWellPointed k β1 β -> ReWellPointed k α β
- WellPointedSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReWellPointed k (α1, β1) (β1, α1)
- WellPointedAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReWellPointed k α (α, u)
- WellPointedDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReWellPointed k (β, u) β
- WellPointedRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReWellPointed k (α1, (β1, γ)) ((α1, β1), γ)
- WellPointedRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReWellPointed k ((α1, β1), γ) (α1, (β1, γ))
- WellPointedPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => ReWellPointed k α1 β1 -> ReWellPointed k γ δ -> ReWellPointed k (α1, γ) (β1, δ)
- WellPointedFanout :: forall (k :: Type -> Type -> Type) α β1 γ. (Object k α, ObjectPair k β1 γ) => ReWellPointed k α β1 -> ReWellPointed k α γ -> ReWellPointed k α (β1, γ)
- WellPointedTerminal :: forall (k :: Type -> Type -> Type) α. Object k α => ReWellPointed k α (UnitObject k)
- WellPointedFst :: forall (k :: Type -> Type -> Type) β β1. ObjectPair k β β1 => ReWellPointed k (β, β1) β
- WellPointedSnd :: forall (k :: Type -> Type -> Type) α1 β. ObjectPair k α1 β => ReWellPointed k (α1, β) β
- WellPointedConst :: forall (k :: Type -> Type -> Type) α β. (Object k α, ObjectPoint k β) => β -> ReWellPointed k α β

Reified versions of the category classes

data ReCategory (k :: Type -> Type -> Type) α β where Source #

Constructors

ReCategory :: forall (k :: Type -> Type -> Type) α β. k α β -> ReCategory k α β
CategoryId :: forall (k :: Type -> Type -> Type) α. Object k α => ReCategory k α α
CategoryCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReCategory k α β1 -> ReCategory k β1 β -> ReCategory k α β

Instances

Instances details

Category k => Category (ReCategory k :: Type -> Type -> Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

id :: Object (ReCategory k) a => ReCategory k a a Source #

(.) :: (Object (ReCategory k) a, Object (ReCategory k) b, Object (ReCategory k) c) => ReCategory k b c -> ReCategory k a b -> ReCategory k a c Source #

HasAgent k => HasAgent (ReCategory k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

alg :: (Object (ReCategory k) a, Object (ReCategory k) b) => (forall q. Object (ReCategory k) q => AgentVal (ReCategory k) q a -> AgentVal (ReCategory k) q b) -> ReCategory k a b Source #

($~) :: (Object (ReCategory k) a, Object (ReCategory k) b, Object (ReCategory k) c) => ReCategory k b c -> AgentVal (ReCategory k) a b -> AgentVal (ReCategory k) a c Source #

Category k => CRCategory (ReCategory k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Associated Types

type SpecificCat (ReCategory k)
Instance details Defined in Control.Category.Constrained.Reified.PolyPattern type SpecificCat (ReCategory k) = k

Methods

fromSpecific :: SpecificCat (ReCategory k) α β -> ReCategory k α β Source #

match_concrete :: ReCategory k α β -> Maybe (SpecificCat (ReCategory k) α β) Source #

match_id :: ReCategory k α β -> IdPattern (ReCategory k) α β Source #

match_compose :: ReCategory k α β -> CompoPattern (ReCategory k) α β Source #

Category k => EnhancedCat (ReCategory k) k Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

arr :: (Object k b, Object k c, Object (ReCategory k) b, Object (ReCategory k) c) => k b c -> ReCategory k b c Source #

type Object (ReCategory k :: Type -> Type -> Type) (α :: Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type Object (ReCategory k :: Type -> Type -> Type) (α :: Type) = Object k α

type SpecificCat (ReCategory k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

type SpecificCat (ReCategory k) = k

type AgentVal (ReCategory k) α ω Source #

Instance details

Defined in Control.Category.Constrained.Reified

type AgentVal (ReCategory k) α ω = GenericAgent (ReCategory k) α ω

data ReCartesian (k :: Type -> Type -> Type) α β where Source #

Constructors

ReCartesian :: forall (k :: Type -> Type -> Type) α β. k α β -> ReCartesian k α β
CartesianId :: forall (k :: Type -> Type -> Type) α. Object k α => ReCartesian k α α
CartesianCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReCartesian k α β1 -> ReCartesian k β1 β -> ReCartesian k α β
CartesianSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReCartesian k (α1, β1) (β1, α1)
CartesianAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReCartesian k α (α, u)
CartesianDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReCartesian k (β, u) β
CartesianRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReCartesian k (α1, (β1, γ)) ((α1, β1), γ)
CartesianRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReCartesian k ((α1, β1), γ) (α1, (β1, γ))

Instances

Instances details

Cartesian k => Category (ReCartesian k :: Type -> Type -> Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

id :: Object (ReCartesian k) a => ReCartesian k a a Source #

(.) :: (Object (ReCartesian k) a, Object (ReCartesian k) b, Object (ReCartesian k) c) => ReCartesian k b c -> ReCartesian k a b -> ReCartesian k a c Source #

Cartesian k => Cartesian (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Associated Types

type UnitObject (ReCartesian k)
Instance details Defined in Control.Category.Constrained.Reified type UnitObject (ReCartesian k) = UnitObject k

Methods

swap :: (ObjectPair (ReCartesian k) a b, ObjectPair (ReCartesian k) b a) => ReCartesian k (a, b) (b, a) Source #

attachUnit :: (unit ~ UnitObject (ReCartesian k), ObjectPair (ReCartesian k) a unit) => ReCartesian k a (a, unit) Source #

detachUnit :: (unit ~ UnitObject (ReCartesian k), ObjectPair (ReCartesian k) a unit) => ReCartesian k (a, unit) a Source #

regroup :: (ObjectPair (ReCartesian k) a b, ObjectPair (ReCartesian k) b c, ObjectPair (ReCartesian k) a (b, c), ObjectPair (ReCartesian k) (a, b) c) => ReCartesian k (a, (b, c)) ((a, b), c) Source #

regroup' :: (ObjectPair (ReCartesian k) a b, ObjectPair (ReCartesian k) b c, ObjectPair (ReCartesian k) a (b, c), ObjectPair (ReCartesian k) (a, b) c) => ReCartesian k ((a, b), c) (a, (b, c)) Source #

(HasAgent k, Cartesian k) => HasAgent (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

alg :: (Object (ReCartesian k) a, Object (ReCartesian k) b) => (forall q. Object (ReCartesian k) q => AgentVal (ReCartesian k) q a -> AgentVal (ReCartesian k) q b) -> ReCartesian k a b Source #

($~) :: (Object (ReCartesian k) a, Object (ReCartesian k) b, Object (ReCartesian k) c) => ReCartesian k b c -> AgentVal (ReCartesian k) a b -> AgentVal (ReCartesian k) a c Source #

Cartesian k => CRCartesian (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_swap :: ReCartesian k α β -> SwapPattern (ReCartesian k) α β Source #

match_attachUnit :: ReCartesian k α β -> AttachUnitPattern (ReCartesian k) α β Source #

match_detachUnit :: ReCartesian k α β -> DetachUnitPattern (ReCartesian k) α β Source #

match_regroup :: ReCartesian k α β -> RegroupPattern (ReCartesian k) α β Source #

match_regroup' :: ReCartesian k α β -> Regroup'Pattern (ReCartesian k) α β Source #

Cartesian k => CRCategory (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Associated Types

type SpecificCat (ReCartesian k)
Instance details Defined in Control.Category.Constrained.Reified.PolyPattern type SpecificCat (ReCartesian k) = k

Methods

fromSpecific :: SpecificCat (ReCartesian k) α β -> ReCartesian k α β Source #

match_concrete :: ReCartesian k α β -> Maybe (SpecificCat (ReCartesian k) α β) Source #

match_id :: ReCartesian k α β -> IdPattern (ReCartesian k) α β Source #

match_compose :: ReCartesian k α β -> CompoPattern (ReCartesian k) α β Source #

Cartesian k => EnhancedCat (ReCartesian k) k Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

arr :: (Object k b, Object k c, Object (ReCartesian k) b, Object (ReCartesian k) c) => k b c -> ReCartesian k b c Source #

type Object (ReCartesian k :: Type -> Type -> Type) (a :: Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type Object (ReCartesian k :: Type -> Type -> Type) (a :: Type) = Object k a

type UnitObject (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type UnitObject (ReCartesian k) = UnitObject k

type SpecificCat (ReCartesian k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

type SpecificCat (ReCartesian k) = k

type AgentVal (ReCartesian k) α ω Source #

Instance details

Defined in Control.Category.Constrained.Reified

type AgentVal (ReCartesian k) α ω = GenericAgent (ReCartesian k) α ω

type PairObjects (ReCartesian k) α β Source #

Instance details

Defined in Control.Category.Constrained.Reified

type PairObjects (ReCartesian k) α β = PairObjects k α β

data ReMorphism (k :: Type -> Type -> Type) α β where Source #

Constructors

ReMorphism :: forall (k :: Type -> Type -> Type) α β. k α β -> ReMorphism k α β
MorphismId :: forall (k :: Type -> Type -> Type) α. Object k α => ReMorphism k α α
MorphismCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReMorphism k α β1 -> ReMorphism k β1 β -> ReMorphism k α β
MorphismSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReMorphism k (α1, β1) (β1, α1)
MorphismAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReMorphism k α (α, u)
MorphismDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReMorphism k (β, u) β
MorphismRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReMorphism k (α1, (β1, γ)) ((α1, β1), γ)
MorphismRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReMorphism k ((α1, β1), γ) (α1, (β1, γ))
MorphismPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => ReMorphism k α1 β1 -> ReMorphism k γ δ -> ReMorphism k (α1, γ) (β1, δ)

Instances

Instances details

Morphism k => Category (ReMorphism k :: Type -> Type -> Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

id :: Object (ReMorphism k) a => ReMorphism k a a Source #

(.) :: (Object (ReMorphism k) a, Object (ReMorphism k) b, Object (ReMorphism k) c) => ReMorphism k b c -> ReMorphism k a b -> ReMorphism k a c Source #

Morphism k => Morphism (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

first :: (ObjectPair (ReMorphism k) b d, ObjectPair (ReMorphism k) c d) => ReMorphism k b c -> ReMorphism k (b, d) (c, d) Source #

second :: (ObjectPair (ReMorphism k) d b, ObjectPair (ReMorphism k) d c) => ReMorphism k b c -> ReMorphism k (d, b) (d, c) Source #

(***) :: (ObjectPair (ReMorphism k) b b', ObjectPair (ReMorphism k) c c') => ReMorphism k b c -> ReMorphism k b' c' -> ReMorphism k (b, b') (c, c') Source #

Morphism k => Cartesian (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Associated Types

type UnitObject (ReMorphism k)
Instance details Defined in Control.Category.Constrained.Reified type UnitObject (ReMorphism k) = UnitObject k

Methods

swap :: (ObjectPair (ReMorphism k) a b, ObjectPair (ReMorphism k) b a) => ReMorphism k (a, b) (b, a) Source #

attachUnit :: (unit ~ UnitObject (ReMorphism k), ObjectPair (ReMorphism k) a unit) => ReMorphism k a (a, unit) Source #

detachUnit :: (unit ~ UnitObject (ReMorphism k), ObjectPair (ReMorphism k) a unit) => ReMorphism k (a, unit) a Source #

regroup :: (ObjectPair (ReMorphism k) a b, ObjectPair (ReMorphism k) b c, ObjectPair (ReMorphism k) a (b, c), ObjectPair (ReMorphism k) (a, b) c) => ReMorphism k (a, (b, c)) ((a, b), c) Source #

regroup' :: (ObjectPair (ReMorphism k) a b, ObjectPair (ReMorphism k) b c, ObjectPair (ReMorphism k) a (b, c), ObjectPair (ReMorphism k) (a, b) c) => ReMorphism k ((a, b), c) (a, (b, c)) Source #

(HasAgent k, Morphism k) => HasAgent (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

alg :: (Object (ReMorphism k) a, Object (ReMorphism k) b) => (forall q. Object (ReMorphism k) q => AgentVal (ReMorphism k) q a -> AgentVal (ReMorphism k) q b) -> ReMorphism k a b Source #

($~) :: (Object (ReMorphism k) a, Object (ReMorphism k) b, Object (ReMorphism k) c) => ReMorphism k b c -> AgentVal (ReMorphism k) a b -> AgentVal (ReMorphism k) a c Source #

Morphism k => CRCartesian (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_swap :: ReMorphism k α β -> SwapPattern (ReMorphism k) α β Source #

match_attachUnit :: ReMorphism k α β -> AttachUnitPattern (ReMorphism k) α β Source #

match_detachUnit :: ReMorphism k α β -> DetachUnitPattern (ReMorphism k) α β Source #

match_regroup :: ReMorphism k α β -> RegroupPattern (ReMorphism k) α β Source #

match_regroup' :: ReMorphism k α β -> Regroup'Pattern (ReMorphism k) α β Source #

Morphism k => CRCategory (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Associated Types

type SpecificCat (ReMorphism k)
Instance details Defined in Control.Category.Constrained.Reified.PolyPattern type SpecificCat (ReMorphism k) = k

Methods

fromSpecific :: SpecificCat (ReMorphism k) α β -> ReMorphism k α β Source #

match_concrete :: ReMorphism k α β -> Maybe (SpecificCat (ReMorphism k) α β) Source #

match_id :: ReMorphism k α β -> IdPattern (ReMorphism k) α β Source #

match_compose :: ReMorphism k α β -> CompoPattern (ReMorphism k) α β Source #

Morphism k => CRMorphism (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_par :: ReMorphism k α β -> ParPattern (ReMorphism k) α β Source #

Morphism k => EnhancedCat (ReMorphism k) k Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

arr :: (Object k b, Object k c, Object (ReMorphism k) b, Object (ReMorphism k) c) => k b c -> ReMorphism k b c Source #

type Object (ReMorphism k :: Type -> Type -> Type) (a :: Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type Object (ReMorphism k :: Type -> Type -> Type) (a :: Type) = Object k a

type UnitObject (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type UnitObject (ReMorphism k) = UnitObject k

type SpecificCat (ReMorphism k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

type SpecificCat (ReMorphism k) = k

type AgentVal (ReMorphism k) α ω Source #

Instance details

Defined in Control.Category.Constrained.Reified

type AgentVal (ReMorphism k) α ω = GenericAgent (ReMorphism k) α ω

type PairObjects (ReMorphism k) α β Source #

Instance details

Defined in Control.Category.Constrained.Reified

type PairObjects (ReMorphism k) α β = PairObjects k α β

data RePreArrow (k :: Type -> Type -> Type) α β where Source #

Constructors

RePreArrow :: forall (k :: Type -> Type -> Type) α β. k α β -> RePreArrow k α β
PreArrowId :: forall (k :: Type -> Type -> Type) α. Object k α => RePreArrow k α α
PreArrowCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => RePreArrow k α β1 -> RePreArrow k β1 β -> RePreArrow k α β
PreArrowSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => RePreArrow k (α1, β1) (β1, α1)
PreArrowAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => RePreArrow k α (α, u)
PreArrowDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => RePreArrow k (β, u) β
PreArrowRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => RePreArrow k (α1, (β1, γ)) ((α1, β1), γ)
PreArrowRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => RePreArrow k ((α1, β1), γ) (α1, (β1, γ))
PreArrowPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => RePreArrow k α1 β1 -> RePreArrow k γ δ -> RePreArrow k (α1, γ) (β1, δ)
PreArrowFanout :: forall (k :: Type -> Type -> Type) α β1 γ. (Object k α, ObjectPair k β1 γ) => RePreArrow k α β1 -> RePreArrow k α γ -> RePreArrow k α (β1, γ)
PreArrowTerminal :: forall (k :: Type -> Type -> Type) α. Object k α => RePreArrow k α (UnitObject k)
PreArrowFst :: forall (k :: Type -> Type -> Type) β β1. ObjectPair k β β1 => RePreArrow k (β, β1) β
PreArrowSnd :: forall (k :: Type -> Type -> Type) α1 β. ObjectPair k α1 β => RePreArrow k (α1, β) β

Instances

Instances details

PreArrow k => Category (RePreArrow k :: Type -> Type -> Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

id :: Object (RePreArrow k) a => RePreArrow k a a Source #

(.) :: (Object (RePreArrow k) a, Object (RePreArrow k) b, Object (RePreArrow k) c) => RePreArrow k b c -> RePreArrow k a b -> RePreArrow k a c Source #

PreArrow k => Morphism (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

first :: (ObjectPair (RePreArrow k) b d, ObjectPair (RePreArrow k) c d) => RePreArrow k b c -> RePreArrow k (b, d) (c, d) Source #

second :: (ObjectPair (RePreArrow k) d b, ObjectPair (RePreArrow k) d c) => RePreArrow k b c -> RePreArrow k (d, b) (d, c) Source #

(***) :: (ObjectPair (RePreArrow k) b b', ObjectPair (RePreArrow k) c c') => RePreArrow k b c -> RePreArrow k b' c' -> RePreArrow k (b, b') (c, c') Source #

PreArrow k => PreArrow (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

(&&&) :: (Object (RePreArrow k) b, ObjectPair (RePreArrow k) c c') => RePreArrow k b c -> RePreArrow k b c' -> RePreArrow k b (c, c') Source #

terminal :: Object (RePreArrow k) b => RePreArrow k b (UnitObject (RePreArrow k)) Source #

fst :: ObjectPair (RePreArrow k) x y => RePreArrow k (x, y) x Source #

snd :: ObjectPair (RePreArrow k) x y => RePreArrow k (x, y) y Source #

PreArrow k => Cartesian (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Associated Types

type UnitObject (RePreArrow k)
Instance details Defined in Control.Category.Constrained.Reified type UnitObject (RePreArrow k) = UnitObject k

Methods

swap :: (ObjectPair (RePreArrow k) a b, ObjectPair (RePreArrow k) b a) => RePreArrow k (a, b) (b, a) Source #

attachUnit :: (unit ~ UnitObject (RePreArrow k), ObjectPair (RePreArrow k) a unit) => RePreArrow k a (a, unit) Source #

detachUnit :: (unit ~ UnitObject (RePreArrow k), ObjectPair (RePreArrow k) a unit) => RePreArrow k (a, unit) a Source #

regroup :: (ObjectPair (RePreArrow k) a b, ObjectPair (RePreArrow k) b c, ObjectPair (RePreArrow k) a (b, c), ObjectPair (RePreArrow k) (a, b) c) => RePreArrow k (a, (b, c)) ((a, b), c) Source #

regroup' :: (ObjectPair (RePreArrow k) a b, ObjectPair (RePreArrow k) b c, ObjectPair (RePreArrow k) a (b, c), ObjectPair (RePreArrow k) (a, b) c) => RePreArrow k ((a, b), c) (a, (b, c)) Source #

(HasAgent k, PreArrow k) => HasAgent (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

alg :: (Object (RePreArrow k) a, Object (RePreArrow k) b) => (forall q. Object (RePreArrow k) q => AgentVal (RePreArrow k) q a -> AgentVal (RePreArrow k) q b) -> RePreArrow k a b Source #

($~) :: (Object (RePreArrow k) a, Object (RePreArrow k) b, Object (RePreArrow k) c) => RePreArrow k b c -> AgentVal (RePreArrow k) a b -> AgentVal (RePreArrow k) a c Source #

PreArrow k => CRCartesian (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_swap :: RePreArrow k α β -> SwapPattern (RePreArrow k) α β Source #

match_attachUnit :: RePreArrow k α β -> AttachUnitPattern (RePreArrow k) α β Source #

match_detachUnit :: RePreArrow k α β -> DetachUnitPattern (RePreArrow k) α β Source #

match_regroup :: RePreArrow k α β -> RegroupPattern (RePreArrow k) α β Source #

match_regroup' :: RePreArrow k α β -> Regroup'Pattern (RePreArrow k) α β Source #

PreArrow k => CRCategory (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Associated Types

type SpecificCat (RePreArrow k)
Instance details Defined in Control.Category.Constrained.Reified.PolyPattern type SpecificCat (RePreArrow k) = k

Methods

fromSpecific :: SpecificCat (RePreArrow k) α β -> RePreArrow k α β Source #

match_concrete :: RePreArrow k α β -> Maybe (SpecificCat (RePreArrow k) α β) Source #

match_id :: RePreArrow k α β -> IdPattern (RePreArrow k) α β Source #

match_compose :: RePreArrow k α β -> CompoPattern (RePreArrow k) α β Source #

PreArrow k => CRMorphism (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_par :: RePreArrow k α β -> ParPattern (RePreArrow k) α β Source #

PreArrow k => CRPreArrow (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_fan :: RePreArrow k α β -> FanPattern (RePreArrow k) α β Source #

match_fst :: RePreArrow k α β -> FstPattern (RePreArrow k) α β Source #

match_snd :: RePreArrow k α β -> SndPattern (RePreArrow k) α β Source #

match_terminal :: RePreArrow k α β -> TerminalPattern (RePreArrow k) α β Source #

PreArrow k => EnhancedCat (RePreArrow k) k Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

arr :: (Object k b, Object k c, Object (RePreArrow k) b, Object (RePreArrow k) c) => k b c -> RePreArrow k b c Source #

type Object (RePreArrow k :: Type -> Type -> Type) (a :: Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type Object (RePreArrow k :: Type -> Type -> Type) (a :: Type) = Object k a

type UnitObject (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

type UnitObject (RePreArrow k) = UnitObject k

type SpecificCat (RePreArrow k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

type SpecificCat (RePreArrow k) = k

type AgentVal (RePreArrow k) α ω Source #

Instance details

Defined in Control.Category.Constrained.Reified

type AgentVal (RePreArrow k) α ω = GenericAgent (RePreArrow k) α ω

type PairObjects (RePreArrow k) α β Source #

Instance details

Defined in Control.Category.Constrained.Reified

type PairObjects (RePreArrow k) α β = PairObjects k α β

data ReWellPointed (k :: Type -> Type -> Type) α β where Source #

Constructors

ReWellPointed :: forall (k :: Type -> Type -> Type) α β. k α β -> ReWellPointed k α β
WellPointedId :: forall (k :: Type -> Type -> Type) α. Object k α => ReWellPointed k α α
WellPointedCompo :: forall (k :: Type -> Type -> Type) β1 α β. Object k β1 => ReWellPointed k α β1 -> ReWellPointed k β1 β -> ReWellPointed k α β
WellPointedSwap :: forall (k :: Type -> Type -> Type) α1 β1. (ObjectPair k α1 β1, ObjectPair k β1 α1) => ReWellPointed k (α1, β1) (β1, α1)
WellPointedAttachUnit :: forall (k :: Type -> Type -> Type) α u. (Object k α, UnitObject k ~ u, ObjectPair k α u) => ReWellPointed k α (α, u)
WellPointedDetachUnit :: forall (k :: Type -> Type -> Type) β u. (Object k β, UnitObject k ~ u, ObjectPair k β u) => ReWellPointed k (β, u) β
WellPointedRegroup :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReWellPointed k (α1, (β1, γ)) ((α1, β1), γ)
WellPointedRegroup_ :: forall (k :: Type -> Type -> Type) α1 β1 γ. (ObjectPair k α1 β1, ObjectPair k β1 γ, ObjectPair k α1 (β1, γ), ObjectPair k (α1, β1) γ) => ReWellPointed k ((α1, β1), γ) (α1, (β1, γ))
WellPointedPar :: forall (k :: Type -> Type -> Type) α1 γ β1 δ. (ObjectPair k α1 γ, ObjectPair k β1 δ) => ReWellPointed k α1 β1 -> ReWellPointed k γ δ -> ReWellPointed k (α1, γ) (β1, δ)
WellPointedFanout :: forall (k :: Type -> Type -> Type) α β1 γ. (Object k α, ObjectPair k β1 γ) => ReWellPointed k α β1 -> ReWellPointed k α γ -> ReWellPointed k α (β1, γ)
WellPointedTerminal :: forall (k :: Type -> Type -> Type) α. Object k α => ReWellPointed k α (UnitObject k)
WellPointedFst :: forall (k :: Type -> Type -> Type) β β1. ObjectPair k β β1 => ReWellPointed k (β, β1) β
WellPointedSnd :: forall (k :: Type -> Type -> Type) α1 β. ObjectPair k α1 β => ReWellPointed k (α1, β) β
WellPointedConst :: forall (k :: Type -> Type -> Type) α β. (Object k α, ObjectPoint k β) => β -> ReWellPointed k α β

Instances

Instances details

WellPointed k => Category (ReWellPointed k :: Type -> Type -> Type) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

id :: Object (ReWellPointed k) a => ReWellPointed k a a Source #

(.) :: (Object (ReWellPointed k) a, Object (ReWellPointed k) b, Object (ReWellPointed k) c) => ReWellPointed k b c -> ReWellPointed k a b -> ReWellPointed k a c Source #

WellPointed k => Morphism (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

first :: (ObjectPair (ReWellPointed k) b d, ObjectPair (ReWellPointed k) c d) => ReWellPointed k b c -> ReWellPointed k (b, d) (c, d) Source #

second :: (ObjectPair (ReWellPointed k) d b, ObjectPair (ReWellPointed k) d c) => ReWellPointed k b c -> ReWellPointed k (d, b) (d, c) Source #

(***) :: (ObjectPair (ReWellPointed k) b b', ObjectPair (ReWellPointed k) c c') => ReWellPointed k b c -> ReWellPointed k b' c' -> ReWellPointed k (b, b') (c, c') Source #

WellPointed k => PreArrow (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

(&&&) :: (Object (ReWellPointed k) b, ObjectPair (ReWellPointed k) c c') => ReWellPointed k b c -> ReWellPointed k b c' -> ReWellPointed k b (c, c') Source #

terminal :: Object (ReWellPointed k) b => ReWellPointed k b (UnitObject (ReWellPointed k)) Source #

fst :: ObjectPair (ReWellPointed k) x y => ReWellPointed k (x, y) x Source #

snd :: ObjectPair (ReWellPointed k) x y => ReWellPointed k (x, y) y Source #

WellPointed k => WellPointed (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

globalElement :: ObjectPoint (ReWellPointed k) x => x -> ReWellPointed k (UnitObject (ReWellPointed k)) x Source #

unit :: CatTagged (ReWellPointed k) (UnitObject (ReWellPointed k)) Source #

const :: (Object (ReWellPointed k) b, ObjectPoint (ReWellPointed k) x) => x -> ReWellPointed k b x Source #

WellPointed k => Cartesian (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Associated Types

type UnitObject (ReWellPointed k)
Instance details Defined in Control.Category.Constrained.Reified type UnitObject (ReWellPointed k) = UnitObject k

Methods

swap :: (ObjectPair (ReWellPointed k) a b, ObjectPair (ReWellPointed k) b a) => ReWellPointed k (a, b) (b, a) Source #

attachUnit :: (unit ~ UnitObject (ReWellPointed k), ObjectPair (ReWellPointed k) a unit) => ReWellPointed k a (a, unit) Source #

detachUnit :: (unit ~ UnitObject (ReWellPointed k), ObjectPair (ReWellPointed k) a unit) => ReWellPointed k (a, unit) a Source #

regroup :: (ObjectPair (ReWellPointed k) a b, ObjectPair (ReWellPointed k) b c, ObjectPair (ReWellPointed k) a (b, c), ObjectPair (ReWellPointed k) (a, b) c) => ReWellPointed k (a, (b, c)) ((a, b), c) Source #

regroup' :: (ObjectPair (ReWellPointed k) a b, ObjectPair (ReWellPointed k) b c, ObjectPair (ReWellPointed k) a (b, c), ObjectPair (ReWellPointed k) (a, b) c) => ReWellPointed k ((a, b), c) (a, (b, c)) Source #

(HasAgent k, WellPointed k) => HasAgent (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified

Methods

alg :: (Object (ReWellPointed k) a, Object (ReWellPointed k) b) => (forall q. Object (ReWellPointed k) q => AgentVal (ReWellPointed k) q a -> AgentVal (ReWellPointed k) q b) -> ReWellPointed k a b Source #

($~) :: (Object (ReWellPointed k) a, Object (ReWellPointed k) b, Object (ReWellPointed k) c) => ReWellPointed k b c -> AgentVal (ReWellPointed k) a b -> AgentVal (ReWellPointed k) a c Source #

WellPointed k => CRCartesian (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Methods

match_swap :: ReWellPointed k α β -> SwapPattern (ReWellPointed k) α β Source #

match_attachUnit :: ReWellPointed k α β -> AttachUnitPattern (ReWellPointed k) α β Source #

match_detachUnit :: ReWellPointed k α β -> DetachUnitPattern (ReWellPointed k) α β Source #

match_regroup :: ReWellPointed k α β -> RegroupPattern (ReWellPointed k) α β Source #

match_regroup' :: ReWellPointed k α β -> Regroup'Pattern (ReWellPointed k) α β Source #

WellPointed k => CRCategory (ReWellPointed k) Source #

Instance details

Defined in Control.Category.Constrained.Reified.PolyPattern

Associated Types

type SpecificCat (ReWellPointed k)
Instance details Defined in Control.Category.Constrained.Reified.PolyPattern type SpecificCat (ReWellPointed k) = k