oalg-base-3.0.0.0: Algebraic structures on oriented entities and limits as a tool kit to solve algebraic problems.
Copyright(c) Erich Gut
LicenseBSD3
Maintainerzerich.gut@gmail.com
Safe HaskellNone
LanguageHaskell2010

OAlg.Entity.Definition

Description

definition of entities. All algebraic structures defined here are based on them. They are showable, distinguishable, validable and typeable.

Synopsis

Entity

type Entity a = (Object a, Eq a, Typeable a) Source #

entity.

type Object x = (Show x, Validable x) Source #

object.

data Ent Source #

indexing Entitys.

Instances

Instances details
Transformable Abl Ent Source # 
Instance details

Defined in OAlg.Structure.Additive.Definition

Methods

tau :: Struct Abl x -> Struct Ent x Source #

Transformable Add Ent Source # 
Instance details

Defined in OAlg.Structure.Additive.Definition

Methods

tau :: Struct Add x -> Struct Ent x Source #

Transformable Dst Ent Source # 
Instance details

Defined in OAlg.Structure.Distributive.Definition

Methods

tau :: Struct Dst x -> Struct Ent x Source #

Transformable Fbr Ent Source # 
Instance details

Defined in OAlg.Structure.Fibred.Definition

Methods

tau :: Struct Fbr x -> Struct Ent x Source #

Transformable FbrOrt Ent Source # 
Instance details

Defined in OAlg.Structure.FibredOriented

Methods

tau :: Struct FbrOrt x -> Struct Ent x Source #

Transformable Mlt Ent Source # 
Instance details

Defined in OAlg.Structure.Multiplicative.Definition

Methods

tau :: Struct Mlt x -> Struct Ent x Source #

Transformable Ort Ent Source # 
Instance details

Defined in OAlg.Structure.Oriented.Definition

Methods

tau :: Struct Ort x -> Struct Ent x Source #

Transformable (Alg k) Ent Source # 
Instance details

Defined in OAlg.Structure.Algebraic.Definition

Methods

tau :: Struct (Alg k) x -> Struct Ent x Source #

Transformable (Vec k) Ent Source # 
Instance details

Defined in OAlg.Structure.Vectorial.Definition

Methods

tau :: Struct (Vec k) x -> Struct Ent x Source #

type Structure Ent x Source # 
Instance details

Defined in OAlg.Entity.Definition

type Structure Ent x = Entity x

data EntOrd Source #

indexing orderd entities.

Instances

Instances details
TransformableG [] EntOrd EntOrd Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

tauG :: Struct EntOrd x -> Struct EntOrd [x] Source #

ApplicativeG Set (Map EntOrd) (->) Source # 
Instance details

Defined in OAlg.Entity.Sequence.Set

Methods

amapG :: Map EntOrd x y -> Set x -> Set y Source #

FunctorialG Set (Map EntOrd) (->) Source # 
Instance details

Defined in OAlg.Entity.Sequence.Set

type Structure EntOrd x Source # 
Instance details

Defined in OAlg.Entity.Definition

type Structure EntOrd x = (Entity x, Ord x)

Entity1

type Entity1 (a :: Type -> Type) = (Show1 a, Eq1 a, Validable1 a, Typeable a) Source #

entity for parameterized types.

Entity2

type Entity2 (h :: Type -> Type -> Type) = (Show2 h, Eq2 h, Validable2 h, Typeable h) Source #

entity for two parameterized types.

Basic Entities

Empty

data EntEmpty Source #

the empty entity.

Instances

Instances details
Show EntEmpty Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

showsPrec :: Int -> EntEmpty -> ShowS #

show :: EntEmpty -> String #

showList :: [EntEmpty] -> ShowS #

Eq EntEmpty Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

(==) :: EntEmpty -> EntEmpty -> Bool #

(/=) :: EntEmpty -> EntEmpty -> Bool #

Ord EntEmpty Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

compare :: EntEmpty -> EntEmpty -> Ordering #

(<) :: EntEmpty -> EntEmpty -> Bool #

(<=) :: EntEmpty -> EntEmpty -> Bool #

(>) :: EntEmpty -> EntEmpty -> Bool #

(>=) :: EntEmpty -> EntEmpty -> Bool #

max :: EntEmpty -> EntEmpty -> EntEmpty #

min :: EntEmpty -> EntEmpty -> EntEmpty #

Validable EntEmpty Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

valid :: EntEmpty -> Statement Source #

fromEmpty :: EntEmpty -> x Source #

the empty function.

data EntEmpty2 a b Source #

the empty entity2.

Instances

Instances details
Eq2 EntEmpty2 Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

eq2 :: EntEmpty2 x y -> EntEmpty2 x y -> Bool Source #

EqExt EntEmpty2 Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

(.=.) :: EntEmpty2 x y -> EntEmpty2 x y -> Statement Source #

Show2 EntEmpty2 Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

show2 :: EntEmpty2 a b -> String Source #

Validable2 EntEmpty2 Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

valid2 :: EntEmpty2 x y -> Statement Source #

ApplicativeG t EntEmpty2 b Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

amapG :: EntEmpty2 x y -> b (t x) (t y) Source #

Show (EntEmpty2 a b) Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

showsPrec :: Int -> EntEmpty2 a b -> ShowS #

show :: EntEmpty2 a b -> String #

showList :: [EntEmpty2 a b] -> ShowS #

Eq (EntEmpty2 a b) Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

(==) :: EntEmpty2 a b -> EntEmpty2 a b -> Bool #

(/=) :: EntEmpty2 a b -> EntEmpty2 a b -> Bool #

Validable (EntEmpty2 x y) Source # 
Instance details

Defined in OAlg.Entity.Definition

Methods

valid :: EntEmpty2 x y -> Statement Source #

fromEmpty2 :: EntEmpty2 a b -> x Source #

the empty function.