Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Data.Constructable

Contents

Constructable
Exposable

Description

constructing values by there Form..

Synopsis

class Exposable x => Constructable x where
- make :: Form x -> x
cmap :: (Constructable x, Constructable y) => (Form x -> Form y) -> x -> y
class Exposable x where
- type Form x
- form :: x -> Form x
restrict :: Exposable x => (Form x -> y) -> x -> y

Constructable

class Exposable x => Constructable x where Source #

types with an associated form, which serves as a blueprint to construct a corresponding value.

A common setting for this structure is a module with a reducible type f (see Reducible) with public constructors - which serves as a form to be filled out - and in the same module a type e with a private constructor - lets say E - to hold the reduced f. Than an implementation would be

make f = E (reduce f)

and

form (E f) = f

Property Let x be an instance of the class Constructable than holds: For all x in x holds: make (form x) == x.

Methods

make :: Form x -> x Source #

constructor.

Instances

Instances details

Oriented x => Constructable (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods make :: Form (GLT x) -> GLT x Source #
Entity x => Constructable (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol Methods make :: Form (ProductSymbol x) -> ProductSymbol x Source #
Eq i => Constructable (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Methods make :: Form (Permutation i) -> Permutation i Source #
(Oriented a, Integral r) => Constructable (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods make :: Form (Product r a) -> Product r a Source #
(Fibred a, Ord a, Semiring r, Commutative r) => Constructable (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods make :: Form (Sum r a) -> Sum r a Source #
Constructable (IsoOp s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Methods make :: Form (IsoOp s a b) -> IsoOp s a b Source #
Constructable (IsoOpMap f s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Methods make :: Form (IsoOpMap f s a b) -> IsoOpMap f s a b Source #

cmap :: (Constructable x, Constructable y) => (Form x -> Form y) -> x -> y Source #

restriction of a f in Form x -> Form y.

Exposable

class Exposable x where Source #

types with an associated form type and a function form which exposes its values to its form.

Associated Types

type Form x Source #

the form.

Methods

form :: x -> Form x Source #

the associated form.

Instances

Instances details

Exposable (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Associated Types type Form (GLT x) Source # Methods form :: GLT x -> Form (GLT x) Source #
Exposable (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol Associated Types type Form (ProductSymbol x) Source # Methods form :: ProductSymbol x -> Form (ProductSymbol x) Source #
Exposable (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Associated Types type Form (Permutation i) Source # Methods form :: Permutation i -> Form (Permutation i) Source #
Exposable (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Associated Types type Form (Product r a) Source # Methods form :: Product r a -> Form (Product r a) Source #
Exposable (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Associated Types type Form (Sum r a) Source # Methods form :: Sum r a -> Form (Sum r a) Source #
Exposable (IsoOp s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Associated Types type Form (IsoOp s a b) Source # Methods form :: IsoOp s a b -> Form (IsoOp s a b) Source #
Exposable (IsoOpMap f s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Associated Types type Form (IsoOpMap f s a b) Source # Methods form :: IsoOpMap f s a b -> Form (IsoOpMap f s a b) Source #

restrict :: Exposable x => (Form x -> y) -> x -> y Source #

restriction of a f in Form x -> y.