Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Structure.Oriented.Path

Contents

Path

Description

Paths

Synopsis

data Path q = Path (Point q) [q]
pthLength :: Path q -> N
pthOne :: Point q -> Path q
pthMlt :: Oriented q => Path q -> Path q -> Path q

Path

data Path q Source #

a path in a Oriented structure q starting at a given point.

Definition Let q be a Oriented structure and p = Path s [a 0..a (n-1)] a path in q, then p is valid if and only if

s is valid and a i are valid for all i = 0..n-1.
start (a (n-1)) == s and start (a i) == end (a (n+1)) for all i = 0..n-2.

furthermore n is called the length of p.

Note Paths admit a canonical embedding in to Product.

Constructors

Path (Point q) [q]

Instances

Instances details

Foldable Path Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods fold :: Monoid m => Path m -> m # foldMap :: Monoid m => (a -> m) -> Path a -> m # foldMap' :: Monoid m => (a -> m) -> Path a -> m # foldr :: (a -> b -> b) -> b -> Path a -> b # foldr' :: (a -> b -> b) -> b -> Path a -> b # foldl :: (b -> a -> b) -> b -> Path a -> b # foldl' :: (b -> a -> b) -> b -> Path a -> b # foldr1 :: (a -> a -> a) -> Path a -> a # foldl1 :: (a -> a -> a) -> Path a -> a # toList :: Path a -> [a] # null :: Path a -> Bool # length :: Path a -> Int # elem :: Eq a => a -> Path a -> Bool # maximum :: Ord a => Path a -> a # minimum :: Ord a => Path a -> a # sum :: Num a => Path a -> a # product :: Num a => Path a -> a #
Oriented q => Embeddable q (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods inj :: q -> Path q Source #
(Show q, ShowPoint q) => Show (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods showsPrec :: Int -> Path q -> ShowS # show :: Path q -> String # showList :: [Path q] -> ShowS #
(Eq q, EqPoint q) => Eq (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods (==) :: Path q -> Path q -> Bool # (/=) :: Path q -> Path q -> Bool #
Oriented q => Dualisable (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods toDual :: Path q -> Dual (Path q) Source # fromDual :: Dual (Path q) -> Path q Source #
Reflexive (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods toBidual :: Path q -> Dual (Dual (Path q)) Source # fromBidual :: Dual (Dual (Path q)) -> Path q Source #
LengthN (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods lengthN :: Path q -> N Source #
Oriented q => Validable (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods valid :: Path q -> Statement Source #
Oriented q => Multiplicative (Path q) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods one :: Point (Path q) -> Path q Source # (*) :: Path q -> Path q -> Path q Source # npower :: Path q -> N -> Path q Source #
Oriented q => Oriented (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods orientation :: Path q -> Orientation (Point (Path q)) Source # start :: Path q -> Point (Path q) Source # end :: Path q -> Point (Path q) Source #
EqPoint q => EqPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
ShowPoint q => ShowPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
SingletonPoint q => SingletonPoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
TypeablePoint q => TypeablePoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
ValidablePoint q => ValidablePoint (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path
(Oriented a, Integral r) => Embeddable (Path a) (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: Path a -> Product r a Source #
Embeddable (Path a) (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: Path a -> ProductForm r a Source #
Oriented a => Projectible (Path a) (Product N a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: Product N a -> Path a Source #
Oriented a => Projectible (Path a) (ProductForm N a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: ProductForm N a -> Path a Source #
(Oriented a, Integral r) => Projectible (Product r a) (Path a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: Path a -> Product r a Source #
type Dual (Path q :: Type) Source #
Instance details Defined in OAlg.Structure.Oriented.Path type Dual (Path q :: Type) = Path (Op q)
type Point (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path type Point (Path q) = Point q

pthLength :: Path q -> N Source #

the length of a path.

pthOne :: Point q -> Path q Source #

path of length 0 at the given point.

pthMlt :: Oriented q => Path q -> Path q -> Path q Source #

composition of two paths.