Copyright	(c) David Janin, 2016
License	see the LICENSE file in the distribution
Maintainer	janin@labri.fr
Stability	experimental
Safe Haskell	Safe
Language	Haskell2010

Tile.TCategories

Contents

Category instances

Description

Haskell instances of the categorical properties of duration or delay preserving function over tiles, using the various packages Control.Category.* by Edward Kmett.

Synopsis

Category instances

newtype FuncT d iv v1 v2 Source #

The category of functions over tiles

Constructors

FuncT (Tile d iv v1 -> Tile d iv v2)

Instances

Category * (FuncT d iv) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #

newtype FuncDurP d iv v1 v2 Source #

The category of duration preserving functions over tiles. A tile function is a duration preserving tile function when

durationT t == durationT (f t)

Constructors

FuncDurP (Tile d iv v1 -> Tile d iv v2)

Instances

(Eq d, Num d, Lattice d) => PFunctor Either (FuncDurP d iv) (FuncDurP d iv) Source #
Methods first :: FuncDurP d iv a b -> FuncDurP d iv (Either a c) (Either b c) #
(Eq d, Num d, Lattice d) => QFunctor Either (FuncDurP d iv) (FuncDurP d iv) Source #
Methods second :: FuncDurP d iv a b -> FuncDurP d iv (Either c a) (Either c b) #
(Eq d, Num d, Lattice d) => Bifunctor Either (FuncDurP d iv) (FuncDurP d iv) (FuncDurP d iv) Source #
Methods bimap :: FuncDurP d iv a b -> FuncDurP d iv c d -> FuncDurP d iv (Either a c) (Either b d) #
Category * (FuncDurP d iv) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
(Eq d, Num d, Lattice d) => CCC (FuncDurP d iv) Source #
Associated Types type Exp (FuncDurP d iv :: * -> * -> ) :: -> * -> * # Methods apply :: FuncDurP d iv (Product (FuncDurP d iv) (Exp (FuncDurP d iv) a b) a) b # curry :: FuncDurP d iv (Product (FuncDurP d iv) a b) c -> FuncDurP d iv a (Exp (FuncDurP d iv) b c) # uncurry :: FuncDurP d iv a (Exp (FuncDurP d iv) b c) -> FuncDurP d iv (Product (FuncDurP d iv) a b) c #
(Eq d, Num d, Lattice d) => Cartesian (FuncDurP d iv) Source #
Associated Types type Product (FuncDurP d iv :: * -> * -> ) :: -> * -> * # Methods fst :: FuncDurP d iv (Product (FuncDurP d iv) a b) a # snd :: FuncDurP d iv (Product (FuncDurP d iv) a b) b # diag :: FuncDurP d iv a (Product (FuncDurP d iv) a a) # (&&&) :: FuncDurP d iv a b -> FuncDurP d iv a c -> FuncDurP d iv a (Product (FuncDurP d iv) b c) #
(Eq d, Num d, Lattice d) => Braided (FuncDurP d iv) Either Source #
Methods braid :: FuncDurP d iv (Either a b) (Either b a) #
(Eq d, Num d, Lattice d) => Symmetric (FuncDurP d iv) Either Source #

(Eq d, Num d, Lattice d) => Monoidal (FuncDurP d iv) Either Source #
Associated Types type Id (FuncDurP d iv :: * -> * -> ) (Either :: -> * -> ) :: # Methods idl :: FuncDurP d iv (Either (Id (FuncDurP d iv) Either) a) a # idr :: FuncDurP d iv (Either a (Id (FuncDurP d iv) Either)) a # coidl :: FuncDurP d iv a (Either (Id (FuncDurP d iv) Either) a) # coidr :: FuncDurP d iv a (Either a (Id (FuncDurP d iv) Either)) #
(Eq d, Num d, Lattice d) => Associative (FuncDurP d iv) Either Source #
Methods associate :: FuncDurP d iv (Either (Either a b) c) (Either a (Either b c)) # disassociate :: FuncDurP d iv (Either a (Either b c)) (Either (Either a b) c) #
(Eq d, Fractional d, Lattice d) => Fractional (FuncDurP d iv v1 v2) Source #
Methods (/) :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # recip :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # fromRational :: Rational -> FuncDurP d iv v1 v2 #
(Eq d, Num d, Lattice d) => Num (FuncDurP d iv v1 v2) Source #
Methods (+) :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # (-) :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # (*) :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # negate :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # abs :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # signum :: FuncDurP d iv v1 v2 -> FuncDurP d iv v1 v2 # fromInteger :: Integer -> FuncDurP d iv v1 v2 #
type Exp (FuncDurP d iv) Source #
type Exp (FuncDurP d iv) = FuncDurP d iv
type Product (FuncDurP d iv) Source #
type Product (FuncDurP d iv) = Either
type Id (FuncDurP d iv) Either Source #
type Id (FuncDurP d iv) Either = Void

toFuncDurP :: (Eq d, Num d, Lattice d, POrd v1) => Functile d iv v1 v2 -> FuncDurP d iv v1 v2 Source #

Lifts any function over tiles to a duration preserving function over tiles.

newtype FuncDelayP d iv v1 v2 Source #

The category of delay preserving functions over tiles. A tile function is a delay preserving tile function when

f (delayT t) == delayT (f t)

Constructors

FuncDelayP (Tile d iv v1 -> Tile d iv v2)

Instances

(Eq d, Num d, Lattice d) => PFunctor Either (FuncDelayP d iv) (FuncDelayP d iv) Source #
Methods first :: FuncDelayP d iv a b -> FuncDelayP d iv (Either a c) (Either b c) #
(Eq d, Num d, Lattice d) => QFunctor Either (FuncDelayP d iv) (FuncDelayP d iv) Source #
Methods second :: FuncDelayP d iv a b -> FuncDelayP d iv (Either c a) (Either c b) #
(Eq d, Num d, Lattice d) => Bifunctor Either (FuncDelayP d iv) (FuncDelayP d iv) (FuncDelayP d iv) Source #
Methods bimap :: FuncDelayP d iv a b -> FuncDelayP d iv c d -> FuncDelayP d iv (Either a c) (Either b d) #
Category * (FuncDelayP d iv) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
(Eq d, Num d, Lattice d) => Cartesian (FuncDelayP d iv) Source #
Associated Types type Product (FuncDelayP d iv :: * -> * -> ) :: -> * -> * # Methods fst :: FuncDelayP d iv (Product (FuncDelayP d iv) a b) a # snd :: FuncDelayP d iv (Product (FuncDelayP d iv) a b) b # diag :: FuncDelayP d iv a (Product (FuncDelayP d iv) a a) # (&&&) :: FuncDelayP d iv a b -> FuncDelayP d iv a c -> FuncDelayP d iv a (Product (FuncDelayP d iv) b c) #
(Eq d, Num d, Lattice d) => CoCartesian (FuncDelayP d iv) Source #
Associated Types type Sum (FuncDelayP d iv :: * -> * -> ) :: -> * -> * # Methods inl :: FuncDelayP d iv a (Sum (FuncDelayP d iv) a b) # inr :: FuncDelayP d iv b (Sum (FuncDelayP d iv) a b) # codiag :: FuncDelayP d iv (Sum (FuncDelayP d iv) a a) a # (\|\|\|) :: FuncDelayP d iv a c -> FuncDelayP d iv b c -> FuncDelayP d iv (Sum (FuncDelayP d iv) a b) c #
(Eq d, Num d, Lattice d) => Braided (FuncDelayP d iv) Either Source #
Methods braid :: FuncDelayP d iv (Either a b) (Either b a) #
(Eq d, Num d, Lattice d) => Symmetric (FuncDelayP d iv) Either Source #

(Eq d, Num d, Lattice d) => Monoidal (FuncDelayP d iv) Either Source #
Associated Types type Id (FuncDelayP d iv :: * -> * -> ) (Either :: -> * -> ) :: # Methods idl :: FuncDelayP d iv (Either (Id (FuncDelayP d iv) Either) a) a # idr :: FuncDelayP d iv (Either a (Id (FuncDelayP d iv) Either)) a # coidl :: FuncDelayP d iv a (Either (Id (FuncDelayP d iv) Either) a) # coidr :: FuncDelayP d iv a (Either a (Id (FuncDelayP d iv) Either)) #
(Eq d, Num d, Lattice d) => Associative (FuncDelayP d iv) Either Source #
Methods associate :: FuncDelayP d iv (Either (Either a b) c) (Either a (Either b c)) # disassociate :: FuncDelayP d iv (Either a (Either b c)) (Either (Either a b) c) #
(Eq d, Fractional d, Lattice d) => Fractional (FuncDelayP d iv v1 v2) Source #
Methods (/) :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # recip :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # fromRational :: Rational -> FuncDelayP d iv v1 v2 #
(Eq d, Num d, Lattice d) => Num (FuncDelayP d iv v1 v2) Source #
Methods (+) :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # (-) :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # (*) :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # negate :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # abs :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # signum :: FuncDelayP d iv v1 v2 -> FuncDelayP d iv v1 v2 # fromInteger :: Integer -> FuncDelayP d iv v1 v2 #
type Product (FuncDelayP d iv) Source #
type Product (FuncDelayP d iv) = Either
type Sum (FuncDelayP d iv) Source #
type Sum (FuncDelayP d iv) = Either
type Id (FuncDelayP d iv) Either Source #
type Id (FuncDelayP d iv) Either = Void

toFuncDelayP :: (Eq d, Num d, Lattice d, POrd v1) => Functile d iv v1 v2 -> FuncDelayP d iv v1 v2 Source #

Lifts any function over tiles to a delay preserving function over tiles.