Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Interval

Description

Interval analysis

Documentation

type family Iv a Source #

Instances

Instances details

type Iv () Source #
Instance details Defined in ConCat.Interval type Iv () = ()
type Iv Double Source #
Instance details Defined in ConCat.Interval type Iv Double = Double :* Double
type Iv Float Source #
Instance details Defined in ConCat.Interval type Iv Float = Float :* Float
type Iv Int Source #
Instance details Defined in ConCat.Interval type Iv Int = Int :* Int
type Iv (Par1 a) Source #
Instance details Defined in ConCat.Interval type Iv (Par1 a) = Iv (O (Par1 a))
type Iv (a :* b) Source #
Instance details Defined in ConCat.Interval type Iv (a :* b) = Iv a :* Iv b
type Iv (a :+ b) Source #
Instance details Defined in ConCat.Interval type Iv (a :+ b) = Iv a :+ Iv b
type Iv (a -> b) Source #
Instance details Defined in ConCat.Interval type Iv (a -> b) = Iv a -> Iv b
type Iv (L s a b) Source #
Instance details Defined in ConCat.Interval type Iv (L s a b) = Iv (O (L s a b))

data IF a b Source #

Constructors

IF
Fields unIF :: Iv a -> Iv b

Instances

Instances details

AssociativePCat IF Source #
Instance details Defined in ConCat.Interval Methods lassocP :: Ok3 IF a b c => IF (Prod IF a (Prod IF b c)) (Prod IF (Prod IF a b) c) Source # rassocP :: Ok3 IF a b c => IF (Prod IF (Prod IF a b) c) (Prod IF a (Prod IF b c)) Source #
BraidedPCat IF Source #
Instance details Defined in ConCat.Interval Methods swapP :: Ok2 IF a b => IF (Prod IF a b) (Prod IF b a) Source #
BraidedSCat IF Source #
Instance details Defined in ConCat.Interval Methods swapS :: Ok2 IF a b => IF (Coprod IF a b) (Coprod IF b a) Source #
Category IF Source #
Instance details Defined in ConCat.Interval Associated Types type Ok IF :: Type -> Constraint Source # Methods id :: Ok IF a => IF a a Source # (.) :: forall b c a. Ok3 IF a b c => IF b c -> IF a b -> IF a c Source #
ClosedCat IF Source #
Instance details Defined in ConCat.Interval Methods apply :: Ok2 IF a b => IF (Prod IF (Exp IF a b) a) b Source # curry :: Ok3 IF a b c => IF (Prod IF a b) c -> IF a (Exp IF b c) Source # uncurry :: Ok3 IF a b c => IF a (Exp IF b c) -> IF (Prod IF a b) c Source #
CoproductCat IF Source #
Instance details Defined in ConCat.Interval Methods inl :: Ok2 IF a b => IF a (Coprod IF a b) Source # inr :: Ok2 IF a b => IF b (Coprod IF a b) Source # jam :: Ok IF a => IF (Coprod IF a a) a Source #
DistribCat IF Source #
Instance details Defined in ConCat.Interval Methods distl :: Ok3 IF a u v => IF (Prod IF a (Coprod IF u v)) (Coprod IF (Prod IF a u) (Prod IF a v)) Source # distr :: Ok3 IF u v b => IF (Prod IF (Coprod IF u v) b) (Coprod IF (Prod IF u b) (Prod IF v b)) Source #
MonoidalPCat IF Source #
Instance details Defined in ConCat.Interval Methods (***) :: Ok4 IF a b c d => IF a c -> IF b d -> IF (Prod IF a b) (Prod IF c d) Source # first :: forall a a' b. Ok3 IF a b a' => IF a a' -> IF (Prod IF a b) (Prod IF a' b) Source # second :: Ok3 IF a b b' => IF b b' -> IF (Prod IF a b) (Prod IF a b') Source #
MonoidalSCat IF Source #
Instance details Defined in ConCat.Interval Methods (+++) :: Ok4 IF a b c d => IF c a -> IF d b -> IF (Coprod IF c d) (Coprod IF a b) Source # left :: forall a a' b. Oks IF '[a, b, a'] => IF a a' -> IF (Coprod IF a b) (Coprod IF a' b) Source # right :: Oks IF '[a, b, b'] => IF b b' -> IF (Coprod IF a b) (Coprod IF a b') Source #
ProductCat IF Source #
Instance details Defined in ConCat.Interval Methods exl :: Ok2 IF a b => IF (Prod IF a b) a Source # exr :: Ok2 IF a b => IF (Prod IF a b) b Source # dup :: Ok IF a => IF a (Prod IF a a) Source #
Iv b ~ (b :* b) => ConstCat IF b Source #
Instance details Defined in ConCat.Interval Methods const :: Ok IF a => b -> IF a (ConstObj IF b) Source # unitArrow :: b -> IF (Unit IF) (ConstObj IF b) Source #
(Iv a ~ (a :* a), Num a, Ord a) => NumCat IF a Source #
Instance details Defined in ConCat.Interval Methods negateC :: IF a a Source # addC :: IF (Prod IF a a) a Source # subC :: IF (Prod IF a a) a Source # mulC :: IF (Prod IF a a) a Source # powIC :: IF (Prod IF a Int) a Source #
Coercible (Iv a) (Iv b) => CoerceCat IF (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.Interval Methods coerceC :: IF a b Source #
Newtype (IF a b) Source #
Instance details Defined in ConCat.Interval Associated Types type O (IF a b) Source # Methods pack :: O (IF a b) -> IF a b Source # unpack :: IF a b -> O (IF a b) Source #
type Ok IF Source #
Instance details Defined in ConCat.Interval type Ok IF = Yes1 :: Type -> Constraint
type O (IF a b) Source #
Instance details Defined in ConCat.Interval type O (IF a b) = Iv a -> Iv b

min4 :: Ord a => ((a :* a) :* (a :* a)) -> a Source #

max4 :: Ord a => ((a :* a) :* (a :* a)) -> a Source #

minMax2 :: Ord a => a -> a -> a :* a Source #

minMax4 :: Ord a => a -> a -> a -> a -> a :* a Source #

ivFun :: (a -> b) -> Iv a -> Iv b Source #