Iso.Deriving

Documentation

newtype As a b

As a b is represented at runtime as b, but we know we can in fact convert it into an a with no loss of information. We can think of it has having a *dual representation* as either a or b.

type As1 :: k -> Type -> Type

Constructors

As b

Instances

(Project a b, Eq a) => Eq (As a b)

Defined in Iso.Deriving

Methods

(==) :: As a b -> As a b -> Bool

(/=) :: As a b -> As a b -> Bool

(Isomorphic a b, Num a) => Num (As a b)

Defined in Iso.Deriving

Methods

(+) :: As a b -> As a b -> As a b

(-) :: As a b -> As a b -> As a b

(*) :: As a b -> As a b -> As a b

negate :: As a b -> As a b

abs :: As a b -> As a b

signum :: As a b -> As a b

fromInteger :: Integer -> As a b

(Project a b, Ord a) => Ord (As a b)

Defined in Iso.Deriving

Methods

compare :: As a b -> As a b -> Ordering

(<) :: As a b -> As a b -> Bool

(<=) :: As a b -> As a b -> Bool

(>) :: As a b -> As a b -> Bool

(>=) :: As a b -> As a b -> Bool

max :: As a b -> As a b -> As a b

min :: As a b -> As a b -> As a b

(Isomorphic a b, Real a) => Real (As a b)

Defined in Iso.Deriving

Methods

toRational :: As a b -> Rational

(Project a b, Show a) => Show (As a b)

Defined in Iso.Deriving

Methods

showsPrec :: Int -> As a b -> ShowS

show :: As a b -> String

showList :: [As a b] -> ShowS

(Isomorphic a b, Semigroup a) => Semigroup (As a b)

Defined in Iso.Deriving

Methods

(<>) :: As a b -> As a b -> As a b

sconcat :: NonEmpty (As a b) -> As a b

stimes :: Integral b0 => b0 -> As a b -> As a b

(Isomorphic a b, Monoid a) => Monoid (As a b)

Defined in Iso.Deriving

Methods

mempty :: As a b

mappend :: As a b -> As a b -> As a b

mconcat :: [As a b] -> As a b

newtype As1 f g a

Like As for kind k -> Type.

type As1 :: k1 -> (k2 -> Type) -> k2 -> Type

Constructors

As1

Fields

• getAs1 :: g a

Instances

(forall x. Isomorphic (f x) (g x), Monad f) => Monad (As1 f g)

Defined in Iso.Deriving

Methods

(>>=) :: As1 f g a -> (a -> As1 f g b) -> As1 f g b

(>>) :: As1 f g a -> As1 f g b -> As1 f g b

return :: a -> As1 f g a

fail :: String -> As1 f g a

(forall x. Isomorphic (f x) (g x), Functor f) => Functor (As1 f g)

Defined in Iso.Deriving

Methods

fmap :: (a -> b) -> As1 f g a -> As1 f g b

(<$) :: a -> As1 f g b -> As1 f g a

(forall x. Isomorphic (f x) (g x), Applicative f) => Applicative (As1 f g)

Defined in Iso.Deriving

Methods

pure :: a -> As1 f g a

(<*>) :: As1 f g (a -> b) -> As1 f g a -> As1 f g b

liftA2 :: (a -> b -> c) -> As1 f g a -> As1 f g b -> As1 f g c

(*>) :: As1 f g a -> As1 f g b -> As1 f g b

(<*) :: As1 f g a -> As1 f g b -> As1 f g a

(forall x. Isomorphic (f x) (g x), Alternative f) => Alternative (As1 f g)

Defined in Iso.Deriving

Methods

empty :: As1 f g a

(<|>) :: As1 f g a -> As1 f g a -> As1 f g a

some :: As1 f g a -> As1 f g [a]

many :: As1 f g a -> As1 f g [a]

newtype As2 f g a b

Like As for kind k1 -> k2 -> Type.

type As2 :: k1 -> (k2 -> k3 -> Type) -> k2 -> k3 -> Type

Constructors

As2 (g a b)

Instances

(forall (x :: k) (y :: k). Isomorphic (f x y) (g x y), Category f) => Category (As2 f g :: k -> k -> Type)

Defined in Iso.Deriving

Methods

id :: As2 f g a a

(.) :: As2 f g b c -> As2 f g a b -> As2 f g a c

class Inject a b where

Methods

inj :: a -> b

class Project a b where

Methods

prj :: b -> a

class (Inject a b, Project a b) => Isomorphic a b where

Laws: isom is an isomorphism, that is:

view isom . view (from isom) = id = view (from isom) . view isom

Minimal complete definition

Nothing

Methods

isom :: Iso' a b