Safe Haskell	None
Language	Haskell2010

Iso.Deriving

Synopsis

newtype As a b = As b
newtype As1 f g a = As1 {
- getAs1 :: g a
}
newtype As2 f g a b = As2 (g a b)
class Inject a b where
- inj :: a -> b
class Project a b where
- prj :: b -> a
class (Inject a b, Project a b) => Isomorphic a b where
- isom :: Iso' a b

Documentation

newtype As a b Source #

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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Iso.Deriving Methods toRational :: As a b -> Rational #
(Project a b, Show a) => Show (As a b) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 Source #

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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 Source #

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) Source #
Instance details 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 Source #

Methods

inj :: a -> b Source #

class Project a b where Source #

Methods

prj :: b -> a Source #

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

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 Source #