Iso.Deriving

Documentation

type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)

type Iso' s a = Iso s s a a

newtype As (a :: Type) 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 as having a dual representation as either a or b.

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 :: k1 -> Type) (g :: k1 -> Type) (a :: k1)

Like As for kind k -> Type.

Constructors

As1

Fields

• getAs1 :: g a

Instances

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

Defined in Iso.Deriving

Methods

writer :: (a, s) -> As1 f g a

tell :: s -> As1 f g ()

listen :: As1 f g a -> As1 f g (a, s)

pass :: As1 f g (a, s -> s) -> As1 f g a

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

Defined in Iso.Deriving

Methods

get :: As1 f g s

put :: s -> As1 f g ()

state :: (s -> (a, s)) -> As1 f g a

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

Defined in Iso.Deriving

Methods

ask :: As1 f g s

local :: (s -> s) -> As1 f g a -> As1 f g a

reader :: (s -> a) -> As1 f g a

(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.

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

Class of isomorphic types.

Laws

right-inverse

inj . prj = id

left-inverse

prj . inj = id

compatibility

isom = dimap inj (fmap prj)

Minimal complete definition

Nothing

Methods

isom :: Iso' a b