Copyright	(C) 2025 - Eitan Chatav
License	BSD-style (see the file LICENSE)
Maintainer	Eitan Chatav <eitan.chatav@gmail.com>
Stability	provisional
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Control.Lens.PartialIso

Contents

PartialIso
Actions
Patterns
Iterations
Orphan instances

Description

See Rendel & Ostermann, Invertible syntax descriptions

Synopsis

dimapMaybe :: (Choice p, Cochoice p) => (s -> Maybe a) -> (b -> Maybe t) -> p a b -> p s t
type PartialIso s t a b = forall p f. (Choice p, Cochoice p, Applicative f, Filterable f) => p a (f b) -> p s (f t)
type PartialIso' s a = PartialIso s s a a
type APartialIso s t a b = PartialExchange a b a (Maybe b) -> PartialExchange a b s (Maybe t)
data PartialExchange a b s t = PartialExchange (s -> Maybe a) (b -> Maybe t)
partialIso :: (s -> Maybe a) -> (b -> Maybe t) -> PartialIso s t a b
withPartialIso :: APartialIso s t a b -> ((s -> Maybe a) -> (b -> Maybe t) -> r) -> r
clonePartialIso :: APartialIso s t a b -> PartialIso s t a b
coPartialIso :: APartialIso b a t s -> PartialIso s t a b
crossPartialIso :: APartialIso s t a b -> APartialIso u v c d -> PartialIso (s, u) (t, v) (a, c) (b, d)
altPartialIso :: APartialIso s t a b -> APartialIso u v c d -> PartialIso (Either s u) (Either t v) (Either a c) (Either b d)
(>?) :: Choice p => APrism s t a b -> p a b -> p s t
(?<) :: Cochoice p => APrism b a t s -> p a b -> p s t
(>?<) :: (Choice p, Cochoice p) => APartialIso s t a b -> p a b -> p s t
mapIso :: Profunctor p => AnIso s t a b -> p a b -> p s t
coPrism :: (Profunctor p, Filterable f) => APrism b a t s -> p a (f b) -> p s (f t)
satisfied :: (a -> Bool) -> PartialIso' a a
nulled :: (AsEmpty s, AsEmpty t) => PartialIso s t () ()
notNulled :: (AsEmpty s, AsEmpty t) => PartialIso s t s t
streamed :: (AsEmpty s, AsEmpty t, Cons s s c c, Cons t t c c) => Iso' s t
maybeEot :: Iso (Maybe a) (Maybe b) (Either () a) (Either () b)
listEot :: (Cons s s a a, AsEmpty t, Cons t t b b) => Iso s t (Either () (a, s)) (Either () (b, t))
iterating :: APartialIso a b a b -> Iso a b a b
difoldl1 :: Cons s t a b => APartialIso (c, a) (d, b) c d -> Iso (c, s) (d, t) (c, s) (d, t)
difoldr1 :: Cons s t a b => APartialIso (a, c) (b, d) c d -> Iso (s, c) (t, d) (s, c) (t, d)
difoldl :: (AsEmpty s, AsEmpty t, Cons s t a b) => APartialIso (c, a) (d, b) c d -> PartialIso (c, s) (d, t) c d
difoldr :: (AsEmpty s, AsEmpty t, Cons s t a b) => APartialIso (a, c) (b, d) c d -> PartialIso (s, c) (t, d) c d
difoldl' :: (AsEmpty s, Cons s s a a) => APrism' (c, a) c -> Prism' (c, s) c
difoldr' :: (AsEmpty s, Cons s s a a) => APrism' (a, c) c -> Prism' (s, c) c

PartialIso

dimapMaybe :: (Choice p, Cochoice p) => (s -> Maybe a) -> (b -> Maybe t) -> p a b -> p s t Source #

The dimapMaybe function endows Choice & Cochoice "partial profunctors" with an action >?< of PartialIsos.

type PartialIso s t a b = forall p f. (Choice p, Cochoice p, Applicative f, Filterable f) => p a (f b) -> p s (f t) Source #

PartialIso is a first class inexhaustive pattern, similar to how Prism is a first class exhaustive pattern, by combining Prisms and coPrisms.

Every Iso & Prism is APartialIso.

PartialIsos are isomorphic to PartialExchanges.

type PartialIso' s a = PartialIso s s a a Source #

A simple PartialIso' s a is an identification of a subset of s with a subset of a.

Given a simple PartialIso', partialIso f g, has properties:

Just = f <=< g

Just = g <=< f

These are left and right inverse laws for proper PartialIso's. However, sometimes an improper PartialIso' will be useful. For an improper PartialIso', only the left inverse law holds.

Just = f <=< g

For an improper PartialIso', norm = g <=< f is an idempotent

norm = norm <=< norm

and can be regarded as a normalization within some equivalence class of terms.

type APartialIso s t a b = PartialExchange a b a (Maybe b) -> PartialExchange a b s (Maybe t) Source #

If you see APartialIso in a signature for a function, the function is expecting a PartialIso.

data PartialExchange a b s t Source #

A PartialExchange provides efficient access to the two functions that make up a PartialIso.

Constructors

PartialExchange (s -> Maybe a) (b -> Maybe t)

Instances

Instances details

Tokenized a b (PartialExchange a b) Source #
Instance details Defined in Data.Profunctor.Distributor Methods anyToken :: PartialExchange a b a b Source #
Filtrator (PartialExchange a b) Source #
Instance details Defined in Data.Profunctor.Distributor Methods filtrate :: PartialExchange a b (Either a0 c) (Either b0 d) -> (PartialExchange a b a0 b0, PartialExchange a b c d) Source #
Choice (PartialExchange a b) Source #
Instance details Defined in Control.Lens.PartialIso Methods left' :: PartialExchange a b a0 b0 -> PartialExchange a b (Either a0 c) (Either b0 c) # right' :: PartialExchange a b a0 b0 -> PartialExchange a b (Either c a0) (Either c b0) #
Cochoice (PartialExchange a b) Source #
Instance details Defined in Control.Lens.PartialIso Methods unleft :: PartialExchange a b (Either a0 d) (Either b0 d) -> PartialExchange a b a0 b0 # unright :: PartialExchange a b (Either d a0) (Either d b0) -> PartialExchange a b a0 b0 #
Profunctor (PartialExchange a b) Source #
Instance details Defined in Control.Lens.PartialIso Methods dimap :: (a0 -> b0) -> (c -> d) -> PartialExchange a b b0 c -> PartialExchange a b a0 d # lmap :: (a0 -> b0) -> PartialExchange a b b0 c -> PartialExchange a b a0 c # rmap :: (b0 -> c) -> PartialExchange a b a0 b0 -> PartialExchange a b a0 c # (#.) :: forall a0 b0 c q. Coercible c b0 => q b0 c -> PartialExchange a b a0 b0 -> PartialExchange a b a0 c # (.#) :: forall a0 b0 c q. Coercible b0 a0 => PartialExchange a b b0 c -> q a0 b0 -> PartialExchange a b a0 c #
Functor (PartialExchange a b s) Source #
Instance details Defined in Control.Lens.PartialIso Methods fmap :: (a0 -> b0) -> PartialExchange a b s a0 -> PartialExchange a b s b0 # (<$) :: a0 -> PartialExchange a b s b0 -> PartialExchange a b s a0 #
Filterable (PartialExchange a b s) Source #
Instance details Defined in Control.Lens.PartialIso Methods mapMaybe :: (a0 -> Maybe b0) -> PartialExchange a b s a0 -> PartialExchange a b s b0 # catMaybes :: PartialExchange a b s (Maybe a0) -> PartialExchange a b s a0 # filter :: (a0 -> Bool) -> PartialExchange a b s a0 -> PartialExchange a b s a0 # drain :: PartialExchange a b s a0 -> PartialExchange a b s b0 #

partialIso :: (s -> Maybe a) -> (b -> Maybe t) -> PartialIso s t a b Source #

Build a PartialIso.

withPartialIso :: APartialIso s t a b -> ((s -> Maybe a) -> (b -> Maybe t) -> r) -> r Source #

Convert APartialIso to the pair of functions that characterize it.

clonePartialIso :: APartialIso s t a b -> PartialIso s t a b Source #

Clone APartialIso so that you can reuse the same monomorphically typed partial isomorphism for different purposes.

coPartialIso :: APartialIso b a t s -> PartialIso s t a b Source #

Clone and invert APartialIso.

crossPartialIso :: APartialIso s t a b -> APartialIso u v c d -> PartialIso (s, u) (t, v) (a, c) (b, d) Source #

Construct a PartialIso on pairs from components.

altPartialIso :: APartialIso s t a b -> APartialIso u v c d -> PartialIso (Either s u) (Either t v) (Either a c) (Either b d) Source #

Construct a PartialIso on Eithers from components.

Actions

(>?) :: Choice p => APrism s t a b -> p a b -> p s t infixl 4 Source #

Action of APrism on Choice Profunctors.

(?<) :: Cochoice p => APrism b a t s -> p a b -> p s t infixl 4 Source #

Action of a coPrism on Cochoice Profunctors.

(>?<) :: (Choice p, Cochoice p) => APartialIso s t a b -> p a b -> p s t infixl 4 Source #

Action of APartialIso on Choice and Cochoice Profunctors.

mapIso :: Profunctor p => AnIso s t a b -> p a b -> p s t Source #

Action of AnIso on Profunctors.

coPrism :: (Profunctor p, Filterable f) => APrism b a t s -> p a (f b) -> p s (f t) Source #

Action of a coPrism on the composition of a Profunctor and Filterable.

Patterns

satisfied :: (a -> Bool) -> PartialIso' a a Source #

satisfied is the prototypical proper partial isomorphism, identifying a subset which satisfies a predicate.

nulled :: (AsEmpty s, AsEmpty t) => PartialIso s t () () Source #

nulled matches an Empty pattern, like _Empty.

notNulled :: (AsEmpty s, AsEmpty t) => PartialIso s t s t Source #

notNulled matches a non-Empty pattern.

streamed :: (AsEmpty s, AsEmpty t, Cons s s c c, Cons t t c c) => Iso' s t Source #

streamed is an isomorphism between two stream types with the same token type.

maybeEot :: Iso (Maybe a) (Maybe b) (Either () a) (Either () b) Source #

The either-of-tuples representation of Maybe.

listEot :: (Cons s s a a, AsEmpty t, Cons t t b b) => Iso s t (Either () (a, s)) (Either () (b, t)) Source #

The either-of-tuples representation of list-like streams.

Iterations

iterating :: APartialIso a b a b -> Iso a b a b Source #

Iterate the application of a partial isomorphism, useful for constructing fold/unfold isomorphisms.

difoldl1 :: Cons s t a b => APartialIso (c, a) (d, b) c d -> Iso (c, s) (d, t) (c, s) (d, t) Source #

Left fold & unfold APartialIso to an Iso.

difoldr1 :: Cons s t a b => APartialIso (a, c) (b, d) c d -> Iso (s, c) (t, d) (s, c) (t, d) Source #

Right fold & unfold APartialIso to an Iso.

difoldl :: (AsEmpty s, AsEmpty t, Cons s t a b) => APartialIso (c, a) (d, b) c d -> PartialIso (c, s) (d, t) c d Source #

Left fold & unfold APartialIso to a PartialIso.

difoldr :: (AsEmpty s, AsEmpty t, Cons s t a b) => APartialIso (a, c) (b, d) c d -> PartialIso (s, c) (t, d) c d Source #

Right fold & unfold APartialIso to a PartialIso.

difoldl' :: (AsEmpty s, Cons s s a a) => APrism' (c, a) c -> Prism' (c, s) c Source #

Left fold & unfold APrism' to a Prism'.

difoldr' :: (AsEmpty s, Cons s s a a) => APrism' (a, c) c -> Prism' (s, c) c Source #

Right fold & unfold APrism' to a Prism'.

Orphan instances

(Profunctor p, Filterable f) => Cochoice (WrappedPafb f p) Source #
Instance details Methods unleft :: WrappedPafb f p (Either a d) (Either b d) -> WrappedPafb f p a b # unright :: WrappedPafb f p (Either d a) (Either d b) -> WrappedPafb f p a b #
(Profunctor p, Filterable (p a)) => Filterable (Coyoneda p a) Source #
Instance details Methods mapMaybe :: (a0 -> Maybe b) -> Coyoneda p a a0 -> Coyoneda p a b # catMaybes :: Coyoneda p a (Maybe a0) -> Coyoneda p a a0 # filter :: (a0 -> Bool) -> Coyoneda p a a0 -> Coyoneda p a a0 # drain :: Coyoneda p a a0 -> Coyoneda p a b #
(Profunctor p, Filterable (p a)) => Filterable (Yoneda p a) Source #
Instance details Methods mapMaybe :: (a0 -> Maybe b) -> Yoneda p a a0 -> Yoneda p a b # catMaybes :: Yoneda p a (Maybe a0) -> Yoneda p a a0 # filter :: (a0 -> Bool) -> Yoneda p a a0 -> Yoneda p a a0 # drain :: Yoneda p a a0 -> Yoneda p a b #
(Profunctor p, Functor f) => Functor (WrappedPafb f p a) Source #
Instance details Methods fmap :: (a0 -> b) -> WrappedPafb f p a a0 -> WrappedPafb f p a b # (<$) :: a0 -> WrappedPafb f p a b -> WrappedPafb f p a a0 #
(Profunctor p, Functor (p a), Filterable f) => Filterable (WrappedPafb f p a) Source #
Instance details Methods mapMaybe :: (a0 -> Maybe b) -> WrappedPafb f p a a0 -> WrappedPafb f p a b # catMaybes :: WrappedPafb f p a (Maybe a0) -> WrappedPafb f p a a0 # filter :: (a0 -> Bool) -> WrappedPafb f p a a0 -> WrappedPafb f p a a0 # drain :: WrappedPafb f p a a0 -> WrappedPafb f p a b #
Filterable (Forget r a :: Type -> Type) Source #
Instance details Methods mapMaybe :: (a0 -> Maybe b) -> Forget r a a0 -> Forget r a b # catMaybes :: Forget r a (Maybe a0) -> Forget r a a0 # filter :: (a0 -> Bool) -> Forget r a a0 -> Forget r a a0 # drain :: Forget r a a0 -> Forget r a b #
Filterable f => Filterable (Star f a) Source #
Instance details Methods mapMaybe :: (a0 -> Maybe b) -> Star f a a0 -> Star f a b # catMaybes :: Star f a (Maybe a0) -> Star f a a0 # filter :: (a0 -> Bool) -> Star f a a0 -> Star f a a0 # drain :: Star f a a0 -> Star f a b #