Package com.jnape.palatable.lambda.optics

Interface Iso<S,T,A,B>

Type Parameters:
S - the larger type for focusing
T - the larger type for mirrored focusing
A - the smaller type for focusing
B - the smaller type for mirrored focusing
All Superinterfaces:
Applicative<T,Iso<S,?,A,B>>, Contravariant<S,Profunctor<?,T,Iso<?,?,A,B>>>, Functor<T,Iso<S,?,A,B>>, Monad<T,Iso<S,?,A,B>>, MonadRec<T,Iso<S,?,A,B>>, Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>, Profunctor<S,T,Iso<?,?,A,B>>
All Known Subinterfaces:
Iso.Simple<S,A>, TypeSafeKey<A,B>, TypeSafeKey.Simple<A>
Functional Interface:
This is a functional interface and can therefore be used as the assignment target for a lambda expression or method reference.
@FunctionalInterface public interface Iso<S,T,A,B> extends Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>, MonadRec<T,Iso<S,?,A,B>>, Profunctor<S,T,Iso<?,?,A,B>>
An Iso (short for "isomorphism") is an invertible Lens: an Optic encoding of a bi-directional focusing of two types, and like Lenses, can be Viewed, Set, and updated.

As an example, consider the isomorphism between valid Strings and Integers: 

 
 Iso<String, String, Integer, Integer> stringIntIso = Iso.iso(Integer::parseInt, Object::toString);
 Integer asInt = view(stringIntIso, "123"); // 123
 String asString = view(stringIntIso.mirror(), 123); // "123"
In the previous example, stringIntIso can be viewed as an Optic<String, String, Integer, Integer>, and can be mirror()ed and viewed as a Optic<Integer, Integer, String, String>.

As with Lens, variance is supported between S/T and A/B, and where these pairs do not vary, a Iso.Simple iso can be used (for instance, in the previous example, stringIntIso could have had the simplified Iso.Simple<String, Integer> type).

For more information, read about isos.

See Also:

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Interface
    Description
    static interface 
    Iso.Simple<S,A>
    A convenience type with a simplified type signature for common isos with both unified "larger" values and unified "smaller" values.

  • Method Summary

    Modifier and Type
    Method
    Description
    default <Z, C> Iso<S,T,Z,C>
    andThen(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,A,B,Z,C> f)
    Left-to-right composition of optics.
    default <R, U> Iso<R,U,A,B>
    compose(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,R,U,S,T> g)
    Right-to-Left composition of optics.
    default <R> Iso<R,T,A,B>
    contraMap(Fn1<? super R,? extends S> fn)
    Contravariantly map A <- B.
    default <R, U> Iso<R,U,A,B>
    diMap(Fn1<? super R,? extends S> lFn, Fn1<? super T,? extends U> rFn)
    Dually map contravariantly over the left parameter and covariantly over the right parameter.
    default <R> Iso<R,T,A,B>
    diMapL(Fn1<? super R,? extends S> fn)
    Contravariantly map over the left parameter.
    default <U> Iso<S,U,A,B>
    diMapR(Fn1<? super T,? extends U> fn)
    Covariantly map over the right parameter.
    default <U> Iso<S,U,A,B>
    discardL(Applicative<U,Iso<S,?,A,B>> appB)
    Sequence both this Applicative and appB, discarding this Applicative's result and returning appB.
    default <U> Iso<S,T,A,B>
    discardR(Applicative<U,Iso<S,?,A,B>> appB)
    Sequence both this Applicative and appB, discarding appB's result and returning this Applicative.
    default <U> Iso<S,U,A,B>
    flatMap(Fn1<? super T,? extends Monad<U,Iso<S,?,A,B>>> fn)
    Chain dependent computations that may continue or short-circuit based on previous results.
    default <U> Iso<S,U,A,B>
    fmap(Fn1<? super T,? extends U> fn)
    Covariantly transmute this functor's parameter using the given mapping function.
    static <S, T, A, B>
    Iso<S,T,A,B>
    iso(Fn1<? super S,? extends A> f, Fn1<? super B,? extends T> g)
    Static factory method for creating an iso from a function and it's inverse.
    static <S, T, A, B>
    Iso<S,T,A,B>
    iso(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,S,T,A,B> optic)
    Promote an optic with compatible bounds to an Iso.
    default <C> Iso<S,T,C,B>
    mapA(Fn1<? super A,? extends C> fn)
    Covariantly map A to C, yielding a new optic.
    default <Z> Iso<S,T,A,Z>
    mapB(Fn1<? super Z,? extends B> fn)
    Contravariantly map B to Z, yielding a new optic.
    default <R> Iso<R,T,A,B>
    mapS(Fn1<? super R,? extends S> fn)
    Contravariantly map S to R, yielding a new optic.
    default <U> Iso<S,U,A,B>
    mapT(Fn1<? super T,? extends U> fn)
    Covariantly map T to U, yielding a new optic.
    default Iso<B,A,T,S>
    mirror()
    Flip this Iso around.
    default <U> Iso<S,U,A,B>
    pure(U u)
    Lift the value b into this applicative functor.
    static <S, A, B> Pure<Iso<S,?,A,B>>
    pureIso(Fn1<? super S,? extends A> sa)
    The canonical Pure instance for Iso.
    static <S, A> Iso.Simple<S,A>
    simpleIso(Fn1<? super S,? extends A> f, Fn1<? super A,? extends S> g)
    Static factory method for creating a simple Iso from a function and its inverse.
    default Lens<S,T,A,B>
    toLens()
    Convert this Iso into a Lens.
    default <U> Iso<S,U,A,B>
    trampolineM(Fn1<? super T,? extends MonadRec<RecursiveResult<T,U>,Iso<S,?,A,B>>> fn)
    Given some operation yielding a RecursiveResult inside this MonadRec, internally trampoline the operation until it yields a termination instruction.
    default Tuple2<Fn1<? super S,? extends A>,Fn1<? super B,? extends T>>
    unIso()
    Destructure this Iso into the two functions S -< A and B -< T that constitute the isomorphism.
    default <U> Iso<S,U,A,B>
    zip(Applicative<Fn1<? super T,? extends U>,Iso<S,?,A,B>> appFn)
    Given another instance of this applicative over a mapping function, "zip" the two instances together using whatever application semantics the current applicative supports.

    Methods inherited from interface com.jnape.palatable.lambda.functor.Functor

    coerce

    Methods inherited from interface com.jnape.palatable.lambda.monad.MonadRec

    lazyZip

    Methods inherited from interface com.jnape.palatable.lambda.optics.Optic

    apply, monomorphize

  • Method Details

    • toLens

      default Lens<S,T,A,B> toLens()
      Convert this Iso into a Lens.
      Returns:
      the equivalent lens

    • mirror

      default Iso<B,A,T,S> mirror()
      Flip this Iso around.
      Returns:
      the mirrored Iso

    • unIso

      default Tuple2<Fn1<? super S,? extends A>,Fn1<? super B,? extends T>> unIso()
      Destructure this Iso into the two functions S -< A and B -< T that constitute the isomorphism.
      Returns:
      the destructured iso

    • fmap

      default <U> Iso<S,U,A,B> fmap(Fn1<? super T,? extends U> fn)
      Covariantly transmute this functor's parameter using the given mapping function. Generally this method is specialized to return an instance of the class implementing Functor.
      Specified by:
      fmap in interface Applicative<S,T>
      Specified by:
      fmap in interface Functor<S,T>
      Specified by:
      fmap in interface Monad<S,T>
      Specified by:
      fmap in interface MonadRec<S,T>
      Type Parameters:
      U - the new parameter type
      Parameters:
      fn - the mapping function
      Returns:
      a functor over B (the new parameter type)

    • pure

      default <U> Iso<S,U,A,B> pure(U u)
      Lift the value b into this applicative functor.
      Specified by:
      pure in interface Applicative<S,T>
      Specified by:
      pure in interface Monad<S,T>
      Specified by:
      pure in interface MonadRec<S,T>
      Type Parameters:
      U - the type of the returned applicative's parameter
      Parameters:
      u - the value
      Returns:
      an instance of this applicative over b

    • zip

      default <U> Iso<S,U,A,B> zip(Applicative<Fn1<? super T,? extends U>,Iso<S,?,A,B>> appFn)
      Given another instance of this applicative over a mapping function, "zip" the two instances together using whatever application semantics the current applicative supports.
      Specified by:
      zip in interface Applicative<S,T>
      Specified by:
      zip in interface Monad<S,T>
      Specified by:
      zip in interface MonadRec<S,T>
      Type Parameters:
      U - the resulting applicative parameter type
      Parameters:
      appFn - the other applicative instance
      Returns:
      the mapped applicative

    • discardL

      default <U> Iso<S,U,A,B> discardL(Applicative<U,Iso<S,?,A,B>> appB)
      Sequence both this Applicative and appB, discarding this Applicative's result and returning appB. This is generally useful for sequentially performing side-effects.
      Specified by:
      discardL in interface Applicative<S,T>
      Specified by:
      discardL in interface Monad<S,T>
      Specified by:
      discardL in interface MonadRec<S,T>
      Type Parameters:
      U - the type of the returned Applicative's parameter
      Parameters:
      appB - the other Applicative
      Returns:
      appB

    • discardR

      default <U> Iso<S,T,A,B> discardR(Applicative<U,Iso<S,?,A,B>> appB)
      Sequence both this Applicative and appB, discarding appB's result and returning this Applicative. This is generally useful for sequentially performing side-effects.
      Specified by:
      discardR in interface Applicative<S,T>
      Specified by:
      discardR in interface Monad<S,T>
      Specified by:
      discardR in interface MonadRec<S,T>
      Type Parameters:
      U - the type of appB's parameter
      Parameters:
      appB - the other Applicative
      Returns:
      this Applicative

    • flatMap

      default <U> Iso<S,U,A,B> flatMap(Fn1<? super T,? extends Monad<U,Iso<S,?,A,B>>> fn)
      Chain dependent computations that may continue or short-circuit based on previous results.
      Specified by:
      flatMap in interface Monad<S,T>
      Specified by:
      flatMap in interface MonadRec<S,T>
      Type Parameters:
      U - the resulting monad parameter type
      Parameters:
      fn - the dependent computation over A
      Returns:
      the new monad instance

    • trampolineM

      default <U> Iso<S,U,A,B> trampolineM(Fn1<? super T,? extends MonadRec<RecursiveResult<T,U>,Iso<S,?,A,B>>> fn)
      Given some operation yielding a RecursiveResult inside this MonadRec, internally trampoline the operation until it yields a termination instruction.

      Stack-safety depends on implementations guaranteeing that the growth of the call stack is a constant factor independent of the number of invocations of the operation. For various examples of how this can be achieved in stereotypical circumstances, see the referenced types.

      Specified by:
      trampolineM in interface MonadRec<S,T>
      Type Parameters:
      U - the ultimate resulting carrier type
      Parameters:
      fn - the function to internally trampoline
      Returns:
      the trampolined MonadRec
      See Also:

    • diMapL

      default <R> Iso<R,T,A,B> diMapL(Fn1<? super R,? extends S> fn)
      Contravariantly map over the left parameter.
      Specified by:
      diMapL in interface Profunctor<S,T,A>
      Type Parameters:
      R - the new left parameter type
      Parameters:
      fn - the mapping function
      Returns:
      a profunctor over Z (the new left parameter type) and C (the same right parameter type)

    • diMapR

      default <U> Iso<S,U,A,B> diMapR(Fn1<? super T,? extends U> fn)
      Covariantly map over the right parameter. For all profunctors that are also functors, it should hold that diMapR(f) == fmap(f).
      Specified by:
      diMapR in interface Profunctor<S,T,A>
      Type Parameters:
      U - the new right parameter type
      Parameters:
      fn - the mapping function
      Returns:
      a profunctor over A (the same left parameter type) and C (the new right parameter type)

    • diMap

      default <R, U> Iso<R,U,A,B> diMap(Fn1<? super R,? extends S> lFn, Fn1<? super T,? extends U> rFn)
      Dually map contravariantly over the left parameter and covariantly over the right parameter. This is isomorphic to diMapL(lFn).diMapR(rFn).
      Specified by:
      diMap in interface Profunctor<S,T,A>
      Type Parameters:
      R - the new left parameter type
      U - the new right parameter type
      Parameters:
      lFn - the left parameter mapping function
      rFn - the right parameter mapping function
      Returns:
      a profunctor over Z (the new left parameter type) and C (the new right parameter type)

    • contraMap

      default <R> Iso<R,T,A,B> contraMap(Fn1<? super R,? extends S> fn)
      Contravariantly map A <- B.
      Specified by:
      contraMap in interface Contravariant<S,T>
      Specified by:
      contraMap in interface Profunctor<S,T,A>
      Type Parameters:
      R - the new parameter type
      Parameters:
      fn - the mapping function
      Returns:
      the mapped Contravariant functor instance

    • mapS

      default <R> Iso<R,T,A,B> mapS(Fn1<? super R,? extends S> fn)
      Contravariantly map S to R, yielding a new optic.
      Specified by:
      mapS in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      R - the new left side of the output profunctor
      Parameters:
      fn - the mapping function
      Returns:
      the new optic

    • mapT

      default <U> Iso<S,U,A,B> mapT(Fn1<? super T,? extends U> fn)
      Covariantly map T to U, yielding a new optic.
      Specified by:
      mapT in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      U - the new right side's functor embedding of the output profunctor
      Parameters:
      fn - the mapping function
      Returns:
      the new optic

    • mapA

      default <C> Iso<S,T,C,B> mapA(Fn1<? super A,? extends C> fn)
      Covariantly map A to C, yielding a new optic.
      Specified by:
      mapA in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      C - the new left side of the input profunctor
      Parameters:
      fn - the mapping function
      Returns:
      the new optic

    • mapB

      default <Z> Iso<S,T,A,Z> mapB(Fn1<? super Z,? extends B> fn)
      Contravariantly map B to Z, yielding a new optic.
      Specified by:
      mapB in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      Z - the new right side's functor embedding of the input profunctor
      Parameters:
      fn - the mapping function
      Returns:
      the new optic

    • andThen

      default <Z, C> Iso<S,T,Z,C> andThen(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,A,B,Z,C> f)
      Left-to-right composition of optics. Requires compatibility between S and T.
      Specified by:
      andThen in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      Z - the new left side of the input profunctor
      C - the new right side's functor embedding of the input profunctor
      Parameters:
      f - the other optic
      Returns:
      the composed optic

    • compose

      default <R, U> Iso<R,U,A,B> compose(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,R,U,S,T> g)
      Right-to-Left composition of optics. Requires compatibility between A and B.
      Specified by:
      compose in interface Optic<Profunctor<?,?,?>,Functor<?,?>,S,T,A,B>
      Type Parameters:
      R - the new left side of the output profunctor
      U - the new right side's functor embedding of the output profunctor
      Parameters:
      g - the other optic
      Returns:
      the composed optic

    • iso

      static <S, T, A, B> Iso<S,T,A,B> iso(Fn1<? super S,? extends A> f, Fn1<? super B,? extends T> g)
      Static factory method for creating an iso from a function and it's inverse.
      Type Parameters:
      S - the larger type for focusing
      T - the larger type for mirrored focusing
      A - the smaller type for focusing
      B - the smaller type for mirrored focusing
      Parameters:
      f - the function
      g - f's inverse
      Returns:
      the iso

    • iso

      static <S, T, A, B> Iso<S,T,A,B> iso(Optic<? super Profunctor<?,?,?>,? super Functor<?,?>,S,T,A,B> optic)
      Promote an optic with compatible bounds to an Iso.
      Type Parameters:
      S - the larger type for focusing
      T - the larger type for mirrored focusing
      A - the smaller type for focusing
      B - the smaller type for mirrored focusing
      Parameters:
      optic - the Optic
      Returns:
      the Iso

    • simpleIso

      static <S, A> Iso.Simple<S,A> simpleIso(Fn1<? super S,? extends A> f, Fn1<? super A,? extends S> g)
      Static factory method for creating a simple Iso from a function and its inverse.
      Type Parameters:
      S - one side of the isomorphism
      A - the other side of the isomorphism
      Parameters:
      f - a function
      g - f's inverse
      Returns:
      the simple iso

    • pureIso

      static <S, A, B> Pure<Iso<S,?,A,B>> pureIso(Fn1<? super S,? extends A> sa)
      The canonical Pure instance for Iso.
      Type Parameters:
      S - the larger type for focusing
      A - the smaller type for focusing
      B - the smaller type for mirrored focusing
      Parameters:
      sa - one side of the isomorphism
      Returns:
      the Pure instance