Iso
An Iso
is an optic which converts elements of type S
into elements of type A
without loss.
Consider a case class Person
with two fields:
case class Person(name: String, age: Int)
Person
is equivalent to a tuple (String, Int)
and a tuple (String, Int)
is equivalent to Person
.
So we can create an Iso
between Person
and (String, Int)
using two total functions:
get: Person => (String, Int)
reverseGet (aka apply): (String, Int) => Person
import monocle.Iso
val personToTuple = Iso[Person, (String, Int)](p => (p.name, p.age)){case (name, age) => Person(name, age)}
personToTuple.get(Person("Zoe", 25))
// res0: (String, Int) = ("Zoe", 25)
personToTuple.reverseGet(("Zoe", 25))
// res1: Person = Person(name = "Zoe", age = 25)
Or simply:
personToTuple(("Zoe", 25))
// res2: Person = Person(name = "Zoe", age = 25)
Another common use of Iso
is between collection. List
and Vector
represent the same concept, they are both an
ordered sequence of elements but they have different performance characteristics. Therefore, we can define an Iso
between
a List[A]
and a Vector[A]
:
def listToVector[A] = Iso[List[A], Vector[A]](_.toVector)(_.toList)
listToVector.get(List(1,2,3))
// res3: Vector[Int] = Vector(1, 2, 3)
We can also reverse
an Iso
since it defines a symmetric transformation:
def vectorToList[A] = listToVector[A].reverse
vectorToList.get(Vector(1,2,3))
// res4: List[Int] = List(1, 2, 3)
Iso
are also convenient to lift methods from one type to another, for example a String
can be seen as a List[Char]
so we should be able to transform all functions List[Char] => List[Char]
into String => String
:
val stringToList = Iso[String, List[Char]](_.toList)(_.mkString(""))
stringToList.modify(_.tail)("Hello")
// res5: String = "ello"
Iso Generation
We defined several macros to simplify the generation of Iso
between a case class and its Tuple
equivalent. All macros
are defined in a separate module (see modules).
case class MyString(s: String)
case class Foo()
case object Bar
import monocle.macros.GenIso
First of all, GenIso.apply
generates an Iso
for newtype
i.e. case class with a single type parameter:
GenIso[MyString, String].get(MyString("Hello"))
// res6: String = "Hello"
Then, GenIso.unit
generates an Iso
for object or case classes with no field:
GenIso.unit[Foo]
// res7: Iso[Foo, Unit] = monocle.PIso$$anon$9@53b3b6dd
GenIso.unit[Bar.type]
// res8: Iso[Bar.type, Unit] = monocle.PIso$$anon$9@42f1e1ea
Finally, GenIso.fields
is a whitebox macro which generalise GenIso.apply
to all case classes:
GenIso.fields[Person].get(Person("John", 42))
// res9: (String, Int) = ("John", 42)
Be aware that whitebox macros are not supported by all IDEs.
Laws
An Iso
must satisfy all properties defined in IsoLaws
from the core
module.
You can check the validity of your own Iso
using IsoTests
from the law
module.
In particular, an Iso
must verify that get
and reverseGet
are inverse. This is done via
roundTripOneWay
and roundTripOtherWay
laws:
def roundTripOneWay[S, A](i: Iso[S, A], s: S): Boolean =
i.reverseGet(i.get(s)) == s
def roundTripOtherWay[S, A](i: Iso[S, A], a: A): Boolean =
i.get(i.reverseGet(a)) == a