We introduce the Lens type, which is used for handling objects in functional programming, using the functional programming language Haskell.

In fact, MyLens can be written from Lens and is already defined in libraries named as Lens'.

In short, both get and set can be replaced using a single MyLens type. However, Lens type in Haskell is different from this MyLens.

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Functionallenses

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Let s be the type of an object and a be the type of a variable, the getter function get and the setter function set have the following types.

The Lens type is beneficial for representing objects in functional programming languages.

While functions like set and get are straightforward for handling objects, we can create a function of type MyLens by combining these two, as shown below.

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In fact, the functions get and set can be defined from MyLens, and vice versa.

While view is defined only on Lens s s a a in the library, we can generalize it on Lens s t a b as myView.

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The first is that getting after setting the value a in the object, should output the same value. The second is that setting the value obtained from get directly using set should result in an object equal to the original one. The third is that repeating multiple set operations is equivalent to applying only the last set.

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However, get and set need to satisfy for any object s and input a, b.

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Actually, get and set can also be defined from Lens, and vice versa.

Furthermore, the following properties also hold for any get and set.

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In Haskell, we generally use Lens type which is generalized from the previous MyLens type.

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First, we show the types of getter and setter, which are the features of object-oriented programming.

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As with MyLens, the following properties also hold for any get and set.

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