Data.Function.Between.Types

This module defines types that behave as a precursors to types defined in lens library.

Since version 0.11.0.0.

PreIso

type PreIso r s t a b = ((b -> t) -> (s -> a) -> r) -> r

Family of types that can construct isomorphism between types.

Since version 0.11.0.0.

type PreIso' r s a = PreIso r s s a a

A simple PreIso.

Since version 0.11.0.0.

PreLens

type PreLens r s t a b = ((b -> s -> t) -> (s -> a) -> r) -> r

We can also view PreLens as a special kind of PreIso:

PreLens r s t a b = PreIso r s (s -> t) a b

Since version 0.11.0.0.

type PreLens' r s a = PreLens r s s a a

A simple PreLens, where we can not change the type of the information we are focusing on. As a consequence neither the type of the container data type can be changed.

Since version 0.11.0.0.

PrePrism

type PrePrism r s t a b = ((b -> t) -> (s -> Either t a) -> r) -> r

We can also get PrePrism by specializing PreIso:

PrePrism r s t a b = PreIso r s t (Either t a) b

This fact is not surprising, since Prisms are actually a special case of isomorphism between two types.

Let's have a type s, and we want to extract specific information out of it, but that information may not be there. Because of the fact that the type s can be a sum type. Imagine e.g. standard Maybe data type:

Maybe a = Nothing | Just a

How do we create something that can extrat that information from a sum type, and if necessary, also reconstructs that sum type. The answer is Prism, which is defined as an isomorphism between that type s and Either t a where a is the information we want to extract and t is the rest that we don't care about.

You may have noticed, that definition of PrePrism contains some type variables that aren't mentioned in the above definition. The reason for this is that, as with Lenses we may want to extract value of type a, but when constructing new data type we may want to change the type of that value in to b and therefore type s may not fit, which is the reason why we have type t in there. Once again we can ilustrate this with Maybe. Lets say that we have a value of s = Maybe a, but if we change the type of a in to b, and try to create Maybe again, then it would have type Maybe b = t.

Since version 0.11.0.0.

type PrePrism' r s a = PrePrism r s s a a

A simple PrePrism, where we can not change the type of the information we are focusing on. As a consequence neither the type of the container data type can be changed.

If we define PrePrism' in terms of PreIso' then we have even better ilustration of Prism concept in terms of isomorphism:

PrePrism' r s a = PreIso' r s (Either t a)

Since version 0.11.0.0.