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Explain purpose of Kleisli Categories from the programmer's perspective #191

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Explain purpose of Kleisli Categories from the programmer's perspective #191

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19 changes: 18 additions & 1 deletion src/content/1.4/kleisli-categories.tex
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Expand Up @@ -400,6 +400,23 @@ \section{Kleisli Categories}
programs that in imperative languages are traditionally implemented
using side effects.

But, what is the real purpose of this concept from the perspective of a
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I partially agree with this statement because I believe the real purpose of this concept for programmers is a composition for a monadic functions.
e.g.(code is scala)
type Foo = Kleisli[IO, Int, String]
type Bar = Kleisli[IO, String, String]
can be easily composed like Bar compose Foo

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If that is the case it would be good if you can add on upon the content I’ve written.

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If that is the case it would be good if you can add on upon the content I’ve written.

Hi, I'll try to add a description tomorrow

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@a-nigredo a-nigredo May 19, 2019 •
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Fortunately, I have time to write today:

But, what is the real purpose of this concept from the perspective of a programmer?
Since arrows in Kleisli category is monadic functions and we know from a category definition that arrows have to be composable inside a category.
So the Kleisli category just gives us a composition for monadic function.

Let's say we have to read text from a file and save it to a database.

We have 2 arrows:

type FileReader = String=> IO[String]
type DbWriter = String => IO[Unit]

It is not possible to compose them since FileReader returns IO[String] not String as DbWriter expects. So what can we do?
Just wrapped functions by Kleisli

type FileReaderKleisli = Kleisli[IO, String, String]
type DbWriterKleisli = Kleisli[IO, String, Unit]

and now we can easily compose them as DbWriterKleisli(DbWriter) compose FileReaderKleisli(FileReader)

All code is written in Scala(https://www.scala-lang.org/) and Kleisli type signature is taken from https://typelevel.org/cats/datatypes/kleisli.html

but I don't have time to change pull request directly.
@wongjiahau could you please add and correct if needed my text and add to your pull request?

programmer? Improved code maintainability. Recall that the \code{process}
function can actually be written without using the fish operator:

\begin{snip}{hs}
process :: String -> Writer [String]
process s =
let (s' , log) = upCase s in
let (s'', log') = toWords s' in
(s'', log ++ log')
\end{snip}

However, this piece of code is not only harder to comprehend, it is also
difficult to modify (imagine that you want to add new operations or
change the sequence of exisitng operations). That is why we need to leverage
the power of Kleisli Categories along with the fish operator.

\section{Challenge}

A function that is not defined for all possible values of its argument
Expand Down Expand Up @@ -443,4 +460,4 @@ \section{Challenge}
Compose the functions \code{safe\_root} and \code{safe\_reciprocal} to implement
\code{safe\_root\_reciprocal} that calculates \code{sqrt(1/x)}
whenever possible.
\end{enumerate}
\end{enumerate}