if it can form one you can fold without providing an accumulator or empty value because you can use ...

# arrow

[raulraja]

if it can form one you can fold without providing an accumulator or empty value because you can use the monoid empty identity as the empty value and the associative operation as the accumulator

[CLOVIS]

So fold acts on a Functor which contains data, and a Monoid which is the morphism applied to it?

So in listOf(2, 3, 4).fold(sum)

List<Int> is a Functor that contains Ints, and sum is a Monoid which admits a function Int -> Int -> Int and an identity value (0) ?

[raulraja]

yep

[raulraja]

but fold itself requires an empty start value, that is the Monoid empty identity

[CLOVIS]

Thanks, that explains a lot 👍

[raulraja]

I suppose there sum provides it

[raulraja]

same notion as map reduce

[raulraja]

and all these techniques. They are all catamorphisms, and there are other recursion schemes

[raulraja]

What helps clarify all this is learning recursion schemes with Algebras and Coalgebras

[raulraja]

Data, Co-data, Fold, un-fold… it’s all conceptually the same

[CLOVIS]

How would you write sum in Arrow? I guess it's some type of typeclass that holds a function

[raulraja]

a kind of recursion scheme and their duals

[raulraja]

Sum is currently the default monoid for Int

[raulraja]

so you just use the int monoid

[CLOVIS]

I'll try to go deeper in the theory so I can read the Wikipedia pages

[raulraja]

There may be a Mult somewhere you’d have to pass by hand

[raulraja]

Check out this if you are interested

[raulraja]

https://www.47deg.com/blog/basic-recursion-schemes-in-scala/

[raulraja]

https://www.47deg.com/blog/recursion-schemes-introduction/

[CLOVIS]

You mean this; https://arrow-kt.io/docs/apidocs/arrow-core/arrow.core.extensions/kotlin.-int/monoid.html ?

[CLOVIS]

Thanks I'll watch them 😊

[raulraja]

yes, that is the int monoid

[raulraja]

Also this talk is gold

https://www.youtube.com/watch?v=XZ9nPZbaYfE▾

[CLOVIS]

Thanks ^^

[raulraja]

You can also put them to practice if you feel like it with one of the incubating modules in Arrow https://arrow-kt.io/docs/recursion/intro/