do i have this right? ```/** left identity */ obje...

# arrow

[jimn]

do i have this right?

/** left identity */
object `⟳` {
      operator fun <T> invoke(t: T) = { t: T -> t } 
}

/** left identity */
val <T> T.`⟳` get() =   `⟳` ( this) 
/**right identity*/
val <T> T.`⟲` get() = { this }

[raulraja]

I’ve never seen it it encoded like that. We usually encode it like this:

fun <A> A.identity(): A = this
fun <A> identity(ev: A): A = ev

[jimn]

https://wiki.haskell.org/Monad_laws plus also milos whiteboarded the circle arrows for left and right.

[jimn]

my haskellize is less than perfect

[jimn]

plus it starts to get deep here. https://planetmath.org/leftidentityandrightidentity

[raulraja]

I see, in our case we have these https://arrow-kt.io/docs/apidocs/arrow-test/arrow.test.laws/-monoid-laws/index.html

[raulraja]

those are in the monoid laws

[jimn]

i noted in the lecture that right identity was being used to lift a into a .⟲ ( G ⚬ F) verbatim. This works in kotlin type checking for my Vector abstraction which appears to fulfil the semigroup where a ( G ⚬ F) does not cooperate on an infix viable basis.

i have backwards and forards composition of the same basic functors as below.

IOMemento.IoLocalDate to Tokenized(
dateMapper ⚬ trim ⚬ btoa ⚬ bb2ba,
{ a, b -> a.putLong(b.toEpochDay()) }),
IOMemento.IoInstant to Tokenized(
bb2ba → btoa → trim → instantMapper,
{ a, b -> a.putLong(b.toEpochMilli()) })

[jimn]

im assuming that if i am following the same basic cat thoery blueprints as arrow that i will be in range of type-aliasing much of this onto arrow constructs, or at least will learn where it's different

[raulraja]

yes, there may be differences or missing abstractions in Arrow as well