Is this a Functor

Question

Recently I am learning functors and monads but it seems a little bit confusing. I have written this to chain multiple operations and wonder if it is a functor and I understand it correctly?

function Init(store = {}) {
  const map = (fn) => {
    const result = fn(store)
    return Init(result ? {...store, ...result} : store)
  }
  const unwrap = () => store
  return {
    map,
    unwrap
  }
}

// example usage
Init()
.map(fetchData)
.map(fetchOtherData)
.map(compareTwoData)
.map(saveAllData)
// ...etc

Answer 1

I don't think it is, because Functors must preserve composition map(g°h)=map(g)°map(h), which yours does not:

function Init(store = {}) {
    const map = (fn) => {
        const result = fn(store)
        return Init(result ? {...store, ...result} : store)
    }
    const unwrap = () => store
    return {
        map,
        unwrap
    }
}

a = x => ({...x, a:1})
b = x => 0


console.log(Init({X:1}).map(a).map(b).unwrap())
console.log(Init({X:1}).map(x => b(a(x))).unwrap())

Here's an example of a basic Functor that satisfies both functor laws:

function Functor(value) {
    const fmap = (fn) => {
        const result = fn(value)
        return Functor(result)
    }
    return {fmap, value}
}

//

let id = x => x
let a = x => x * 5
let b = x => x + 3


// identity
console.log(
    Functor(7).value === Functor(7).fmap(id).value
)

// composition
console.log(
    Functor(7).fmap(a).fmap(b).value ===
    Functor(7).fmap(x => b(a(x))).value
)