An example of Functor in TypeScript. You can run this on https://www.typescriptlang.org/play/

Functor.ts

// ==============================================
//  PROPOSAL OF SOLUTION
// ==============================================

// ================================
// Emulate nominal type-system
// ================================

type Kind<K> = { kind: K }
type Value<T> = { value: T }
type Container<K, T> = Kind<K> & Value<T> 

type Unit<K> = <T>(value: T) => Container<K, T>
const Unit = 
    <K extends string>(kind: K):Unit<K> => <T>(value: T) => 
        ({kind, value})

// ================================
//  The map (aka: Functor)
// ================================

// curied version
const map_ =
    <KB extends string>(unit: Unit<KB>) =>
    <A, B>(fn: (_: A) => B) =>
    <KA extends string>(m: Container<KA, A>): Container<KB, B> =>
        unit(fn(m.value))

// uncuried version
const map =
    <KB extends string, KA extends string, A, B>
    (unit: Unit<KB>,
    fn: (_: A) => B,
    m: Container<KA, A>): Container<KB, B> =>
        unit(fn(m.value))


// ================================
//  Use
// ================================

// Box now is a polimorphic nominal type constructor 
const Box = Unit("Box")
const OtherBox = Unit("OtherBox")

// example
const boxedString = Box("hello world") 
const boxedNumber = Box(10) 

// Functor map can't fail now
const mapbox = map(Box, (x:number) => x * 2, Box(3))
const mapOtherBox = map(OtherBox, (x:number) => x * 2, Box(3))

// You can use partially aplied version
const mapBox_ = map_(Box)
const mapOtherBox_ = map_(OtherBox)

// Use of curried version
const mapped = mapBox_((x:string) => x + "world")(Box("hello"))