Possible to implement overloaded call signature with an arrow function?

[bcherny]

TypeScript Version: 4.0.0-dev

Search Terms: Function overload, signature, declaration

Code

type CreateElement = {
  (tag: 'a'): HTMLAnchorElement
  (tag: string): HTMLElement
}

/*
  Error TS2322:
    Type '(tag: string) => HTMLAnchorElement | HTMLDivElement' is not assignable to type 'CreateElement'.
      Type 'HTMLAnchorElement | HTMLDivElement' is not assignable to type 'HTMLAnchorElement'.
*/
const createElement: CreateElement = (tag: string) => {
  if (tag === 'a') {
    return document.createElement('a')
  }
  return document.createElement('div')
}

TS infers createElement's signature as (tag: string) => HTMLAnchorElement | HTMLDivElement, which is not assignable to CreateElement. Could there be a way to treat this case similarly to how TS treats function-based overloads, so instead of checking that the right-hand-side of the assignment is compatible with the left-hand type (CreateElement), TS instead checks that each case of the overload (in CreateElement) is assignable to the right-hand-side? Or if this is too radical of a departure from TS's assignability checking, could there be another way to make this work?

Expected behavior: TS should treat function and function expression overloads the same. This code should work, the same way that the following code works:

function createElement(tag: 'a'): HTMLAnchorElement
function createElement(tag: string): HTMLElement {
   return document.createElement(tag)
}

Actual behavior: TypeError

Playground Link

Related Issues:

• Overloaded union type does not resolve overloads #37704
• Function implementation that returns literal types is not assignable to widened overload #37394
• Describe function signature using an interface  #34319

[RyanCavanaugh]

The posted "equivalent" has only one overload; it is not at all equivalent 😐

The only way to detect that this is a valid assignment is to read the function body and understand that it behaves correctly in each overload case; it is far beyond TS's capabilities to do this.