Support overload resolution with type union arguments

[johnendev]

TypeScript Version: 2.1.6

Code

interface Foo {
    bar(s: string): void;
    bar(n: number): number;
    bar(b: boolean): boolean;
}
type SN = string | number;

var sn1: string | number;
var sn2: SN;
var foo: Foo;

var x1 = foo.bar(sn1); // error
var x2 = foo.bar(sn2); // error

Expected behavior:
This should be allowed.
The type of x1 and x2 should be void | number, the union of the matching overload return types.

All 3 overloads can be seen as a single overload with a union type. It should try to fallback to a union when it can't match one of the originally defined overloads.

Actual behavior:
error TS2345: Argument of type 'string | number' is not assignable to parameter of type 'boolean'.
Type 'string' is not assignable to type 'boolean'.

[DanielRosenwasser]

I can't find other issues where this discussion's been had, but I'll try to give some context. The single-parameter case always tends to be the most frustrating one for people, and the most obvious one to fix. The problem occurs when you have multiple overloads.

For example, suppose you had the following overloads

interface Foo {
    bar(s1: string, s2: string): void;
    bar(n1: number, n2: number): number;
}

and you tried calling with the following:

declare var sn1: string | number;
declare var sn2: string | number;
declare var foo: Foo

foo(sn1, sn2);

Should our call to foo succeed? Probably not, since we can't guarantee that sn1 and sn2 share the same type.

So we could come up with a way of trying to collapse overloads that differ by exactly one parameter into unions and retying the overload process, but I think our concerns are

1. It seems a little ad-hoc, and ideally we'd like to generalize the behavior.
2. That process could be expensive (although this is less of a concern - this could be lazily done if overload resolution fails).
3. This process is potentially not as trivial as it sounds at face value.

[johnendev]

Ok. I think a more general way to look at it would be this:
When resolving overloads, an overload must match for every tuple in the cartesian product of all union argument types. Again the return type would be the union of all matching overloads.

For your example, it would look for overloads for each of (string, string), (string, number), (number, string), (number, number). It would fail as 2 of them don't have a matching overload.

The problem space would grow exponentially, but functions generally don't have a large number of parameters with a large number of types in each union. It could be short-circuited to ensure that every necessary type exists at each positional parameter first, before computing permutations. For generic parameters short-circuiting might not always be possible.

[RyanCavanaugh]

#1805 was the prior incarnation of this

[masaeedu]

@DanielRosenwasser Say we treat functions of the form (a: A, b: B) => R identically to functions of the form (a: A) => (b: B) => R for the purposes of overload resolution. We only need a sensible specification for the return type of the overloaded function ((a1: A1) => R1) & ((a2: A2) => R2) when invoked with A1 | A2, and we can then apply this recursively to the return type until we've exhausted the parameter list.

I propose that the return type of the overloaded function ((a1: A1) => R1) & ((a2: A2) => R2), when invoked with argument A1 | A2 be R1 | R2 (when invoked with A1, be R1, etc). Note that R1 | R2 is a union of the partially applied remainders from each overload, so this is a union of functions.

Now we need a sensible rule for the return type of a union of functions R1 | R2 == ((b1: B1) => S1) | ((b2: B2) => S2), and what it can be invoked with. I propose that the union ((b1: B1) => S1) | ((b2: B2) => S2), be invocable with an intersection of the parameter types B1 & B2, and that it return S1 | S2. Note that this is not a perfect dual of the previous rule; the uncertainty that was introduced due to invocation with a union propagates throughout the remaining parameters.

Let's apply this to your example and see what we come up with:

1. (s1: string, s2: string) => void & (n1: number, n2: number) => number; will be substituted with (s1: string) => (s2: string) => void & (n1: number) => (n2: number) => number; for the purposes of overload resolution
2. We apply the argument string | number to the function type (s1: string) => S & (n1: number) => N to obtain the return type S | N, for S == (s2: string) => void and N == (n2: number) => number
3. We try to apply the argument string | number to the function type (s2: string) => void | (n2: number) => number, but find that we cannot, since it can only accept a parameter of type string & number. The program does not succeed type checking
4. If we had provided string & number for the second argument, type checking would succeed and the overall return type would be void | number

The requirement for the second argument to be of type string & number intuitively makes sense, and simply falls out of the rules described above. I think this would generalize fairly well to any number of overloads and any number of parameters.

[jcalz]

It seems like this issue keeps being reported occasionally. Folks expect TypeScript to notice that an overloaded or generic function (essentially an intersection of functions) can take an argument of a union of possible argument types; and that a union of functions can take an intersection of possible argument types.

The former case is mentioned in this issue and in some of the references above.

The latter case shows up when you have something like this:

var someArray = Math.random() < 0.5 ? [1,2,3] : ['a','b','c']; // number[] | string[]
var filteredArray = someArray.filter(x:any => typeof x !== 'undefined') // nope!

(see #16716, #16644)

---

You can force TypeScript to notice this in specific cases:

function intersectFunction<A1, R1, A2, R2>
  (f: ((a: A1) => R1) & ((a: A2) => R2)) :    
  ((a: A1 | A2) => (R1 | R2)) {
  return f;
}

function uniteFunction<A1, R1, A2, R2>
  (f: ((a: A1) => R1) | ((a: A2) => R2)) :    
  ((a: A1 & A2) => (R1 | R2)) {
  return f;
}

which is, I think, the translation of part of @masaeedu's method into explicit functions.

Then @johnendev's case could be forcibly fixed like this:

// behold ugliness:
var boundBar = foo.bar.bind(foo) as typeof foo.bar; // have to bind to call later
var x1 = intersectFunction<string, void, number, number>(boundBar)(sn1); // number | void
var x2 = intersectFunction<string, void, number, number>(boundBar)(sn2); // number | void
// correct, but at what cost?

and the case with Array.filter() would be similarly mangled into type checking like this:

// behold ugliness:
var boundFilter = someArray.filter.bind(someArray) as typeof someArray.filter; // ditto
var filteredArray = uniteFunction
  <(n: number) => any, number[], (x: string) => any, string[]>
  (boundFilter)((x: any) => typeof x !== 'undefined'); // number[] | string[]
// correct, but at what cost?

---

But it would be much nicer all around if TypeScript could infer this itself. @masaeedu's idea about using currying/uncurrying to do this inference of polyadic functions is pretty neat. Does anyone think this would be incorrect as opposed to just possibly too expensive for the type checker?

Thanks!

[aj-r]

I think that this union type argument check should only be done if all of the following apply:

1. An exact match on any one overload was not found. This not only saves a bunch on compiler performance; it also lowers the risk of breaking backwards compatibility.
2. Two or more overloads have almost the same signature, with exactly one argument being different. This cuts down on the number of combinations we need to check for. I'm not sure if it will cover all use cases - just an idea at this point.