Consider the following TypeScript function:

function example<T>(
  ...[callback, batch]:
    | [callback: (param: T) => void, batch?: false]
    | [callback: (param: T[]) => void, batch: true]
) {
  if (batch) {
    callback([]);
  } else {
    callback({} as T);
  }
}

The callback type definition specifies its argument type, so one would expect the argument type to be inferred in the following calls:

example<string>((param) => {});        // Param should be inferred as string
example<string>((param) => {}, true);  // Param should be inferred as string[]

However TypeScript complains it cannot infer the type of param:

error TS7006: Parameter 'param' implicitly has an 'any' type.

example<string>((param) => {});
                 ~~~~~

error TS7006: Parameter 'param' implicitly has an 'any' type.

example<string>((param) => {}, true);
                 ~~~~~

Providing a explicit type does fix the problem but I believe TypeScript has enough information to infer it by itself. In fact, TypeScript does report incorrect typings when providing an invalid explicit type:

error TS2345: Argument of type '[(param: number) => void]' is not assignable to parameter of type '[callback: (c: string) => void, batch?: false | undefined] | [callback: (c: string[]) => void, batch: true]'.
  Type '[(param: number) => void]' is not assignable to type '[callback: (c: string) => void, batch?: false | undefined]'.
    Type at position 0 in source is not compatible with type at position 0 in target.
      Type '(param: number) => void' is not assignable to type '(c: string) => void'.
        Types of parameters 'param' and 'c' are incompatible.
          Type 'string' is not assignable to type 'number'.

example<string>((param: number) => {});
                ~~~~~~~~~~~~~~~~~~~~~

error TS2345: Argument of type '[(param: number[]) => void, true]' is not assignable to parameter of type '[callback: (c: string) => void, batch?: false | undefined] | [callback: (c: string[]) => void, batch: true]'.
  Type '[(param: number[]) => void, true]' is not assignable to type '[callback: (c: string[]) => void, batch: true]'.
    Type at position 0 in source is not compatible with type at position 0 in target.
      Type '(param: number[]) => void' is not assignable to type '(c: string[]) => void'.
        Types of parameters 'param' and 'c' are incompatible.
          Type 'string[]' is not assignable to type 'number[]'.
            Type 'string' is not assignable to type 'number'.

example<string>((param: number[]) => {}, true);
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Is there any way to get this to work without the explicit argument type?