is there any way to let Typescript infer the return type from the function argument value?

is there any way to let Typescript infer the return type from the valueType argument instead of overloads?

 type ValueType = 'integer' | 'string' | 'number' | 'date' | 'dateTime' | 'boolean' | '';

   function toValueType<S>(v: S, valueType: 'integer'): number;
   function toValueType<S>(v: S, valueType: 'number'): number;
   function toValueType<S>(v: S, valueType: 'date'): Date | undefined;
   function toValueType<S>(v: S, valueType: 'dateTime'): Date | undefined;
   function toValueType<S>(v: S, valueType: 'string'): string;
   function toValueType<S>(v: S, valueType: ''): S;
   function toValueType<S>(v: S, valueType: ValueType): any {
        switch (valueType) {
            case 'integer':
                return To.int(v); // return number
            case 'number':
                return To.number(v); // return number
            case 'date':
                return To.date(v); // return Date|undefined
            case 'dateTime':
                return To.dateTime(v); // return Date|undefined
            case 'string':
                return To.string(v); // return string
            case 'boolean':
                return To.boolean(v); // return boolean
            default:
                return v; // return source
        }
    } 

You can create a type alias which represents a mapping of each string literal in your ValueType union to its corresponding expected return type, and create another generic type parameter to use for selecting the appropriate type in a conditional return type:

TS Playground

type ValueMap = {
  boolean: boolean;
  date: Date | undefined;
  dateTime: Date | undefined;
  integer: number;
  number: number;
  string: string;
};

type ValueType = keyof ValueMap | "";

declare function toValueType<T, K extends ValueType>(
  v: T,
  valueType: K,
): K extends keyof ValueMap ? ValueMap[K] : T;

declare const v: { _type: "example" };

const r0 = toValueType(v, "boolean");
    //^? const r0: boolean

const r1 = toValueType(v, "date");
    //^? const r1: Date | undefined

const r2 = toValueType(v, "dateTime");
    //^? const r2: Date | undefined

const r3 = toValueType(v, "integer");
    //^? const r3: number

const r4 = toValueType(v, "number");
    //^? const r4: number

const r5 = toValueType(v, "string");
    //^? const r5: string

const r6 = toValueType(v, "");
    //^? const r6: { _type: "example"; }

toValueType(v, "something else"); /* Error
               ~~~~~~~~~~~~~~~~
Argument of type '"something else"' is not assignable to parameter of type 'ValueType'.(2345) */