Typescript index signatures

The only way to do both restrict values, and preserve type information about what keys are actually in the implementing type is to use a generic helper function. The function will enforce that the object literal extends the interface, but it will infer the actual type of the object literal:

interface NumberMap {
    [key: string]: number;
}

function createNumberMap<T extends NumberMap>(v: T) {
    return v;
}
const map = createNumberMap({
    one: 1,
    two: 2,
    three: 3,
    // no: '' // error
});
map.one //ok
map.no //error