// This is a contrived class. We could do the same thing with Observables, etc.
class SetOf<A> {
  _store: A[];

  add(a: A) {
    this._store.push(a);
  }

  transform<B>(transformer: (a: SetOf<A>) => SetOf<B>): SetOf<B> {
    return transformer(this);
  }

  forEach(fn: (a: A, index: number) => void) {
      this._store.forEach((a, i) => fn(a, i));
  }
}

function compose<A, B, C, D, E>(
  fnA: (a: SetOf<A>) => SetOf<B>, 
  fnB: (b: SetOf<B>) => SetOf<C>, 
  fnC: (c: SetOf<C>) => SetOf<D>,
  fnD: (c: SetOf<D>) => SetOf<E>,
):(x: SetOf<A>) => SetOf<E>;
/* ... etc ... */
function compose<T>(...fns: ((x: T) => T)[]): (x: T) => T {
  return (x: T) => fns.reduce((prev, fn) => fn(prev), x);
}

function map<A, B>(fn: (a: A) => B): (s: SetOf<A>) => SetOf<B> {
  return (a: SetOf<A>) => {
    const b: SetOf<B> = new SetOf();
    a.forEach(x => b.add(fn(x)));
    return b;
  }
}

function filter<A>(predicate: (a: A) => boolean): (s: SetOf<A>) => SetOf<A> {
  return (a: SetOf<A>) => {
    const result = new SetOf<A>();
    a.forEach(x => {
      if (predicate(x)) result.add(x);
    });
   return result;
  }
}

const testSet = new SetOf();
testSet.add(1);
testSet.add(2);
testSet.add(3);

// THE PROBLEM IS HERE
// all functions below are unable to infer any types.
// The user will be required to annotate the types manually at each step.
testSet.transform(
  compose(
    filter(x => x % 1 === 0),
    map(x => x + x),
    map(x => x + '!!!'),
    map(x => x.toUpperCase())
  )
)

testSet.transform(
  compose(
    filter(x => x % 1 === 0),
    map(x => x + x),
    map(x => 123),  // Whoops a bug
    map(x => x.toUpperCase()) // causes an error!
  )
)

// given the same `compose` function from above:

const result = [1, 2, 3, 4].map(
  compose(
    x => x + x,
    x => x + '!!!',
    x => parseInt(x)
  )
);

console.log(result); // [2, 4, 6, 8]