s11hw

function add_streams(s1, s2) {
    return is_null(s1)
            ? s2
            : is_null(s2)
            ? s1
            : pair(head(s1) + head(s2),
            () => add_streams(stream_tail(s1),
            stream_tail(s2)));
}
function scale_stream(c, stream) {
    return stream_map(x => c * x, stream);
}

const add_series = add_streams;
const scale_series = scale_stream;

function negate_series(s) {
    return scale_series(-1, s);
}

function subtract_series(s1, s2) {
    return add_series(s1, negate_series(s2));
}

function coeffs_to_series(list_of_coeffs) {
    const zeros = pair(0, () => zeros);
    function iter(list) {
        return is_null(list)
                ? zeros
                : pair(head(list),
                () => iter(tail(list)));
    }
    return iter(list_of_coeffs);
}

function fun_to_series(fun) {
    return stream_map(fun, non_neg_integers);
}

const non_neg_integers = pair(0, () => stream_map(num => num + 1, non_neg_integers));

const ones = pair(1, () => ones);
const alt1 = pair(1, () => stream_map(num => -num, alt1));
const zeroes = add_series(alt1, stream_tail(alt1));
const zeroes2 = subtract_series(alt1, alt1);
eval_stream(alt1, 5);
eval_stream(zeroes, 5);

const s1 = x => fun_to_series(num => math_pow(x, num));

const s2 = x => {
    return fun_to_series(num => (num + 1) * math_pow(x, num));
};

eval_stream(s2(2), 5);
eval_stream(fun_to_series(num => math_pow(2, num)), 5);
function mul_streams(a,b) {
    return pair(head(a) * head(b),
            () => mul_streams(stream_tail(a), stream_tail(b)));
}
const B = pair(1, () => mul_streams(B, stream_tail(non_neg_integers)));
eval_stream(B, 5);