25thOct_advancedstreams

// seive of eratosthenes

function is_divisible(x, y){
    return x % y === 0;
}

function seive(s){
    return pair(head(s), () => seive(stream_filter(x => !is_divisible(x, head(s)), stream_tail(s))));
}

const primes = seive(integers_from(2));

// square roots by newton's method

/*
function improve(guess, x){
    return average(guess, guess/x);
}

function sqrt_iter(guess, x){
    if (good_enough(guess, x)){ // we dont know what good_enough is?
        return guess;
    }
    
    else {
        return sqrt_iter(improve(guess, x), x);
    }
}


function sqrt(x) {
    return sqrt_iter(1.0, x);
}
*/

// using streams for iteration

function average(a,b){
    return (a + b)/2;
}

function improve(guess, x){
    return average(guess, x/guess);
    
}

function sqrt_stream(x){
    const guesses = pair(1.0, () => stream_map(guess => improve(guess, x), guesses));
    return guesses;
}

eval_stream(sqrt_stream(4), 6);


// approximating pi

// pi/4 = 1 - 1/3 + 1/5 - 1/7 ...

// function to produce a stream of summands
// i.e. 1, -1/3, 1/5...

function pi_summands(n) {
    return pair(1 / n,
        () => stream_map(x => -x, pi_summands(n + 2)));
}

eval_stream(pi_summands(1), 10);


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)));
}

// Returns a stream whose elements are 
// s0, s0 + s1, s0 + s1 + s2, ...

function partial_sums(s) {
    return pair(head(s), () => add_streams(partial_sums(s), stream_tail(s)));
}

// similar to fibonacci


function scale_stream(s, f) {
    return stream_map(x => x * f, s);
} // multiply by 4 cause we find for pi/4

    
const pi_stream =
    scale_stream(partial_sums(pi_summands(1)), 4);

eval_stream(pi_stream, 8);

//should return:
// [4,
// [2.666666666666667,
// [3.466666666666667,
// [2.8952380952380956,
// [3.3396825396825403,
// [2.9760461760461765,
// [3.2837384837384844,
// [3.017071817071818,
// null]]]]]]]]