map,filter,accumulate

// function my_map(f, xs) {
//     return accumulate((x, ys) => pair(f(x), ys), null, xs);
// }

// display(my_map(x => x + 1, list(1, 2, 3)));



// function remove_duplicates(xs) {
//     return is_null(xs)
//             ? null 
//             : pair(head(xs), remove_duplicates(filter(x => x !== head(xs), tail(xs))));
// }


// // display(!is_null(member(3, list(1, 2, 4, 4, 2, 1, 2))));
// remove_duplicates(list(1, 2, 3, 4, 4, 3, 2, 1, 2));

// function makeup_amount(x, coins) {
//     if (x === 0) {
//         return list(null);
//     } else if (x < 0 || is_null(coins)) {
//         return null;
//     } else {
//     // Combinations that do not use the head coin.
//         const combi_A = makeup_amount(x, tail(coins));
//     // Combinations that do not use the head coin
//     // for the remaining amount.
//         const combi_B = makeup_amount(x - head(coins), tail(coins));
//     // Combinations that use the head coin.
//         const combi_C = map(xs => pair(head(coins), xs), combi_B);
//         return append(combi_A, combi_C);
//     }
// }
// display_list(makeup_amount(22, list(1, 10, 5, 20, 1, 5, 1, 50)));


// function removeDuplicates(xs) {
//     return accumulate((x, ys) => pair(x, remove_all(x, ys)), null, xs);
// }

// removeDuplicates(list(1, 2, 3, 4, 4, 3, 2, 1, 2));

function subset(xs) {
    return is_null(xs) 
            ? list(null)
            : append(map(ys => pair(head(xs), ys), subset(tail(xs))), subset(tail(xs))); 
}

display_list(subset(list(1, 2, 3)));

// function permutations(xs) {
//     return is_null(xs) 
//             ? list(null)
//             : map(ys => pair(head(xs), ys), permutations(tail(ys)));
// }

display_list(null);

function flatmap(f, seq) {
    return accumulate(append, null, map(f, seq));
}

function binary(n) {
    return n === 1 
            ? list('0', '1')
            // : append(flatmap(str => str + '0', binary(n - 1)),
            // flatmap(str => str + '1', binary(n - 1)));
            : append(map(str => str + '0', binary(n - 1)), map(str => str + '1', binary(n - 1)));
}

display_list(binary(2));