6th_Sept_data_structure_1

// simplest data structure : pair
// (x,y)

function make_point(x,y){
    
    return component => component === 0 ? x : y;
}

// to get x 

function x_of(p){
    return p(0);
}

function y_of(p){
    return p(1);
}

x_of(make_point(3,4));


const pair = (x,y) => f => f(x,y);

// const p = pair(1,2);
// input to function f needs two arguments
// f => (x,y) => x 

// (f => f(1,2)(lambda expression input for f))

const head = p => p((x,y) => x);
const tail = p => p((x,y) => y);

// rational number 
// a pair consisting of a denominator and numerator

function make_rat(n, d){
    return pair(n, d);
}

function numer(x){
    return head(x);
}

function denom(x){
    return tail(x);
}

// rational number arithmetic system

function add_rat(x, y){
    return make_rat(numer(x) * denom(y) +
                    numer(y) * denom(y),
                    denom(x) * denom(y));
}


// similarly for subtraction, multiplication and division

// equality of rational numbers


// dont have to reduce to lowest form to check
// instead can cross multiply and check

// visualising rational numbers


function rat_to_string(x) {
    return stringify(numer(x)) + '/' + stringify(denom(x));
}

display(rat_to_string(add_rat(make_rat(1,2), make_rat(1,3)))); 
// why is the above giving wrong answer?

// gcd

// implementation details of this invisible to user