Currying vs partial application vs factory

currying.js

/**
Example is using Heron's formula for calculating area of triangle
more info: https://en.wikipedia.org/wiki/Heron%27s_formula
*/


// Given a function of type f: (X x Y x Z) -> N,
// currying produces f: X -> (Y -> (Z -> N))

// Num -> (Num -> (Num -> Num))
function triangleArea(a) {
  return function(b) {
    return function(c) {
      const s = (a + b + c) / 2;
      return Math.sqrt(s * (s - a) * (s - b) * (s - c));
    };
  };
}

// Num -> (Num -> Num)
const withAequal5 = triangleArea(5);

withAequal5(3)(3);
// => 4.14578098794425

withAequal5(4)(2);
// => 3.799671038392666

factory.js

/**
Example is using Heron's formula for calculating area of triangle
more info: https://en.wikipedia.org/wiki/Heron%27s_formula
*/

// Given (X x Y x Z),
// factory THIS produces f: () -> N
function triangleArea(a, b, c) {
    return function() {
        const s = (a + b + c) / 2;
        return Math.sqrt(s * (s - a) * (s - b) * (s - c));
    };
}

// () -> N
const triangle =  triangleArea(5, 3, 3);
const triangle2 = triangleArea(5, 4, 2);

triangle();
// => 4.14578098794425

triangle2();
// => 3.799671038392666

partial-application.js

/**
Example is using Heron's formula for calculating area of triangle
more info: https://en.wikipedia.org/wiki/Heron%27s_formula
*/

// Given a function  of type f: (X x Y x Z) -> N,
// fixingbinding produces fpartial: (Y x Z) -> N


function triangleArea(a, b, c) {
  const s = (a + b + c) / 2;
  return Math.sqrt(s * (s - a) * (s - b) * (s - c));
}

// (X x Y) -> N
const partial = triangleArea.bind(undefined, 5);

partial(3, 3);
// => 4.14578098794425

partial(4, 2);
// => 3.799671038392666