High Order Functions: Break down of Fold (Reduce) in JavaScript

README.high-order-functions.md

Fold

About a high-order functions:

High-Order Function, as a structural transformation, the fold is a polymorphic function.

(The breakdown)

This just means, it takes on different forms (poly = multiple), and can take data from one element and transform it into another.

Specifically, this is speaking to the 'left fold'.

Key points:

• explained in category theory
• catamorphism, uses 'typed calculis' (Lambda) to explain the fold of a list.
• typically a linear function applied to a finite set.

We call this in JavaScript: Reduce

math-fold-left-sequence-map-reduce.js

(() => {
  /**
   * For Reference, I peronsally find it important to
   * understand the background in the tools I use.
   *
   * In this particular case, it's part of discrete math.
   * And the concept is:
   * apply a function, against a sequence of elements
   * and yield (return) a product of that function.
   *
   * Reduce :
   *     ( f x e -> f ) x Seq<e> x f -> f
   */
  const produceSumOfSequenceElements = (sequence, element) => {
    return sequence + element;
  }
  const getTotalSum = (elements = [], operatorFunction) => {
    return elements.reduce(
      operatorFunction,
      0
    )
  };

  // Testing Assumptions
  const testTaskSumOfSequence = (verbose = true) => {
    const elements = [5, 2, 6, 9, 10];
    const expectedSum = 32;
    const sumOfSequence = getTotalSum(elements, produceSumOfSequenceElements);
    if (verbose) {
      console.log(`Task:`);
      console.log(`Get the sum of elements in sequence:\n${elements}.\n\n`);
      console.log(`Expected result:\n${expectedSum}.\n\nActual result:\n${sumOfSequence}.`);
    }
    if (expectedSum === sumOfSequence) {
      console.log(`> Task Status: Passed.`);
    } else {
      console.log(`> Task Status: Failed.`);
    }
  };
  testTaskSumOfSequence(false);

  /**
     Result:
     Task:
     Get the sum of elements in sequence:
     5,2,6,9,10.

     Expected result:
     32.

     Actual result:
     32.

     > Task Status: Passed.
   */

})();