Logic and Multiply-Quantified Statements in JavaScript
Programming has drawn me back into math, and I am really enjoying seeing the parallels between the formal logic of mathematics and the logic we see in code.
I’ve been enjoying working through Sussana S. Epp’s fantastic Discrete Mathematics with Applications and I am seeing how a lot of the mathematical concepts I’m learning were things that I had already seen or played with in functional programming, using Scheme/Racket and JavaScript/TypeScript.
For example, quantified statements using ∃\exists ∃ and ∀\forall ∀ can be expressed using JavaScript’s Array.some and Array.every methods.
Both of these methods work on an array of data and take a predicate function as an argument. Array.some checks to see if the predicate is true for any one of the elements in the array. Array.every checks to see if the predicate is true for all of the elements in the array.
In other words, the opposite of saying, “Q(x) is true for every single element in D” would be to say, “There is at least one element in D for which Q(x) is not true.” Formally,
