Programming

A comprehensive introduction to Higher Kinded Types in TypeScript, exploring how to encode and utilize these powerful abstractions from functional programming. HKTs enable type constructors that take other type constructors as arguments - imagine Functor<F> that works for any F<T> whether it’s Array<T>, Promise<T>, or Option<T>. Through encoding techniques using interface augmentation and symbol keys, we can simulate HKTs in TypeScript, making possible advanced functional patterns like monadic composition and type-safe algebraic structures previously impossible in the language.

How many lambda calculus programs exist with exactly $N$ terms? This exploration dives into deep questions about computational complexity, from counting programs like (λx. x x) (λx. x x) to analyzing the non-computable BB(N) busy beaver function that grows faster than any computable sequence. We examine Chaitin’s constant $Ω$ and why determining program convergence connects to unsolved problems like the Collatz conjecture collatz(3n + 1).