I recently wondered whether the B combinator alone is capable of producing any parenthesization. My intuition was that this should be the case, but I found more or less nothing solid or concise about it, let alone an explicit construction. I’m sure this floats around somewhere, but anyways: The goal of this post is to be discoverable. To be short and intuitive instead of a deep dive.
I certainly had fun figuring all of the following out, so consider not reading the solution if you enjoy a good puzzle!
Imagine a list of terms
t4, … and…
I first read about the Iota combinator years ago and was intrigued by its existence. Recently I wondered what some alternative one-point bases look like and whether Iota is the smallest such combinator. Here is what I found online, in papers, and from writing a small tool that searches for such bases.
Indeed, the tool found some that are smaller than Iota. I’m sure they have been found before, but it seems this information could be more discoverable. So here is a buffet of one-point bases; after a quick, informal recap/definition of what a (one-point) basis is.
Disclaimer: This is…
In this post I assume you know the difference between lazy evaluation and strict/eager evaluation, but here is a quick summary. Skip this if all you care about is the how.
x = 3 + 4 // <- does the addition happen here?
print x // <- or here?
print x // <- or even here?
No matter what your programming background and experience is, you have a mental model about what the above piece of code does, whatever language it may be. We would probably all guess that it prints “7” twice.
This is just a short story about the online Fractional Derivative Playground that I created out of curiosity and wanted to share with other curious minds. Disclaimer: I am not a mathematician, so take everything I claim or the playground shows with a grain of salt.
TL;DR: Fractional derivatives are a thing; I couldn’t find any nice interactive online visualization; I made one; let me know what you think!
One day my YouTube feed contained Dr. Peyam’s Definition of the Half Derivative. I didn’t even know something like that exists, must watch.
Dr. Peyam made my day. Derivatives and…
Have you ever written expressions like
(await t).Select(x => x?.Foo())? Fun fact:
await (async. programming),
Select (list processing) and
?. (null-conditional) are really the same thing. Language designers could make this expression look like
(await each nullable t).Foo(). Read on to find out why and how. Your feedback is highly appreciated!
Consider the following, seemingly independent, programming concepts:
One will a number of solutions fulfilling at least some of the above wishes, such as webpack.js.org, browserify.org or nodular.js. However, all of those approaches are based on some form of the source code transformation — either ahead of time (webpack and browserify)…
I did all work on my Windows 10 laptop (i7–5557U@3.1GHz, 16GB), but made heavy use of WSL a.k.a. “Bash on Ubuntu…
compiler and programming language enthusiast