Brandon Blaylock baetheus

Implementing complex numbers and FFT with just datatypes (no floats)

In this article, I'll explain why implementing numbers with just algebraic datatypes is desirable. I'll then talk about common implementations of FFT (Fast Fourier Transform) and why they hide inherent inefficiencies. I'll then show how to implement integers and complex numbers with just algebraic datatypes, in a way that is extremely simple and elegant. I'll conclude by deriving a pure functional implementation of complex FFT with just datatypes, no floats.

There is nothing more annoying than databases. Absolutely all DBs nowadays are based on some kind of pre-determined data structure (tables, documents, key/val stores, whatever) plus some methods to mutate data on them. They're the functional programmer's worst nightmare and one of the few "imperative" things that still impregnate Haskell programs. I wonder if there isn't, on this human world, a single functional-oriented DB.

I'm thinking of an app-centric, append-only-log database. That is, rather than having tables or documents with operations that mutate the database state - like all DBs nowadays do, and which is completely non-functional - it would merely store an immutable history of transactions. You would then derive the app state from a reducer. Let me explain with an example. Suppose we're programming a collective TODO-list application. In order to create a DB, all you need is the specification of your app and a data path:

Local database

import MyDreamDB

	## USAGE
	# $ nix-build kexec-installer.nix
	# can be deployed remote like this
	# $ rsync -aL -e ssh result/ root@host:
	# $ ssh root@host ./kexec-installer
	## Customize it like this
	# # custom-installer.nix
	# import ./kexec-installer.nix {
	# extraConfig = {pkgs, ... } {
	# user.extraUsers.root.openssh.authorizedKeys.keys = [ "<your-key>" ];

	On why stateful code is bad
	===========================

	STUDENT: Sir, can I ask a question?
	TEACHER: Yes!
	STUDENT: How do you put an elephant inside a fridge?
	TEACHER: I don't know.
	STUDENT: It's easy, you just open the fridge and put it in. I have another question!
	TEACHER: Ok, ask.
	STUDENT: How to put a donkey inside the fridge?