Rudi Grinberg rgrinberg

A quadratic space is a real vector space V with a quadratic form Q(x), e.g. V = R^n with Q as the squared length. The Clifford algebra Cl(V) of a quadratic space is the associative algebra that contains V and satisfies x^2 = Q(x) for all x in V. We're imposing by fiat that the square of a vector should be the quadratic form's value and seeing where it takes us. Treat x^2 = Q(x) as a symbolic rewriting rule that lets you replace x^2 or x x with Q(x) and vice versa whenever x is a vector. Beyond that Cl(V) satisfies the standard axioms of an algebra: it lets you multiply by scalars, it's associative and distributive, but not necessarily commutative.

Remarkably, this is all you need to derive everything about Clifford algebras.

Let me show you how easy it is to bootstrap the theory from nothing.

We know Cl(V) contains a copy of V. Since x^2 = Q(x) for all x, it must also contain a copy of some nonnegative reals.

A couple months ago, I had an idea for a monad transformer, and sunk a good deal of time into figuring out how to make it work. I started getting it ready for Hackage before I realized I didn't have an immediate use case for it, and so I didn't have a good sense for what sensible defaults would be. I put the project aside to work on other things and let my brain churn on it.

What I'm going to do here is describe the idea and some implementation notes to get a sense of how useful it'd be as a package, so I know whether it's worth my time.

This blog post series has moved here.

You might also be interested in the 2016 version.

Give me back my sanity

One of the many things I do for my group at work is to take care of automating as many things as possible. It usually brings me a lot of satisfaction, mostly because I get a kick out of making people's lives easier.

But sometimes, maybe too often, I end up in drawn-out struggles with machines and programs. And sometimes, these struggles bring me to the edge of despair, so much so that I regularly consider living on a computer-less island growing vegetables for a living.

This is the story of how I had to install Pandoc in a CentOS 6 Docker container. But more generally, this is the story of how I think computing is inherently broken, how programmers (myself included) tend to think that their way is the way, how we're ultimately replicating what most of us think is wrong with society, building upon layers and layers of (best-case scenario) obscure and/or weak foundations.

*I would like to extend my gratitude to Google, StackOverflow, GitHub issues but mostly, the people who make the

The introduction to Reactive Programming you've been missing

(by @andrestaltz)

This tutorial as a series of videos

If you prefer to watch video tutorials with live-coding, then check out this series I recorded with the same contents as in this article: Egghead.io - Introduction to Reactive Programming.

Caml-inspect symbolizer

Symbolizes closure blocks. Works only on native executables.

Build

ocamlfind ocamlopt -syntax camlp4o -package lwt -package lwt.syntax -package lwt.unix str.cmxa -linkpkg symbolizer.ml -o symbolizer
ocamlfind ocamlopt -package inspect -linkpkg foo.ml -o foo

	(* An initial attempt at universal algebra in Coq.
	Author: Andrej Bauer <[email protected]>

	If someone knows of a less painful way of doing this, please let me know.

	We would like to define the notion of an algebra with given operations satisfying given
	equations. For example, a group has of three operations (unit, multiplication, inverse)
	and five equations (associativity, unit left, unit right, inverse left, inverse right).
	*)

	public static Observable<List<String>> paginatedThings(final Observable<Void> onNextObservable) {
	return Observable.create(new Observable.OnSubscribe<List<String>>() {
	@Override
	public void call(final Subscriber<? super List<String>> subscriber) {

	onNextObservable.subscribe(new Observer<Void>() {
	int latestPage = -1;
	@Override
	public void onCompleted() {
	subscriber.onCompleted();

	(* Database provides key-generation and table-instantiation,
	* so that a key can be associated to various properties.
	*)

	(* This is for a fully-controlled specification...
	*
	* module Db = Database.Make (Database.IntKey)
	* module Prop = Db.MultiInherit
	* module PropHash = Prop.Table(Database.Hash)
	* module Size = (val PropHash.create ~default:0 () : Db.Sig with type t = int)