Viewing profile — matt-noonan

This is really a non-issue in practice. In the olden days, you’d just make the change and then spend a pleasant hour or two fixing the callsites by responding to compiler errors in…

As somebody who has helped hire many Haskell devs, I can say that lots of Haskell experience isn't always a positive. We have to filter carefully to make sure that we end up with d…

This is particularly funny because arXiv doesn't just predate Web 2.0, it nearly predates the public web entirely (only missing it by about two weeks)

I just realized I botched the description of Brzozowski's algorithm, step (b) should be "determinize the NFA using the powerset construction". Mea culpa.

There is a very useful perspective in which categories are just typed monoids, and the monoid operation can only be applied when the types "line up". For example, here are some use…

Yes, there are a number of them. Here are some examples off the top of my head: - Moggi was studying the problem of equivalence of programs, and noted that the traditional approach…

That is definitely not what Galois Fields are about.

No, it's quite different. A super rough but somewhat accurate starting point is to think of a lens as being like the `.foo.bar.baz` in `myobject.foo.bar.baz`: a way to describe som…

A common failure mode is for people to think Haskell is some special snowflake that requires reading 50 books and papers to understand. It doesn’t. Learning by doing is definitely …

There are some interesting solutions out there, such as bit-banding used in some ARM Cortex CPUs. This maps entire bytes in the high part of the address space to single bits in the…

It's almost correct, but misses the point in an annoying way that kind of ruins the example. What does work is something like the subset of the plane given by { (x, y) | x real, y …

It gives a set-theoretic bijection, but not one that plays by all the rules I mentioned above. In particular, you don't get a bijection that corresponds to a finite, non-looping pr…

It's definitely surprising, for a couple of reasons: 1. It isn't just the uninteresting result that the set of trees has the same cardinality as the set of 7-tuples of trees; the b…

Here are a few off the top of my head, as a mathematician-turned-programmer who never has been an algebraic geometer. - Elliptic curve cryptography ( https://en.wikipedia.org/wiki/…

Another vote here for the matrixanalysis.com book. It is a really excellent book and takes a reasonably pragmatic approach to linear algebra. Coming from a programming background, …

Yes, I meant that equation to be interpreted in the GA used in the article. But essentially all geometric algebras also have zero divisors, for similar reasons.

> it is deficient in various ways when compared to [...] differential forms (e.g. if you want to work basis-free) There is nothing basis-dependent in Geometric Algebra. This presen…

No, this is wrong. Geometric algebras aren't division algebras in general: they usually have zero divisors. Objects that live in a single grade are invertible, but composite object…

A more accurate translation to food would be something like “does it feel weird to call a physical plate of spaghetti a recipe?”

Inside the model, “the reals are uncountable” means you have two sets R and N, and there is no surjective function from N onto R. That function would be a set as well; a certain su…

I learned it originally from Jim Henle, and iirc he had a textbook on the hyperreals (“Infinitessimal Analysis”, possibly?) This honors project has what looks like an accurate writ…

Although the original statement about “infinitesimals being functions that vanish at 0” was stated with confidence, it is wrong. The usual construction of the hyperreals replaces r…

The principle was certainly known, but I think Alexis really does deserve the credit for the catchy "parse, don't validate" wording. A Google search for that phrase, restricted to …

This is exactly right. The relevant quote from the article is this: > The reason we care about Church-encoding is because not all programming languages natively support sum types o…