matt-noonan

5 ms·

1.
by matt-noonan 5mo ago
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 a pretty low-thought, mechanistic way. Nowadays you can out
2.
by matt-noonan 5mo ago
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 developers who want to build real things, not developers
3.
by matt-noonan 7mo ago
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)
4.
by matt-noonan 2y ago
I just realized I botched the description of Brzozowski's algorithm, step (b) should be "determinize the NFA using the powerset construction". Mea culpa.
5.
by matt-noonan 2y ago
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 useful operations which do not form a monoid: - PUSH(
6.
by matt-noonan 2y ago
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 to modeling a program as a total function Input -> Outpu
7.
by matt-noonan 2y ago
That is definitely not what Galois Fields are about.
8.
by matt-noonan 2y ago
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 some "location" inside of a data structure, in a
9.
by matt-noonan 2y ago
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 the way to go. LYAH is fine but not great at practical probl
10.
by matt-noonan 2y ago
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 low part of the address space, so that you can make an at
11.
by matt-noonan 3y ago
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 rational } U { (0, y) | y real }. This is connected, be
12.
by matt-noonan 4y ago
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 program. Generally speaking, Cantor–Schröder–Bernstein do
13.
by matt-noonan 4y ago
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 bijection here is given by a finite, non-looping pr
14.
by matt-noonan 4y ago
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/Elliptic-curve_cryptography ) - Grobner
15.
by matt-noonan 4y ago
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, you're more likely to find some things that resonate wi
16.
by matt-noonan 5y ago
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.
17.
by matt-noonan 5y ago
> 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 presentation started from a basis, but then again so do many pr
18.
by matt-noonan 5y ago
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 objects don't always have multiplicative inverses. As a
19.
by matt-noonan 5y ago
A more accurate translation to food would be something like “does it feel weird to call a physical plate of spaghetti a recipe?”
20.
by matt-noonan 5y ago
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 subset F of NxR, say. But even if we can externally enumerate
21.
by matt-noonan 5y ago
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 write up of the construction along with proofs of some of the ma
22.
by matt-noonan 5y ago
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 real numbers with sequences of real numbers, and also introdu
23.
by matt-noonan 5y ago
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 October 2019 and earlier, has no results (o
24.
by matt-noonan 6y ago
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 or recursion (although most programming languages support
25.
by matt-noonan 6y ago
This is good advice. It seems like many people get stuck in a rut of thinking they need to study, study, study before they will be productive. That's backwards. Start building things right away; you'll immediately perceive what yo
26.
by matt-noonan 6y ago
The point is really that lenses are values that represent locations in a data structure. And, as values, they can be combined, transformed, serialized, etc etc. Imagine having a type that represents a chain of method selectors, and that g
27.
by matt-noonan 6y ago
I'm pretty sure you're reading this line wrong (though I don't blame you; the wording could probably be improved here). But I believe what the author is saying is "you can use these techniques in any language, but if you
28.
by matt-noonan 6y ago
Just to be totally explicit here, there are no FP languages that require learning category theory. There is no reason to conflate [a small subset of] research on programming languages with the practice of using those languages day-to-day
29.
by matt-noonan 7y ago
David Kelly [1] once told me that as a grad student at Princeton, he somehow managed to get the Sunday New York Times delivered to him late Saturday night. He'd stay up all night solving the crossword puzzle, then dazzle everybody who
30.
by matt-noonan 7y ago
And the only reason the language pragma is deprecated is because TypeInType is now just how things are, by default, with no opt-out.

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