Writing Prettier Haskell with Unicode Syntax and Vim

Re:Writing Prettier Haskell with Unicode Syntax and Vim by jandrese on Thursday June 22, 2023 @05:41PM (#36439453)

IMHO the mathematical language is an impediment for learning math for exactly this reason. It's chock full of cryptic symbols with no obvious meaning that make it incomprehensible to anyone who has not taken years to learn it and also surprisingly difficult to enter into a computer. Math is hard to read because quill pens were difficult to use and much of the syntax was made up on the spot by people who were better at thinking mathematically than communicating ideas. But so many people have spent the effort to learn it that nobody wants to create a "dumbed down" version that a layman might understand.

It is kind of like everyone in the 60s decided that APL was the one true computer language and all interest in other languages died off entirely and when anybody complains about the syntax they are told that they just need to go to school for 4 years and they'll appreciate the beauty.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by xchkr1337 on Thursday June 22, 2023 @05:59PM (#36439673)

If you open any reasonable math textbook (except for maybe logic related ones), chances are, you won't see the ∀ symbol anywhere at all. It's often considered bad taste to write a symbol like this when you can just write "for all". The main obstacle in learning math comes from not understanding the background material enough and basically never from not understanding the notation.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by skydhash on Thursday June 22, 2023 @06:17PM (#36439915)

And the notation are introduced to you gradually. Even books that do not have a chapter on the notation used, will have a reference page. If not, you’re not reading introductory material and some background is assumed.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by marssaxman on Friday June 23, 2023 @09:09AM (#36446345)

How would the notation be "introduced to you" at all, when reading source code? What book would there be? How would you know how to find it?

This is a serious drawback to the traditional math notation: if you didn't come up along one specific educational pathway, it seems to be effectively impossible to work your way in and figure out what any of it means. You can't pronounce any of it, you can't look it up; even if you can work out the names of the symbols, they often mean different things in different contexts. It is a mess.

For many years now, the way I have ingested CS papers is to read the introduction closely, getting my head around the concept, then bail out once the inscrutable symbols show up and go find an actual implementation in some real, documented, parseable programming language - any one will do - from which I can readily infer what the rest of the paper was supposed to mean.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by todd8 on Friday June 23, 2023 @09:36AM (#36446657)

Perhaps this is true for some texts, but take a look at math journals where mathematicians are writing for other mathematicians within their own field. They reuse symbols, sometime an integral symbol is for Riemann integration and sometimes it's for Lebesgue integration. The subject of the paper will make it clear which is which.

Even in our own field, Computer Science, there are too many confusing cases: Knuth uses |S| to mean the cardinality of set S, |f| to be the number of solutions when f is a boolean, |x| to be the absolute value of x, |z| to be the absolute value of a complex number, and |a| to be the length of a. All within the same book, TAOCP vol 4A Part 1.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by jlokier on Friday June 23, 2023 @12:17PM (#36448952)

Those notations are well-known standard notation for the same general concept, "the size of".

What "the size of" means is different applied to each type of object, and may have to be defined to explain some of them (esp. |f|), but it's common in math that general concepts apply differently to different things, while having some properties in common.

I think the notation is helpful rather than confusing because "the size of" carries with it some intuitive connotations which are common to each of those examples.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by agentultra on Thursday June 22, 2023 @07:13PM (#36440517)

You can go back and read maths texts from before algebra was in common use. Before people had these symbols they had to write out their proofs and derivations using the plain language of their day.

tldr; it’s tedious reading those proofs. And it’s laborious to write them. Such labour limits the thoughts one can have. Once algebra has solidified there was an explosion in the pace and depth of mathematics.

The symbols are there for a good reason.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by jandrese on Thursday June 22, 2023 @11:20PM (#36442397)

Yeah, but reading novels from those days is also tedious. Doesn't mean they can't be improved.

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Re:Writing Prettier Haskell with Unicode Syntax and Vim by Skeime on Friday June 23, 2023 @02:43AM (#36443619)

Sure: And the best way we have found (maybe just so far?) has been to introduce more symbolism. But even today, all guides on good mathematical writing urge you not to go overboard with them; a well-written mathematical text is a reasonable mixture of symbols and prose.

In fact, it’s pretty common for math students to want to use only symbols at some point. What they write becomes unintelligible to everyone else (and maybe even themselves) and at some point they (usually) wise up.

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