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Moved the bergamot article to new math delimiters

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-05-13 18:52:21 -07:00
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@ -36,9 +36,9 @@ but whenever I read a paper, my eyes search for the rules first and foremost.
But to those just starting their PL journey, inference rules can be quite cryptic But to those just starting their PL journey, inference rules can be quite cryptic
-- I know they were to me! The first level of difficulty are the symbols: we have -- I know they were to me! The first level of difficulty are the symbols: we have
lots of Greek (\\(\\Gamma\\) and \\(\\Delta\\) for environments, \\(\\tau\\) and perhaps \\(\\sigma\\) lots of Greek (\(\Gamma\) and \(\Delta\) for environments, \(\tau\) and perhaps \(\sigma\)
for types), and the occasional mathematical symbol (the "entails" symbol \\(\\vdash\\) is the most for types), and the occasional mathematical symbol (the "entails" symbol \(\vdash\) is the most
common, but for operational semantics we can have \\(\\leadsto\\) and \\(\\Downarrow\\)). common, but for operational semantics we can have \(\leadsto\) and \(\Downarrow\)).
If you don't know what they mean, or if you're still getting used to them, symbols If you don't know what they mean, or if you're still getting used to them, symbols
in judgements are difficult enough to parse. in judgements are difficult enough to parse.
@ -49,8 +49,8 @@ Inductive Constructions is a doozy, for instance.
{{< figure src="CIC.png" caption="The `match` inference rule from [Introduction to the Calculus of Inductive Constructions](https://inria.hal.science/hal-01094195/document) by Christine Paulin-Mohring" class="fullwide" >}} {{< figure src="CIC.png" caption="The `match` inference rule from [Introduction to the Calculus of Inductive Constructions](https://inria.hal.science/hal-01094195/document) by Christine Paulin-Mohring" class="fullwide" >}}
Just look at the metavariables! We have \\(\\textit{pars}\\), \\(t_1\\) through \\(t_p\\), Just look at the metavariables! We have \(\textit{pars}\), \(t_1\) through \(t_p\),
\\(x_1\\) through \\(x_n\\), plain \\(x\\), and at least two other sets of variables. Not \(x_1\) through \(x_n\), plain \(x\), and at least two other sets of variables. Not
only this, but the rule requires at least some familiarity with [GADTs](https://en.wikipedia.org/wiki/Generalized_algebraic_data_type) to understand only this, but the rule requires at least some familiarity with [GADTs](https://en.wikipedia.org/wiki/Generalized_algebraic_data_type) to understand
completely. completely.
@ -85,8 +85,8 @@ Let me show you both, and try to explain the two. First, here's the wrong way:
{{< /latex >}} {{< /latex >}}
This says that the type of adding two _variables_ of type `string` is still `string`. This says that the type of adding two _variables_ of type `string` is still `string`.
Here, \\(\\Gamma\\) is a _context_, which keeps track of which variable has what Here, \(\Gamma\) is a _context_, which keeps track of which variable has what
type. Writing \\(x : \\text{string} \\in \\Gamma\\) is the same as saying type. Writing \(x : \text{string} \in \Gamma\) is the same as saying
"we know the variable `x` has type `string`". The whole rule reads, "we know the variable `x` has type `string`". The whole rule reads,
> If the variables `x` and `y` both have type `string`, > If the variables `x` and `y` both have type `string`,
@ -301,8 +301,8 @@ expression is rendered__. For one, this is a losing battle: we can't possibly
keep up with all the notation that people use in PL literature, and even if keep up with all the notation that people use in PL literature, and even if
we focused ourselves on only "beginner" notation, there wouldn't be one way to do it! we focused ourselves on only "beginner" notation, there wouldn't be one way to do it!
Different PL papers and texts use slightly different variations of notation. Different PL papers and texts use slightly different variations of notation.
For instance, I render my pairs as \\((a, b)\\), but the very first screenshot For instance, I render my pairs as \((a, b)\), but the very first screenshot
in this post demonstrates a PL paper that writes pairs as \\(\\langle a, b \\rangle\\). in this post demonstrates a PL paper that writes pairs as \(\langle a, b \rangle\).
Neither way (as far as I know!) is right or wrong. But if we hardcode one, Neither way (as far as I know!) is right or wrong. But if we hardcode one,
we lose the ability to draw the other. we lose the ability to draw the other.