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Start explaining exercises in types intro.

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2023-12-27 23:31:28 -08:00
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@ -6,6 +6,9 @@ series: "Everything I Know About Types"
draft: true draft: true
--- ---
{{< katex_component_js >}}
{{< bergamot_js_css >}}
I am in love with types and type systems. They are, quite probably, I am in love with types and type systems. They are, quite probably,
my favorite concept in the world. Most of us mere my favorite concept in the world. Most of us mere
mortals use types as a way to make sure we aren't writing mortals use types as a way to make sure we aren't writing
@ -141,3 +144,39 @@ understanding how to use a crate; check out the
[documentation page for `Vec`](https://doc.rust-lang.org/std/vec/struct.Vec.html), for instance. [documentation page for `Vec`](https://doc.rust-lang.org/std/vec/struct.Vec.html), for instance.
Documentation of Elm packages always lists functions' types (see [documentation for `Parser`](https://package.elm-lang.org/packages/elm/parser/latest/Parser), for example). Even C++ type signatures Documentation of Elm packages always lists functions' types (see [documentation for `Parser`](https://package.elm-lang.org/packages/elm/parser/latest/Parser), for example). Even C++ type signatures
listed by Doxygen can be quite useful; I, for one, got a lot out of the [LLVM documentation](https://llvm.org/doxygen/classllvm_1_1IRBuilderBase.html). listed by Doxygen can be quite useful; I, for one, got a lot out of the [LLVM documentation](https://llvm.org/doxygen/classllvm_1_1IRBuilderBase.html).
### Exercises, Bergamot and You
One of the reasons I love the [Software Foundations](https://softwarefoundations.cis.upenn.edu/)
series are the exercises. They are within the text, and they are machine-checked:
if you use a computer tool to work through the tasks, and verify that you did
them correctly. I hope to do something similar. Exercises will look something
like this:
{{< bergamot_exercise label="sample exercise" id="exercise-1" >}}
Here I tell you to do something that I believe would be instructive.
{{< /bergamot_exercise >}}
To achieve my ideal of interactive exercises, I developed a tool called Bergamot.
It's a tiny little programming language for writing _inference rules_, which are an invaluable tool
in a type theorist's toolbox. I introduced the tool in [a separate post on this
site]({{< relref "bergamot" >}}). Throughout this series, I'll be using Bergamot
for exercises and mild amounts of interactive content. This is completely optional:
My aim is to make everything I write self-contained and useful without various
tools. However, I think that having a way to interactively play with inference
rules is conducive to learning the concepts.
The unfortunate problem with making a tool for exercises is that you also need
to teach others how to use the tool. Some exercises will be more specific
to the tool than to type theory itself; I will denote these exercises as such where
possible. Also, whenever the context of the exercise can be loaded into
Bergamot, I will denote this with a play button.
{{< bergamot_preset name="intro-preset" prompt="PromptConverter @ prompt(type(?term, ?t)) <- input(?term);" >}}
TNumber @ type(lit(?n), number) <- num(?n);
TPlusI @ type(plus(?e_1, ?e_2), number) <-
type(?e_1, number), type(?e_2, number);
{{< /bergamot_preset >}}
{{< bergamot_exercise label="bergamot; sample exercise" preset="intro-preset" id="exercise-2" >}}
Try typing <code>1+1</code> into the input field!
{{< /bergamot_exercise >}}