More Agda Tips

Posted on March 14, 2019

Literate Agda

For including Agda code in LaTeX files, Agda’s built-in literate programming support is a great tool. It typesets code well, and ensures that it typechecks which can help avoid typos.

Embedding Agda Code in LaTeX

I write the LaTeX document in one file, and the Agda code in another .lagda file. Using the catchfilebetweentags LaTeX package, I can then embed snippets of the Agda code into the LaTeX document. For instance, in a file named Lists.lagda I can have the following:

% \ begin { code } begincode : List A → Maybe A headList AMaybe A \ end { code } endcode % \ begin { code } begincode = nothing head []nothing ( x ∷ xs ) = just x headx ∷ xsjust x \ end { code } endcode

Then, after compiling the Agda file with agda --latex --output-dir=. Lists.lagda , I can embed the snippet head : List A → Maybe A into the TeX file like so:

Dealing with Unicode

Most Agda source code will be Unicode-heavy, which doesn’t work well in LaTeX. There are a few different ways to deal with this: you could use XeTeX, which handles Unicode better, for instance. I found it easier to use the ucs package, and write a declaration for each Unicode character as I came across it. For the ∷ character above, for instance, you can write:

\usepackage { ucs } \DeclareUnicodeCharacter {8759}{ \ensuremath{ \squaredots } } {8759}{

Live Reloading

For plain LaTeX code, I use Spacemacs and Skim to get live reloading. When I save the LaTeX source code, the Skim window refreshes and jumps to the point my editing cursor is at. I use elisp code from this blog post.

For Agda code, live reloading gets a little trickier. If I edit an Agda source file, the LaTeX won’t automatically recompile it. However, based on this stack exchange answer, you can put the following .latexmkrc file in the same directory as your .lagda files and your .tex file:

' lagda ' , ' tex ' , 0 , ' lagda2tex ' ); add_cus_dep(); sub lagda2tex { my $base = shift @_ ; return system ( ' agda ' , ' --latex ' , ' --latex-dir=. ' , " $base .lagda " ); ); }

This will recompile the literate Agda files whenever they’re changed. Unfortunately, it doesn’t automate it the first time you do it: it needs to see the .tex files to see the dependency. You can fix this yourself, by running agda --latex --output-dir=. when you add a new .lagda file (just once, after that the automation will take over), or you can use a script like the following:

#!/bin/bash find . -type f -name '*.lagda' | while read -r code ; do . -type f -name-r dir=$( dirname " $code " ) file=$( basename " $code " .lagda ) .tex .lagda.tex if [ ! -e " $dir / $file " ] then agda --latex --latex-dir=. " $code " --latex --latex-dir=. fi done

This will compile any .lagda file it finds that doesn’t have a corresponding .tex file (so it won’t slow things down). Then call that script on the first line of your .latexmkrc , like so:

system ( " bash ./init-missing-lagda.sh " ); ); ' lagda ' , ' tex ' , 0 , ' lagda2tex ' ); add_cus_dep(); sub lagda2tex { my $base = shift @_ ; return system ( ' agda ' , ' --latex ' , ' --latex-dir=. ' , " $base .lagda " ); ); }

Flags for Debugging

There are a number of undocumented flags you can pass to Agda which are absolutely invaluable when it comes to debugging. One of them can tell you more about termination checking, another reports on type checking ( tc ), another for profiling ( profile ), and so on. Set the verbosity level ( agda -v 100 ) to get more or less info.

Type Checking Order

Agda does type checking from left to right. This isn’t always desired: as an example, if we want to annotate a value with its type, we can use the following function:

: ∀ { a } ( A : Set a ) → A → A the _ x = x the : _ example = the ℕ 3 examplethe ℕ

Coming from Haskell, though, this is the wrong way around. We usually prefer to write something like 3 :: Int . We can’t write that as a simple function in Agda, though, so we instead use a syntax declaration:

syntax the ty x = x ∷ ty the ty xx ∷ ty : _ example = 3 ∷ ℕ example∷ ℕ

Changing the order of type checking can also speed up typechecking in some cases. There’s more information about syntax declarations in Agda’s documentation.