Arrows to Arrows, Categories to Queries
Quick read
A blog post describing catlang, a small programming language whose compiler desugars programs into a categorical intermediate language and emits a single SQL SELECT that executes the program. The author explains how arrows, products, coproducts, and a stack-based nameless IL make it easy to target unusual backends like Postgres SQL.
- Shows an example program compiled into a looping SQL query
- Explains arrow-based IL operations and their algebraic meanings
- Describes desugaring to a nameless stack representation
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A closer look at Arrows to Arrows, Categories to Queries
catlang: a programming language that compiles to SQL
This post describes catlang, a programming language whose compiler emits a single large SELECT statement. Running that query in Postgres returns the program output; the author demonstrates a program that returns 100 by actually looping in SQL. The language is presented as a programming language (not a new query language) whose intermediary representation is built from category-theory-inspired primitives.
what you can do on the page
The page walks through an example program (a count function) and its desugaring into an intermediate language (IL) made of categorical operators. It shows the IL, explains symbols like A ⨟ B (compose and pipe results), △ (fork to build pairs), ▽ (join for coproducts/branching), and discusses how loops desugar into category-theory primitives such as cochoice. It also links the IL to a generated SQL example and explains that the generated SQL can be run in Postgres to observe the behavior.
who will find this useful
People interested in category theory applied to programming, those curious about unconventional compilation targets (compiling programs to SQL), and readers with a Haskell or functional-programming background will get the most from the post. The writeup focuses on how desugaring removes variable names, represents values as a stack of projections, and why that makes retargeting to domains without naming natural (the author gives the example of routing bit ribbons in electronic circuits).
Questions people ask about Arrows to Arrows, Categories to Queries
- Does the post show the generated SQL?
- Yes - the author says you can take a peek at the generated SQL and that running it in Postgres 17 returns the expected result.
- Is catlang introduced as a new query language?
- No - the author explicitly calls catlang a programming language whose compiler spits out a single SELECT statement, not a new query language.
- Do I need to know category theory to follow the post?
- Familiarity with Haskell or basic category-theory concepts will help, since the exposition uses arrows, coproducts, products, and composition, but the author also explains the primitives and the desugaring process.
Arrows to Arrows, Categories to Queries was shared on NexURLs by Nexis on November 5, 2026, in Learning & Books.
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What is Arrows to Arrows, Categories to Queries?
Arrows to Arrows, Categories to Queries (reasonablypolymorphic.com): A blog post describing catlang, a small programming language whose compiler desugars programs into a categorical intermediate language and emits a single SQL SELECT that executes the program. The author explains how arrows, products, coproducts, and a stack-based nameless IL make it easy to target...
Who shared Arrows to Arrows, Categories to Queries on NexURLs?
It was shared by Nexis in November 2026. Every link on NexURLs is shared by a real member and passes a safety check before it goes out.
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