From Reasonablypolymorphic · · 1m 30s
Arrows to Arrows, Categories to Queries
A programming language compiles to SQL using category theory.
In brief
A programming language compiles to SQL using category theory. Author created catlang, a programming language that compiles to SQL via category theory. Originally reported by Reasonablypolymorphic.
Catlang Compiles to SQL
Author created catlang, a programming language that compiles to one giant SQL SELECT statement.
“I’ve written a little programming language that compiles to sql”
Count Function Example
Count function returns 100 using arrow notation with loops and conditionals.
“count : Int -> Int”
Category Theory Basics
Category theory uses arrows and types without function application.
“We do not have the notion of function application”
Product and Coproduct
Product types use projections, coproducts use injections and branching.
“prj₁ :: (a, b) ~> a”
Stack-Based Compilation
Compiler eliminates variable names using stack-based representation.
“No variable names anywhere to be found”
Cochoice for Loops
Cochoice operation implements loops by recursively processing either values.
“cochoice :: ( Either a c ~> Either b c) -> (a ~> b)”
SQL Implementation
SQL implements category theory operations with nested queries and unions.
“Composition corresponds to a nested query”
Recursive CTE for Loops
Loops use recursive CTEs with clock timestamps to track iterations.
“clock_timestamp() as step”
Brainfuck in Postgres
Author plans to compile brainfuck to sql for postgres execution.
“Write a little brainfuck interpreter in catlang”
Haskell Inspiration
Catlang is inspired by haskell's arrow syntax and category theory.
“Source language of catlang is heavily inspired by haskell's arrow syntax”
Compiler Backend
Compiler backend uses stack representation for efficient sql generation.
“No compiler backend needs to deal with names”
Future Plans
Author plans to add string-crunching primitives for brainfuck interpreter.
“Compiler still needs a few string-crunching primitives”
GitHub Repository
Code available on github with template-thaskell backend for haskell.
“All of the code is available on github”
Category Theory Background
Category theory underpins programming language design and compilation.
“Lambda calculus corresponds to cartesian-closed categories”
Compiler Limitations
Compiler has limitations in handling complex data structures and loops.
“Cochoice is the only really tricky thing”
Next Steps
Author will focus on improving compiler and adding new features.
“I’ve run out of vacation time to work on this project”
Here's the gist
Author created catlang, a programming language that compiles to SQL via category theory.
