Top 42 type-theory open source projects

The People's Refinement Logic

"Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory

Homepage Theorem Proving in Lean FAQ

Lecture notes on univalent foundations of mathematics with Agda

A Super Kawaii Dependently Typed Programming Language

A selection of formal proofs in Coq.

List of resources about foundational knowledge for programmers (supposed to last a few decades)

A modern proof language

Agda is a dependently typed programming language / interactive theorem prover.

A SuperCompiler for Martin-Löf's Type Theory

😎TT

Formalising Type Theory in a modular way for translations between type theories

A collection of papers on modules.

Normalization by evaluation for Martin-Löf Type Theory with dependent records

(WIP) Dependently-typed programming language with Agda style dependent pattern matching

Towards changing things and see if it proofs

Homotopy type theory

A friendly little systems language with first-class types. Very WIP! 🚧 🚧 🚧

λΠ Programming Language Theory

Experimental implementation of Cubical Type Theory

Programming language agnostic type construction language based on polynomials.

Research on integrating datalog & lambda calculus via monotonicity types

Building a modern functional compiler from first principles. (http://dev.stephendiehl.com/fun/)

Fine-grain implementations of common lambda calculi in Haskell, tested with QuickCheck

Exercises from Benjamin Pierce's "Types and Programming Languages" textbook + extras!

Lecture note on Lambda Calculus and Types for FLOLAC

The MLPolyR programming language, revived

An experimental implementation of homotopy type theory in the interactive proof assistant Isabelle

Variant types in TypeScript

A research project in path semantics, a re-interpretation of functions for expressing mathematics

Cicada Language

Type Theory in Type Theory using Cubical Agda

Homotopy Type Theory proofs in Idris

Logical manifestations of topological concepts, and other things. This version adopts the univalent point of view.

A categorical semantics library in Agda.

Univalent mathematics in Agda

SHAPE/S∀F∃: static prover/type-checker for N-D array programming in Scala, a use case of intuitionistic type theory

Dependently-typed row-polymorphic programming language, evolved from minitt-rs

Dependently-typed lambda calculus, Mini-TT, extended and implemented in Rust

Book: Gentle Introduction to Dependent Types with Idris

Reading schedule and our library of pdfs

My undergradate thesis on coinductive types in univalent type theory