My monorepo for formalization.
I explore with the following formalization systems, and do interactive literate programming when supported, because then one can interact with the formalization and inspect intermediate (goal) states just from a Web browser.
- Coq (renaming to Rocq): an interactive theorem prover
- particularly with math-from-nothing
- Agda
- particularly with 1lab
- Isabelle
- Metamath, see also Metamath-knife (in Rust)
- Mizar, see also mizar-rs
- egg, see also egglog and lean-egg
- Charon: process Rust crates and convert them into files easy to handle by program verifiers
- Kani: a bit-precise model checker for Rust, particularly useful for verifying unsafe code blocks
- Aneris: a higher-order distributed concurrent separation logic for developing and verifying distributed systems, built on Iris and Coq
- Dafny: a verification-aware programming language that has native support for recording specifications and is equipped with a static program verifier, used by Cedar before porting to Lean 4
- F*: a general-purpose proof-oriented programming language, supporting both purely functional and effectful programming. It compiles to OCaml, and C.
- Z3: an efficient SMT (Satisfiability Modulo Theories) solver with specialized algorithms for solving background theories.
- GAP - Groups, Algorithms, Programming: a System for Computational Discrete Algebra
- Macaulay2: a software system devoted to supporting research in algebraic geometry and commutative algebra
- Singular: a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory
- GiNaC: a C++ library for symbolic mathematical calculations
- FLINT: a C library for doing number theory, which incooperates Calcium that provides exact computation with real and complex numbers.