constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
Arend is a proof assistant system for homotopy type theory with native support for higher inductive types and some cubical type theory.
based on plain type theory/set theory:
based on dependent type theory/homotopy type theory:
based on cubical type theory:
based on modal type theory:
For monoidal category theory:
projects for formalization of mathematics with proof assistants:
Archive of Formal Proofs (using Isabelle)
ForMath project (using Coq)
UniMath project (using Coq and Agda)
Xena project (using Lean)
Other proof assistants
Historical projects that died out:
Created on September 12, 2019 at 02:48:21. See the history of this page for a list of all contributions to it.