Editing Type theory (section)

===Proof assistants===
{{main|Proof assistant}}
Much of the current research into type theory is driven by [[Automated proof checking|proof checkers]], interactive [[proof assistant]]s, and [[Automated theorem proving|automated theorem provers]]. Most of these systems use a type theory as the mathematical foundation for encoding proofs, which is not surprising, given the close connection between type theory and programming languages:
* [[Logical framework|LF]] is used by [[Twelf]], often to define other type theories;
* many type theories which fall under [[higher-order logic]] are used by the [[HOL (proof assistant)|HOL family of provers]] and [[Prototype Verification System|PVS]];
* computational type theory is used by [[NuPRL]];
* [[calculus of constructions]] and its derivatives are used by [[Rocq (software)|Rocq]] (previously known as ''Coq''), [[Matita]], and [[Lean (proof assistant)|Lean]];
* UTT (Luo's Unified Theory of dependent Types) is used by [[Agda (programming language)|Agda]] which is both a programming language and proof assistant

Many type theories are supported by [[LEGO (proof assistant)|LEGO]] and [[Isabelle (proof assistant)|Isabelle]]. Isabelle also supports foundations besides type theories, such as [[Zermelo–Fraenkel set theory|ZFC]]. [[Mizar system|Mizar]] is an example of a proof system that only supports set theory.