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
A dependently typed functional programming language with applications to certified programming. It is also used as a proof assistant.
Besides Coq, Agda is one of the languages in which homotopy type theory has been implementsed (Brunerie). Agda can be compiled to Haskell, Epic or Javascript.
General information on Agda is at
Ulf Norell, James Chapman, Dependently Typed Programming in Agda (pdf)
Dan Licata, Ian Voysey, Programming and proving in Agda
Ulf Norell, Towards a practical programming language based on dependent type theory, 2007 (pdf)
A tutorial for use of Agda as an implementation of homotopy type theory is at
Guillaume Brunerie, Agda for homotopy type theory (web)
Guillaume Brunerie, The Agda proof assistant, slides, pdf