nLab HOL




HOL (short for higher-order logic) is a kind of simply typed lambda calculus. There are various proof assistants that implement this language. The most known one is Isabelle, that has HOL or Isabelle/HOL as its main application.

Other proof assistants of this kind are HOL4, HOL Light, HOL Zero, and ProofPower.

proof assistants:

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:

based on simplicial type theory:

For monoidal category theory:

For higher category theory:

projects for formalization of mathematics with proof assistants:

Other proof assistants

Historical projects that died out:


  • T. Nipkow, L. Paulson, M. Wenzel. Isabelle/HOL — A Proof Assistant for Higher-Order Logic, Springer (2002)

  • Wikipedia, HOL (proof assistant)

  • Florian Rabe and Mihnea Iancu, A Formalized Set-Theoretical Semantics of Isabelle/HOL (pdf)

  • M. J. C. Gordon and T. F. Melham (editors), Introduction to HOL: A Theorem Proving Environment for Higher Order Logic, 1993

Last revised on September 12, 2019 at 07:00:05. See the history of this page for a list of all contributions to it.