ProofPeer - A Cloud-based Interactive Theorem Proving System

Probably the most popular ITP systems these days are Isabelle [4a] and Coq [5]. Isabelle is a descendant of Edinburgh LCF. Its declarative extension Isabelle/Isar [4b] has been heavily influenced by Mizar. Coq can be viewed as a descendant of the Automath system in that both systems are based on the Curry-Howard correspondence [6] (a proof is a program, the formula it proves is a type for the program). Coq is implemented in OCaml [7], which is a dialect of Standard ML [8] which is one of the results of the Edinburgh LCF project, therefore Coq has been heavily influenced by Edinburgh LCF as well. Recently Coq has also gained declarative features similar to those found in Mizar and Isabelle/Isar. Another ITP system is HOL-light, another Edinburgh LCF system which has a small and actually formally verified kernel [17].