Automated Reasoning - Proof Systems

Proof Systems

Boyer-Moore Theorem Prover (NQTHM)
The design of this system was influenced by John McCarthy and Woody Bledsoe. Started in 1971 at Edinburgh, Scotland, this was a fully automatic theorem prover built using Pure Lisp. The main aspects of NQTHM were:

1. the use of Lisp as a working logic.

2. the reliance on a principle of definition for total recursive functions.

3. the extensive use of rewriting and "symbolic evaluation".

4. an induction heuristic based the failure of symbolic evaluation.

HOL Light
Written in Objective CAML, HOL Light is designed to have a simple and clean logical foundation and an uncluttered implementation. It is essentially another proof assistant for classical higher order logic.

Coq
Developed in France, Coq is another automated proof assistant, which can automatically extract executable programs from specifications, as either Objective CAML or Haskell source code. Properties, programs and proofs are formalized in the same language called the Calculus of Inductive Constructions (CIC).