Computational logic: its origins and applications

Abstract

Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

Formalising Mathematics – in Praxis; A Mathematician’s First Experiences with Isabelle/HOL and the Why and How of Getting Started

“…I will not elaborate further on a general discussion about this topic -I rather restrict to mentioning the inspiring papers by Avigad [3], Paulson [50], Lamport [42], Barendregt and Wiedijk [4] and the classical QED Manifesto from the mid-90's [6].…”

TPL: A Trust Policy Language

“…One could argue that this is not necessary since RP x is formally verified, however, one should, as e.g. Paulson [15] recently pointed out, not see formal verification as a replacement for testing. Indeed we have run RP x on a number of encoded triples but more systematic testing would be needed to ensure a production quality certifier.…”

Michael John Caldwell Gordon. 28 February 1948—22 August 2017

“…Additional information on the history of this period has been written by Mike himself (22, 32) and by his colleagues (Harrison et al 2014;Paulson 2018).…”