Computational Logic: Its Origins and Applications

TL;DR

Computational Logic, originating from 19th-century mathematical reasoning, now encompasses diverse formalisms and techniques, primarily used for verifying hardware, software, and mathematical correctness with increasing automation and flexibility.

Contribution

The paper reviews the historical development, core formalisms, and modern applications of computational logic, highlighting the evolution from LCF to Isabelle and their impact.

Findings

LCF approach enables interactive proof construction without compromising correctness

Isabelle offers flexible formalism choice and enhanced automation

Applications extend from hardware/software verification to mathematical proofs

Abstract

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-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 "LCF approach" pioneered by Robin Milner FRS, 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.