Introduction to Pylog

Abstract: PyLog is a minimal experimental proof assistant based on linearised natural deduction for intuitionistic and classical first-order logic extended with a comprehension operator. PyLog is interesting as a tool to be used in conjunction with other more complex proof assistants and formal mathematics projects (such as Coq and Coq-based projects). Proof assistants based on dependent type theory are at once very different and profoundly connected to the one employed by Pylog via the Curry-Howard correspondence. The Tactic system of Coq presents us with a top-down approach to proofs (finding a term inhabiting a given type via backtracking the rules, typability and type-inference being automated) whilst the classical approach of Pylog follows how mathematical proofs are usually written. Pylog should be further developed along the lines of Coq in particular through the introduction of many "micro-automatisations" and a nice IDE.