Siddhataa: Automatic theorem prover based on equational reasoning

Abstract

Siddhata is an automatic theorem prover that can serve as a teaching aid for learning Dijkstra's philosophy of equational reasoning and proofs based on textual substitution [1]. Written in a dialect of the purely functional programming language Haskell, Siddhata implements a term rewriting system that uses a temporal rule-base to repeatedly rewrite a given proposition in an attempt to reduce it to the truth value T, thus proving the proposition. The functionality of Siddhata has been tested by automatically generating proofs for all the theorems in two Chapters of a textbook on discrete mathematics [2]. It has also been used as a teaching aid in a Master's degree course on the mathematical foundations of programming, with encouraging results.