🤖 AI Summary
This study addresses the longstanding absence of unified formal verification support for Turing machines and the lambda calculus, two foundational pillars of computation theory. Leveraging the Dafny programming language, this work presents the first unified formal modeling of both classical computational models and employs automated theorem proving techniques to resolve core theoretical problems. Specifically, the research successfully achieves termination proofs for Turing machines, mechanized verification of Church encoding, and a rigorous machine-checked proof of the Church-Rosser theorem. By bridging the gap between computational models and program verification, this work establishes a novel paradigm for the mechanized verification of classical computation theory.
📝 Abstract
We describe the formalization in Dafny of two computational models, Turing Machines and the Lambda Calculus. We present several application of the formalizations: machine proofs of termination for Turing machines, Dafny proofs for Church encodings, and a mechanized proof of the Church-Rosser theorem.