A Proof of the Church-Rosser Theorem for the Lambda Calculus in Higher Order Logic

This paper describes a proof of the Church-Rosser theorem within the Higher Order Logic (HOL) theorem prover. This follows the proof by Tait/Martin-Lof, preserving the elegance of the classic presentation by Barendregt. We model the lambda calculus with a name-carrying syntax, as in practical languages. The proof is simpli ed by forming a quotient of the name-carrying syntax by the -equivalence relation, thus separating the concerns of -equivalence and -reduction.