A Proof of the Church-Rosser Theorem and its Representation in a Logical Framework
Frank Pfenning · 1992
We give a detailed, informal proof of the Church-Rosser property for the untyped lambda-calculus and show its representation in LF. The proof is due to Tait and Martin-Löf and is based on the notion of parallel reduction. The representation employs higher-order abstract syntax and the judgments-as-types principle and takes advantage of term reconstruction as it is provided in the Elf implementation of LF. Proofs of meta-theorems are represented as higher-level judgments which relate sequences of reductions and conversions.