Abstract
We present a new proof of confluence of the untyped lambda calculus by reducing the confluence of s-reduction in the untyped lambda calculus to the confluence of s-reduction in the simply typed lambda calculus. This is achieved by embedding typed lambda terms into simply typed lambda terms. Using this embedding, an auxiliary reduction, and s-reduction on simply typed lambda terms we define a new reduction on all lambda terms. The transitive closure of the reduction defined is s-reduction on all lambda terms. This embedding allows us to use the confluence of s-reduction on simply typed lambda terms and thus prove the confluence of the reduction defined. As a consequence we obtain the confluence of s-reduction in the untyped lambda calculus.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
