Textbook examples of recursion
Donald E. Knuth
TL;DR
This paper explores properties of recursive schemas, including McCarthy's 91 function and Takeuchi's triple recursion, proposing theorems for verification and raising open questions about their characteristics.
Contribution
It introduces new theorems related to recursive schemas and highlights open questions, advancing understanding of recursion in computation.
Findings
Proposed theorems for recursive schemas verification
Identified intriguing open questions in recursion properties
Analyzed properties of McCarthy's 91 function and Takeuchi's triple recursion
Abstract
We discuss properties of recursive schemas related to McCarthy's ``91 function'' and to Takeuchi's triple recursion. Several theorems are proposed as interesting candidates for machine verification, and some intriguing open questions are raised.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, programming, and type systems · semigroups and automata theory