I am aghast to discover that “coding camp” type publications on proof assistants, like #Agda and #Lean, do exist, complete with the all-too-common modern #IT anthem, “No need to know any mathematics”, emblazoned across the introduction, and subsequent pages littered with code samples, without proofs.
There are two primary uses of a proof assistant: to do mathematics and to write verified programmes. Both uses are built upon writing formal proofs. Without writing proofs, a proof assistant is almost an inconvenient, inefficient #programming language.
Want to learn more about the latest developments on using AI and (interactive) theorem proving in Mathematics? Wait no longer!
We have a great line-up of speakers at our online Workshop on AI and Theorem Provers in Mathematics. The workshop will be held online from 8th to 10th of April and attendance is free (registration required). For more details, visit the workshop website: https://aitpm.github.io/
#math #itp #theoremProving #isabelleHOL #lean #llm #ai #formal_mehods #agda #hol #mathematics

We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate the relationships between them and their classical counterparts. We identify, and eliminate where possible, the use of classical logic in the proofs of standard ARS results. Our analysis leads to refinements and mild generalizations of classical termination and confluence criteria. We investigate logical relationships between several notions of termination, arising from different formulations of the concept of a well-founded relation. We illustrate general applicability of our ARS development with an example formalization of the lambda calculus.