Lifting and Lowering Functions with The Dump Calculus

This article discusses a set of functional combinators called lifting and dumping, which are used to add or remove arguments from functions. The author aims to use these combinators to create a nameless de Bruijn-style e-graph that supports binders and alpha equivalence. Lifting adds redundant arguments to functions via thinnings, while dumping partially applies functions to junk values, forming a one-sided inverse relationship. The article provides Python examples and mathematical interpretations, and introduces Co-de Bruijn as a normal form for lifting expressions. This content is highly relevant to IT/technology, specifically programming, functional programming, and graph-based computation.