Thinnings: Sublist Witnesses and de Bruijn Index Shift Clumping

4 days ago

Thinnings are witnesses to a sublist question, providing a way to verify if one list is a sublist of another.
Thinnings can be represented in various forms, such as bit vectors, prefix sums, or index selector lists, and they support operations like composition and identity.
De Bruijn indices are used in lambda calculus to represent variables by counting the binders they must cross, and thinnings can compact multiple shifts into a single operation.
Thinnings have applications in lambda egraphs, hash consing, and union finds, offering a way to manage variable bindings and substitutions efficiently.
The concept of thinnings is related to proof objects in logic programming and can be used to optimize verification processes in programming languages.

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