# Override and update

## TL;DR

This paper establishes a complete set of axioms for the first order theory of override and update operations on partial functions, connecting these concepts with combinatorial geometry to solve a longstanding problem.

## Contribution

It introduces a novel connection between override/update operations and combinatorial geometry, providing the first comprehensive axiomatization for their theory.

## Key findings

- Complete finite axiomatization of override and update theory
- Connection between partial functions and combinatorial geometry
- Resolution of a major open problem in the area

## Abstract

Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms for the first order theory of the override and update constructions on partial functions, resolving the main unsolved problem in the area.