Date of Submission

Spring 2022

Academic Program

Mathematics

Project Advisor 1

Robert McGrail

Abstract/Artist's Statement

Type unification takes type inference a step further by allowing non-local flow of information. By exposing the algebraic structure of type unification, we obtain even more flexibility as well as clarity in the implementation. In particular, the main contribution is an explicit description of the arithmetic of universe levels and consistency of constraints of universe levels, with hints at how row types and general unification/subsumption can fit into the same framework of constraints. The compositional nature of the algebras involved ensure correctness and reduce arbitrariness: properties such as associativity mean that implementation details of type inference do not leak in error messages, for example. This project is a discovery and implementation of these ideas by extending the type theory of the Dhall programming language, with implementation in PureScript.

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Open Access

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