Logic and Foundations Commons^™

The Algebra Of Type Unification, Verity James Scheel

Senior Projects Spring 2022

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 …

Constructing A Categorical Framework Of Metamathematical Comparison Between Deductive Systems Of Logic, Alex Gabriel Goodlad

Senior Projects Spring 2016

The topic of this paper in a broad phrase is “proof theory". It tries to theorize the general

notion of “proving" something using rigorous definitions, inspired by previous less general

theories. The purpose for being this general is to eventually establish a rigorous framework

that can bridge the gap when interrelating different logical systems, particularly ones

that have not been as well defined rigorously, such as sequent calculus. Even as far as

semantics go on more formally defined logic such as classic propositional logic, concepts

like “completeness" and “soundness" between the “semantic" and the “deductive system"

is too arbitrarily defined …