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Universe Subtyping in Martin-Lof Type Theory Internship Report

Summary: Universe Subtyping in Martin-L®of Type Theory
Internship Report
Gabriel Scherer
under the supervision of Andreas Abel
Revised version: August 24, 2011
The pragmatic goal of this internship was to establish the theoretical soundness
of a particular feature of the Agda proof assistant, the so-called universe polymor-
phism. This is part of a series of work by my supervisor Andreas Abel [ACD07]
aiming to provide a coherent metatheory for the different features implemented or
desired in this proof assistant. More precisely, we first considered universe cumu-
lativity, a well-known feature for universe hierarchy, then universe polymorphism,
which is a less explored area, and finally attempted to add irrelevance to the type
system, to ease universe levels manipulations.
All those notions will be introduced in more detail in the first section. I will
highlight the main goals and constraints of the desired theory, in comparison to
related works. I will also have to discuss some of the technical choices and issues
we have faced; those technical decisions have large consequences ≠ often unforeseen
≠ on the technical development and its structure.
The second section will describe the formal type system ≠ or type systems, as
we will consider variants ≠ used throughout the report. To this declarative type


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen


Collections: Computer Technologies and Information Sciences