Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internalizing Representation Independence with Univalence   In their usual form, representation independence metatheorems provide an
external guarantee that two implementations of an abstract interface are
interchangeable when they are related by an operation-preserving
correspondence. If our programming language is dependently-typed, however, we
would like to appeal to such invariance results within the language itself, in
order to obtain correctness theorems for complex implementations by
transferring them from simpler, related implementations. Recent work in proof
assistants has shown that Voevodsky's univalence principle allows transferring
theorems between isomorphic types, but many instances of representation
independence in programming involve non-isomorphic representations.
  In this paper, we develop techniques for establishing internal relational
representation independence results in dependent type theory, by using higher
inductive types to simultaneously quotient two related implementation types by
a heterogeneous correspondence between them. The correspondence becomes an
isomorphism between the quotiented types, thereby allowing us to obtain an
equality of implementations by univalence. We illustrate our techniques by
considering applications to matrices, queues, and finite multisets. Our results
are all formalized in Cubical Agda, a recent extension of Agda which supports
univalence and higher inductive types in a computationally well-behaved way.

13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin