Quotients, subtypes, and other forms of type abstraction are ubiquitous in formal reasoning
with higher-order logic. Typically, users want to build a library of operations and theorems …

Formal verification of algorithms often requires a choice between definitions that are easy to
reason about and definitions that are computationally efficient. One way to reconcile both …

In their usual form, representation independence metatheorems provide an external
guarantee that two implementations of an abstract interface are interchangeable when they …

The days of verifying only toy programs are long gone. The last two decades have marked a
new era of verification at scale, bringing strong guarantees to large and critical systems—an …

Reasoning modulo equivalences is natural for everyone, including mathematicians.
Unfortunately, in proof assistants based on type theory, which are frequently used to …

Homotopy Type Theory promises a unification of the concepts of equality and equivalence in
Type Theory, through the introduction of the univalence principle. However, existing proof …

This article presents Trocq, a new proof transfer framework for dependent type theory. Trocq
is based on a novel formulation of type equivalence, used to generalize the univalent …

Ornaments express relations between inductive types with the same inductive structure. We
implement fully automatic proof reuse for a particular class of ornaments in a Coq plugin …

Proof reuse addresses the issue of how proofs of theorems in a specific setting can be used
to prove other theorems in different settings. This paper proposes an approach where …

Proof assistants based on type theory such as Coq or Lego, put emphasis on inductive
specifications and proofs by featuring expressive inductive types. It is frequent to modify an …