Related papers: Tactics for Reasoning modulo AC in Coq

interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

While transformer models have been highly successful, they are computationally inefficient. We observe that for each layer, the full width of the layer may be needed only for a small subset of tokens inside a batch and that the "effective"…

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In…

Interactive Theorem Proving was repeatedly shown to be fruitful when combined with Generative Artificial Intelligence. This paper assesses multiple approaches to Rocq generation and illuminates potential avenues for improvement. We identify…

Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…

The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an $\hbar$ expansion of Liouville space generating functions, we show how…

Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for…

The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…

This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a…

Reynold's abstraction theorem is now a well-established result for a large class of type systems. We propose here a definition of relational parametricity and a proof of the abstraction theorem in the Calculus of Inductive Constructions…

We present a refinement of the Calculus of Inductive Constructions in which one can easily define a notion of relational parametricity. It provides a new way to automate proofs in an interactive theorem prover like Coq.

We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…

In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…

Common functional languages incentivize tail-recursive functions, as opposed to general recursive functions that consume stack space and may not scale to large inputs. This distinction occasionally requires writing functions in a…

We present ViCAR, a library for working with monoidal categories in the Coq proof assistant. ViCAR provides definitions for categorical structures that users can instantiate with their own verification projects. Upon verifying relevant…

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…

We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By…