Related papers: Mechanically Verified Calculational Abstract Inter…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
From a set of technical drawings and expert knowledge, we automatically learn a parser to interpret such a drawing. This enables automatic reasoning and learning on top of a large database of technical drawings. In this work, we develop a…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Abstraction is an important and useful concept in the field of artificial intelligence. To the best of our knowledge, there is no syntactic method to compute a sound and complete abstraction from a given low-level basic action theory and a…
Graphical calculus is an intuitive visual notation for manipulating tensors and index contractions. Using graphical calculus leads to simple and memorable derivations, and with a bit of practice one can learn to prove complex identities…
Binary-level pointer analysis can be of use in symbolic execution, testing, verification, and decompilation of software binaries. In various such contexts, it is crucial that the result is trustworthy, i.e., it can be formally established…
Understanding and manipulating concrete and abstract concepts is fundamental to human intelligence. Yet, they remain challenging for artificial agents. This paper introduces a multimodal generative approach to high order abstract concept…
We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…
We show how static analysis for secure information flow can be expressed and proved correct entirely within the framework of abstract interpretation. The key idea is to define a Galois connection that directly approximates the hyperproperty…
Multiplicative-Additive System Virtual (MAV) is a logic that extends Multiplicative-Additive Linear Logic with a self-dual non-commutative operator expressing the concept of "before" or "sequencing". MAV is also an extenson of the the logic…
Understanding AI systems' inner workings is critical for ensuring value alignment and safety. This review explores mechanistic interpretability: reverse engineering the computational mechanisms and representations learned by neural networks…
Abstract interpretation is a well-established technique for performing static analyses of logic programs. However, choosing the abstract domain, widening, fixpoint, etc. that provides the best precision-cost trade-off remains an open…