Related papers: Automating the Functional Correspondence between H…
Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large…
We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines. To demonstrate the technique and support our claim, we transform…
Abstraction plays an important role in the generalisation of knowledge and skills and is key to sample efficient learning. In this work, we study joint temporal and state abstraction in reinforcement learning, where temporally-extended…
The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive…
Context-free approaches to static analysis gain precision over classical approaches by perfectly matching returns to call sites---a property that eliminates spurious interprocedural paths. Vardoulakis and Shivers's recent formulation of…
We present an abstract machine that implements a full-reducing (a.k.a. strong) call-by-value strategy for pure $\lambda$-calculus. It is derived using Danvy et al.'s functional correspondence from Cr\'egut's KN by: (1) deconstructing KN to…
The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…
A language model (LM) is a mapping from a linguistic context to an output token. However, much remains to be known about this mapping, including how its geometric properties relate to its function. We take a high-level geometric approach to…
We present work on summarising deliberative processes for non-English languages. Unlike commonly studied datasets, such as news articles, this deliberation dataset reflects difficulties of combining multiple narratives, mostly of poor…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce $\textit{space}$ efficiencies, the price being $\textit{time}$ performances often poorer than those…
Quantitative analysis of computing systems is an emerging area in automated formal analysis. Such properties address aspects such as costs and rewards, quality measures, resource consumption, distance metrics, etc. Existing solutions for…
The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead,…
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…