Related papers: Controlling unfolding in type theory
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
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…
The unfolding problem formulation for correcting experimental data distortions due to finite resolution and limited detector acceptance is discussed. A novel validation of the problem solution is proposed. Attention is drawn to fact that…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
In recent years, Homotopy Type Theory (HoTT) has had great success both as a foundation of mathematics and as internal language to reason about $\infty$-groupoids (a.k.a. spaces). However, in many areas of mathematics and computer science,…
Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make…
Machine learning has enabled differential cross section measurements that are not discretized. Going beyond the traditional histogram-based paradigm, these unbinned unfolding methods are rapidly being integrated into experimental workflows.…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
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…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
To ensure decidability and consistency of its type theory, a proof assistant should only accept terminating recursive functions and productive corecursive functions. Most proof assistants enforce this through syntactic conditions, which can…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Colimits are a fundamental construction in category theory. They provide a way to construct new objects by gluing together existing objects that are related in some way. We introduce a complementary notion of anticolimits, which provide a…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
This paper presents a novel technique for process discovery. In contrast to the current trend, which only considers an event log for discovering a process model, we assume two additional inputs: an independence relation on the set of logged…
We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…