Related papers: Guarded Dependent Type Theory with Coinductive Typ…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
The goal of this manuscript is to conduct a controltheoretic analysis of Temporal Difference (TD) learning algorithms. TD-learning serves as a cornerstone in the realm of reinforcement learning, offering a methodology for approximating the…
Dependently typed programming languages have become increasingly relevant in recent years. They have been adopted in industrial strength programming languages and have been extremely successful as the basis for theorem provers. There are…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…
Erasure enriches type theory with a distinction between runtime relevant and irrelevant data, allowing the compilation step to safely erase the latter. Versions of this feature are implemented by many systems, including Agda, Idris, and…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive…
We present a type system and inference algorithm for a rich subset of JavaScript equipped with objects, structural subtyping, prototype inheritance, and first-class methods. The type system supports abstract and recursive objects, and is…
Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…
Guarded tuple-generating dependencies (GTGDs) are a natural extension of description logics and referential constraints. It has long been known that queries over GTGDs can be answered by a variant of the chase - a quintessential technique…
We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
Ordinary differential equations (ODE) models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the…
In this tutorial I will present how a combination of linear and dependent type can be useful to describe different properties about higher order programs. Linear types have been proved particularly useful to express properties of functions;…
We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…
We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive…
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…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope,…