Related papers: Modular implicits
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
Multi-stage programming is a proven technique that provides predictable performance characteristics by controlling code generation. We propose a core semantics for Typed Template Haskell, an extension of Haskell that supports multi staged…
The Unified Modelling Language is emerging as a de-facto standard for modelling object-oriented systems. However, the semantics document that a part of the standard definition primarily provides a description of the language's syntax and…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
Some years ago, Borcherds described in [Bo1] two methods for constructing modular forms on modular varieties related to the orthogonal group ${\O}(2,n)$. They are the so called Borcherds' additive and multiplicative lifting. The…
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
Multilingual pre-trained models are known to suffer from the curse of multilinguality, which causes per-language performance to drop as they cover more languages. We address this issue by introducing language-specific modules, which allows…
Both humans and large language models are able to learn language without explicit structural supervision. What inductive biases make this learning possible? We address this fundamental cognitive question by leveraging transformer language…
Many complex mechatronic systems consist of multiple interconnected dynamical subsystems, which are designed, developed, analyzed, and manufactured by multiple independent teams. To support such a design approach, a modular model framework…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
This study utilizes the game Codenames as a benchmarking tool to evaluate large language models (LLMs) with respect to specific linguistic and cognitive skills. LLMs play each side of the game, where one side generates a clue word covering…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about…
We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
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…
In conventional formulations of multilayer feedforward neural networks, the individual layers are customarily defined by explicit functions. In this paper we demonstrate that defining individual layers in a neural network \emph{implicitly}…
Type classes are a popular tool for implementing generic algorithms and data structures without loss of efficiency, bridging the gap between parametric and ad-hoc polymorphism. Since their initial development in Haskell, they now feature…