Related papers: Modalities, Cohesion, and Information Flow
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes…
Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of…
In this essay, I present the advantages and, I dare say, the beauty of programming in a language with set-theoretic types, that is, types that include union, intersection, and negation type connectives. I show by several examples how…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
Logic-based models can be used to build verification tools for machine learning classifiers employed in the legal field. ML classifiers predict the outcomes of new cases based on previous ones, thereby performing a form of case-based…
Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…