Related papers: Guarded Cubical Type Theory: Path Equality for Gua…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We…
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…
Click-Through Rate (CTR) prediction models are integral to a myriad of industrial settings, such as personalized search advertising. Current methods typically involve feature extraction from users' historical behavior sequences combined…
Inductive knowledge graph completion (KGC) aims to predict missing triples with unseen entities. Recent works focus on modeling reasoning paths between the head and tail entity as direct supporting evidence. However, these methods depend…
A fundamental challenge in deep metric learning is the generalization capability of the feature embedding network model since the embedding network learned on training classes need to be evaluated on new test classes. To address this…
As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
We consider the conversion problem for multimodal type theory (MTT) by characterizing the normal forms of the type theory and proving normalization. Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability…
Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by…
This is the third in a series of papers extending Martin-L\"of's meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higher-dimensional types. We extend this framework to include a…
We develop game-theoretic semantics (GTS) for the fragment ATL+ of the full Alternating-time Temporal Logic ATL*, essentially extending a recently introduced GTS for ATL. We first show that the new game-theoretic semantics is equivalent to…
This paper proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the…
We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq,…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
Computational paths treat propositional equality as explicit paths built from labelled deduction steps and rewrite rules. This view originates in work by de Queiroz and collaborators [1] and yields a weak groupoid structure for equality,…
In modern OCaml, single-argument datatype declarations (variants with a single constructor, records with a single field) can sometimes be `unboxed'. This means that their memory representation is the same as their single argument (omitting…
This paper explores the relationship between C++ templates and partial evaluation. Templates were designed to support generic programming, but unintentionally provided the ability to perform compile-time computations and code generation.…
The research on gradual typing has led to many variations on the Gradually Typed Lambda Calculus (GTLC) of Siek and Taha (2006) and its underlying cast calculus. For example, Wadler and Findler (2009) added blame tracking, Siek et al.…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…