Related papers: Denotational semantics for guarded dependent type …
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…
An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact…
Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away.…
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…
Guarded Interaction Trees are a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Rocq. We present an extension of Guarded Interaction Trees to support formal reasoning about…
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…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
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,…
In recent years, languages like Haskell have seen a dramatic surge of new features that significantly extends the expressive power of their type systems. With these features, the challenge of kind inference for datatype declarations has…
Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical…
In the impredicative type theory of System F ({\lambda}2), it is possible to create inductive data types, such as natural numbers and lists. It is also possible to create coinductive data types such as streams. They work well in the sense…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers [Nuyts, Vezzosi and Devriese, 2017]. It is well-known that any presheaf category constitutes a model of dependent…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to…
We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a…
We formulate an attention mechanism for continuous and ordered sequences that explicitly functions as an alignment model, which serves as the core of many sequence-to-sequence tasks. Standard scaled dot-product attention relies on…
Two novel descriptions of weak {\omega}-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are {\omega}-categories. The second is a recursive description of a…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…