Related papers: The clocks they are adjunctions:Denotational seman…

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…

The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…

Timed Concurrent Constraint Programming (tcc) is a declarative model for concurrency offering a logic for specifying reactive systems, i.e. systems that continuously interact with the environment. The universal tcc formalism (utcc) is an…

We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This…

We present a derivation of the structure and dynamics of a ticking clock by showing that for finite systems a single natural principle serves to distinguish what we understand as ticking clocks from time-keeping systems in general. As a…

Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…

A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…

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…

Type classes are an elegant extension to traditional, Hindley-Milner based typing systems. They are used in modern, typed languages such as Haskell to support controlled overloading of symbols. Haskell 98 supports only single-parameter and…

We consider type inference for guarded recursive data types (GRDTs) -- a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference.…

Connectionist temporal classification (CTC) is a popular sequence prediction approach for automatic speech recognition that is typically used with models based on recurrent neural networks (RNNs). We explore whether deep convolutional…

Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…

When scripts in untyped languages grow into large programs, maintaining them becomes difficult. A lack of explicit type annotations in typical scripting languages forces programmers to must (re)discover critical pieces of design information…

Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…

Abstracting Gradual Typing (AGT) is an approach to systematically deriving gradual counterparts to static type disciplines. The approach consists of defining the semantics of gradual types by interpreting them as sets of static types, and…

In this paper we combine the principled approach to modalities from multimodal type theory (MTT) with the computationally well-behaved realization of identity types from cubical type theory (CTT). The result -- cubical modal type theory…

Continuous clocks, i.e. the clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the…

Nakano's later modality allows types to express that the output of a function does not immediately depend on its input, and thus that computing its fixpoint is safe. This idea, guarded recursion, has proved useful in various contexts, from…

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…

Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…