Related papers: Native Type Theory
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
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…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
We reformulate recent advances in directed type theory--a type theory where the types have the structure of synthetic (higher) categories--as a logical calculus with multiple context 'zones', following the example of Pfenning and Davies.…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…
The ability to cast values between related types is a leitmotiv of many flavors of dependent type theory, such as observational type theories, subtyping, or cast calculi for gradual typing. These casts all exhibit a common structural…
Applications of narrative theories using large language models (LLMs) deliver promising use-cases in automatic story generation and understanding tasks. Our survey examines how natural language processing (NLP) research engages with fields…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
Topological collections allow to consider uniformly many data structures in programming languages and are handled by functions defined by pattern matching called transformations. We present two type systems for languages with topological…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
Asking good questions in large-scale, open-domain conversational systems is quite significant yet rather untouched. This task, substantially different from traditional question generation, requires to question not only with various patterns…
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…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
The study of homotopy theoretic phenomena in the language of type theory is sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type theory is only one of the many aspects of homotopy type theory, which also includes…
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…
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known…
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…