Related papers: Multimodal Dependent Type Theory
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it…
While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach…
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…
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…
Human perception of the empirical world involves recognizing the diverse appearances, or 'modalities', of underlying objects. Despite the longstanding consideration of this perspective in philosophy and cognitive science, the study of…
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…
Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the…
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…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
We introduce Displayed Type Theory (dTT), a multi-modal homotopy type theory with discrete and simplicial modes. In the intended semantics, the discrete mode is interpreted by a model for an arbitrary $\infty$-topos, while the simplicial…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
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.
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
We introduce Masked Trajectory Models (MTM) as a generic abstraction for sequential decision making. MTM takes a trajectory, such as a state-action sequence, and aims to reconstruct the trajectory conditioned on random subsets of the same…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
A neural multimodal machine translation (MMT) system is one that aims to perform better translation by extending conventional text-only translation models with multimodal information. Many recent studies report improvements when equipping…