Related papers: DeLaM: A Dependent Layered Modal Type Theory for M…
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.
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
As Large Language Models (LLMs) become increasingly integrated into our daily lives, the potential harms from deceptive behavior underlie the need for faithfully interpreting their decision-making. While traditional probing methods have…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
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…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
In this tutorial I will present how a combination of linear and dependent type can be useful to describe different properties about higher order programs. Linear types have been proved particularly useful to express properties of functions;…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
Latent Class Models (LCMs) are used to cluster multivariate categorical data (e.g. group participants based on survey responses). Traditional LCMs assume a property called conditional independence. This assumption can be restrictive,…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
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…
This technical report investigates Kripke-style modal type theories, both simply typed and dependently typed. We examine basic meta-theories of the type theories, develop their substitution calculi, and give normalization by evaluation…
Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…
Dependently typed programming languages have become increasingly relevant in recent years. They have been adopted in industrial strength programming languages and have been extremely successful as the basis for theorem provers. There are…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
Dependent types help programmers write highly reliable code. However, this reliability comes at a cost: it can be challenging to write new prototypes in (or migrate old code to) dependently-typed programming languages. Gradual typing makes…