相关论文: Constructing Recursion Operators in Intuitionistic…

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…

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…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

It is quite well-known from Kurt Godel's (1931) ground-breaking result on the Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are…

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually…

It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL.…

We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capturesome programming patterns used in untyped languages. Although occurrence typing was tied from its inceptionto set-theoretic…

In this paper, I establish the categorical structure necessary to interpret dependent inductive and coinductive types. It is well-known that dependent type theories \`a la Martin-L\"of can be interpreted using fibrations. Modern theorem…

We present an extension of Martin-L\"of Type Theory that contains a tiny object; a type for which there is a right adjoint to the formation of function types as well as the expected left adjoint. We demonstrate the practicality of this type…

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…

Curry-Howard correspondences between Linear Logic (LL) and session types provide a firm foundation for concurrent processes. As the correspondences hold for intuitionistic and classic versions of LL (ILL and CLL), we obtain two different…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

In this note we provide an algorithm for translating relational structures into "proper" relational structures, i.e., those such that there is no pair of worlds w and u such that w is accessible from u for every agent. In particular, our…

Machine learning has made major advances in categorizing objects in images, yet the best algorithms miss important aspects of how people learn and think about categories. People can learn richer concepts from fewer examples, including…

To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only…