Related papers: A Two-Level Linear Dependent Type Theory

Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…

We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…

Whilst there have been great advances in HPC hardware and software in recent years, the languages and models that we use to program these machines have remained much more static. This is not from a lack of effort, but instead by virtue of…

We propose a notion of state distinguishability that does not refer to probabilities, but rather to the ability of a set of states to serve as programs for a desired set of gates. Using this notion, we reconstruct the structural features of…

An oblivious computation is one that is free of direct and indirect information leaks, e.g., due to observable differences in timing and memory access patterns. This paper presents Lambda Obliv, a core language whose type system enforces…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…

Asynchronous programming has appeared as a programming style that overcomes undesired properties of concurrent programming. Typically in asynchronous models of programming, methods are posted into a post list for latter execution. The order…

There are various kinds of type analysis of logic programs. These include for example inference of types that describe an over-approximation of the success set of a program, inference of well-typings, and abstractions based on given types.…

This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…

Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…

Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…

Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…

Hierarchy is a common and effective way of organizing data and representing their relationships at different levels of abstraction. However, hierarchical data dependencies cause difficulties in the estimation of "separable" models that can…

We show how systems of session types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as…