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This paper considers parametricity and its consequent free theorems for nested data types. Rather than representing nested types via their Church encodings in a higher-kinded or dependently typed extension of System F, we adopt a functional…
Structured outputs are essential for large language models (LLMs) in critical applications like agents and information extraction. Despite their capabilities, LLMs often generate outputs that deviate from predefined schemas, significantly…
Developing and maintaining software commonly requires (1) adding new data type constructors to existing applications, but also (2) adding new functions that work on existing data. Most programming languages have native support for defining…
The dependency core calculus (DCC), a simple extension of the computational lambda calculus, captures a common notion of dependency that arises in many programming language settings. This notion of dependency is closely related to the…
We present Turnstile+, a high-level, macros-based metaDSL for building dependently typed languages. With it, programmers may rapidly prototype and iterate on the design of new dependently typed features and extensions. Or they may create…
This study provides a detailed analysis of current advancements in dynamic object tracking (DOT) and trajectory prediction (TP) methodologies, including their applications and challenges. It covers various approaches, such as feature-based,…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…
Context-Oriented Programming (COP) is a programming paradigm to encourage modularization of context-dependent software. Key features of COP are layers---modules to describe context-dependent behavioral variations of a software system---and…
Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
When writing programs involving matrices or tensors in general, it is desirable to rule out the inconsistency of tensor shapes (i.e., the generalization of matrix sizes) before actual computation. For this purpose, some languages provide…
Dropout has been demonstrated as a simple and effective module to not only regularize the training process of deep neural networks, but also provide the uncertainty estimation for prediction. However, the quality of uncertainty estimation…
A demand-driven approach to program analysis have been viewed as efficient algorithms to compute only the information required to serve a target demand. In contrast, an exhaustive approach computes all information in anticipation of it…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
Unsupervised Domain Adaptation (UDA) aims to adapt models from labeled source domains to unlabeled target domains. When adapting to adverse scenes, existing UDA methods fail to perform well due to the lack of instructions, leading their…