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Dependently-typed host languages empower users to verify a wide range of properties of embedded languages and programs written in them. Designers of such embedded languages are faced with a difficult choice between using a shallow or a deep…
The development of programming languages can be quite complicated and costly. Hence, much effort has been devoted to the modular definition of language features that can be reused in various combinations to define new languages and…
We explore a method for improving the performance of large language models through self-reflection and reinforcement learning. By incentivizing the model to generate better self-reflections when it answers incorrectly, we demonstrate that a…
Large language models (LLMs) exhibit remarkable generative capabilities but often suffer from hallucinations. Retrieval-augmented generation (RAG) offers an effective solution by incorporating external knowledge, but existing methods still…
We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver…
Code generation plays a crucial role in various tasks, such as code auto-completion and mathematical reasoning. Previous work has proposed numerous methods to enhance code generation performance, including integrating feedback from the…
Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…
Code reproduction is a cornerstone of scientific validity, yet it remains a formidable challenge in computer networking research due to the scarcity of open-source implementations and the complexity of heterogeneous system architectures.…
Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…
Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high…
The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…
It has been shown that Large Language Models' (LLMs) performance can be improved for many tasks using Chain of Thought (CoT) or In-Context Learning (ICL), which involve demonstrating the steps needed to solve a task using a few examples.…
Existing technology can parse arbitrary context-free grammars, but only a single, static grammar per input. In order to support more powerful syntax-extension systems, we propose reflective grammars, which can modify their own syntax during…
Probabilistic programming and the formal analysis of probabilistic algorithms are active areas of research, driven by the widespread use of randomness to improve performance. While functional correctness has seen substantial progress,…
Large Language Models (LLMs) are showing remarkable performance in generating source code, yet the generated code often has issues like compilation errors or incorrect code. Researchers and developers often face wasted effort in…
Large Language Models (LLMs) have recently made significant advances in code generation through the 'Chain-of-Thought' prompting technique. This technique empowers the model to autonomously devise "solution plans" to tackle intricate…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
Reflective systems allow their own structures to be altered from within. Here we are concerned with a style of reflection, called linguistic reflection, which is the ability of a running program to generate new program fragments and to…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…