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In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
This paper describes the design and implementation of a comprehensive OCaml interface to the Sundials library of numeric solvers for ordinary differential equations, differential algebraic equations, and non-linear equations. The interface…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Large Language Models (LLMs) have showcased impressive capabilities in handling straightforward programming tasks. However, their performance tends to falter when confronted with more challenging programming problems. We observe that…
Inferring reward functions from demonstrations is a key challenge in reinforcement learning (RL), particularly in multi-agent RL (MARL), where large joint state-action spaces and complex inter-agent interactions complicate the task. While…
The Core Imaging Library (CIL) is an open-source versatile Python framework for solving inverse problems with special emphasis on imaging applications such as computed tomography (CT), using a plug-in architecture for data and operators,…
In recent years, various computing-in-memory (CIM) processors have been presented, showing superior performance over traditional architectures. To unleash the potential of various CIM architectures, such as device precision, crossbar size,…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…
Recent advances in Transformer-based large language models (LLMs) have led to significant performance improvements across many tasks. These gains come with a drastic increase in the models' size, potentially leading to slow and costly use…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
In this paper the reversibility of executable Interval Temporal Logic (ITL) specifications is investigated. ITL allows for the reasoning about systems in terms of behaviours which are represented as non-empty sequences of states. It allows…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We present Step-Back Prompting, a simple prompting technique that enables LLMs to do abstractions to derive high-level concepts and first principles from instances containing specific details. Using the concepts and principles to guide…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic…
<Q>_e is the effective list of all finite predicate logic programs. <T_e> is the list of recursive trees. We modify constructions of Marek, Nerode, and Remmel [25] to construct recursive functions f and g such that for all indices e, (i)…
Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…