Lambdas at the Far Edge: a Tale of Flying Lambdas and Lambdas on Wheels

Multi-robot systems are becoming increasingly relevant within diverse application domains, such as healthcare, exploration, and rescue missions. However, building such systems is still a significant challenge, since it adds the complexities of the physical nature of robots and their environments to those inherent in coordinating any distributed (multi-agent) system. Aggregate Programming (AP) has recently emerged as a promising approach to engineering resilient, distributed systems with proximity-based communication, and is notably supported by practical frameworks. In this paper we present a prototype of a multi-robot service system, which adopts AP for the design and implementation of its coordination software. The prototype has been validated both with simulations, and with tests in a University library.

Aggregate programming is a field-based coordination paradigm with over a decade of exploration and successful applications across domains including sensor networks, robotics, and IoT, with implementations in various programming languages, such as Protelis, ScaFi (Scala), and FCPP (C++). A recent research direction integrates machine learning with aggregate computing, aiming to support large-scale distributed learning and provide new abstractions for implementing learning algorithms. However, existing implementations do not target data science practitioners, who predominantly work in Python--the de facto language for data science and machine learning, with a rich and mature ecosystem. Python also offers advantages for other use cases, such as education and robotics (e.g., via ROS). To address this gap, we present Phyelds, a Python library for aggregate programming. Phyelds offers a fully featured yet lightweight implementation of the field calculus model of computation, featuring a Pythonic API and an architecture designed for seamless integration with Python's machine learning ecosystem. We describe the design and implementation of Phyelds and illustrate its versatility across domains, from well-known aggregate computing patterns to federated learning coordination and integration with a widely used multi-agent reinforcement learning simulator.

Existing LLM agent frameworks lack formal semantics: there is no principled way to determine whether an agent configuration is well-formed or will terminate. We present $λ_A$, a typed lambda calculus for agent composition that extends the simply-typed lambda calculus with oracle calls, bounded fixpoints (the ReAct loop), probabilistic choice, and mutable environments. We prove type safety, termination of bounded fixpoints, and soundness of derived lint rules, with full Coq mechanization (1,519 lines, 42 theorems, 0 Admitted). As a practical application, we derive a lint tool that detects structural configuration errors directly from the operational semantics. An evaluation on 835 real-world GitHub agent configurations shows that 94.1% are structurally incomplete under $λ_A$, with YAML-only lint precision at 54%, rising to 96--100% under joint YAML+Python AST analysis on 175 samples. This gap quantifies, for the first time, the degree of semantic entanglement between declarative configuration and imperative code in the agent ecosystem. We further show that five mainstream paradigms (LangGraph, CrewAI, AutoGen, OpenAI SDK, Dify) embed as typed $λ_A$ fragments, establishing $λ_A$ as a unifying calculus for LLM agent composition.