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Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI

Ehud Shapiro

TL;DR

GLP introduces a concurrent logic programming paradigm with writer/reader variable pairs enabling single-assignment communication; the paper develops two implementation-ready semantics, $\text{dGLP}$ for single-agent and $\text{madGLP}$ for multiagent, and proves them correct with respect to their abstract counterparts. It then shows how these semantics map onto deterministic agent-level implementations using globalization/localization and a global link infrastructure, including an index-0 serializer for cold-calls, ensuring correct dataflow and forwarding without central coordination. The methodology advocates a human-AI co-design workflow, deriving English+code specs from formal semantics and then Dart implementations, with iterative refinement driving major redesigns. Overall, the work provides a rigorous foundation and practical blueprint for implementing Grassroots Logic Programs on distributed smartphone networks.

Abstract

Grassroots Logic Programs (GLP) is a concurrent logic programming language with variables partitioned into paired \emph{readers} and \emph{writers}, conjuring both linear logic and futures/promises: an assignment is produced at most once via the sole occurrence of a writer (promise) and consumed at most once via the sole occurrence of its paired reader (future), and may contain additional readers and/or writers, enabling the concise expression of rich multidirectional communication modalities. GLP was designed as a language for grassroots platforms -- distributed systems with multiple instances that can operate independently of each other and of any global resource, and can coalesce into ever larger instances -- with its target architecture being smartphones communicating peer-to-peer. The operational semantics of Concurrent (single-agent) GLP and of multiagent GLP (maGLP) were defined via transition systems/multiagent transition systems, respectively. Here, we describe the mathematics developed to facilitate the workstation- and smartphone-based implementations of GLP by AI in Dart. We developed dGLP -- implementation-ready deterministic operational semantics for single-agent GLP -- and proved it correct with respect to the Concurrent GLP operational semantics; dGLP was used by AI as a formal spec, from which it developed a workstation-based implementation of GLP. We developed madGLP -- an implementation-ready multiagent operational semantics for maGLP -- and proved it correct with respect to the maGLP operational semantics; madGLP is deterministic at the agent level (not at the system level due to communication asynchrony), and is being used by AI as a formal spec from which it develops a smartphone-based implementation of maGLP.

Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI

TL;DR

GLP introduces a concurrent logic programming paradigm with writer/reader variable pairs enabling single-assignment communication; the paper develops two implementation-ready semantics, for single-agent and for multiagent, and proves them correct with respect to their abstract counterparts. It then shows how these semantics map onto deterministic agent-level implementations using globalization/localization and a global link infrastructure, including an index-0 serializer for cold-calls, ensuring correct dataflow and forwarding without central coordination. The methodology advocates a human-AI co-design workflow, deriving English+code specs from formal semantics and then Dart implementations, with iterative refinement driving major redesigns. Overall, the work provides a rigorous foundation and practical blueprint for implementing Grassroots Logic Programs on distributed smartphone networks.

Abstract

Grassroots Logic Programs (GLP) is a concurrent logic programming language with variables partitioned into paired \emph{readers} and \emph{writers}, conjuring both linear logic and futures/promises: an assignment is produced at most once via the sole occurrence of a writer (promise) and consumed at most once via the sole occurrence of its paired reader (future), and may contain additional readers and/or writers, enabling the concise expression of rich multidirectional communication modalities. GLP was designed as a language for grassroots platforms -- distributed systems with multiple instances that can operate independently of each other and of any global resource, and can coalesce into ever larger instances -- with its target architecture being smartphones communicating peer-to-peer. The operational semantics of Concurrent (single-agent) GLP and of multiagent GLP (maGLP) were defined via transition systems/multiagent transition systems, respectively. Here, we describe the mathematics developed to facilitate the workstation- and smartphone-based implementations of GLP by AI in Dart. We developed dGLP -- implementation-ready deterministic operational semantics for single-agent GLP -- and proved it correct with respect to the Concurrent GLP operational semantics; dGLP was used by AI as a formal spec, from which it developed a workstation-based implementation of GLP. We developed madGLP -- an implementation-ready multiagent operational semantics for maGLP -- and proved it correct with respect to the maGLP operational semantics; madGLP is deterministic at the agent level (not at the system level due to communication asynchrony), and is being used by AI as a formal spec from which it develops a smartphone-based implementation of maGLP.
Paper Structure (56 sections, 30 theorems, 7 equations, 1 figure)

This paper contains 56 sections, 30 theorems, 7 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Transition Systems and Implementations
  3. Transition Systems
  4. Implementations
  5. Concurrent GLP and Its Implementation
  6. Concurrent GLP
  7. Deterministic Implementation of GLP
  8. Multiagent Transition Systems
  9. Agents, Local States, and Configurations
  10. Multiagent Transition Systems
  11. Multiagent GLP and Its Implementation
  12. Multiagent GLP
  13. Implementing Multiagent GLP with Deterministic Agents
  14. Related Work
  15. Conclusion
  16. ...and 41 more sections

Key Result

Lemma 14

GLP is persistent.

Figures (1)

  • Figure 1: maGLP vs madGLP variable linking through three stages. Left: maGLP shared variable pairs. Right: madGLP local pairs with global links (arrows from reader to writer, labeled with global names). Dashed lines separate agents $p$ and $q$. "gs" denotes global_send goals watching readers. In Stage 2, the V link arrow points from $q$ to $p$ (callback): when $q$ assigns $\mathsf{V_q}$, the goal gs($\mathsf{V_q?}$) sends the value back to $p$.

Theorems & Definitions (105)

  • Definition 1: Transition System
  • Definition 2: Implementation
  • Definition 3: Live, Complete, and Correct Implementation
  • Definition 4: GLP Variables
  • Definition 5: GLP Terms and Goals
  • Definition 6: Single-Occurrence (SO) Invariant
  • Definition 7: GLP Program
  • Definition 8: Writers Substitution, Assignment, Readers Substitution and Counterpart
  • Definition 9: GLP Renaming, Renaming Apart
  • Definition 10: Writer MGU
  • ...and 95 more