Higher-Order, Data-Parallel Structured Deduction (2211.11573v1)

Abstract: State-of-the-art Datalog engines include expressive features such as ADTs (structured heap values), stratified aggregation and negation, various primitive operations, and the opportunity for further extension using FFIs. Current parallelization approaches for state-of-art Datalogs target shared-memory locking data-structures using conventional multi-threading, or use the map-reduce model for distributed computing. Furthermore, current state-of-art approaches cannot scale to formal systems which pervasively manipulate structured data due to their lack of indexing for structured data stored in the heap. In this paper, we describe a new approach to data-parallel structured deduction that involves a key semantic extension of Datalog to permit first-class facts and higher-order relations via defunctionalization, an implementation approach that enables parallelism uniformly both across sets of disjoint facts and over individual facts with nested structure. We detail a core language, $DL_s$, whose key invariant (subfact closure) ensures that each subfact is materialized as a top-class fact. We extend $DL_s$ to Slog, a fully-featured language whose forms facilitate leveraging subfact closure to rapidly implement expressive, high-performance formal systems. We demonstrate Slog by building a family of control-flow analyses from abstract machines, systematically, along with several implementations of classical type systems (such as STLC and LF). We performed experiments on EC2, Azure, and ALCF's Theta at up to 1000 threads, showing orders-of-magnitude scalability improvements versus competing state-of-art systems.

• The paper presents Slog, a novel Datalog extension that implements subfact closure with defunctionalization and higher-order relations.
• The paper demonstrates significant scalability gains over tools like Soufflé by leveraging distributed MPI for efficient data indexing and processing.
• The paper showcases practical applications in formal analysis, enabling advanced control-flow analyses and type system development through its innovative approach.

Overview of "Higher-Order, Data-Parallel Structured Deduction"

The paper "Higher-Order, Data-Parallel Structured Deduction" by Gilray et al. investigates an innovative approach to enhancing the performance and expressiveness of Datalog-based logical deduction systems. The authors empirically demonstrate the scalability of this approach using their language and system called Slog, which leverages higher-order relations and subfact indexing, leading to significant performance improvements over contemporary state-of-the-art Datalog engines such as Soufflé and Radlog.

Core Innovations

The primary innovation proposed in the paper is the extension of Datalog to support "subfact closure", enabling first-class facts and higher-order relations. This extension involves the creation of the core language DL, which ensures all subfacts are indexed and treated as first-class entities. This is achieved through defunctionalization, and implemented via data parallelism using MPI (Message Passing Interface), effectively balancing the computational workload across many threads.

1. Defunctionalization and subfact closure: These concepts allow structured data manipulation akin to higher-order functions, essential for implementing sophisticated program analyses and abstract machines.
2. Distributed and parallel execution: Slog’s reliance on MPI facilitates scalable parallelism on both multi-core and distributed computing platforms by leveraging subfact internment to optimize data indexing and retrieval.
3. Embedded formal verification and analysis: By illustrating the systematic development of control-flow analyses and type systems using Slog, the paper showcases expressive possibilities for formal methods and program analysis.
4. Comparison with other systems: The paper provides comprehensive experimental results in which Slog outperforms current tools like Soufflé, particularly in structured data contexts, due to its efficient subfact indexing.

Experimental Evaluation

The authors conducted extensive experiments across different computing platforms (including Amazon EC2, Azure, and ALCF’s Theta) to demonstrate Slog’s scalability. Notably, the system showed orders-of-magnitude performance gains on tasks involving large structured datasets compared to Soufflé and Radlog. Some of these benchmarks included:

• Transitive closure computations on varying datasets, demonstrating its strong scalability and competitive performance even when compared to conventional systems optimized for such tasks.
• $k$-CFA and $m$-CFA analyses, where contexts and execution stacks were efficiently handled using their extended Datalog approach, showcasing superior runtime scalability and efficiency against Soufflé.

Theoretical and Practical Implications

The research suggests significant theoretical advancements in logical deduction systems:

• The introduction of subfact closure extends the usability of Datalog to handle more complex, recursive data structures efficiently, fitting advanced applications in both declarative programming and semantic web environments.
• These advances hint at broader applicability of logic programming paradigms to real-world large-scale data analysis tasks, where traditional Datalog extensions would fall short due to performance bottlenecks introduced by lack of efficient data indexing and control.

In practice, Slog’s scalable architecture offers direct applications to formal reasoning systems, potentially transforming how programs are analyzed and verified for correctness. The system thrives under large-scale deployment conditions, proved by experiments with up to 1000 computational threads, indicating its readiness for integration into large compute ecosystems.

Future Prospects

The direction posited by this research opens avenues for further enhancements and broader adoption in AI and software engineering practices. Future work could explore deeper integration of Slog with solver-based systems, potentially enabling hybrid deductive/constraint-solving frameworks. Additionally, continuous refinements in handling distributed data could reduce overhead and ensure higher efficiency. The innovative mechanisms of Slog may also serve as a template for other logic-based systems aiming to transition to data-parallel architectures.

In conclusion, by pushing the boundaries of what is achievable with declarative logic programming languages, Gilray et al. present a formidable case for adopting higher-order, data-parallel structured deduction in tackling increasingly complex computational problems. Their results emphasize the importance of marrying theoretical advancements with robust, scalable implementations to address the growing computational challenges in data-heavy domains.