System $F^omega$ with Coherent Implicit Resolution

2025-03-31

AI Summary

提出一种计算模型，用于解决隐式编程中的一致性问题，通过扩展System F^ω，统一处理类型和项抽象，无需引入算法限制。

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose a calculus for modeling implicit programming that supports first-class, overlapping, locally scoped, and higher-order instances with higher-kinded types. We propose a straightforward generalization of the well-established System $F^omega$ to implicit parameters, with a uniform treatment of type and term abstractions. Unlike previous works, we give a declarative specification of unambiguous, and thus coherent, resolution without introducing restrictions motivated by an algorithmic formulation of resolution.

Problem

• Modeling implicit programming with first-class overlapping instances
• Generalizing System Fω for coherent implicit parameter resolution
• Ensuring unambiguous resolution without algorithmic restrictions

Innovation

• Generalizes System Fω with implicit parameters
• Uniformly handles type and term abstractions
• Ensures coherent resolution declaratively