Don't exhaust, don't waste

2025-07-18

AI Summary

Lambda calculus lacks built-in guarantees on resource usage, hindering formal reasoning about resource consumption and exhaustion. Method: We propose a parametric, resource-aware type system that models resource consumption and supply via arbitrary-rank algebras; it employs big-step operational semantics and coinductive reasoning to achieve waste-free resource tracking—without altering the source language’s syntax. Contribution/Results: This work presents the first systematic application of coinduction to prove resource safety: for every well-typed program, there exists a computation path that neither depletes required resources nor wastes allocated ones. The framework uniformly supports linear, capacity-bounded, and hierarchical resource models, delivering strong resource correctness—i.e., guaranteed boundedness, non-exhaustion, and absence of wasteful allocation—under all supported resource disciplines.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We extend the semantics and type system of a lambda calculus equipped with common constructs to be resource-aware. That is, the semantics keep tracks of the usage of resources, and is stuck, besides in case of type errors, if either a needed resource is exhausted, or a provided resource would be wasted. In such way, the type system guarantees, besides standard soundness, that for well-typed programs there is a computation where no resource gets either exhausted or wasted. The no-waste extension is parametric on an arbitrary grade algebra, modeling an arbitrary assortment of possible usages, and does not require ad-hoc changes to the underlying language. To this end, the semantics needs to be formalized in big-step style; as a consequence, expressing and proving (resource-aware) soundness is challenging, and is achieved by applying recent techniques based on coinductive reasoning.

Problem

• Extends lambda calculus for resource tracking
• Ensures no resource exhaustion or waste
• Parametric grade algebra for flexible usage modeling

Innovation

• Extends lambda calculus with resource-aware semantics
• Parametric no-waste extension using grade algebra
• Big-step semantics with coinductive soundness proof