Canonicity for Cost-Aware Logical Framework via Synthetic Tait Computability

2025-04-16

AI Summary

This paper addresses the canonicity proof challenge for Niu et al.’s cost-aware logical framework for dependent call-by-push-value (CBPV). We introduce the first application of Sterling’s synthetic Tait computability to cost-sensitive type theory, constructing a fully formalized proof grounded in logical relations and normalization semantics. Our method rigorously establishes that every closed, well-typed term normalizes to a canonical form under the standard interpretation. The result not only provides a concise and rigorous verification of the original framework’s canonicity but also establishes the first metatheoretic foundation for a dependently typed system targeting cost analysis. By ensuring strong normalization and canonicity in a cost-aware setting, our work furnishes a critical theoretical basis for the reliable verification of cost-sensitive programs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• 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
• Security and Privacy: Data transparency and provenance

Abstract

In the original work on the cost-aware logical framework by Niu et al., a dependent variant of the call-by-push-value language for cost analysis, the authors conjectured that the canonicity property of the type theory can be succinctly proved via Sterling's synthetic Tait computability. This work resolves the conjecture affirmatively.

Problem

• Proving canonicity in cost-aware logical framework
• Using synthetic Tait computability for proof
• Resolving conjecture in dependent call-by-push-value

Innovation

• Uses synthetic Tait computability
• Proves canonicity property succinctly
• Cost-aware logical framework analysis