Core Concepts
Structured data representations, such as sparse and compressed tensors, can be efficiently manipulated by exploiting their structural properties. The authors develop a relational logic, LGTM, that enables mechanised proofs of hypersafety properties for such computations.
Abstract
The content discusses the problem of formally verifying computations that manipulate structured data, such as sparse and compressed tensors. The key observations are:
- Specifications for structured data manipulations can be phrased as hypersafety properties, which relate traces of multiple programs.
- The authors develop the Logic for Graceful Tensor Manipulation (LGTM), a new Hoare-style relational separation logic for specifying and verifying computations over structured data.
- The key idea in LGTM is the notion of parametrised hypersafety specifications, where the number of program components can depend on program variables.
- LGTM is mechanised in Coq, including its meta-theory, rules, and soundness proof.
- The authors develop a library of domain-specific tactics that automate computer-aided hypersafety reasoning, enabling short and reusable proof scripts.
- The effectiveness of LGTM is demonstrated by mechanically proving the correctness of 13 case studies involving computations on compressed arrays and sparse tensors.