What the study found
The paper presents a way to represent abstraction functions as types in univalent dependent type theory, using a phase distinction and related modalities to separate concrete and abstract parts of a type.
Why the authors say this matters
The authors say this supports modular verification at scale by preserving abstraction between libraries and client code, and they conclude it can help hide private details while still allowing precise specifications of program behavior and cost.
What the researchers tested
The researchers developed a synthetic account of Hoare's methodology within univalent dependent type theory. They used a gluing construction to encode abstraction-function data in types, and they introduced a phase distinction, a noninterference theorem, and a monadic sealing effect to study modularity.
What worked and what didn't
The abstract says the approach scales to verification of cost and allows analysis of client cost relative to a cost-aware specification. It also says a monadic sealing effect permits an implementation to be upper-bounded by its specification when private details affect observable cost.
What to keep in mind
The abstract does not describe experimental evaluation, benchmarks, or comparisons with other systems. It also does not state detailed limitations beyond the scope of the presented theory.
Key points
- Abstraction functions are encoded as types in univalent dependent type theory.
- The approach uses a phase distinction and gluing construction to separate concrete and abstract parts.
- A noninterference theorem is used to characterize modularity guarantees.
- The theory is described as scaling to verification of cost as well as behavior.
- A monadic sealing effect is said to support upper bounds on implementation cost.
Disclosure
- Research title:
- A type-theoretic account of abstraction functions and cost verification
- Authors:
- Harrison Grodin, Runming Li, Robert Harper
- Institutions:
- Carnegie Mellon University
- Publication date:
- 2026-01-08
- DOI:
- 10.1145/3776673
- OpenAlex record:
- View
- Image credit:
- Photo by TheDigitalWay on Pixabay · Pixabay License
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