https://calfproject.github.io/runmingl/ runmingl /runmingl/ Runming Li Person https://www.cs.cmu.edu/~runmingl/ Carnegie Mellon University 0000-0001-7600-9069 Ph.D. Student Runming Li is a second-year Ph.D. student in the Computer Science Department at Carnegie Mellon University, advised by Prof. Robert Harper. He studies semantics of programming languages from the perspectives of (dependent) type theory and category theory. More broadly, he is interested in the design and implementation of functional programming languages and proof assistants that facilitate the construction and verification of correct and efficient programs. References Context https://calfproject.github.io/team-phd-current/ team-phd-current /team-phd-current/ Current Ph.D. Students Team https://calfproject.github.io/hgrodin/ hgrodin /hgrodin/ Harrison Grodin Person https://www.harrisongrodin.com Carnegie Mellon University 0000-0002-0947-3520 Ph.D. Student Harrison Grodin is a fourth-year Ph.D. student in the Principles of Programming group in the Computer Science Department at Carnegie Mellon University, advised by Robert Harper. His research is on programming language semantics, drawing inspiration from ideas in type theory and category theory. https://calfproject.github.io/runmingl/ runmingl /runmingl/ Runming Li Person https://www.cs.cmu.edu/~runmingl/ Carnegie Mellon University 0000-0001-7600-9069 Ph.D. Student Runming Li is a second-year Ph.D. student in the Computer Science Department at Carnegie Mellon University, advised by Prof. Robert Harper. He studies semantics of programming languages from the perspectives of (dependent) type theory and category theory. More broadly, he is interested in the design and implementation of functional programming languages and proof assistants that facilitate the construction and verification of correct and efficient programs. https://calfproject.github.io/ethanchu/ ethanchu /ethanchu/ Ethan Chu Person https://gediminas19.github.io Carnegie Mellon University 0009-0005-6041-0313 Ph.D. Student Ethan Chu is a 2nd-year PhD student in the Principles of Programming (PoP) group in Carnegie Mellon University’s Computer Science Department (CMU CSD), advised by Jan Hoffmann. His research areas are programming languages and verification, with a focus on type systems and static resource analysis of programs. Backlinks Lukas Kebuladze https://calfproject.github.io/kebuladze-2025/ kebuladze-2025 /kebuladze-2025/ Amortized Analysis of Splay Trees via a Lax Homomorphism Reference Technical Report, Carnegie Mellon University https://www.cs.cmu.edu/~runmingl/student/kebuladze-splay.pdf 2025, title = {Amortized Analysis of Splay Trees via a Lax Homomorphism}, author = {Lukas Kebuladze}, year = {2025}, month = {aug}, url = {https://www.cs.cmu.edu/~runmingl/student/kebuladze-splay.pdf}, institution = {Carnegie Mellon University} }]]> CMU undergraduate summer SURA project report by Lukas Kebuladze, supervised by Runming Li. Extended abstract, poster, and presentation: 3rd place winner in the undergraduate category of the 2026 POPL Student Research Competition. Andrew Zhou https://calfproject.github.io/zhou-2025/ zhou-2025 /zhou-2025/ Formally Verified Cost of the Parallel Prefix Sum Algorithm Reference Technical Report, Carnegie Mellon University https://www.cs.cmu.edu/~runmingl/student/zhou-scan.pdf 2025, title = {Formally Verified Cost of the Parallel Prefix Sum Algorithm}, author = {Andrew Zhou}, year = {2025}, month = {aug}, url = {https://www.cs.cmu.edu/~runmingl/student/zhou-scan.pdf}, institution = {Carnegie Mellon University} }]]> CMU undergraduate summer SURA project report by Andrew Zhou, supervised by Runming Li. Related https://calfproject.github.io/cmu/ cmu /cmu/ Carnegie Mellon University Institution https://www.cmu.edu/ Pittsburgh, PA, USA https://calfproject.github.io/rwh/ rwh /rwh/ Robert Harper Person https://www.cs.cmu.edu/~rwh/ Carnegie Mellon University 0000-0002-9400-2941 Professor Contributions Runming Li Harrison Grodin Robert Harper https://calfproject.github.io/li-grodin-harper-2023/ li-grodin-harper-2023 /li-grodin-harper-2023/ A Verified Cost Analysis of Joinable Red-Black Trees Reference Manuscript 10.48550/arXiv.2309.11056 2023, title = {A Verified Cost Analysis of Joinable Red-Black Trees}, author = {Runming Li and Harrison Grodin and Robert Harper}, year = {2023}, url = {https://arxiv.org/abs/2309.11056}, eprint = {2309.11056}, archiveprefix = {arXiv}, primaryclass = {cs.PL} }]]> Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in Calf, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of Calf in the Agda theorem prover. Harrison Grodin Runming Li Robert Harper https://calfproject.github.io/grodin-li-harper-2026/ grodin-li-harper-2026 /grodin-li-harper-2026/ Abstraction Functions as Types: Modular Verification of Cost and Behavior in Dependent Type Theory Reference POPL ’26: 53rd ACM SIGPLAN Symposium on Principles of Programming Languages 10.1145/3776673 2026, title = {Abstraction Functions as Types: Modular Verification of Cost and Behavior in Dependent Type Theory}, author = {Grodin, Harrison and Li, Runming and Harper, Robert}, year = 2026, month = jan, journal = {Proc. ACM Program. Lang.}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, volume = 10, number = {POPL}, doi = {10.1145/3776673}, url = {https://doi.org/10.1145/3776673}, issue_date = {January 2026}, articleno = 31, numpages = 28, keywords = {abstract data type, abstraction, abstraction function, algorithm, algorithm analysis, call-by-push-value, concrete type, cost analysis, data structure, dependent type theory, equational reasoning, information flow, modal type theory, modularity, noninterference, phase distinction, verification} }]]> Software development depends on the use of libraries whose public specifications inform client code and impose obligations on private implementations; it follows that verification at scale must also be modular, preserving such abstraction. Hoare’s influential methodology uses abstraction functions to demonstrate the coherence between such concrete implementations and their abstract specifications. However, the Hoare methodology relies on a conventional separation between implementation and specification, providing no linguistic support for ensuring that this convention is obeyed. This paper proposes a synthetic account of Hoare’s methodology within univalent dependent type theory by encoding the data of abstraction functions within types themselves. This is achieved via a phase distinction, which gives rise to a gluing construction that renders an abstraction function as a type and a pair of modalities that fracture a type into its concrete and abstract parts. A noninterference theorem governing the phase distinction characterizes the modularity guarantees provided by the theory. This approach scales to verification of cost, allowing the analysis of client cost relative to a cost-aware specification. A monadic sealing effect facilitates modularity of cost, permitting an implementation to be upper-bounded by its specification in cases where private details influence observable cost. The resulting theory supports modular development of programs and proofs in a manner that hides private details of no concern to clients while permitting precise specifications of both the cost and behavior of programs. Runming Li Robert Harper https://calfproject.github.io/li-harper-2025/ li-harper-2025 /li-harper-2025/ Canonicity for Cost-Aware Logical Framework via Synthetic Tait Computability Reference Manuscript 10.48550/arXiv.2504.12464 2025, title = {Canonicity for Cost-Aware Logical Framework via Synthetic Tait Computability}, author = {Runming Li and Robert Harper}, year = {2025}, url = {https://arxiv.org/abs/2504.12464}, eprint = {2504.12464}, archiveprefix = {arXiv}, primaryclass = {cs.PL} }]]> 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. Runming Li Yue Yao Robert Harper https://calfproject.github.io/li-yao-harper-2026/ li-yao-harper-2026 /li-yao-harper-2026/ Mechanizing Synthetic Tait Computability in Istari Reference CPP '26: the 15th ACM SIGPLAN International Conference on Certified Programs and Proofs 10.1145/3779031.3779085 2026, title = {Mechanizing Synthetic Tait Computability in Istari}, author = {Li, Runming and Yao, Yue and Harper, Robert}, year = 2026, booktitle = {Proceedings of the 15th ACM SIGPLAN International Conference on Certified Programs and Proofs}, location = {Rennes, France}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, series = {CPP '26}, pages = {231–247}, doi = {10.1145/3779031.3779085}, isbn = 9798400723414, url = {https://doi.org/10.1145/3779031.3779085}, numpages = 17, keywords = {Istari, cost-aware logical framework, equality reflection, extensional type theory, gluing, logical relations, meta-theory, synthetic Tait computability} }]]> Categorical gluing is a powerful technique for proving meta- theorems of type theories such as canonicity and normaliza- tion. Synthetic Tait Computability (STC) provides an abstract treatment of the complex gluing models by internalizing the gluing category into a modal dependent type theory with a phase distinction. This work presents a mechanization of STC in the Istari proof assistant. Istari is a Martin-Löf- style extensional type theory with equality reflection, which avoids much of the explicit transport reasoning typically found in intensional proof assistants. This work develops a reusable library for synthetic phase distinction, including modalities, extension types, and strict glue types, and applies it to two case studies: (1) a canonicity model for dependent type theory with dependent products and booleans with large elimination, and (2) a Kripke canonicity model for the cost-aware logical framework. Our results demonstrate that the core STC constructions can be formalized essentially verbatim in Istari, preserving the elegance of the on-paper arguments while ensuring machine-checked correctness.