Ph.D. Candidate at Boston UniversityI am a Ph.D. student in the Department of Computer Science at Boston University, advised by Prof. Hongwei Xi. My research interests lie in programming languages, type systems, and verification.
These days research is mainly focused on the design of languages and type systems that tackle issues in memory safety and concurrency as well as the development of novel language features that aid programmer productivity and reasoning. A common thread between my works is that they are guided by ideas from substructural logics while also drawing influences from other areas such as dependent type theory, session types, probabilistic programming, etc.
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Boston UniversityDepartment of Computer Science
Ph.D. StudentSep. 2019 - present -
North China University of TechnologyB.E. in Computer ScienceSep. 2015 - Jul. 2019
Experience
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Institute of Computing Technology, Chinese Academy of SciencesResearch AssistantSep. 2018 - Jul. 2019
Selected Publications (view all )
Probabilistic Refinement Session Types
Qiancheng Fu, Ankush Das, Marco Gaboardi
ACM SIGPLAN Conference on Programming Language Design and Implementation 2025
Session types provide a formal type system to define and verify communication protocols between message-passing processes. In order to analyze randomized systems, recent works have extended session types with probabilistic type constructors. Unfortunately, all the proposed extensions only support constant probabilities which limits their applicability to real-world systems. Our work addresses this limitation by introducing probabilistic refinement session types which enable symbolic reasoning for concurrent probabilistic systems in a core calculus we call PReST. The type system is carefully designed to be a conservative extension of refinement session types and supports both probabilistic and regular choice type operators. We also implement PReST in a prototype which we use for validating probabilistic concurrent programs. The added expressive power leads to significant challenges, both in the meta theory and implementation of PReST, particularly with type checking: it requires reconstructing intermediate types for channels when type checking probabilistic branching expressions. The theory handles this by semantically quantifying refinement variables in probabilistic typing rules, a deviation from standard refinement type systems. The implementation relies on a bi-directional type checker that uses an SMT solver to reconstruct the intermediate types minimizing annotation overhead and increasing usability. To guarantee that probabilistic processes are almost-surely terminating, we integrate cost analysis into our type system to obtain expected upper bounds on recursion depth. We evaluate PReST on a wide variety of benchmarks from 4 categories: (i) randomized distributed protocols such as Itai and Rodeh's leader election, bounded retransmission, etc., (ii) parametric Markov chains such as random walks, (iii) probabilistic analysis of concurrent data structures such as queues, and (iv) distributions obtained by composing uniform distributions using operators like max, and sum. Our experiments show that the PReST type checker scales to large programs with sophisticated probabilistic distributions.
Probabilistic Refinement Session Types
Qiancheng Fu, Ankush Das, Marco Gaboardi
ACM SIGPLAN Conference on Programming Language Design and Implementation 2025
Session types provide a formal type system to define and verify communication protocols between message-passing processes. In order to analyze randomized systems, recent works have extended session types with probabilistic type constructors. Unfortunately, all the proposed extensions only support constant probabilities which limits their applicability to real-world systems. Our work addresses this limitation by introducing probabilistic refinement session types which enable symbolic reasoning for concurrent probabilistic systems in a core calculus we call PReST. The type system is carefully designed to be a conservative extension of refinement session types and supports both probabilistic and regular choice type operators. We also implement PReST in a prototype which we use for validating probabilistic concurrent programs. The added expressive power leads to significant challenges, both in the meta theory and implementation of PReST, particularly with type checking: it requires reconstructing intermediate types for channels when type checking probabilistic branching expressions. The theory handles this by semantically quantifying refinement variables in probabilistic typing rules, a deviation from standard refinement type systems. The implementation relies on a bi-directional type checker that uses an SMT solver to reconstruct the intermediate types minimizing annotation overhead and increasing usability. To guarantee that probabilistic processes are almost-surely terminating, we integrate cost analysis into our type system to obtain expected upper bounds on recursion depth. We evaluate PReST on a wide variety of benchmarks from 4 categories: (i) randomized distributed protocols such as Itai and Rodeh's leader election, bounded retransmission, etc., (ii) parametric Markov chains such as random walks, (iii) probabilistic analysis of concurrent data structures such as queues, and (iv) distributions obtained by composing uniform distributions using operators like max, and sum. Our experiments show that the PReST type checker scales to large programs with sophisticated probabilistic distributions.
A Two-Level Linear Dependent Type Theory
Qiancheng Fu, Hongwei Xi
arXiv 2023
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system to assume tight resource bounds. A natural notion of irrelevancy is established where all proofs and types occurring inside programs are fully erasable without compromising their operational behavior. Through a heap-based operational semantics, we show that extracted programs always make computational progress and run memory clean. Additionally, programs can be freely reflected into the logical level for conducting deep proofs in the style of standard dependent type theories. This enables one to write resource safe programs and verify their correctness using a unified language.
A Two-Level Linear Dependent Type Theory
Qiancheng Fu, Hongwei Xi
arXiv 2023
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system to assume tight resource bounds. A natural notion of irrelevancy is established where all proofs and types occurring inside programs are fully erasable without compromising their operational behavior. Through a heap-based operational semantics, we show that extracted programs always make computational progress and run memory clean. Additionally, programs can be freely reflected into the logical level for conducting deep proofs in the style of standard dependent type theories. This enables one to write resource safe programs and verify their correctness using a unified language.
A Calculus of Inductive Linear Constructions
Qiancheng Fu, Hongwei Xi
Workshop on Type-Driven Development 2023
In this paper, we present a novel calculus of inductive linear constructions (CILC), combining linear types and dependent types. Our type theory addresses a looming issue in the research on linear dependent types: the lack of a general mechanism for defining sound linear inductive types. CILC allows one to encode in a straightforward manner the linear connectives that must be baked into the core of other systems. This greatly lowers the difficulty of encoding various data structures and makes writing non-trivial programs humanly feasible. We study the standard meta theory of our calculus, showing that it is sound in the usual sense. Through a heap-based operational semantics, we show that CILC safely manipulates resources and runs memory clean. We have formalized and proven correct most of the reported results in the Coq Proof Assistant.
A Calculus of Inductive Linear Constructions
Qiancheng Fu, Hongwei Xi
Workshop on Type-Driven Development 2023
In this paper, we present a novel calculus of inductive linear constructions (CILC), combining linear types and dependent types. Our type theory addresses a looming issue in the research on linear dependent types: the lack of a general mechanism for defining sound linear inductive types. CILC allows one to encode in a straightforward manner the linear connectives that must be baked into the core of other systems. This greatly lowers the difficulty of encoding various data structures and makes writing non-trivial programs humanly feasible. We study the standard meta theory of our calculus, showing that it is sound in the usual sense. Through a heap-based operational semantics, we show that CILC safely manipulates resources and runs memory clean. We have formalized and proven correct most of the reported results in the Coq Proof Assistant.