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Tobias Reinhard

Publications and source records attributed to Tobias Reinhard.

9 recordsLinked to original sources
arXiv2026

DeCo: A Core Calculus for Incremental Functional Programming with Generic Data Types

Incrementalization speeds up computations by avoiding unnecessary recomputations and by efficiently reusing previous results. While domain-specific techniques achieve impressive speedups, e.g., in the context of database queries, they are difficult to generalize. Meanwhile, general approaches offer little support for incrementalizing domain-specific operations. In this work, we present DeCo, a novel core calculus for incremental functional programming with support for a wide range of user-defined data types. Despite its generic nature, our approach statically incrementalizes domain-specific operations on user-defined data types. It is, hence, more fine-grained than other generic techniques which resort to treating domain-specific operations as black boxes. We mechanized our work in Lean and proved it sound, meaning incrementalized execution computes the same result as full reevaluation. We also provide an executable implementation with case studies featuring examples from linear algebra, relational algebra, dictionaries, trees, and conflict-free replicated data types, plus a brief performance evaluation on linear and relational algebra and on trees.

cs.PL↗
arXiv2024

Semi-Automated Modular Formal Verification of Critical Software: Liveness and Completeness Thresholds

In this dissertation we describe two contributions to the state of the art in reasoning about liveness and safety, respectively. Programs for multiprocessor machines commonly perform busy waiting for synchronization. We propose the first separation logic for modularly verifying termination of such programs under fair scheduling. Our logic requires the proof author to associate a ghost signal with each busy-waiting loop and allows such loops to iterate while their corresponding signal $s$ is not set. The proof author further has to define a well-founded order on signals and to prove that if the looping thread holds an obligation to set a signal $s'$, then $s'$ is ordered above $s$. By using conventional shared state invariants to associate the state of ghost signals with the state of data structures, programs busy-waiting for arbitrary conditions over arbitrary data structures can be verified. Moreover, we present the first study of completeness thresholds for bounded memory safety proofs. Specifically, we consider heap-manipulating programs that iterate over arrays without allocating or freeing memory. In this setting, we present the first notion of completeness thresholds for program verification which reduce unbounded memory safety proofs to bounded ones. Furthermore, we demonstrate that we can characterise completeness thresholds for simple classes of array traversing programs. Finally, we suggest avenues of research to scale this technique theoretically, i.e., to larger classes of programs (heap manipulation, tree-like data structures), and practically by highlighting automation opportunities.

cs.LO↗
arXiv2023

Completeness Thresholds for Memory Safety: Unbounded Guarantees via Bounded Proofs (Extended Abstract)

Bounded proofs are convenient to use due to the high degree of automation that exhaustive checking affords. However, they fall short of providing the robust assurances offered by unbounded proofs. We sketch how completeness thresholds serve as a bridge, allowing us to derive unbounded guarantees from bounded proofs. Using a bubble sort implementation as example, we demonstrate that a bounded proof only needs to consider a few specific inputs to yield unbounded guarantees.

cs.LO↗
arXiv2023

Completeness Thresholds for Memory Safety of Array Traversing Programs

We report on intermediate results of -- to the best of our knowledge -- the first study of completeness thresholds for (partially) bounded memory safety proofs. Specifically, we consider heap-manipulating programs that iterate over arrays without allocating or freeing memory. In this setting, we present the first notion of completeness thresholds for program verification which reduce unbounded memory safety proofs to (partially) bounded ones. Moreover, we demonstrate that we can characterise completeness thresholds for simple classes of array traversing programs. Finally, we suggest avenues of research to scale this technique theoretically, i.e., to larger classes of programs (heap manipulation, tree-like data structures), and practically by highlighting automation opportunities.

cs.LO↗
arXiv2023

Completeness Thresholds for Memory Safety of Array Traversing Programs: Early Technical Report

In this early technical report on an ongoing project, we present -- to the best of our knowledge -- the first study of completeness thresholds for memory safety proofs. Specifically we consider heap-manipulating programs that iterate over arrays without allocating or freeing memory. We present the first notion of completeness thresholds for program verification which reduce unbounded memory safety proofs to bounded ones. Moreover, we present some preliminary ideas on how completeness thresholds can be computed for concrete programs.

cs.LO↗
arXiv2021

Ghost Signals: Verifying Termination of Busy-Waiting (Extended Version)

Programs for multiprocessor machines commonly perform busy waiting for synchronization. We propose the first separation logic for modularly verifying termination of such programs under fair scheduling. Our logic requires the proof author to associate a ghost signal with each busy-waiting loop and allows such loops to iterate while their corresponding signal $s$ is not set. The proof author further has to define a well-founded order on signals and to prove that if the looping thread holds an obligation to set a signal $s^\prime$, then $s^\prime$ is ordered above $s$. By using conventional shared state invariants to associate the state of ghost signals with the state of data structures, programs busy-waiting for arbitrary conditions over arbitrary data structures can be verified.

cs.LO↗
arXiv2020

A Separation Logic to Verify Termination of Busy-Waiting for Abrupt Program Exit

Programs for multiprocessor machines commonly perform busy-waiting for synchronisation. In this paper, we make a first step towards proving termination of such programs. We approximate (i) arbitrary waitable events by abrupt program termination and (ii) busy-waiting for events by busy-waiting to be abruptly terminated. We propose a separation logic for modularly verifying termination (under fair scheduling) of programs where some threads eventually abruptly terminate the program, and other threads busy-wait for this to happen.

cs.LO↗
arXiv2020

A Core Calculus for Static Latency Tracking with Placement Types

Developing efficient geo-distributed applications is challenging as programmers can easily introduce computations that entail high latency communication. We propose a language design which makes latency explicit and extracts type-level bounds for a computation's runtime latency. We present our initial steps with a core calculus that enables extracting provably correct latency bounds and outline future work.

cs.PL↗
arXiv2020

A Separation Logic to Verify Termination of Busy-Waiting for Abrupt Program Exit: Technical Report

Programs for multiprocessor machines commonly perform busy-waiting for synchronisation. In this paper, we make a first step towards proving termination of such programs. We approximate (i) arbitrary waitable events by abrupt program termination and (ii) busy-waiting for events by busy-waiting to be abruptly terminated. We propose a separation logic for modularly verifying termination (under fair scheduling) of programs where some threads eventually abruptly terminate the program, and other threads busy-wait for this to happen.

cs.LO↗