arXiv subjects

Rose Bohrer

Publications and source records attributed to Rose Bohrer.

13 recordsLinked to original sources

arXiv2026

Hybrid Spatiotemporal Logic for Automotive Applications: Modeling and Model-Checking

We introduce a hybrid spatiotemporal logic for automotive safety applications (HSTL), focused on highway driving. Spatiotemporal logic features specifications about vehicles throughout space and time, while hybrid logic enables precise references to individual vehicles and their historical positions. We define the semantics of HSTL and provide a baseline model-checking algorithm for it. We propose two optimized model-checking algorithms, which reduce the search space based on the reachable states and possible transitions from one state to another. All three model-checking algorithms are evaluated on a series of common driving scenarios such as safe following, safe crossings, overtaking, and platooning. An exponential performance improvement is observed for the optimized algorithms.

cs.LO↗

arXiv2025

Proceedings 14th International Workshop on Trends in Functional Programming in Education

The goal of TFPIE is to gather researchers, teachers and professionals that use, or are interested in the use of, functional programming in education. TFPIE aims to be a venue where novel ideas, classroom-tested ideas and work-in-progress on the use of functional programming in education are discussed. The one-day workshop will foster a spirit of open discussion by having a review process for publication after the workshop.

cs.PL↗

arXiv2025

A Coq Formalization of Unification Modulo Exclusive-Or

Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory contains an operator with the properties Associativity, Commutativity, Nilpotency, and the presence of an identity. In the proof assistant Coq, we implement an algorithm that solves XOR unification problems, whose design was inspired by Liu and Lynch, and prove it sound, complete, and terminating. Using Coq's code extraction capability we obtain an implementation in the programming language OCaml.

cs.LO↗

arXiv2024

Pronoun Logic

Particularly in transgender and nonbinary (TGNB) communities, it is an increasingly common practice to publicly share one's personal pronouns so that we may be gendered correctly in others' speech. Many of us have nuanced desires for how we are gendered, leading us to use more complex descriptions of our wishes; for example, the descriptor 'she/they'. We observe that these descriptions of our wishes have the structure of a little language all their own. We thus propose formal logic as a tool for expressing one's personal pronouns and potentially other aspects of gender. We explore three potential logical foundations (linear logic, temporal logic, and free logic with definite descriptions) and their trade-offs. Our foremost motivation for this proposal is play, affirming that one can be both a logician and TGNB at the same time. We present formalization as something that can continue to evolve over time with society's understanding of gender. This implies that outreach is a major potential application: we can show TGNB youth that they belong in logic and have a unique contribution to make. Tools for evaluating whether one's pronouns are respected are an application as well.

cs.CL↗

arXiv2024

Programming Language Case Studies Can Be Deep

In the pedagogy of programming languages, one well-known course structure is to tour multiple languages as a means of touring paradigms. This tour-of-paradigms approach has long received criticism as lacking depth, distracting students from foundational issues in language theory and implementation. This paper argues for disentangling the idea of a tour-of-languages from the tour-of-paradigms. We make this argument by presenting, in depth, a series of case studies included in the Human-Centered Programming Languages curriculum. In this curriculum, case studies become deep, serving to tour the different intellectual foundations through which a scholar can approach programming languages, which one could call the tour-of-humans. In particular, the design aspect of programming languages has much to learn from the social sciences and humanities, yet these intellectual foundations would yield far fewer deep contributions if we did not permit them to employ case studies.

cs.PL↗

arXiv2022

Goal-Aware RSS for Complex Scenarios via Program Logic

We introduce a goal-aware extension of responsibility-sensitive safety (RSS), a recent methodology for rule-based safety guarantee for automated driving systems (ADS). Making RSS rules guarantee goal achievement -- in addition to collision avoidance as in the original RSS -- requires complex planning over long sequences of manoeuvres. To deal with the complexity, we introduce a compositional reasoning framework based on program logic, in which one can systematically develop RSS rules for smaller subscenarios and combine them to obtain RSS rules for bigger scenarios. As the basis of the framework, we introduce a program logic dFHL that accommodates continuous dynamics and safety conditions. Our framework presents a dFHL-based workflow for deriving goal-aware RSS rules; we discuss its software support, too. We conducted experimental evaluation using RSS rules in a safety architecture. Its results show that goal-aware RSS is indeed effective in realising both collision avoidance and goal achievement.

cs.RO↗

arXiv2022

Chemical Case Studies in KeYmaera X

Safety-critical chemical processes are the backbone of multi-billion-dollar industries, thus society deserves the strongest possible guarantees that they are safe. To that end, models of chemical processes are well-studied in the formal methods literature, including hybrid systems models which combine discrete and continuous dynamics. This paper is the first to use the KeYmaera X theorem-prover to verify chemical models with differential dynamic logic. Our case studies are novel in combining the following: we provide strong general-case correctness theorems, use particularly rich hybrid dynamics, and have particularly rigorous proofs. This novel combination is made possible by KeYmaera X. Simultaneously, we tell a general story about KeYmaera X: recent advances in automated reasoning about safety and liveness for differential equations have enabled elegant proofs about reaction dynamics.

cs.LO↗

arXiv2021

Structured Proofs for Adversarial Cyber-Physical Systems

Many cyber-physical systems (CPS) are safety-critical, so it is important to formally verify them, e.g. in formal logics that show a model's correctness specification always holds. Constructive Differential Game Logic (CdGL) is such a logic for (constructive) hybrid games, including hybrid systems. To overcome undecidability, the user first writes a proof, for which we present a proof-checking tool. We introduce Kaisar, the first language and tool for CdGL proofs, which until now could only be written by hand with a low-level proof calculus. Kaisar's structured proofs simplify challenging CPS proof tasks, especially by using programming language principles and high-level stateful reasoning. Kaisar exploits CdGL's constructivity and refinement relations to build proofs around models of game strategies. The evaluation reproduces and extends existing case studies on 1D and 2D driving. Proof metrics are compared and reported experiences are discussed for the original studies and their reproductions.

cs.LO↗

arXiv2020

Constructive Game Logic

Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's actions. We thus develop Constructive Game Logic which extends Parikh's Game Logic (GL) with constructivity and with first-order programs a la Pratt's first-order dynamic logic (DL). Our major contributions include: 1) a novel realizability semantics capturing the adversarial dynamics of games, 2) a natural deduction calculus and operational semantics describing the computational meaning of strategies via proof-terms, and 3) theoretical results including soundness of the proof calculus w.r.t. realizability semantics, progress and preservation of the operational semantics of proofs, and Existence Properties on support of the extraction of computational artifacts from game proofs. Together, these results provide the most general account of a Curry-Howard interpretation for any program logic to date, and the first at all for Game Logic.

cs.LO↗

arXiv2020

Refining Constructive Hybrid Games

We extend the constructive differential game logic (CdGL) of hybrid games with a refinement connective that relates two hybrid games. We use this connective to prove a folk theorem relating hybrid games to hybrid systems.

cs.LO↗

arXiv2020

Constructive Hybrid Games

Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where proofs that a player can win the game correspond to computable winning strategies. This is the logical foundation for synthesis of correct control and monitoring code for safety-critical cyber-physical systems. Our contributions include novel static and dynamic semantics as well as soundness and consistency.

cs.LO↗

arXiv2019

Toward Structured Proofs for Dynamic Logics

We present Kaisar, a structured interactive proof language for differential dynamic logic (dL), for safety-critical cyber-physical systems (CPS). The defining feature of Kaisar is *nominal terms*, which simplify CPS proofs by making the frequently needed historical references to past program states first-class. To support nominals, we extend the notion of structured proof with a first-class notion of *structured symbolic execution* of CPS models. We implement Kaisar in the theorem prover KeYmaera X and reproduce an example on the safe operation of a parachute and a case study on ground robot control. We show how nominals simplify common CPS reasoning tasks when combined with other features of structured proof. We develop an extensive metatheory for Kaisar. In addition to soundness and completeness, we show a formal specification for Kaisar's nominals and relate Kaisar to a nominal variant of dL.

cs.PL↗

arXiv2018

TWAM: A Certifying Abstract Machine for Logic Programs

Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of our approach is a new certifying abstract machine which we call the Typed Warren Abstract Machine (TWAM). The TWAM has a dependent type system strong enough to specify the semantics of a logic program in the logical framework LF. We present a soundness metatheorem which constitutes a partial correctness guarantee: well-typed programs implement the logic program specified by their type. This metatheorem justifies our design and implementation of a certifying compiler from T-Prolog to TWAM.

cs.PL↗