arXiv subjects

Anders Alnor Mathiasen

Publications and source records attributed to Anders Alnor Mathiasen.

4 recordsLinked to original sources

arXiv2026

Yarrow: Reconciling Effect Handlers and Region-Based Memory Management

We present a new ML-like programming language Yarrow with algebraic effects and region-based memory management. Reconciling these programming language features into one language is challenging: the non-local control flow of algebraic effects break the stack discipline of function calls and returns that region-based memory management relies on, and multi-shot effect handlers break the invariant that regions can be exited at most once. We present a program logic, called Yarrow Logic (YL), that supports safe and modular reasoning about regions in the presence of one-shot and multi-shot effect handlers. We prove the logic sound w.r.t. the operational semantics of Yarrow which is inspired by the runtime of OCaml but refined for regions. We use YL to prove correctness of a number of case studies with algebraic effects, including checkpointing, asynchronous computation and a LIFO data structure implementation. Since all memory locations used in these case studies are allocated in regions, these case studies avoid using the less efficient garbage collected heap memory. We have formalized Yarrow's operational semantics, the Yarrow program logic, and all our case studies using the Iris separation logic framework on top of the Rocq Prover.

cs.PL↗

arXiv2026

Verifying Isolation Levels of Database Implementations for Free Using Separation Logic

Modern databases are highly concurrent and provide transactions as a mean of grouping several database operations into atomically applied units. Database vendors and software engineers use isolation levels to describe the consistency guarantees of transactions. The popular isolation levels give weak guarantees, with intricate semantics, to optimize performance of applications. The problem of assuring that database implementations actually implement the isolation level guarantees that application developers build their systems upon has received a great deal of attention from the testing community. But until now, there exists no method for formally verifying that a database implementation actually implements the isolation level that database vendors says it provides. In this paper, we present a method for verifying that a database implements an isolation level: we derive isolation levels directly, as formalized in transactional consistency models by the database community, from the structure of separation logic specifications. By doing so, we consider all program executions that a database and arbitrary clients of the database could produce. The result is a so-called free theorem meaning that any database implementation, whose operations are verified against a specific set of separation logic specifications, actually implements its isolation level. As all proofs in this paper are mechanized in the Rocq proof assistant and build upon a detailed semantic model of program execution, we believe this contribution raises the bar for the achievable robustness of databases.

cs.DB↗

arXiv2025

Reasoning about Weak Isolation Levels in Separation Logic

Consistency guarantees among concurrently executing transactions in local- and distributed systems, commonly referred to as isolation levels, have been formalized in a number of models. Thus far, no model can reason about executable implementations of databases or local transaction libraries providing weak isolation levels. Weak isolation levels are characterized by being highly concurrent and, unlike their stronger counterpart serializability, they are not equivalent to the consistency guarantees provided by a transaction library implemented using a global lock. Industrial-strength databases almost exclusively implement weak isolation levels as their default level. This calls for formalism as numerous bugs violating isolation have been detected in these databases. In this paper, we formalize three weak isolation levels in separation logic, namely read uncommitted, read committed, and snapshot isolation. We define modular separation logic specifications that are independent of the underlying transaction library implementation. Historically, isolation levels have been specified using examples of executions between concurrent transactions that are not allowed to occur, and we demonstrate that our specifications correctly prohibit such examples. To show that our specifications are realizable, we formally verify that an executable implementation of a key-value database running the multi-version concurrency control algorithm from the original snapshot isolation paper satisfies our specification of snapshot isolation. Moreover, we prove implications between the specifications -- snapshot isolation implies read committed and read committed implies read uncommitted -- and thus the verification effort of the database serves as proof that all of our specifications are realizable. All results are mechanized in the Rocq proof assistant on top of the Iris separation logic framework.

cs.PL↗

arXiv2020

The Fine-Grained and Parallel Complexity of Andersen's Pointer Analysis

Pointer analysis is one of the fundamental problems in static program analysis. Given a set of pointers, the task is to produce a useful over-approximation of the memory locations that each pointer may point-to at runtime. The most common formulation is Andersen's Pointer Analysis (APA), defined as an inclusion-based set of $m$ pointer constraints over a set of $n$ pointers. Existing algorithms solve APA in $O(n^2\cdot m)$ time, while it has been conjectured that the problem has no truly sub-cubic algorithm, with a proof so far having remained elusive. In this work we draw a rich fine-grained and parallel complexity landscape of APA, and present upper and lower bounds. First, we establish an $O(n^3)$ upper-bound for general APA, improving over $O(n^2\cdot m)$ as $n=O(m)$. Second, we show that even on-demand APA ("may a specific pointer $a$ point to a specific location $b$?") has an $Ω(n^3)$ (combinatorial) lower bound under standard complexity-theoretic hypotheses. This formally establishes the long-conjectured "cubic bottleneck" of APA, and shows that our $O(n^3)$-time algorithm is optimal. Third, we show that under mild restrictions, APA is solvable in $\tilde{O}(n^ω)$ time, where $ω<2.373$ is the matrix-multiplication exponent. It is believed that $ω=2+o(1)$, in which case this bound becomes quadratic. Fourth, we show that even under such restrictions, even the on-demand problem has an $Ω(n^2)$ lower bound under standard complexity-theoretic hypotheses, and hence our algorithm is optimal when $ω=2+o(1)$. Fifth, we study the parallelizability of APA and establish lower and upper bounds: (i) in general, the problem is P-complete and hence unlikely parallelizable, whereas (ii) under mild restrictions, the problem is parallelizable. Our theoretical treatment formalizes several insights that can lead to practical improvements in the future.

cs.PL↗