Covers programming language semantics, language features, programming approaches, and compiler techniques.
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2604.04345Several recently proposed program logics have incorporated notions of underapproximation into their design, enabling them to reason about reachability rather than safety. In this paper, we explore how similar ideas can be integrated into an expressive type and effect system. We use the resulting underapproximate type specifications to guide the synthesis of test generators that probe the behavior of effectful black-box systems. A key novelty of our type language is its ability to capture underapproximate behaviors of effectful operations using symbolic traces that expose latent data and control dependencies, constraints that must be preserved by the test sequences the generator outputs. We implement this approach in a tool called Clouseau, and evaluate it on a diverse range of applications by integrating Clouseau's synthesized generators into property-based testing frameworks like QCheck and model-checking tools like P. In both settings, the generators synthesized by Clouseau are significantly more effective than the default testing strategy, and are competitive with state-of-the-art, handwritten solutions.
Generating performant executables from high level languages is critical to software performance across a wide range of domains. Modern compilers perform this task by passing code through a series of well-studied optimizations at progressively lower levels of abstraction, but may miss optimization opportunities that require high-level reasoning about a program's purpose. Recent work has proposed using LLMs to fill this gap. While LLMs can achieve large speedups on some programs, they frequently generate code that is incorrect. In this work, we propose a method to balance the correctness of conventional compiler optimizations with the ``creativity'' of LLM-based code generation: compiler-LLM cooperation. Our approach integrates existing compiler optimization passes with LLM-based code generation at multiple levels of abstraction, retaining the best features of both types of code optimization. We realize our approach with a multi-agent system that includes (1) LLM-based optimization agents for each level of abstraction, (2) individual compiler constituents as tools, (3) an LLM-based test generation agent that probes the correctness and performance of generated code, and (4) a guiding LLM that orchestrates the other components. The strategy enables LLM-based optimization of input programs at multiple levels of abstraction and introduces a method for distributing computational budget between levels. Our extensive evaluation shows that compiler-LLM cooperation outperforms both existing compiler optimizations and level-specific LLM-based baselines, producing speedups up to 1.25x.
Coarse-Grained Reconfigurable Architectures (CGRAs) are a promising and versatile accelerator platform, offering a balance between the performance and efficiency of specialized accelerators and the software programmability. However, their full potential is severely hindered by control flow in accelerated kernels, as the control flow (e.g., loops, branches) is fundamentally incompatible with the parallel, data-driven CGRA fabric. Prior strategies to resolve this mismatch in CGRA kernel acceleration are either inefficient, sacrificing performance for generality, or lack generality due to the difficulty of adapting them across different execution models. Thus, a general and unified solution for efficient CGRA kernel acceleration remains elusive. This paper introduces NEURA, a unified and retargetable compilation framework that systematically resolves the control-dataflow mismatch in CGRAs. NEURA's core innovation is a novel, pure dataflow intermediate representation (IR) built on a predicated type system. In this IR, control contexts are embedded as a predicate within each data, making control an intrinsic property of data. This mechanism enables NEURA to systematically flatten complex control flow into a single unified dataflow graph. This unified representation decouples kernel representation from hardware, empowering NEURA to retarget diverse CGRAs with different execution models and microarchitectural features. When targeted to a high-performance spatio-temporal CGRA, NEURA delivers a 2.20x speedup on kernel benchmarks and up to 2.71x geometric mean speedup on real-world applications over state-of-the-art (SOTA) high-performance baselines. It also provides a competitive solution against the SOTA low-power CGRA when retargeted to a spatial-only CGRA. NEURA is open-source and available at https://github.com/coredac/neura.
In recent years, quantum computing has gained a substantial amount of momentum, and the capabilities of quantum devices are continually expanding and improving. Nevertheless, writing a quantum program from scratch remains tedious and error-prone work, showcasing the clear demand for automated tool support. We present Qet, a fully automated static program analysis tool that yields a precise expected cost analysis of mixed classical-quantum programs. Qet supports programs with advanced features like mid-circuit measurements and classical control flow. The methodology of our prototype implementation is based on a recently proposed quantum expectation transformer framework, generalising Dijkstra's predicate transformer and Hoare logic. The prototype implementation Qet is evaluated on a number of case studies taken from the literature and online references. Qet is able to fully automatically infer precise upper bounds on the expected costs that previously could only be derived by tedious manual calculations.
2604.02955This technical report contains the formal definitions and metatheory for the act specification and verification language. It documents the syntax, the operational pointer semantics, the type system and the main metatheoretic results (type-safety).
Current LLM-based coding agents follow a serial execution paradigm: the model first generates the complete code, then invokes an interpreter to execute it. This sequential workflow leaves the executor idle during generation and the generator idle during execution, resulting in unnecessary end-to-end latency. We observe that, unlike human developers, LLMs produce code tokens sequentially without revision, making it possible to execute code as it is being generated. We formalize this parallel execution paradigm, modeling it as a three-stage pipeline of generation, detection, and execution, and derive closed-form latency bounds that characterize its speedup potential and operating regimes. We then present Eager, a concrete implementation featuring AST-based chunking, dynamic batching with gated execution, and early error interruption. We evaluate Eager across four benchmarks, seven LLMs, and three execution environments. Results show that Eager reduces the non-overlapped execution latency by up to 99.9% and the end-to-end latency by up to 55% across seven LLMs and four benchmarks.
ErgoAI is a high level, multi-paradigm logic programming language and system developed by Coherent Knowledge Systems as an enhancement of and a successor to the popular Flora-2 system. ErgoAI is oriented towards scalable knowledge representation and reasoning, and can exploit both structured knowledge as well as knowledge derived from external sources such as vector embeddings. From the start, ErgoAI (and Flora-2 before it) were designed to exploit the well-founded semantics for reasoning in a multi-paradigm environment, including object-based logic (F-logic) with non-monotonic inheritance; higher order syntax in the style of HiLog; defeasibility of rules; semantically clean transactional updates; extensive use of subgoal delay for handling unsafe queries and for better performance; and optional support for bounded rationality at a module level. Although Flora-2 programs are compiled into XSB and adopt many Prolog features, ErgoAI is altogether a different language and system. Under consideration in Theory and Practice of Logic Programming (TPLP).
2603.28326The Rust programming language is famous for its strong ownership regime: at each point, each value is either exclusively owned, exclusively borrowed through a mutable reference, or borrowed as read-only through one or more shared references. These rules, known as Rust's pointer-aliasing rules, are exploited by the Rust compiler to generate more efficient machine code, and enforced by Rust's static type system, except inside unsafe blocks. In this paper, we present our work in progress towards the first program logic for modularly verifying that Rust programs that use unsafe blocks comply with the pointer-aliasing rules.
Reverse engineering tools remain monolithic and imperative compared to the advancement of modern compiler architectures: analyses are tied to a single mutable representation, making them difficult to extend or refine, and forcing premature choices between soundness and precision. We observe that decompilation is the reverse of compilation and can be structured as a sequence of modular passes, each performing a granular and clearly defined interpretation of the binary at a progressively higher level of abstraction. We formalize this as provenance-guided superset decompilation (PGSD), a framework that monotonically derives facts about the binary into a relation store. Instead of committing early to a single interpretation, the pipeline retains ambiguous interpretations as parallel candidates with provenance, deferring resolution until the final selection phase. Manifold implements PGSD as a declarative reverse engineering framework that lifts Linux ELF binaries to C99 through a granular intermediate representation in ~35K lines of Rust and Datalog. On GNU coreutils, Manifold's output quality matches Ghidra, IDA Pro, angr, and RetDec on multiple metrics while producing fewer compiler errors, and generalizes across compilers and optimization levels.
Non-Axiomatic Reasoning Systems (NARS) provide a framework for building adaptive agents that operate under insufficient knowledge and resources. However, the standard input language, Narsese, poses a usability barrier: its dense symbolic notation, overloaded punctuation, and implicit conventions make programs difficult to read, write, and maintain. We present DriftScript, a Lisp-like domain-specific language that compiles to Narsese. DriftScript provides source-level constructs covering the major sentence and term forms used in Non-Axiomatic Logic (NAL) levels 1 through 8, including inheritance, temporal implication, variable quantification, sequential conjunction, and operation invocation, while replacing symbolic syntax with readable keyword-based S-expressions. The compiler is a zero-dependency, four-stage pipeline implemented in 1,941 lines of C99. When used with the DriftNARS engine, DriftScript programs connect to external systems through four structured callback types and an HTTP operation registry, enabling a sense-reason-act loop for autonomous agents. We describe the language design and formal grammar, detail the compiler architecture, and evaluate the compiler through a 106-case test suite, equivalence testing against hand-written Narsese, a NAL coverage analysis, structural readability metrics, and compilation benchmarks. The source code is available at https://github.com/seamus-brady/DriftNARS. This paper focuses on the design and implementation of the DriftScript language and its embedding into DriftNARS, rather than on new inference algorithms for NARS itself.
The Heighway dragon curve is one of the most known fractal curves. There are two ways to construct the curve: repeatedly make a copy of the current curve, rotate it by 90 degrees, and connect them; or repeatedly replace each straight segment in the curve by two segments with a right angle. A natural question is how do we prove the equivalence of the two approaches? We generalise the construction of the curve to allow rotations to both sides. It then turns out that the two approaches are respectively a foldr and a foldl, and the key property for proving their equivalence, using the second duality theorem, is the distributivity of an "interleave" operator.
Designing correct replicated data types (RDTs) is challenging because replicas evolve independently and must be merged while preserving application intent. A promising approach is correct-by-construction development in a proof-oriented programming language such as F*, Dafny and Lean, where desired correctness guarantees are specified and checked as the RDTs are implemented. Recent work Neem proposes the use of replication-aware linearizability (RA linearizability) as the correctness condition for state-based CRDTs and mergeable replicated data types (MRDTs), with automation in the SMT-aided, proof-oriented programming language F*. However, SMT-centric workflows can be opaque when automation fails to discharge a verification condition (VC), and they enlarge the trusted computing base (TCB). We present Sal, a multi-modal workflow to design and verify state-based CRDTs and MRDTs in Lean. Sal combines (i) kernel-checkable automation with proof reconstruction, (ii) SMT-aided automation when needed, and (iii) AI-assisted interactive theorem proving for remaining proof obligations. When a verification condition is shown to be invalid, we leverage Lean's property-based testing to automatically generate and visualize counterexamples, helping developers debug incorrect specifications or implementations. We report on our experience verifying a suite of 13 CRDTs and MRDTs with Sal: 69% of verification conditions are discharged by kernel-verified automation without SMT, and counterexamples automatically expose subtle bugs such as the well-known enable-wins flag anomaly. The codebase for Sal is open-sourced, and is available at \href{https://github.com/fplaunchpad/sal}{https://github.com/fplaunchpad/sal}
For high-assurance software, source-level reasoning is insufficient: we need binary-level guarantees. Despite constrained Horn clause (CHC) solving being one of the most popular forms of automated verification, prior work has not evaluated the viability of CHC solving for binary analysis. To fill this gap, we assemble a pipeline that encodes binary analysis problems as CHCs in the SMT logic of quantifier-free bit vectors, and show that off-the-shelf CHC solvers achieve reasonable success on binaries compiled from 983 C invariant inference benchmarks: a portfolio solves 59.5% and 66.1% of the problems derived from the unoptimized and optimized binaries, respectively -- roughly equal to the success rate of a leading C verifier on the source code (60.1%). Moreover, we show that binary analysis provides a valuable source of bit-vector CHC benchmarks (which are in short supply): binary-derived problems differ from existing benchmarks both structurally and in solver success rates and rankings. Augmenting CHC solving competitions with binary-derived benchmarks will encourage solver developers to improve bit-vector reasoning, in turn making CHC solving a more effective tool for binary analysis.
2603.27015We present a framework in which program analysis -- type checking, bug finding, and equivalence verification -- is organized as computing the Čech cohomology of a semantic presheaf over a program's site category. The presheaf assigns refinement-type information to observation sites and restricts it along data-flow morphisms. The cohomology group $H^{0}$ is the space of globally consistent typings. The first cohomology group $H^{1}$ classifies gluing obstructions -- bugs, type errors, and equivalence failures -- each localized to a specific pair of disagreeing sites. This formulation yields three concrete results unavailable in prior work: (1) the rank of $H^1$ over $F_{2}$ counts the minimum independent fixes; (2) $H_{1}(U, Iso) = 0$ is sound and complete for behavioral equivalence; (3) Mayer-Vietoris enables compositional, incremental obstruction counting. We implement the framework in Deppy, a Python analysis tool, and evaluate it on a suite of 375~benchmarks: 133~bug-detection programs, 134~equivalence pairs, and 108~specification-satisfaction checks. Deppy achieves {100% bug-detection recall} (69% precision, F1 = 81%), 99% equivalence accuracy with zero false equivalences, and 98% spec accuracy with zero false satisfactions -- outperforming mypy and pyright, which report zero findings on unannotated code. The analysis models Python semantics as algebraic geometry: variables live on the generic fiber (non-None) unless on the closed nullable subscheme, integers form Spec($\mathbb{Z}$) with no bounded section (no overflow), and short-circuit evaluation defines an open-set topology on the presheaf.
2603.26215Differential privacy (DP) has established itself as one of the standards for ensuring privacy of individual data. However, reasoning about DP is a challenging and error-prone task, hence methods for formal verification and refutation of DP properties have received significant interest in recent years. In this work, we present a novel method for automated formal refutation of $ε$-DP. Our method refutes $ε$-DP by searching for a pair of inputs together with a non-negative function over outputs whose expected value on these two inputs differs by a significant amount. The two inputs and the non-negative function over outputs are computed simultaneously, by utilizing upper expectation supermartingales and lower expectation submartingales from probabilistic program analysis, which we leverage to introduce a sound and complete proof rule for $ε$-DP refutation. To the best of our knowledge, our method is the first method for $ε$-DP refutation to offer the following four desirable features: (1)~it is fully automated, (2)~it is applicable to stochastic mechanisms with sampling instructions from both discrete and continuous distributions, (3)~it provides soundness guarantees, and (4)~it provides semi-completeness guarantees. Our experiments show that our prototype tool SuperDP achieves superior performance compared to the state of the art and manages to refute $ε$-DP for a number of challenging examples collected from the literature, including ones that were out of the reach of prior methods.
Despite widespread use, the complexity class of modern regular expression matching was not well-understood. Previous work proved that regular expression matching with backreferences and lookarounds was PSPACE-complete, but the proof was not mechanized and applied to an abstract regex language. This paper clarifies the question for JavaScript regular expressions. In this paper, we prove the following new results, with most core proofs mechanized in the Rocq proof assistant. We prove that JavaScript regex matching is indeed PSPACE-hard, even without negative lookarounds, and OptP-hard as well; that JavaScript regex matching without lower-bounded quantifiers (i.e. quantifiers with a non-zero minimum number of repetitions) is PSPACE-complete; and that JavaScript regex matching without lower-bounded quantifiers and without lookarounds is OptP-complete.
Large Language Models (LLMs) have shown promising results in automating formal verification. However, existing approaches treat proof generation as a static, end-to-end prediction over source code, relying on limited verifier feedback and lacking access to concrete program behaviors. We present EXVERUS, a counterexample-guided framework that enables LLMs to reason about proofs using behavioral feedback via counterexamples. When a proof fails, EXVERUS automatically generates and validates counterexamples, and then guides the LLM to generalize them into inductive invariants to block these failures. Our evaluation shows that EXVERUS significantly improves proof accuracy, robustness, and token efficiency over the state-of-the-art prompting-based Verus proof generator.
A prevailing assumption in machine learning is that model correctness must be enforced after the fact. We observe that the properties determining whether an AI model is numerically stable, computationally correct, or consistent with a physical domain do not necessarily demand post hoc enforcement. They can be verified at design time, before training begins, at marginal computational cost, with particular relevance to models deployed in high-leverage decision support and scientifically constrained settings. These properties share a specific algebraic structure: they are expressible as constraints over finitely generated abelian groups $\mathbb{Z}^n$, where inference is decidable in polynomial time and the principal type is unique. A framework built on this observation composes three prior results (arXiv:2603.16437, arXiv:2603.17627, arXiv:2603.18104): a dimensional type system carrying arbitrary annotations as persistent codata through model elaboration; a program hypergraph that infers Clifford algebra grade and derives geometric product sparsity from type signatures alone; and an adaptive domain model architecture preserving both invariants through training via forward-mode coeffect analysis and exact posit accumulation. We believe this composition yields a novel information-theoretic result: Hindley-Milner unification over abelian groups computes the maximum a posteriori hypothesis under a computable restriction of Solomonoff's universal prior, placing the framework's type inference on the same formal ground as universal induction. We compare four contemporary approaches to AI reliability and show that each imposes overhead that can compound across deployments, layers, and inference requests. This framework eliminates that overhead by construction.
2603.25337We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching theory. The second is an inductive style, which follows a more traditional mathematical approach. We also discuss several optimizations for these representations. Furthermore, we present a case study that demonstrates the potential applications of our approach across various domains.
Numerical software depends on fast, accurate implementations of mathematical primitives like sin, exp, and log. Modern superoptimizers can optimize floating-point kernels against a given set of such primitives, but a more fundamental question remains open: which new primitives are worth implementing in the first place? We formulate this as numerical library learning: given a workload of floating-point kernels, identify the mathematical primitives whose expert implementations would most improve speed and accuracy. Our key insight is that numerical superoptimizers already have the machinery well-suited to this problem. Their search procedures happen to enumerate candidate primitives, their equivalence procedures can generalize and deduplicate candidates, and their cost models can estimate counterfactual utility: how much the workload would improve if a given primitive were available. We present GrowLibm, which repurposes the Herbie superoptimizer as a numerical library learner. GrowLibm mines candidate primitives from the superoptimizer's intermediate search results, ranks them by counterfactual utility, and prunes redundant candidates. Across three scientific applications (PROJ, CoolProp, and Basilisk), GrowLibm identifies compact, reusable primitives that can be implemented effectively using standard numerical techniques. When Herbie is extended with these expert implementations, kernel speed improves by up to 2.2x at fixed accuracy, and maximum achievable accuracy also improves, in one case from 56.0% to 93.5%. We also prototype an LLVM matcher that recognizes learned primitives in optimized IR, recovering 26 replacement sites across five PROJ projections and improving end-to-end application performance by up to 5%.