Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2408.11007

Extending the Quantitative Pattern-Matching Paradigm

Sandra Alves·Delia Kesner·Miguel Ramos
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming languages, we use a (weak and closed) $\lambda$-calculus integrating a pattern matching mechanism on algebraic data types (ADTs). Remarkably, we also show that this language not only encodes Plotkin's CBV and CBN $\lambda$-calculus as well as other subsuming frameworks, such as the bang-calculus, but can also be used to interpret the semantics of effectful languages with exceptions. After a thorough study of the untyped language, we introduce a type system based on intersection types, and we show through purely logical methods that the set of terminating terms of the language corresponds exactly to that of well-typed terms. Moreover, by considering non-idempotent intersection types, this characterization turns out to be quantitative, i.e. the size of the type derivation of a term t gives an upper bound for the number of evaluation steps from t to its normal form.

Explore related subjects

cs.PLcs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sandra Alves, Delia Kesner, Miguel Ramos. 2024-08-20. Extending the Quantitative Pattern-Matching Paradigm. https://arxiv.org/abs/2408.11007

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

UnsafeChecker: Finding Soundness Bugs in Rust Safe Abstractions

Rust guarantees memory safety without garbage collection through a strict ownership and borrowing system. However, for low-level systems programming, many widely used libraries rely on the unsafe keyword. These libraries encapsulate raw-pointer operations behind safe APIs to form safe abstractions. A single mistake in this internal unsafe code can break its safety contract, rendering the abstraction unsound and allowing safe clients to trigger undefined behavior. Detecting these potential soundness violations is challenging. Existing static analysis tools for C/C++ ignore Rust-specific safety contracts, while current Rust tools lack the deep semantic modeling required to track the contexts that raw pointers erase. To address this gap, we present UnsafeChecker, a compiler-integrated static analysis framework for detecting potential soundness violations in Rust safe abstractions. UnsafeChecker analyzes Rust MIR using a flow-sensitive abstract interpretation that maintains a shared state with three components: ownership, object validity, and layout. Each warning rule consumes the subset of facts needed for the corresponding Rust safety obligation. UnsafeChecker reports both instruction-level undefined behavior and boundary-level contract violations that may escape through safe APIs. We evaluate UnsafeChecker on a benchmark of 46 RustSec vulnerabilities, which contain 53 ground-truth bugs. UnsafeChecker outperforms several state-of-the-art tools, detecting 32 CVEs and covering 36 bugs (67.9% recall) with 51.6% alert-level precision. Furthermore, in a large-scale scan of real-world crates on crates.io, UnsafeChecker uncovered 114 previously unknown bugs across 83 crates, with 45 confirmed and 27 already fixed by maintainers.

cs.PL↗
arXiv2026

Mapping Dynamic, Hierarchical Quantum Circuits

Qubit mapping is a critical pass in quantum compilation. Despite various advances, dynamic circuits, those exhibiting data dependent control-flow, often resulting from qubit measurements, are not yet supported by the vast majority of available qubit mappers. The crucial limitation to overcome is the dependence on flat, one-dimensional representations of circuits. Further, qubit mappers currently lack compiler abstractions that capture the hierarchical nature of circuits, hindering the qubit mapping process. In this paper, 1 we introduce a new qubit mapping method and analyses to tackle hierarchical dynamic circuits. Our novelty resides in four key aspects: modeling (statically) sub-circuits in disjoint control-flow paths, introducing a novel Qubit Reconciliation pass to maintain consistency between sub-circuit and control-flow boundaries, a loop-entry remapping pass, and a refined cost function enhanced for SWAP count, circuit depth, circuit latency and error. We demonstrate the efficiency of our approach on a wide range of dynamic circuits on two monolithic Quantum Processing Units of 127 and 156 qubits, and on chiplet hexagon-based QPUs. On monolithic QPUs, our qubit mapper improves the SWAP count by up to 52%, depth by up to 18%, latency by up to 18.6%, and error by up to 40%. On chiplet architectures, we achieve improvements of up to 36% on SWAP count, 8.7% on depth, 15% on latency, and 15% of error.

cs.PL↗
arXiv2026

Erased Postulates, Identity Types and Quotients

This text is concerned with the question of whether, in type theory with erasure annotations, one can postulate that some type is inhabited and still have a guarantee that a program will not get stuck. Previous work has provided such guarantees for consistent erased postulates, i.e. postulates that are restricted to be used in erased contexts. Here those guarantees are extended to type theory with identity types. Similar ideas provide a simple way to support quotient types: it is shown that one can let things like "the equivalence classes for two related values are equal" be erased postulates and have an eliminator that only computes for the equivalence class constructor, and still get a guarantee that programs will compute correctly. Another question is whether programs compute correctly if one is allowed to transport (cast) using erased identity proofs. It is shown that this is safe in the absence of quotients and postulates, and in the presence of quotients and erased postulates that can be implemented using equality reflection. However, unrestricted transports of this kind are not compatible with erased, postulated univalence. For that reason the text includes a study of the function []-cong, which encapsulates a limited form of transport for erased identity proofs. The text is accompanied by machine-checked Agda proofs.

cs.PL↗