Related papers: Dependently Typing R Vectors, Arrays, and Matrices

Requirements are inherently interconnected through various types of dependencies. Identifying these dependencies is essential, as they underpin critical decisions and influence a range of activities throughout software development. However,…

Alignment has quickly become a default ingredient in LLM development, with techniques such as reinforcement learning from human feedback making models act safely, follow instructions, and perform ever-better on complex tasks. While these…

Type inference for dynamic programming languages such as Python is an important yet challenging task. Static type inference techniques can precisely infer variables with enough static constraints but are unable to handle variables with…

Writing parallel codes is difficult and exhibits a fundamental trade-off between abstraction and performance. The high level language abstractions designed to simplify the complexities of parallelism make certain assumptions that impacts…

Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…

We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…

Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…

Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…

Dependently typed lambda calculi such as the Edinburgh Logical Framework (LF) are a popular means for encoding rule-based specifications concerning formal syntactic objects. In these frameworks, relations over terms representing formal…

We present a logical framework for the verification of relational properties in imperative programs. Our work is motivated by relational properties which come from security applications and often require reasoning about formulas with…

Design patterns are distilled from many real systems to catalog common programming practice. However, some object-oriented design patterns are distorted or overly complicated because of the lack of supporting programming language constructs…

Redis is an in-memory data structure store, often used as a database, with a Haskell interface Hedis. Redis is dynamically typed --- a key can be discarded and re-associated to a value of a different type, and a command, when fetching a…

Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…

Dynamic code, i.e., code that is created or modified at runtime, is ubiquitous in today's world. The behavior of dynamic code can depend on the logic of the dynamic code generator in subtle and non-obvious ways, with significant security…

This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…

Large language models (LLMs) have shown promising performance in software vulnerability detection, yet their reasoning capabilities remain unreliable. We propose R2Vul, a method that combines reinforcement learning from AI feedback (RLAIF)…

We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…

We propose an amortized analysis that approximates the resource usage of a Haskell expression. Using the plugin API of GHC, we convert the Haskell code into a simplified representation called GHC Core. We then apply a type-based system…

Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…

Modelling term dependence in IR aims to identify co-occurring terms that are too heavily dependent on each other to be treated as a bag of words, and to adapt the indexing and ranking accordingly. Dependent terms are predominantly…