Related papers: Dependent Types in Haskell: Theory and Practice

Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…

Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…

Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…

Deep learning is being used extensively in a variety of software engineering tasks, e.g., program classification and defect prediction. Although the technique eliminates the required process of feature engineering, the construction of…

DEKL 2.0 is a dependent type-theoretic framework for trace-indexed knowledge evolution. Its central claim is that the proof calculus remains monotone under standard structural rules, while non-monotonic behavior arises semantically from…

Quantum Computing (QC) offers the potential to enhance traditional High-Performance Computing (HPC) workloads by leveraging the unique properties of quantum computers, leading to the emergence of a new paradigm: HPC-QC. While this…

This paper brings mathematical tools to bear on the study of package dependencies in software systems. We introduce structures known as Dependency Structures with Choice (DSC) that provide a mathematical account of such dependencies,…

Trusted Execution Environments (TEEs) are hardware-enforced memory isolation units, emerging as a pivotal security solution for security-critical applications. TEEs, like Intel SGX and ARM TrustZone, allow the isolation of confidential code…

Cryptographic techniques have the potential to enable distrusting parties to collaborate in fundamentally new ways, but their practical implementation poses numerous challenges. An important class of such cryptographic techniques is known…

Higher inductive-inductive types (HIITs) generalize inductive types of dependent type theories in two ways. On the one hand they allow the simultaneous definition of multiple sorts that can be indexed over each other. On the other hand they…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…

Refinement type checkers are a powerful way to reason about functional programs. For example, one can prove properties of a slow, specification implementation, porting the proofs to an optimized implementation that behaves the same. Without…

Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…

The problem of code generation from textual program descriptions has long been viewed as a grand challenge in software engineering. In recent years, many deep learning based approaches have been proposed, which can generate a sequence of…

The recent notion of graded modal types provides a framework for extending type theories with fine-grained data-flow reasoning. The Granule language explores this idea in the context of linear types. In this practical setting, we observe…

Parallel programs in high performance computing (HPC) continue to grow in complexity and scale in the exascale era. The diversity in hardware and parallel programming models make developing, optimizing, and maintaining parallel software…

We present a small, formal language for specifying the behavior of simple console I/O programs. The design is driven by the concrete application case of testing interactive Haskell programs written by students. Specifications are…

Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…

The expression problem describes how most types can easily be extended with new ways to produce the type or new ways to consume the type, but not both. When abstract syntax trees are defined as an algebraic data type, for example, they can…