Related papers: Abstracting Extensible Recursive Functions
Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN),…
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…
Languages like F#, C#, and recently also Scala, provide "Async" programming models which aim to make asynchronous programming easier by avoiding an inversion of control that is inherent in callback-based programming models. This paper…
Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
Most ML-like functional languages provide records and overloading as unrelated features. Records not only represent data structures, but are also used to implement dictionary passing, whereas overloading produces type constraints that are…
In this paper, we present the case for a declarative foundation for data-intensive machine learning systems. Instead of creating a new system for each specific flavor of machine learning task, or hardcoding new optimizations, we argue for…
Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Constraint-logic object-oriented programming, for example using Muli, facilitates the integrated development of business software that occasionally involves finding solutions to constraint-logic problems. The availability of object-oriented…
Remora is a higher-order, rank-polymorphic array-processing programming language, in the same general class of languages as APL and J. It is intended for writing programs to be executed on parallel hardware. We provide an example-driven…
Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data…
Existential types are reconstructed in terms of small reflective subuniverses and dependent sums. The folklore decomposition detailed here gives rise to a particularly simple account of first-class modules as a mode of use of traditional…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
While large language models (LLMs) have demonstrated impressive performance in question-answering tasks, their performance is limited when the questions require knowledge that is not included in the model's training data and can only be…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…
In this paper, the branches of recursive and recurrent neural networks are classified in detail according to the network structure, training objective function and learning algorithm implementation. They are roughly divided into three…