We have developed an algebraic framework for the study of recursion. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. We show that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, we are able to have the query answer expressed in an explicit algebr...

Polarized SILL is a programming language that combines functional with session-typed message-passing concurrency. It features general recursion; code and channel transmission; synchronous asynchronous communication. To reason about programs, we develop the first program equivalence framework based on observable communications. We give meaning to programs using an observed communication semantic...

Novice Computer Science (CS) students struggle learning recursion for reasons such as unfamiliarity with recursive thinking and difficulty in visualizing program execution. Many tasks in CS require a thorough understanding of recursion. We introduce the recursion module of ChiQat-Tutor, an environment for learning CS algorithms and data structures. ChiQat-Tutor uses the pedagogical tool of Recu...

We prove that the Langmann-Szabo-Zarembo (LSZ) model with quartic potential, a toy for quantum field theory on noncommutative spaces grasped as complex matrix model, obeys topological recursion of Chekhov, Eynard and Orantin. By introducing two families correlation functions, one corresponding to meromorphic differentials $\omega_{g,n}$ recursion, we obtain Dyson-Schwinger equations eventually ...

A bstract The operator product expansion of massless celestial primary operators arbitrary spin is investigated. Poincaré symmetry found to imply a set recursion relations on the coefficients leading singular terms at tree-level in holomorphic limit. constraints are solved by an Euler beta function with arguments that depend simply right-moving conformal weights product. These symmetry-derived ...

This note reexamines Spector’s remarkable computational interpretation of full classical analysis. Spector’s interpretation makes use of a rather abstruse recursion schema, so-called bar recursion, used to interpret the double negation shift DNS. In this note bar recursion is presented as a generalisation of a simpler primitive recursive functional needed for the interpretation of a finite (int...

We give a recursion-theoretic characterization of the complexity classes NC for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computati...

Recursion is a simple but powerful programming technique used extensively in functional languages. For a number of reasons, however, it is often desirable to use structured forms of recursion in programming, encapsulated in so-called recursion operators, in preference to unrestricted recursion. In particular, using recursion operators has proved invaluable for transforming and reasoning about f...

Syntactic recursion is argued to be a key property of natural languages, allowing us to create an infinite number of utterances from a finite number of words and rules. Some have argued that recursion is uniquely human. There are at least two possibilities for the origins of recursion: 1) Recursion is a property of the language faculty. 2) Recursion is an historical accomplishment and is cultur...