The nature and origin of syntactic recursion in natural languages is a topical problem. Important recent contributions include those of Johansson (2005), Parker (2006), Tomalin (2006; 2007), and Heine and Kuteva (2007). Syntactic recursion will here be discussed especially in relation to its cognate concept of iteration. Their basic common feature is plain structural repetition: “keep on emitti...

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion Graph (RGraph) is one visualization method for re...

A recent proposal (Hauser, Chomsky & Fitch, 2002) suggests that the crucial defining property of human language is recursion. In this paper, following a critical analysis of what is meant by the term, I examine three reasons why the recursion-only hypothesis cannot be correct: (i) recursion is neither unique to language in humans, nor unique to our species, (ii) human language consists of many ...

In this paper we discuss the concept of cosymmetries and co–recursion operators for difference equations and present a co–recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion op...

Several extensions of Gödel’s system T with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion, which include Spector’s original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on...

A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactly characterize the parallel complexity class NC. This is achieved by use of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure and imposing of a linearity constraint.