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...

Martin-Löf’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 recursion over higher types, induction and recursion are formally derived for a large class of well-founded relations. Included are < on natural numbers, and rela...