High-order functions are the sole elements in a class of recursive functions. The functions are related to each other through application, i.e., applying a function to an argument...
Structurally recursive XML queries are an important query class that follows the structure of XML data. At present, it is difficult for XQuery to type and optimize structurally re...
Studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades. Starting with Gold's (1967) model of learning in th...
Abstract. There is a very simple way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over...
We investigate natural systems of fundamental sequences for ordinals below the Howard Bachmann ordinal and study growth rates of the resulting slow growing hierarchies. We consider...
Although formal specification techniques are very useful in software development, the acquisition of formal specification is a difficult task. This paper presents the formal softw...
In Constructive Type Theory, recursive and corecursive definitions are subject to syntactic restrictions which guarantee termination for recursive functions and productivity for c...
In this paper, we present an overview to programming with proofs in the reasoning framework, Beluga. Beluga supports the specification of formal systems given by axioms and inferen...
Abstract. We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool generates from pseudo-code the graph of the in...
Gilles Barthe, Julien Forest, David Pichardie, Vla...
In this paper we first survey recent advances on phase transition phenomena which are related to natural subclasses of the recursive functions. Special emphasis is put on descent ...