Syntactic characterization in Lisp of the polynomial complexity classes and hierarchy

The definition of a class C of functions is syntactic if membership to C can be decided from the construction of its elements. Syntactic characterizations of PTIMEF, of PSPACEF, of the polynomial hierarchy PH, and of its subclasses Delta^p_n are presented. They are obtained by progressive restrictions of recursion in Lisp, and may be regarded as predicative according to a foundational point raised by Leivant