 
Summary: An Elementary Fragment of SecondOrder Lambda
Calculus
KLAUS AEHLIG
and
JAN JOHANNSEN
LudwigMaximiliansUniversitat Munchen
A fragment of secondorder lambda calculus (System F ) is dened that characterizes the elemen
tary recursive functions. Type quantication is restricted to be noninterleaved and stratied,
i.e., the types are assigned levels, and a quantied variable can only be instantiated by a type of
smaller level, with a slightly liberalized treatment of the level zero.
Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
Mathematical Logiccomputational logic; lambda calculus and related systems; F.2.2 [Analy
sis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems
complexity of proof procedures
General Terms: Theory
Additional Key Words and Phrases: elementary recursive functions, complexity, lambda calculus,
second order logic
1. INTRODUCTION AND RELATED WORK
Machineindependent characterizations of computational complexity classes are at
the core of the research area called Implicit Computational Complexity which has
