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Summary: An Elementary Fragment of Second-Order Lambda
Calculus
KLAUS AEHLIG
and
JAN JOHANNSEN
Ludwig-Maximilians-Universitat Munchen
A fragment of second-order lambda calculus (System F ) is de ned that characterizes the elemen-
tary recursive functions. Type quanti cation is restricted to be non-interleaved and strati ed,
i.e., the types are assigned levels, and a quanti ed 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 Logic|computational 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
Machine-independent characterizations of computational complexity classes are at
the core of the research area called Implicit Computational Complexity which has
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