 
Summary: A syntactical analysis of nonsizeincreasing polynomial time computation
Klaus Aehlig Helmut Schwichtenberg
Mathematisches Institut
LudwigMaximiliansUniversit˜at M˜unchen
Email: faehligjschwichtg@rz.mathematik.unimuenchen.de
Abstract
A purely syntactical proof is given that all functions defin
able in a certain affine linear typed –calculus with iteration
in all types are polynomial time computable. The proof also
gives explicit polynomial bounds that can easily be calcu
lated.
1 Summary
In [6] Hofmann presented a linear type system for non
sizeincreasing polynomial time computation allowing un
restricted recursion for inductive datatypes. The proof that
all definable functions of type N ( N are polynomial time
computable essentially used semantic concepts, such as the
settheoretic interpretation of terms.
We present a different proof of the same result for a slightly
modified version of the term system, which uses syntactical
