 
Summary: ParameterFree Polymorphic Types
Klaus Aehlig 1
Department of Computer Science, University of Wales Swansea
Swansea, SA2 8PP, United Kingdom
Abstract
Consider the following restriction of the polymorphically typed lambda calculus
("System F"). All quantifications are parameter free. In other words, in every uni
versal type ., the quantified variable is the only free variable in the scope
of the quantification. This fragment can be locally proven terminating in a system
of intuitionistic secondorder arithmetic known to have strength of finitely iterated
inductive definitions.
1 Introduction and Related Work
The polymorphic lambda calculus ("System F") [8,12] is a very expressive type
system. It nevertheless has the property that all typable terms are strongly
normalising. However, a constructive understanding of polymorphic types is
not easily possible, due to the inherent impredicativity. For the definition of a
type we presuppose knowledge already of all types. Therefore a predica
tive understanding, at least of subsystems of System F, is desirable. Altenkirch
and Coquand proposed a "finitary subsystem of the polymorphic lambda cal
culus" [2] that characterises precisely the functions provably recursive in Peano
