Summary: Axiomatizing Fully Complete Models for
ML Polymorphic Types ?
Samson Abramsky 1 and Marina Lenisa 2
1 Division of Informatics
University of Edinburgh, UK.
2 Dipartimento di Matematica e Informatica
Universit`a di Udine, Italy.
Abstract. We present axioms on models of system F, which are suffi
cient to show full completeness for MLpolymorphic types. These axioms
are given for hyperdoctrine models, which arise as adjoint models, i.e. co
Kleisli categories of linear categories. Our axiomatization consists of two
crucial steps. First, we axiomatize the fact that every relevant morphism
in the model generates, under decomposition, a possibly infinite typed
B¨ohm tree. Then, we introduce an axiom which rules out infinite trees
from the model. Finally, we discuss the necessity of the axioms.
In this paper we address the problem of full completeness (universality) for sys
tem F. A categorical model of a type theory (or logic) is said to be fullycomplete