In this paper the intersection type discipline as defined in
\cite{Barendregt-et.al'83} is studied. We will present two
different and independent complete restrictions of the
intersection type discipline.
The first restricted system, the strict type assignment system,
is presented in section two. Its major feature is the absence
of the derivation rule $(\leq)$ and it is based on a set of
strict types. We will show that these together give rise to a
strict filter lambda model that is essentially different from
the one presented in \cite{Barendregt-et.al'83}. We will show
that the strict type assignment system is the nucleus of the
full system, i.e.\ for every derivation in the intersection
type discipline there is a derivation in which $(\leq)$ is
used only at the very end. Finally we will prove that strict
type assignment is complete for inference semantics.
The second restricted system is presented in section three.
Its major feature is the absence of the type $\omega$. We will
show that this system gives rise to a filter $\lambda$I-model
and that type assignment without $\omega$ is complete for the
$\lambda$I-calculus. Finally we will prove that a lambda term
is typeable in this system if and only if it is strongly
normalizable.
Appeared as:
@Article {Bakel-TCS'92,
Author = "S. van Bakel",
Title = "Complete restrictions of the {I}ntersection {T}ype
{D}iscipline",
Journal = "Theoretical Computer Science",
Volume = "102",
Year = "1992",
Pages = "135-163"
}