This paper studies termination properties of rewrite systems that are
typeable using intersection types. It introduces a notion of partial
type assignment on Curryfied Term Re\-write Systems, that consists of
assigning intersection types to function symbols, and specifying the
way in which types can be assigned to nodes and edges between nodes
in the tree representation of terms. Two operations on types are
specified that are used to define type assignment on terms and rewrite
rules, and are proven to be sound on both terms and rewrite rules.
Using a more liberal approach to recursion, a general scheme for
recursive definitions is presented, that generalizes primitive
recursion, but has full Turing-machine computational power. It will
be proved that, for all systems that satisfy this scheme, every
typeable term is strongly normalizable.
Appeared as:
@Inproceedings {Bakel-Fernandez-HOA'93,
Author = "S. van Bakel and M. Fern\'andez",
Title = "Strong {N}ormalization of {T}ypeable {R}ewrite {S}ystems",
Booktitle = "Proceedings of HOA '93. First {I}nternational {W}orkshop on
{H}igher {O}rder {A}lgebra, {L}ogic and {T}erm {R}ewriting,
{\rm {A}msterdam, the {N}etherlands}. {S}elected {P}apers",
Editor = "Jan Heering and Karl Meinke and Bernhard M{\"o}ller and Tobias
Nipkow",
Series = "Lecture Notes in Computer Science",
Volume = "816",
Publisher = "Springer-Verlag",
Year = "1994",
Pages = "20-39"
}