Abstract
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 Rewrite 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. 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.
Supported by the Netherlands Organisation for the advancement of pure research (N.W.O.).
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van Bakel, S., Fernández, M. (1994). Strong normalization of typeable rewrite systems. In: Heering, J., Meinke, K., Möller, B., Nipkow, T. (eds) Higher-Order Algebra, Logic, and Term Rewriting. HOA 1993. Lecture Notes in Computer Science, vol 816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58233-9_2
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