 
Summary: Syntactical Strong Normalization of
Intersection Types with Term Rewriting Rules
Andreas Abel
Department of Computer Science
LudwigMaximiliansUniversity Munich
4th International Workshop on HigherOrder Rewriting
Paris, France
June 25, 2007
Andreas Abel (LMU Munich) Syntactical Normalization HOR'07 1 / 20
Normalization Proofs in Weak MetaTheories
Weak systems can be shown consistent in (almost as) weak
metatheories.
Normalization implies usually consistency.
Tait's semantical normalization proof for the simplytyped
calculus (STL) is beyond Peano Arithmetic.
Combinatorial/arithmetical/syntactical normalization proofs for the
STL have long been known, e.g., J.J.Levy (1974), Girard, Lafont,
Taylor (1989).
But were better understood for sequent calculus (cut elimination).
No such proof is known for System F; for G¨odel's T, 0induction is
