Summary: Syntactical Strong Normalization of
Intersection Types with Term Rewriting Rules
Department of Computer Science
4th International Workshop on Higher-Order Rewriting
June 25, 2007
Andreas Abel (LMU Munich) Syntactical Normalization HOR'07 1 / 20
Normalization Proofs in Weak Meta-Theories
Weak systems can be shown consistent in (almost as) weak
Normalization implies usually consistency.
Tait's semantical normalization proof for the simply-typed
-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,
But were better understood for sequent calculus (cut elimination).
No such proof is known for System F; for G®odel's T, 0-induction is