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Let N be the natural numbers and A any type in the hierarchy of simple types over N. Let s : (N)N be the successor function and let f : (N)A be arbitrary. Then, for variables x : N, y : A we may form the term [x, y]f(s(x)) : (N)(A)A Let R be the recursor for type A. Then, for any term n : N, we have R( f(0) , [x, y]f(s(x)) , n ) : A By the reduction rules for R one can see that f and R( f(0) , [x, y]f(s(x)) ) agree on the numerals. Suppose we add the following eta-like reduction rule to Gödel's T: R( f(0) , [x, y]f(s(x)) , x ) --> f(x) Is it known whether the resulting system is (strongly) normalizing and confluent? ------------ Ansten Klev Czech Academy of Sciences, Department of Philosophy
