Characterizing complexity classes by general recursive definitions in higher types
General recursive definitions in higher (finite) types, a different notation of finitely typed λ-terms with if-then-else and fixpoints, can be classified into an infinite syntactic hierarchy: A definition is in the n'th stage of this hierarchy, a so called rank-n-definition, iff n is an upper bound on the levels of the types occurring in it.
We restrict attention to definitions defining first-order functions, i.e. functions of type ind x...x ind→ind, ind for individuals, higher types only occur as detour in between.
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