Functions Over Free Algebras Definable in the Simply Typed lambda Calculus

@article{Leivant1993FunctionsOF,
  title={Functions Over Free Algebras Definable in the Simply Typed lambda Calculus},
  author={Daniel Leivant},
  journal={Theor. Comput. Sci.},
  year={1993},
  volume={121},
  pages={309-322}
}
Synopsis. We show that a function over a free algebra is deenable in the simply typed-calculus (modulo the BB ohm-Berarducci embedding) ii it is generated by predicative monotonic recurrence. By monotonic recurrence we mean iteration with parameters, and our predicativity condition uses the notion of tiers introduced in Lei90]. In fact, we show that the same functions are generated by tiered monotonic recurrence whether 2 tiers, or all nite tiers, are used. 

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