The geometry of linear higher-order recursion

@article{Lago2005TheGO,
  title={The geometry of linear higher-order recursion},
  author={Ugo Dal Lago},
  journal={20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)},
  year={2005},
  pages={366-375}
}
Imposing linearity and ramification constraints allows to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polynomial-time computable functions, as the works by Leivant, Hofmann, and others show. This article shows that fine-tuning these two constraints leads to different expressive strengths, some of them lying well beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The… CONTINUE READING
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