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The Geometry of Linear Higher-Order Recursion

U. Dal Lago
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Abstract

Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show 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 framework stems from Gonthier's original work and turns out to be a versatile and powerful tool for the quantitative analysis of normalization in presence of constants and higher-order recursion.

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U. Dal Lago. 2006-10-04. The Geometry of Linear Higher-Order Recursion. https://arxiv.org/abs/cs/0506080

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