Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Imposing linearity and ramification constraints allows to aken 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 ll beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The framework stems from Gonthier's original work (itself a model of Girard's geometry of interaction) and turns out to be a versatile and porful tool for the quantitative analysis of normalization in the lambda calculus with constants and higher-order recursion.
['Ugo Dal Lago']
I am writing a research paper on a idea The geometry of linear higher-order recursion
[{"from": "human", "value": "I am writing a research paper on a idea The geometry of linear higher-order recursion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Imposing linearity and ramification constraints allows to aken 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 ll beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The framework stems from Gonthier's original work (itself a model of Girard's geometry of interaction) and turns out to be a versatile and porful tool for the quantitative analysis of normalization in the lambda calculus with constants and higher-order recursion."}]