Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The lambda-calculus is a widely accepted computational model of higher-order functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda-terms to their normal form is typically studied by reasoning on concrete implementation algorithms. ,  show that when head reduction is the underlying dynamics, the unitary cost model is indeed invariant.#R##N#This improves on known results, which only deal with ak (call-by-value or call-by-name) reduction. Invariance is proved by way of a linear calculus of explicit substitutions, which  allows to nicely decompose any head reduction step in the lambda-calculus into#R##N#more elementary substitution steps, thus making the combinatorics of#R##N#head-reduction easier to reason about. The technique is also a promising tool to attack what  see as the main open problem, namely understanding for which normalizing strategies the unitary cost model is invariant, if any.
['Beniamino Accattoli', 'Ugo Dal Lago']
I am writing a research paper on a idea On the Invariance of the Unitary Cost Model for Head Reduction
[{"from": "human", "value": "I am writing a research paper on a idea On the Invariance of the Unitary Cost Model for Head Reduction"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The lambda-calculus is a widely accepted computational model of higher-order functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda-terms to their normal form is typically studied by reasoning on concrete implementation algorithms. ,  show that when head reduction is the underlying dynamics, the unitary cost model is indeed invariant.#R##N#This improves on known results, which only deal with ak (call-by-value or call-by-name) reduction. Invariance is proved by way of a linear calculus of explicit substitutions, which  allows to nicely decompose any head reduction step in the lambda-calculus into#R##N#more elementary substitution steps, thus making the combinatorics of#R##N#head-reduction easier to reason about. The technique is also a promising tool to attack what  see as the main open problem, namely understanding for which normalizing strategies the unitary cost model is invariant, if any."}]