Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A function on some domain is  λ -definable if the corresponding function of  λ -terms is so definable. Hover, the correspondence is parametrized by a representation of the domain. Often there is a natural choice of representation, but when the domain consists of  λ -terms then they can be represented by either themselves or by the Church numeral of their Godel number. This choice determines whether or not all computable functions are  λ -definable.
['Barry Jay', 'Jose Vergara']
I am writing a research paper on a idea Conflicting accounts of λ-definability
[{"from": "human", "value": "I am writing a research paper on a idea Conflicting accounts of \u03bb-definability"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A function on some domain is  \u03bb -definable if the corresponding function of  \u03bb -terms is so definable. Hover, the correspondence is parametrized by a representation of the domain. Often there is a natural choice of representation, but when the domain consists of  \u03bb -terms then they can be represented by either themselves or by the Church numeral of their Godel number. This choice determines whether or not all computable functions are  \u03bb -definable."}]