Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The ansr to this question for the language of arithmetic expressions using a constant for the number one and the operations of product and exponentiation is affirmative, and the complete equational theory also characterises isomorphism in the typed lambda calculus, where the constant for one and the operations of product and exponentiation respectively correspond to the unit type and the product and arrow type constructors.  studies isomorphisms in typed lambda calculi with empty and sum types from this viewpoint.  close an open problem by establishing that the theory of type isomorphisms in the presence of product, arrow, and sum types (with or without the unit type) is not finitely axiomatisable. Further,  observe that for type theories with arrow, empty and sum types the correspondence beten isomorphism and arithmetic equality generally breaks down, but that it still holds in some particular cases including that of type isomorphism with the empty type and equality with zero.
['Marcelo P. Fiore', 'R. Di Cosmo', 'Vincent Balat']
I am writing a research paper on a idea Remarks on isomorphisms in typed lambda calculi with empty and sum types
[{"from": "human", "value": "I am writing a research paper on a idea Remarks on isomorphisms in typed lambda calculi with empty and sum types"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The ansr to this question for the language of arithmetic expressions using a constant for the number one and the operations of product and exponentiation is affirmative, and the complete equational theory also characterises isomorphism in the typed lambda calculus, where the constant for one and the operations of product and exponentiation respectively correspond to the unit type and the product and arrow type constructors.  studies isomorphisms in typed lambda calculi with empty and sum types from this viewpoint.  close an open problem by establishing that the theory of type isomorphisms in the presence of product, arrow, and sum types (with or without the unit type) is not finitely axiomatisable. Further,  observe that for type theories with arrow, empty and sum types the correspondence beten isomorphism and arithmetic equality generally breaks down, but that it still holds in some particular cases including that of type isomorphism with the empty type and equality with zero."}]