Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a type system with subtyping for a strongly normalizing , Curry-style language. Our type constructors include sum and product types, universal and existential quantifiers, inductive and coinductive types. Soundness and strong normalization are shown semantically by constructing a realizability model.  argue that the system is suitable for practical use based on our experience with a prototype implementation. To support this claim,  consider several examples of applications. For instance, the system is able to type recursors for datatypes encoded in the pure $\lambda$-calculus, using a representation due to Dana Scott. Other examples include injections beten mixed inductive and coinductive types.
['Rodolphe Lepigre', 'Christophe Raffalli']
I am writing a research paper on a idea Subtyping-Based Type-Checking for System F with Induction and Coinduction
[{"from": "human", "value": "I am writing a research paper on a idea Subtyping-Based Type-Checking for System F with Induction and Coinduction"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a type system with subtyping for a strongly normalizing , Curry-style language. Our type constructors include sum and product types, universal and existential quantifiers, inductive and coinductive types. Soundness and strong normalization are shown semantically by constructing a realizability model.  argue that the system is suitable for practical use based on our experience with a prototype implementation. To support this claim,  consider several examples of applications. For instance, the system is able to type recursors for datatypes encoded in the pure $\\lambda$-calculus, using a representation due to Dana Scott. Other examples include injections beten mixed inductive and coinductive types."}]