Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a formulation of simple type theory in which types are just sets. This theory is obtained by relativizing quantifiers and replacing typing predicates by membership of some sets. It can easily be extended to include predicate subtyping.
['Gilles Dowek']
I am writing a research paper on a idea Collections, sets and types
[{"from": "human", "value": "I am writing a research paper on a idea Collections, sets and types"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a formulation of simple type theory in which types are just sets. This theory is obtained by relativizing quantifiers and replacing typing predicates by membership of some sets. It can easily be extended to include predicate subtyping."}]