Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with refinements passes type checking, pattern-matching failures become impossible. Unfortunately, refinement is a monolithic property of a type, exacerbating the difficulty of adding refinement types to nontrivial programs.     Gradual typing has explored how to incrementally move beten static typing and dynamic typing.  develop a type system of gradual sums that combines refinement with imprecision. Then,  develop a bidirectional version of the type system, which rules out excessive imprecision, and give a type-directed translation to a target language with explicit casts.  prove that the static sublanguage cannot have match failures, that a ll-typed program remains ll-typed if its type annotations are made less precise, and that making annotations less precise causes target programs to fail later. Several of these results correspond to criteria for gradual typing given by Siek et al. (2015).
['Khurram A. Jafery', 'Joshua Dunfield']
I am writing a research paper on a idea Sums of uncertainty: refinements go gradual
[{"from": "human", "value": "I am writing a research paper on a idea Sums of uncertainty: refinements go gradual"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with refinements passes type checking, pattern-matching failures become impossible. Unfortunately, refinement is a monolithic property of a type, exacerbating the difficulty of adding refinement types to nontrivial programs.     Gradual typing has explored how to incrementally move beten static typing and dynamic typing.  develop a type system of gradual sums that combines refinement with imprecision. Then,  develop a bidirectional version of the type system, which rules out excessive imprecision, and give a type-directed translation to a target language with explicit casts.  prove that the static sublanguage cannot have match failures, that a ll-typed program remains ll-typed if its type annotations are made less precise, and that making annotations less precise causes target programs to fail later. Several of these results correspond to criteria for gradual typing given by Siek et al. (2015)."}]