Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding operator that is constructed definitionally from a de Bruijn index representation.   make a variety of improvements to Hybrid, culminating in an abstract interface that on one hand makes Hybrid a more mathematically satisfactory theory, and on the other hand has important practical benefits.  start with a modification of Hybrid’s type of terms that better hides its implementation in terms of de Bruijn indices, by excluding at the type level terms with dangling indices.  present an improved set of definitions, and a series of new lemmas that provide a complete characterization of Hybrid’s primitives in terms of properties stated at the HOAS level. Benefits of this new package include a new proof of adequacy and improvements to reasoning about object logics. Such proofs are carried out at the higher level with no involvement of the lor level de Bruijn syntax.
['Alan J. Martin', 'Amy P. Felty']
I am writing a research paper on a idea An Improved Implementation and Abstract Interface for Hybrid
[{"from": "human", "value": "I am writing a research paper on a idea An Improved Implementation and Abstract Interface for Hybrid"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding operator that is constructed definitionally from a de Bruijn index representation.   make a variety of improvements to Hybrid, culminating in an abstract interface that on one hand makes Hybrid a more mathematically satisfactory theory, and on the other hand has important practical benefits.  start with a modification of Hybrid\u2019s type of terms that better hides its implementation in terms of de Bruijn indices, by excluding at the type level terms with dangling indices.  present an improved set of definitions, and a series of new lemmas that provide a complete characterization of Hybrid\u2019s primitives in terms of properties stated at the HOAS level. Benefits of this new package include a new proof of adequacy and improvements to reasoning about object logics. Such proofs are carried out at the higher level with no involvement of the lor level de Bruijn syntax."}]