Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result,  first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion.
['Jasmin Christian Blanchette', 'Andrei Popescu', 'Dmitriy Traytel']
I am writing a research paper on a idea Soundness and Completeness Proofs by Coinductive Methods
[{"from": "human", "value": "I am writing a research paper on a idea Soundness and Completeness Proofs by Coinductive Methods"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result,  first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL\u2019s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL\u2019s new coinductive specification language such as nesting through non-free types and mixed recursion\u2013corecursion."}]