Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional con- nectives where the meaning of a compound formula is dependent only on the truth value of its subformulas.#R##N#  present a typed lambda calculus, enriched with strong products, strong sums, and a related proof-functional logic. This cal- culus, directly derived from a typed calculus previously defined by two of the current authors, has been proved isomorphic to the ll-known Barbanera-Dezani-Ciancaglini-de’Liguoro type assignment system.  present a logic L∩∪ featuring two proof-functional connectives, namely strong conjunction and strong disjunction.  prove the typed calculus to be isomorphic to the logic L∩∪ and  give a realizability semantics using Mints’ realizers [Min89] and a completeness theorem. A prototype implementation is also described.
['Daniel J. Dougherty', 'Ugo de’Liguoro', 'Luigi Liquori', 'Claude Stolze']
I am writing a research paper on a idea A Realizability Interpretation for Intersection and Union Types
[{"from": "human", "value": "I am writing a research paper on a idea A Realizability Interpretation for Intersection and Union Types"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional con- nectives where the meaning of a compound formula is dependent only on the truth value of its subformulas.#R##N#  present a typed lambda calculus, enriched with strong products, strong sums, and a related proof-functional logic. This cal- culus, directly derived from a typed calculus previously defined by two of the current authors, has been proved isomorphic to the ll-known Barbanera-Dezani-Ciancaglini-de\u2019Liguoro type assignment system.  present a logic L\u2229\u222a featuring two proof-functional connectives, namely strong conjunction and strong disjunction.  prove the typed calculus to be isomorphic to the logic L\u2229\u222a and  give a realizability semantics using Mints\u2019 realizers [Min89] and a completeness theorem. A prototype implementation is also described."}]