We study a conservative extension of classical propositional logic distinguishing between four mo... more We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be constructive in some sense, whereas proofs of classical propositions proceed by contradiction. The system, in natural deduction style, is shown to be sound and complete with respect to a Kripke semantics. We develop the system from the perspective of the propositions-as-types correspondence by deriving a term assignment system with confluent reduction. The proof of strong normalization relies on a translation to System F with Mendler-style recursion.
Proceedings of the 17th ACM SIGPLAN International Symposium on Dynamic Languages
Union and intersection types are a staple of gradually typed language such as TypeScript. While i... more Union and intersection types are a staple of gradually typed language such as TypeScript. While it's long been recognized that union and intersection types are difficult to verify statically, it may appear at first that the dynamic part of gradual typing is actually pretty simple. It turns out however, that in presence of higher-order contracts union and intersection are deceptively difficult. The literature on higher-order contracts with union and intersection, while keenly aware of the fact, doesn't really explain why. We point and illustrate the problems and tradeoffs inherent to union and intersection contracts, via example and a survey of the literature. CCS Concepts: • General and reference → Surveys and overviews; • Software and its engineering → Language features; Software verification and validation.
We study a conservative extension of classical propositional logic distinguishing between four mo... more We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be constructive in some sense, whereas proofs of classical propositions proceed by contradiction. The system, in natural deduction style, is shown to be sound and complete with respect to a Kripke semantics. We develop the system from the perspective of the propositions-as-types correspondence by deriving a term assignment system with confluent reduction. The proof of strong normalization relies on a translation to System F with Mendler-style recursion.
Proceedings of the 17th ACM SIGPLAN International Symposium on Dynamic Languages
Union and intersection types are a staple of gradually typed language such as TypeScript. While i... more Union and intersection types are a staple of gradually typed language such as TypeScript. While it's long been recognized that union and intersection types are difficult to verify statically, it may appear at first that the dynamic part of gradual typing is actually pretty simple. It turns out however, that in presence of higher-order contracts union and intersection are deceptively difficult. The literature on higher-order contracts with union and intersection, while keenly aware of the fact, doesn't really explain why. We point and illustrate the problems and tradeoffs inherent to union and intersection contracts, via example and a survey of the literature. CCS Concepts: • General and reference → Surveys and overviews; • Software and its engineering → Language features; Software verification and validation.
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Papers by Teodoro Freund