Player FM 앱으로 오프라인으로 전환하세요!
Identity Inclusion in Relational Type Theory
Manage episode 282601615 series 2823367
Where relational semantics for parametric polymorphism often includes a lemma called Identity Extension (discussed in Episode 10, on the paper "Types, Abstraction, and Parametric Polymorphism"), RelTT instead has a refinement of this called Identity Inclusion. Instead of saying that the interpretation of every closed type is the identity relation (Identity Extension), the Identity Inclusion lemma identifies certain types whose relational meaning is included in the identity relation, and certain types which include the identity relation. So there are two subset relations, going in opposite directions. The two classes of types are first, the ones where all quantifiers occur only positively, and second, where they occur only negatively. Using Identity Inclusion, we can derive transitivity for forall-positive types, which is needed to derive induction following the natural generalization of the scheme in Wadler's paper (last episode).
161 에피소드
Manage episode 282601615 series 2823367
Where relational semantics for parametric polymorphism often includes a lemma called Identity Extension (discussed in Episode 10, on the paper "Types, Abstraction, and Parametric Polymorphism"), RelTT instead has a refinement of this called Identity Inclusion. Instead of saying that the interpretation of every closed type is the identity relation (Identity Extension), the Identity Inclusion lemma identifies certain types whose relational meaning is included in the identity relation, and certain types which include the identity relation. So there are two subset relations, going in opposite directions. The two classes of types are first, the ones where all quantifiers occur only positively, and second, where they occur only negatively. Using Identity Inclusion, we can derive transitivity for forall-positive types, which is needed to derive induction following the natural generalization of the scheme in Wadler's paper (last episode).
161 에피소드
모든 에피소드
×플레이어 FM에 오신것을 환영합니다!
플레이어 FM은 웹에서 고품질 팟캐스트를 검색하여 지금 바로 즐길 수 있도록 합니다. 최고의 팟캐스트 앱이며 Android, iPhone 및 웹에서도 작동합니다. 장치 간 구독 동기화를 위해 가입하세요.