PRELIMINARY DRAFT
Abstract:
Polymorphism enforces a type discipline on the normalizing terms of the-calculus and its many extensions intend to improve the intuition about the behaviour of terms. Parametric polymorphism tries to extend an algebraic property at the first level of types to the higher types. But there seems to be still a striking difference between the syntax of polymorphism and its categorical models: while the type discipline introduced by second-order-calculus is extremely tight and allows intuitions and generalizations such as parametric polymorphism (i.e. terms behaves in the same way on all the types they can be applied) or subtyping (terms have canonical extensions between specific types), the categorical models have produced only partial results in the direction of parametricity. The functorial contra/covariant behaviour of the type contructors has precluded a neat development of models. In particular, it is not known if there is a categorical parametric model. To our knowledge, apart from possibly a syntactic model in [8], the only mention of a parametric model was made by Plotkin in [14] (as he says) adapted from [2] where they state that the standard interpretation of a polymorphic type satisfies [[1X: T]] = 8
Citations
| 103 | Parametricity and local variables – O'Hearn, Tennent - 1995 |
| 53 | Types, abstraction, and parametric polymorphism, part 2 – Ma, Reynolds - 1992 |
| 46 | Polymorphism is set-theoretic, constructively – Pitts |
| 25 | Some free constructions in realizability and proof theory – Carboni - 1995 |
| 24 | Notes on Sconing and Relators – Mitchell, Scedrov - 1993 |
| 16 | A relational approach to strictness analysis for higher-order polymorphic functions – Abramsky, Jensen - 1991 |
| 15 | Connected limits, familial representability and Artin glueing – Carboni, Johnstone - 1995 |
| 13 | Parametricity of extensionally collapsed term models of polymorphism and their categorical properties – Hasegawa - 1991 |
| 10 | Parametricity as subtyping – Ma - 1992 |
| 5 | Functorial parametricity – Freyd, Robinson, et al. - 1992 |
| 5 | About modest sets – Rosolini - 1990 |
| 1 | Categories of separated objects – Carboni, Mantovani - 1992 |
| 1 | order type theory and recursion – Second - 1993 |
