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Polymorphism - Parametric Consider the type of a sort function. sort : IntList IntList Generalize this to sort : Forall(Y) List(Y) List(Y) But what about the comparison operation on elements of Y? That would be of the form compare : Y x Y Bool for any Y. So, sort will take an additional argument: the function compare. sort : Forall(Y) List(Y) x (Y x Y Bool) List(Y) 4/11/2008 Sundar B., BITS, Pilani. CS C362 12
Polymorphism – Parametric Existentials Recall that Existential Quantification captures encapsulation. Can we combine Existentials and Universals? e.g. recall the ADT List PackList = Exists(Y) Y x (Y Int) is the type of ADT List where Y is the hidden representation; and PackList with Y = ArrayZ is the type of ADT List with ArrayZ as the representation. We can abstract out element type of "ArrayZ" ParamPackList = Forall(Z) Exists(Y) Y(Z) x (Y(Z) Int) All combinations are feasible: Z=int, Y=array; Z=int, Y=linkedlist; Z=student,Y=array;
Page 1 and 2: Today’s Agenda Types * Polymorphi
Page 3 and 4: Types and Reuse Consider the follow
Page 5 and 6: Polymorphism - Adhoc Ad-hoc polymor
Page 7 and 8: Polymorphism - Ad hoc Idiosyncracie
Page 9 and 10: Polymorphism - Parametric Consider
Page 11: Polymorphism - Parametric filter =
Page 15 and 16: Polymorphism - Subtyping/Inclusion
Page 17 and 18: Polymorphism - Subtyping Consider f
Page 19 and 20: Subtyping - Rules Function Subtypin
Page 21: Subtyping - Rules Then the general

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