i ;;Quote: a theory of objects as a foundation for object-oriented programming; like lambda calculus but based on objects as primitives; handles classes, self, dynamic dispatch, inheritance, etc.

18 ;;Quote: subsumption is the property that a value of type A is also a value of any supertype B with A<:B

20 ;;Quote: the product type is a covariant type operator on pairs of types; i.e., A x B <: A' x B' provided that A <: A' and B <: B'

21 ;;Quote: a function type is a contravariant type operator on pairs of types; i.e., A -> B <: A' -> B' provided that A' <: A and B <: B'; extends to multiple arguments

21+;;Quote: methods vary contravariantly from classes to subclasses; despite debate to the contrary

21 ;;Quote: an update type is an invariant type operator on pairs of types; i.e., if A * B means A and B may be updated, then A * B <: A' * B' provided A=A' and B=B'

42 ;;Quote: delegation inheritance shares attributes while embedding inheritance copies attributes; can distinguish in object-based languages but not class-based languages

47 ;;Quote: delegation-based object languages like Self and Cecil now distinguish trait objects (like classes), prototype objects (for cloning), and normal objects; enforceable