Com S 641 Lecture -*- Outline -*-

* Subtyping (Ch 8)

** overview

   subsumption is the notion that an object can emulate some object
   with fewer methods.

   Q: what's the relationship between objects and records?
   Q: why don't we want an operation to extract a method from an
   object?

   The subsumption described in this chapter is a simple one based on
   subtyping between object types.

   important theorems: minimum types, and subject-reduction

** type rules for subtyping (8.1)

   Q: what role does the type Top play in the type system?
   Q: is there anything surprising about the subtyping rule for
      function types?
   Q: is there anything surprising about the subtyping rule for object types?
   Q: is subtyping for object types recursive?
        discuss the notions of width and depth subtyping

   Q: what is the equivalent of the notion of context for types?
   Q: how are type contexts used to define covariance and
   contravariance, as well as invariance?
   Q: what can be said about the variance of function and object types?

   Q: does the subtyping relation form a total order? A partial order?
   Q: does every type have an upper bound?
   Q: could we define the meaning of the least upper bound of two types?

   Q: how does the difference in variance affect the translation of
   functions into objects from section 7.7?
	     (It no longer preserves types)

** examples (8.2)
   Q: can you explain the subtyping in the cell example?
   Q: why doesn't to cell example from section 6.5.5 work?
   Q: can you give another example?

** properties of the calculus of subtyping
*** minimum types
   Q: does this calculus have unique types?
   Q: what property could we use to replace that property?
   Q: how can that be formalized?

   Q: what is the difference between the MinOb_1 and Ob_1 systems?
   Q: does the MinOb_1 systems still have subsumption?  Subtyping?
   Q: what are the advantages and disadvantages of using such a
   system?

   Q: how would you go about proving proposition 8.3-1?
   Q: how does this help prove that Ob_1<: has minimum types?
   Q: if we erase the type annotations from a term, does it still have
   a unique minimum type?
   Q: if we omit the type annotations on constant fields in objects do we
   still have unique minimum types?
   Q: is minimum typing important for practical purposes?
   
*** subject reduction (8.3.2)
    Q: what is the importance of the bound weakening lemma?
       is it really weakening?
    Q: can you explain how the environment is used in the substitution lemma?
    Q: can we subsitutute a term having a subtype of the variable's type?
    Q: would that work in MinOb1<:?
    Q: explain the comment after the proof of the subject reduction
    theorem?

** First-order equational theories and subtyping (8.4)
   Q: in what sense does the type point of view matter for the
   equational theory?  Can you give a concrete example?
   Q: how does the formal machinery reflect this?
   Q: in what sense does the formal system allow "an object " to be
   "truncated to its externally visible collection of methods,
   but only if those methods do not depend on the hidden ones"?

   Q: what is the problem with showing the equivalence of terms b and c at
   the top of page 100?

** classes and inheritance (8.5)
*** representing class types and inheritance (8.5.1)
   Q: can you explain the meaning of the class types?
   Q: what is the relationship between inheritance and subtyping for
   class types?
   Q: what is the relation between the "may inherit from" relation and
   informal notion of inheritance?

   Q: what typing requirements apply to subclasses?
   Q: what does this have to say about fields of subclasses in practical
   programming languages like Java?

*** variations on class types (8.5.2)
    Q: How is it possible to model abstract classes and abstract
    methods in a type safe way?
    Q: how could one model final classes in Java?
    Q: how do Abadi and Cardelli modify class types to take such
    considerations into account?
    Q: how can one model public, protected, and private methods?

*** an example (8.5.3)
    Q: what does the private cell example say about the
       relationship between classes, traits and leaf classes?

    Q: what do the restricted cell and no contents cell examples
       say about subsumption and information hiding? 
    Q: does information hiding depend on special type annotations?
    Q: or is the calculus powerful enough by itself?

** objects vs. records (8.6)
   This section discusses two extensions to the calculus Ob1<:, 
   which make its type system unsound.
   These show that "object typing is fundamentally
         different from record typing"

*** records (8.6.1)
    Q: how does the notation for records differ from that of objects?
    Q: what are the operations on records?
    Q: how is field update be "defined from the other operations"?
    Q: why can't that be done for the object calculus?

    Q: what are the differences between the record typing rules and the
       corresponding rules for objects?

    Q: what are the differences between the equational rules for records
       and those for objects?

    Q: how does the derived typing rule for record update differ
       from the typing rule for method update?

*** method extraction (8.6.2)
    Q: how would you read the rules at the bottom of page 107?
    Q: why does the examples show that this is unsound?
    Q: why would this be sound if we do not have subsumption?

*** Elder (8.6.3)
    Q: why would it be useful to refer to the previous value of a method
       during a method update?
    Q: what would the rules look like if we used a keyword "elder" instead of
       the form given in the text?
    Q: would there be any expressive power advantage or disadvantage?

    Q: what does elder have to do with method extraction?
    Q: why is it sound when method extraction is not?
    Q: how would you prove the soundness of elder?

*** covariant object types (8.6.4)
    Q: what does the example show about depth subtyping for objects?
    Q: how do you explain that?

** variance annotations (8.7)
*** object types with variance annotations (8.7.1)
   Q: what is a variance annotation?
   Q: what should the default be?  Why?

   Q: how do you explain the subtyping rule?
   Q: what are the subtyping relationships between
       var =      [get+:int, set-:int->var],
       acceptor = [set-:int->unit] and
       field =    [get+:int] ?
     (this is like an abstract data type for variables)

   Q: why do the typing rules for selection and update have to change?

*** encodings and examples with invariants (8.7.2)
    Q: why are the variance annotations what they are for products?  Records?
    Q: why is the encoding of function types better with variance annotations?

    Q: how can variance annotations be used for preserving invariants?

    Q: how would you encode variant records using variance annotations?

** recursive types (chapter 9)
   we're going to skip this, but you might read: 9.1-2 and 9.4-6
        if you don't have time for the whole chapter