Outline of Class 39: Wrapup

Held: Friday, May 8, 1998

Administrivia

• The final is Monday at 9am. A review sheet is now available.
• I have finished grading assignment six.
  • I only graded the first five problems for a number of reasons.
  • Given the number of times I've tried to emphasize thorough testing of sorting routines, I am extremely disappointed with your tests of the sorting routines.
  • An answer key is available.
• Today we will have a posiquiz. The quiz can only have a positive affect on your grade in the class.
• You will need the the section of the Scheme report on syntax and semantics for today's discussion.
• There are two candidates for a visiting math position coming next week. They will be speaking on Monday night and Wednesday night. I think that the department will be providing Pizza. I'll offer the added incentive that anyone who comes to a talk and sends the department a summary of your reactions to the candidate gets one point of extra credit in the class.
• Note that I've finally determined the meaning of bp's warning singleton_variables. This warning occurs when you only use a variable once in a predicate definition (making it somewhat useless except for notational convenience).

Semantics of Scheme, Revisited

Semantic Domains

• You will note that there are a large number of domains for the Scheme semantics (approximately eightteen). This helps us distinguish the roles of a number of things.
• What are some particularly interesting ones?
• Scheme admits that values will be stored in memory (this is necessary for things like set!) and that there is a separation between variable name and value of the variable.
  • L is used for locations.
  • An environment maps each identifier to a location Surprisingly, it seems that every identifier has a location. A closer reading of the semantics suggests that undefined may be used.
  • A store maps each location to a (value,boolean) pair. It appears that the boolean is used to indicate whether or not the location is allocated.
• There are three kinds of constructed objects: pairs, vectors, and strings.
  • Each has an additional boolean flag. This indicates whether or not the object is mutable (can be changed).
• Continuations are used. There are two kinds,
  • Command continuations map a store to an answer.
  • Expression continuations map a sequence of expressions to a command continuation.
• Scheme (or at least the Scheme semantics) permits a number of kinds of values (symbols, characters, numbers, pairs, vectors, strings, procedures, and some special ones).

Types of Semantic Functions

• Scheme has four semantic functions that assign meaning to variations of the basic syntactic categories.
• A meaning-of-constant function assigns meanings to constants. That function is left as an exercise to the implementer (wich important ones defined on the subsequent page). The meaning of a constant is the value of that constant.
• A meaning-of-expression function assigns meanings to expressions. The meaning of an expression is based on its environment and what is done with the expression. Why "what is done with the expression"? For similar reasons to those in the SIMPLE semantics: an expression may update store or environemnt.
  • You may note that the meaning of an expression doesn't seem to depend on its store. Why not? Because the store is cleverly hidden in the result of the function.
• A meaning-of-expression-sequence function does something similar.
• A meaning-of-command-sequence function also does something similar, but uses a command-continuation instead of the expression continuation. What's the difference? One uses the result of the expression and one doesn't.

A Few Simple Definitions

• Let's consider the first few rules for the meaning-of-expression function.
• What is the meaning of a constant expression?
  • It is a function that takes a environment and an expression continuation and returns a command continuation.
  • The environment isn't needed (sonstants aren't evaluated in the context of an environment).
  • The meaning of the constant is determined. That meaning is a value.
  • The continuation is called on the value using the send helper function.
  • What does send do? It helps support the type structure. Since expression continuations work from sequences of expressions, it turns a single argument into a sequence before calling the continuation.
  • Why didn't they just write cont <meaningK[[K]]>? I have no idea.
• What is the meaning of an identifier?
  • It is a function that takes an environment and an expression continuation and returns a command continuation.
  • It has three steps
    • We look up the identifier in the environment
    • We make sure the identifier is defined
    • We call the continuation
  • How are those expressed?
  • lookup looks up an identifier in an environment. It's not clear why this is all that helpful, except for readability.
  • single takes a single-argument function and makes it an expression continuation.
  • hold takes a location and an expression continuation, grabs the value at that location, and calls the continuation.
    • It has a very strange definition. Note that while it seems to be a function of three arguments, it is typed as a function of two arguments. This is because C is a function type.
    • This is also why the store is repeated in its definition.
• What is the meaning of the application of an expression to a sequence of expressions?
  • It's based on the meaning of all the subexpressions
  • The subexpressions are evaluated in an implementation-dependent order.
  • The meaning of the expressions is determined in the current environment (we'll need to check the meaning-of-expression-sequence definitions to see how each affects the next).
  • The evaluated first subexpression is applied to the rest.
  • The contination is applied to the result.

Wrapup

Our summary of what we learned will be based on the review sheet for the final.

Final Statements

• My mother taught Psychology at Boston University for over thirty years. ("Aha, that explains SamR's personality.") She ended every class with the same statement. I try to do the same, although the statement is filtered through my sensibilities.

  Most of us will take or teach other classes. However, this one is unique; none will ever be quite like this it for a number of reasons. The people in the class made it what it was. We should acknoledge each other's contributions and commit ourselves to making similar contributions in future classes. I thank all of you for your contributions.

• Mom also makes a statement on the order of

  While I enjoyed having you in my class, I'm also happy to have you move on to other things. Like any parent, I've enjoyed seeing you grow, but also want you to test your own wings.

• Mom also tells a story of an elementary school teacher she had worked with who was leaving her job. Mom stopped by to give the teacher a goodbye present. The teacher cried. Mom said "I expect that you've been crying all day as you said goodbye to your students." The teacher said "No, I forgot to say goodbye." Since then mom has always made it a point to say goodbye to her classes. I encourage you to say goodbye to your friends and colleagues who you may not see again.