CSC152 2006S, Class 9: Continuations

Admin:
* Options for Monday: Lab (no reading) or Continuations and the Web (belated readings)
* Disappointed in the lack of responses to the readings.
* Questions on the homework?
* Notes on Church numerals
* Alex and DaveV showed up early.
* Dimitar is late again.

Overview:
* Continuation basics
* Applications of continuations
* Continuations and the Web

/Church Numerals/

* Definition of numbers within the lambda calculus
* Definition based on "zero and successor"
* Each number is a function
* Each number has the form
        \ s z . (s (s .... (s z)))
* Number n has n s's in the rhs

/Continuations/

* Functions that represent 'the state of the program' or
  'what happens next'
> (+ 4 (* 3 (- (+ x x) a)))
  The continuation for (* ...) is "add 4" or (lambda (x) (+ x 4))
  The continuation for (- ...) is multiply by 3 and then add 4, or
    (lambda (x) (+ 4 (* 3 x)))
  The continuation for (+ x x) is ...
* Every language has an implicit notion of continuations (after all, there is always "the next code to execute"
* Scheme makes these continuations first-class objects: You can get them, send them to functions, call them, etc.
  * When you call a continuation, you replace the current continuation with the called continuation
* To get a continuation, use
  (call-with-current-continuation (lambda (cont) ...)) -- Wrap up the current continuation and pass it to lambda (cont)
  (call/cc (lambda (cont) ...)) -- Alias for call-with-....
  (let/cc k body) -- Pack up the current continuation and call it k, then execute body
   - Same as (call/cc (lambda (k) body))

* Simplest useful application of continuations: Exceptions
* Another useful application: Pausing code
  * Create two global continuations: 
    * exit - return to the top level
    * resume - restart the code at the stopped pointa
  * Graham example: You can pause and restart tree traversal
* Another useful application: coroutining

Continuations not necessary, but can make the coding easier (once
you understand them well)

The fun use of continuations: Saving state on the Web
* Write an interactive program that is not Web-based
* Replace each request for input and change it to
  * Grab the current continuation
  * Name and store that continuation for later reuse
  * Generate a Web page with a form that requests input (and has the continuation name in a hidden field)
  * When a page is submitted, get the continuation and call the continuation on the other returned values