15-312 Recitation #10: Monads and Objects
2002-10-30
Joshua Dunfield (joshuad@cs)
Carnegie Mellon University

- Intuition for monads:
      0tau (circle-tau) is like tau susp or 1 -> tau
      val(...) is like delay(...) or lambda _. ...
      let val  is like force(...) or ...()
   
   The correspondence is very rough (tau susp does not separate out
   expressions e that have no effect when evaluated from expressions m
   that may have an effect, as monads do), but may be helpful.

- Common mistakes on asst5:

     1. Applying IH when there are no premises.  You can only apply the
      IH to a *smaller* derivation; if there are no premises, there are no
      smaller derivations and you must prove what you need to prove
      without using the IH.

     2. Making up notation.  Not a big issue, but all the notation you needed
      was in the assignment.

     3. Having write(v) write to the *beginning* of S_O.  I assume this
      was due to people thinking the streams had to work the same way
      as in the SML stream module; you can't add something to the end
      of an SML stream, but the streams in the assignment are just
      abstract objects, so you *can* add something to the end.

     4. Assuming stuff for the store monad carried over to the I/O monad.
      For example, you didn't need a store typing \Lambda since there
      was no store.

     5. In the last two problems, answers that didn't typecheck.
      Practically everybody did this; only one person noticed that
      what they turned in couldn't possibly be well typed (and got
      full credit since I was so glad they were paying attention)
    
- Solutions to last two asst5 problems: to appear

- the Counter object from lecture in a monadic framework:

    counterRep = {x : int ref}
    counter = {get : 0int, inc: 01}           ("01" is "circle unit")
    counterClass : counterRep -> counter
    newCounter : 0counter
   
    ...