For today's OCaml part we briefly covered modules as described in
Hickey, chap.11+12 (and parts of chap.13). You shouldn't spend time on
the gory details of, e.g., "sharing constraints" in chap.13, though.
 
For this afternoon's exercises I ask you to consider the following:

1. Consider the uploaded module implementing Patricia trees.

   You can either copy the source code to your working directory or
   install it using these 5 steps (please ignore the friendly
   instructions printed by ./configure): 

     ./configure
     make ptset.cmi
     make ptmap.cmi
     make
     make install

   then the package should show up within OCaml's toploop if you
   afterwards query it: 

   #use "topfind";;   (* Windows users should instead build a custom #top-level *)
   #list;;

   Alternatively run 'opam install ptset' to install a slightly newer
   version. 

   If you install with 'make' or 'opam' you can afterwards compile a
   file day4.ml that uses ptset with the command:
   
      ocamlbuild -use-ocamlfind -package qcheck,ptset day4.byte


   Test the implementation of integer sets (blackbox over the interface)
   against a model of int sets based on lists. You need
   - to select a set of operations (start small)
   - to implement a little language and an accompanying generator
     of integer set operations
   - to implement an interpreter of these set operations
   - to implement the individual operations in the model
   - to implement abstraction of the Patricia trees
   - and finally to test that for an arbitrary set our observations and
     the set "state" agrees

2. a. Write a shrinker for your language of integer set operations from 1.
   b. Introduce an error in your model
   c. Compare the output (for a fixed seed) with and without shrinking

3. Consider the model for Ptset.mem
   a. Change it to add 'n+1' instead of its parameter 'n'
   b. Does QuickCheck find the error? Why/why not?
   c. Write a classifier that partitions pairs of instruction
      sequences and integers i based on whether i is mentioned in the
      instruction sequence
   d. Change the pair generator to generate more cases in both
      categories of the classifier

4. (for the daring)
   Write an algebraic specification for sets.
   QuickCheck either Patricia trees, Red-black trees, or the Set
   module from OCaml's standard library