Enhancements for PPL 0.12 or later versions
===========================================

- Make all the *affine*image() methods uniform as far as the
  specification is concerned.
- Add the domains of bounded integers and affine spaces.
- Finish the domain of intervals.
- Intervals are best instantiated with checked numbers with
  particular policies: review all the interfaced boxes,
  augment the testsuite, and update the documentation.
- Make the library thread-safe.
- Modify the Makefile.am's to extend silent mode to our own rules.
- Reduce the number of FIXMEs to no more than 20.
- Consider switching to MLGMPIDL for the OCaml interface
  (see https://bugzilla.redhat.com/show_bug.cgi?id=491712).
- Improve the OCaml interface by supporting dynamic loading.
- Enhance the support for systems not providing support for the IEEE
  inexact flag.
- `make check' in ppl_lpsol must run also the incremental version
  of the simplex solver.
- Complete the implementation of the --enable-check configure option.
  Explain it in README.configure.
- Ensure the tests in tests/MIP_Problem/* cover every line of
  code in MIP_Problem.*.
- Define functions rem() and remp() to compute the remainder of division
  in the general case, for rem(), and in the case where the second
  argument is known to be positive, for remp().  In the implementation
  of rem(), if CXX_HAS_REMAINDER_BUG is nonzero, a suitable workaround
  should be implemented to circumvent the INT_MIN % -1 bug.
  rem() and remp() should be used (with a strong preference to the second,
  of course) wherever we now use operator%().
- Suppose we want to sum three numbers, and suppose we do it by

    add(T& to, const T& x, const T& y, const T& z) {
      add(to, x, y);
      add(to, to, z);
    }

  Now suppose that &to == &z, so that we compute the wrong result.
  Perform a code audit to ensure that the above situation never happens.
  In order to ensure that, ensure that the following rule (to be added
  to STANDARDS) is always obeyed:

    if an argument of type T and passed by reference is changed,
    after the change no argument of type U and passed by const or
    non-const reference should be read unless U is incompatible with T
    or we are otherwise 100% sure that the changed argument and the
    argument that is read afterward are not aliases (in the latter
    case an assert(&to != &z) shall be added.
- Improve the handling of the --enable-instantiations configure
  option so that "closure by subdomain" is automatically implemented
  (e.g., if Pointset_Powerset(X) is specified, X should be automatically
  added in case it is not already present).
- Add a "quick assign" function to checked numbers that allows
  to efficiently assign small integer constants (like those in
  the range [-2, 2]) that are guaranteed not to cause any
  rounding or overflow problems.
- Consider whether or not our interface for method time_elapse_assign()
  is the one needed by users: in particular, see if it should take as
  an argument a generator system, instead of an abstract element.
- Provide a generic implementation for the `widening with tokens'.
- Implement the extrapolation operators defined in HenzingerH95
  and HenzingerPW01.
- Implement void Polyhedron::envelope_assign(const Polyhedron& y).
- Provide support for strict inequalities in MIP problems.
- Pointset_Powerset and Partially_Reduced_Product domains:
  Improve and add to the existing methods for the powerset and product domains
  so that they can be subdomains of themselves and of each other;
  tidy the tests directories for these domains and ensure the code
  with all likely instantiations is fully tested;
  add the same functionaity to the C, Java, OCaml and Prolog interfaces.
- Any_Pointset domain: check the interface for lacking or useless methods.


Enhancements for PPL 0.13 or later versions
===========================================

- Find a way to let the GMP and checked-int versions of the PPL coexist
  so as to allow using them in the same application.
- Provide methods computing approximations of the integer convex hull
  of semantic domains for the case where we are only interested in integral
  solutions (as is the case, e.g., in many program analyses).  Then
  cutting-plane methods (Gomory, Chvatal, ...) allow to shrink polyhedra
  still not losing any integral solution.
  See http://www.cs.unipr.it/ppl/Documentation/bibliography#NemhauserW88
  Check the work by Kent Andersen and Gerard Cornuejols on
  reduce-and-split cuts.
- Consider the addition of "constraint-only" methods (e.g., computing
  projections and upper bounds using the MIP solver).
- Consider extending the MIP solver to handle Parametric Integer
  Programming.
- In the OK() methods, instead of having all those #ifndef NDEBUG,
  it is probably worthwhile to use a suitable defined `barf' stream
  that does the right thing.
- Using meta_programming.hh it is possible to define all the swap functions
  "automatically".  Consider whether it is worth doing it.
- Provide a single, generic implementation to replace all our status
  classes.
- Provide optimized implementations of Polyhedron::expand_dimension()
  Polyhedron::fold_dimensions().
- Add an implementation of Minkowski addition.  Check the algorithm
  described in

    K. Fukuda.
    From the zonotope construction to the Minkowski addition
    of convex polytopes.
    J. Symbolic Comput., 38(4):1261-1272, 2004.



Efficiency Issues
=================

- There must be a more efficient way to implement
  bool Polyhedron::is_disjoint_from(const Polyhedron&).
- There must be a more efficient way to compute convex differences.
- We are being rather careless about the creation of temporaries
  as far as the classes Linear_Expression, Constraint and Generator
  are concerned.
- Provide a better implementation of computing squares in MIP_Problem's
  steepest-edge to avoid big numbers.