trs/TODO

# vim: set fileencoding=utf-8 :

 - Fix BisonSyntaxError location tracking.

 - Sort polynom by its exponents?

 - Fix division by zero caused by "0/0": Catch exception in front-end

smvv@multivac ~/work/trs $ printf "a/0\n??" | ./main.py
Traceback (most recent call last):
  File "./main.py", line 75, in <module>
    main()
  File "./main.py", line 64, in main
    node = p.run(debug=args.debug)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 258, in run
    self.report_last_error(filename, e)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 251, in run
    self.engine.runEngine(debug)
  File "bison_.pyx", line 592, in bison_.ParserEngine.runEngine (build/external/pybison/bison_.c:592)
  File "/home/smvv/work/trs/src/parser.py", line 195, in hook_handler
    possibilities = handler(retval)
  File "/home/smvv/work/trs/src/rules/fractions.py", line 23, in match_constant_division
    raise ZeroDivisionError('Division by zero: %s.' % node)
ZeroDivisionError: Division by zero: a / 0.

smvv@multivac ~/work/trs $ printf "0/0\n??" | ./main.py
Traceback (most recent call last):
  File "./main.py", line 75, in <module>
    main()
  File "./main.py", line 64, in main
    node = p.run(debug=args.debug)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 258, in run
    self.report_last_error(filename, e)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 251, in run
    self.engine.runEngine(debug)
  File "bison_.pyx", line 592, in bison_.ParserEngine.runEngine (build/external/pybison/bison_.c:592)
  File "/home/smvv/work/trs/src/parser.py", line 195, in hook_handler
    possibilities = handler(retval)
  File "/home/smvv/work/trs/src/rules/numerics.py", line 73, in match_divide_numerics
    divide = not divmod(n.value, dv)[1]
ZeroDivisionError: integer division or modulo by zero

 - Last possibilities reduce to a similar result.

smvv@multivac ~/work/trs $ printf "0/1\n??" | ./main.py
<Possibility root="0 / 1" handler=divide_numerics args=(0, 1)>
Division of 0 by 1 reduces to 0.
Division of 0 by 1 reduces to 0.

 - ExpressionNode.equals() werkend maken voor alle cases (negatie).

 - validation: preorder traversal implementatie vergelijken met andere
               implementaties.

 - No matches for sin(pi), sin(2pi), sin(4pi), etc...

 - Create unit tests for node inequivalence operator.

 - Line printer: 1 / (n + n)x  ->  1 / (n + n) * x

 - Parser: 'apia' -> 'aa'

 - Unit tests for strategy.

 - Parser: add unit tests for operator associativity (derivatives/integrals).

 - Modules:
   + Equations with substitution
   + Sort
   + Gonio

 - Add parentheses to integral bounds where needed:
   int_(-1)^2 ... dx
   or, fix parser error using the following notation:
   int_-1^2 ... dx

 - Base hint selection on the desired final expression.
   To generate a hint for expression list A, ..., B:
   1. Create a possibility tree for A.
   2. Validate all expressions up to B:
      set ROOT = A

      for each expression C in <A, B] do:
          if final answer of C is not equal to final answer of A:
              validation failes at c

          find C in the possibility tree, traversing from ROOT

          if not found:
              validation continues, but generate an efficiency warning at C
              # FIXME: validation fails at C?

          set ROOT = C
    3. Generate a hint:
      # ROOT should now be equal to B, so lookup of B is unnecessary
      set N = empty dictionary

      for each possibility of ROOT P node do:
          evaluate P(B) until the final expression of A is reached
          set N[P] = the number of explicit possibilities that have been applied in the evaluation

      the hint is that P for which the value of N[P] the smallest

 - Optimization: put possibility tree in hashmap: {'expression': [(handler, args, 'applied_expression')], ...}
   This hashmap can be used to speedup the calculation of possbility trees.

- Fix: int -cf(x) dx (caused infinite loop)

- Idea for validation that is not really working ATM:
  When validating that a => b:
  Apply reductions to a to obtain A, this costs N steps.
  Apply reductions to b to obtain B, this costs M steps.
  if A != B, validation fails (return status 0)
  else if M >= N, the uses has done a useless or bad step (return status 1)
  otherwise (if M < N), the user has reduced the expression correctly (return status 2)