Restored TODO-list

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.
+
+ - MESSAGES needs to be expanded.
+
+ - Use pretty-print for expressions in hint messages.
+
+ - 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
+
+ - Frontend: implicit rules are applied after expicit ones, but are still
+   printed separately. This yields multiple successive occurences of the same
+   expression.
+
+ - 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)