Partial Evaluation With Pyparsing
Solution 1:
1) Yes, it is possible to pickle the results from parsing your expression, and save that to a database. Then you can just fetch and unpickle the expression, rather than reparse the original again.
2) You can do a quick-and-dirty pass at this just using the compile and eval built-ins, as in the following interactive session:
>>>y = compile("m*x+b","","eval")>>>m = 100>>>x = 5>>>b = 1>>>eval(y)
501
Of course, this has the security pitfalls of any eval- or exec-based implementation, in that untrusted or malicious source strings can embed harmful system calls. But if this is your thesis and entirely within your scope of control, just don't do anything foolish.
3) You can get an online example of parsing an expression into a "evaluatable" data structure at the pyparsing wiki's Examples page. Check out simpleBool.py and evalArith.py especially. If you're feeling flush, order a back issue of the May,2008 issue of Python magazine, which has my article "Writing a Simple Interpreter/Compiler with Pyparsing" with a more detailed description of the methods used, plus a description of how pickling and unpickling the parsed results works.
4) The slow part will be the parsing, so you are on the right track in preserving these results in some intermediate and repeatably-evaluatable form. The eval part should be fairly snappy. The second slow part will be in fetching these pickled structures from your database. During your MC run, I would package a single function that takes the selection parameters for an expression, fetches from the database, and unpickles and returns the evaluatable expression. Then once you have this working, use a memoize decorator to cache these query-results pairs, so that any given expression only needs to be fetched/unpickled once.
Good luck with your thesis!
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