Practical Implications of Rice's Theorem

Rice's Theorem -- and what it means for you! :)

Transcript

1. RICE'S THEOREM AND WHAT IT MEANS FOR YOU! :) Created by / Simon Cross @hodgestar
2. WHAT THE HECK IS RICE'S THEOREM?
3. SOME THINGS ARE JUST UNPOSSIBLE! Which things? Glad you asked! :)
4. PROPERTIES OF COMPUTABLE PARTIAL FUNCTIONS
5. FORMAL(ISH) STATEMENT Given a non-trivial property of computable partial functions the problem of whether a particular program computes such a function is undecidable
6. NON-TRIVIAL A least one function that has the property A least one function that doesn't have the property
7. See for the gory details. :) Wikipedia
8. KINDS OF PROPERTIES
9. WORKS FOR: Properties that refer to behaviour Properties that refer to input and output only
10. DOESN'T WORK FOR: Properties that refer to the implementation Number of lines of code Number of for-loops Whether the code is syntactically correct
11. SKETCH OF A PROOF ...
12. ... IN PYTHON! d e f h a s _ c o o l _ p r o p e r t y ( f ) : " " " R e t u r n s T r u e i f f h a s t h i s c o o l p r o p e r t y , F a l s e o t h e r w i s e . " " " # X X X : P u t m a g i c h e r e ! d e f t i n y _ c o o l _ f u n c t i o n ( * a r g s , * * k w ) : " " " T i n y f u n c t i o n w e w r o t e t o s h o w t h e c o o l p r o p e r t y i s s o m e t i m e s m e t . " " " # X X X : W r i t e t h i s . d e f h a l t s ( a , i ) : " " " R e t u r n s T r u e i f a h a l t s g i v e n i n p u t i . " " " d e f t ( * a r g s , * * k w ) : a ( i ) # t h i s i s j u s t h e r e t o m e s s w i t h h a s _ c o o l _ p r o p e r t y r e t u r n t i n y _ c o o l _ f u n c t i o n ( * a r g s , * * k w ) r e t u r n h a s _ c o o l _ p r o p e r t y ( t )
13. SO THESE IMPLICATIONS YOU PROMISED?
14. QA AND TESTING
15. SECURITY AND SANDBOXES
16. COMPILING AND STATIC ANALYSIS
17. NON-IMPLICATIONS a.k.a. things that might work
18. UPFRONT DESIGN If you want a property, design it in up front ... because you won't be able to check later. :/
19. HALT? BY SIMON CROSS / HODGESTAR.ZA.NET
20. WHAT MADE YOU LOOK INTO ALL THIS?!
21. BLAME PERL! It's unparsable. :/
22. ITS GRAMMAR IS AMBIGUOUS IN CRAZY WAYS: w h a t e v e r / 2 5 ; # / ; d i e " t h i s d i e s ! " ;
23. IF YOU EVER NEED TO FEEL GREAT ABOUT USING PYTHON: by Randal Schwartz (2000) by Adam Kennedy by Jeffrey Kegler (2008) On Parsing Perl PPI man page Perl Cannot be Parsed: A Formal Proof
24. AN UNRELATED COOL THING: by John M. Zelle Python as a First Language
25. “Compiling a program and staring at a screenfull of nagging messages is a dull and exasperating activity.”
26. “In fact, I would venture to say that after a couple days playing with Python, many faculty who are now teaching C++ would know Python better.”
27. IDEAS GENERATED BY QUESTIONS AND COMMENTS AFTER THE TALK Scalability is another property one can't tack on to programs afterwards. JIT compilation also benefits from Rice's Theorem since it imposes strong bounds on what static compilation can prove about the algorithm implemented.