1. Possible user modes and options for LEGUP Presented in decreasingly sane order by Ben Blotcky

2. Overview  Solving Varying amounts of interaction with logical tools and solving AI  Display Pretty, clean interface geared towards presentations and lectures  Creation Focus more on user freedom and power

3. Play Mode  For many people, solving grid-based logic puzzles will be a totally new experience.  Give them the opportunity to try solving puzzles before introducing the tree and justification panes  Allow users to develop an intuitive understanding of the puzzles.

4. Option: Check Solution Button  Ignores logic, simply checks if the current state is a valid solution or not.  Allows LEGUP to emulate puzzle applets common on the web  Serves to acquaint users with puzzle rules  Minimal risk of cheating (as far as logic is concerned), as no proof is constructed.

5. How much do we tell them?  Trivial: boolean function compares current state to a solution file, and returns a yes/no answer.  Doable: Show the user where a rule has been violated (like most applets)  Interesting: Display all such violations. Check for completion first! Display one at a time when necessary  Scrollable?

6. Practice Mode  Introduce the rules and tree windows  Essentially what we have now  User justifies changes in puzzle state by rule applications and inductive proof by contradiction/cases.

7. Automated Case Rule Option  Instead of having to split the tree, manually create each case, and then justify the case.  Why not just click a button, then a space, and LEGUP automatically branches and creates the necessary states?

8. Corner Cutting Options  Auto-Check cases for contradiction When the tree splits, prune all the branches that lead to immediate contradictions and don’t display them. Useful for puzzles like Sudoku, which have high branching factors but are easily pruned Results in a cleaner, narrower, easier to follow tree.

9. Solver mode  Uses the solving AI to produce a solution, does not display proof.  Take that, cheaters!  Could be used to implement a hint option Perform a subproof, return

10. Prover mode  Use our AI to automatically generate a proof for a puzzle solution.  Several user-customizable options.  Could be very useful from a research perspective.  But could cripple educational use (automatically does homework)

11. AI options  Adjust when each rule is applied, if ever. One application is testing different sets of rules and comparing the proofs produced from them.  Choose between induction heuristics, assuming we’ll have more than one.

12. Playback mode  Basically a slide show demonstrating how a proof developed Or just the normal interface, full screen.  Could display growth of tree, as well as development of cases side by side. Pruning would be useful for sudoku  Could be used along with AI prover to generate a walkthrough for any given puzzle.

13. Construction Mode  Allow user to create puzzles for a variety of purposes To demonstrate particular tricks, traits, techniques… Creating homework problems Just for fun  Could also be potentially used for…

14. Rule edit mode?  Change order of rule applications  Create small puzzles as test cases  Construct a short proof and use it as a subproof in larger puzzles Somewhat sensible to implement  Change justification rules Necessary to have the proving AI options mentioned earlier

15. Issues with user-edited rules  Requires an expert user to handle  How to make LEGUP understand new rules short of writing the code yourself  Could be one of those crazy ideas that only I care about  At that point, you might as well have…

16. Puzzle Creation Mode  Have an interface for users to add their own puzzles. Very complicated, by necessity. Would be an extremely advanced user feature. Importing new graphics would likely be a pain for everyone involved. Would be incredibly awesome.

17. One last thing…  Timer option  Variety of uses: Research application, see how long it takes to reach certain conclusions or whole puzzles People like to see how fast they can solve