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Automa Automatic V tic Verif erifica ication f tion for or Inter Interactiv active Gr Graphical phical Pr Prog ograms ams Car Carl Eastlund l Eastlund Ma Matthias F tthias Felleisen elleisen cce@ccs.neu.edu

  1. Automa Automatic V tic Verif erifica ication f tion for or Inter Interactiv active Gr Graphical phical Pr Prog ograms ams Car Carl Eastlund l Eastlund Ma Matthias F tthias Felleisen elleisen cce@ccs.neu.edu matthias@ccs.neu.edu Northeastern University Boston, Massachusetts 1

  2. Verification for I/O and Interactive Programs Davis. Reasoning about ACL2 file input. ACL2 ’06. Dowse et al. Reasoning about deterministic concurrent functional I/O. IFL ’04. Dwyer et al. Analyzing interaction orderings with model checking. ASE ’04. Krishnamurthi and Licata. Verifying interactive web programs. ASE ’04. Godefroid et al. VeriWeb: automatically testing dynamic web sites. WWW ’02. Memon. An event-flow model of GUI-based applications for testing. STVR ’07. 2

  3. Cr Crea eating W ting Wor orlds lds 3

  4. Dart Game 4

  5. Dart Game ; A World is either a Natural Number or 'win (big-bang 3 ; : World (on-draw show-game 600 600) (on-mouse throw-dart) (stop-when win-or-lose)) 5

  6. Dart Game ; show-game : World -> Image (defun show-game (w) (cond ((equal w 'win) (text "You win!" 120 'blue)) ((equal w 0) (text "You lose." 120 'blue)) (t (show-darts w (show-target))))) ; throw-dart : ActiveWorld Int Int -> World (defun throw-dart (w x y a) (if (equal a 'button-down) (if (dart-hits x y) 'win (1- w)) w)) ; win-or-lose : World -> Boolean (defun win-or-lose (w) (or (equal w 'win) (equal w 0))) 6

  7. The W he Wor orld Mac ld Machine hine 7

  8. (big-bang *WORLD_0* (on-draw RENDER *WIDTH* *HEIGHT*) (on-tick TOCK *RATE*) (on-key REACT) (on-mouse CLICK) (stop-when DONE)) 8

  9. (on-draw RENDER *WIDTH* *HEIGHT*) ; RENDER : World -> Image ; *WIDTH*, *HEIGHT* : Nat (stop-when DONE) ; DONE : World -> Boolean 9

  10. (on-tick TOCK *RATE*) ; TOCK : ActiveWorld -> World ; *RATE* : Rational (on-key REACT) ; REACT : ActiveWorld String -> World (on-mouse CLICK) ; CLICK : ActiveWorld Int Int Symbol -> World 10

  11. 11

  12. ; event-loop : World EventList -> World (defun event-loop (w es) (cond ((endp es) w) ((DONE w) w) (t (event-loop (event-handler w (car es)) (cdr es))))) 12

  13. ; event-handler : ActiveWorld Event -> World (defun event-handler (w e) (cond ((tickp e) (TOCK w)) ((keyp e) (REACT w e)) ((mousep e) (CLICK w (mouse-x e) (mouse-y e) (mouse-action e))) (t w))) 13

  14. Modeling Darts ; event-handler : ActiveWorld Event -> World (defun event-handler (w e) (cond ((mousep e) (throw-dart w (mouse-x e) (mouse-y e) (mouse-action e))) (t w))) ; event-loop : ActiveWorld EventList -> World (defun event-loop (w es) (cond ((endp es) w) ((win-or-lose w) w) (t (event-loop (event-handler w (car es)) (cdr es))))) 14

  15. No Chea No Cheating! ting! 15

  16. No Cheating! (defthm big-bang-darts-left (implies (>= (count-clicks es) 3) (win-or-lose (event-loop 3 es)))) 16

  17. No Cheating! ; count-clicks : EventList -> Nat (defun count-clicks (es) (cond ((endp es) 0) ((clickp (car es)) (1+ (count-clicks (cdr es)))) (t (count-clicks (cdr es))))) (defthm big-bang-darts-left (implies (>= (count-clicks es) 3) (win-or-lose (event-loop 3 es)))) 17

  18. No Cheating! ; clickp : Event -> Boolean (defun clickp (e) (and (mousep e) (equal (mouse-action e) 'button-down))) ; count-clicks : EventList -> Nat (defun count-clicks (es) (cond ((endp es) 0) ((clickp (car es)) (1+ (count-clicks (cdr es)))) (t (count-clicks (cdr es))))) (defthm big-bang-darts-left (implies (>= (count-clicks es) 3) (win-or-lose (event-loop 3 es)))) 18

  19. No Cheating! (defthm event-loop-darts-left (implies (and (dart-gamep w) (>= (count-clicks es) (darts-left w))) (win-or-lose (event-loop w es)))) 19

  20. No Cheating! ; darts-left : World -> Nat (defun darts-left (w) (if (natp w) w 0)) (defthm event-loop-darts-left (implies (and (dart-gamep w) (>= (count-clicks es) (darts-left w))) (win-or-lose (event-loop w es)))) 20

  21. No Cheating! ; dart-gamep : Any -> Boolean (defun dart-gamep (w) (or (natp w) (equal w 'win))) ; darts-left : World -> Nat (defun darts-left (w) (if (natp w) w 0)) (defthm event-loop-darts-left (implies (and (dart-gamep w) (>= (count-clicks es) (darts-left w))) (win-or-lose (event-loop w es)))) 21

  22. No Cheating! (defthm event-loop-dart-gamep (implies (dart-gamep w) (dart-gamep (event-loop w es)))) (defthm big-bang-dart-gamep (dart-gamep (event-loop 3 es))) 22

  23. No Cheating! (defthm big-bang-dart-gamep (dart-gamep (event-loop 3 es)) :hints (("Goal" :in-theory (disable event-loop-dart-gamep) :use (:instance event-loop-dart-gamep (w 3))))) (defthm big-bang-darts-left (implies (>= (count-clicks es) 3) (win-or-lose (event-loop 3 es))) :hints (("Goal" :in-theory (disable event-loop-darts-left) :use (:instance event-loop-darts-left (w 3))))) 23

  24. Extending Big Bang (big-bang *WORLD_0* (on-draw RENDER *WIDTH* *HEIGHT*) (on-tick TOCK *RATE*) (on-key REACT) (on-mouse CLICK) (stop-when DONE) (world-invariant GOOD) (world-measure MEASURE PROGRESS)) 24

  25. Extending Big Bang (world-invariant GOOD) ; becomes: (defthm event-loop-GOOD (implies (GOOD w) (GOOD (event-loop w es)))) (defthm big-bang-GOOD (GOOD (event-loop *WORLD_0* es)) :hints (("Goal" :in-theory (disable event-loop-GOOD) :use (:instance event-loop-GOOD (w *WORLD_0*))))) 25

  26. Extending Big Bang (world-measure MEASURE PROGRESS) ; becomes: (defun count-PROGRESS (es) ...) (defthm event-loop-MEASURE ...) (defthm big-bang-MEASURE ...) 26

  27. Extending Big Bang (world-measure MEASURE PROGRESS) ; becomes: (defun count-PROGRESS (es) (cond ((endp es) 0) ((PROGRESS (car es)) (1+ (count-PROGRESS (cdr es)))) (t (count-PROGRESS (cdr es))))) (defthm event-loop-MEASURE ...) (defthm big-bang-MEASURE ...) 27

  28. Extending Big Bang (world-measure MEASURE PROGRESS) ; becomes: (defun count-PROGRESS (es) ...) (defthm event-loop-MEASURE (implies (and (GOOD w) (>= (count-PROGRESS es) (MEASURE w))) (DONE (event-loop w es)))) (defthm big-bang-MEASURE ...) 28

  29. Extending Big Bang (world-measure MEASURE PROGRESS) ; becomes: (defun count-PROGRESS (es) ...) (defthm event-loop-MEASURE ...) (defthm big-bang-MEASURE (implies (>= (count-PROGRESS es) (MEASURE *WORLD_0*)) (DONE (event-loop *WORLD_0* es))) :hints (("Goal" :in-theory (disable event-loop-MEASURE) :use (:instance event-loop-MEASURE (w *WORLD_0*))))) 29

  30. Experiments Experiments 30

  31. Experiments Worm: • all segments are adjacent • all segments are on-screen • no segments overlap Blocks: • no blocks overlap • all blocks are on-screen Bikes: • trails run in cardinal directions 31

  32. Experiments UFO: • all objects stay on-screen. • UFO’s descent acts as a time limit. Hangman: • limit of 5 (failed) + word-length (successful) keystrokes 32

  33. Experiments Editor: • partial correctness of typing, selecting, deleting, and navigating • no partial letters are displayed • displayed text is maximal prefix 33

  34. Experiments Pr Project oject Lines Lines Lemmas Lemmas CPU seconds CPU seconds Hangman 365 11 1.48 Blocks 450 16 0.86 UFO 696 23 13.97 Worm 824 34 4.90 Editor 1,117 59 5.04 Bikes 1,354 84 202.11 34

  35. Thank Y hank You. ou. 35

  36. Images ; Basic shape constructors: (circle radius mode color) (rectangle width height mode color) (triangle size mode color) (star inner outer points mode color) ; Combining shapes: (add-line image x1 y1 x2 y2 color) (empty-scene width height) (place-image image x y scene) ; Predicates and accessors: (image? x) (image-width image) (image-height image) 36

  37. Images (defthm circle/image? (implies (and (natp r) (mode? m) (image-color? c)) (image? (circle r m c)))) (defthm circle/image-width (equal (image-width (circle radius mode color)) (* radius 2))) (defthm circle/image-height (equal (image-height (circle radius mode color)) (* radius 2))) 37

  38. Images (defthm empty-text-image-width (implies (and (font-size? size) (image-color? color)) (= (image-width (text "" size color)) 0))) (defthm append-right-text-image-width (implies (and (stringp a) (stringp b) (font-size? size) (image-color? color)) (>= (image-width (text (string-append a b) size color)) (image-width (text a size color))))) (defthm append-left-text-image-width (implies (and (stringp a) (stringp b) (font-size? size) (image-color? color)) (>= (image-width (text (string-append a b) size color)) (image-width (text b size color))))) 38

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