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s str t r s

s strt r - PowerPoint PPT Presentation

Dec 01, 2023 •572 likes •1.63k views

s strt r s Pr sr s

  1. ❚r❛♥s❧❛t✐♊♥ ♊❢ ●♩❛❧s ❝♊❞❡ ● ♣ ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ❊ ✮ ✚ ❂ mark A ❝♊❞❡ ❆ t ✶ ✚ ✳ ✳ ✳ ❝♊❞❡ ❆ t ❊ ✚ call p/k ❆✿ ✳ ✳ ✳ ❊①❛♠♣❧❡✿ ❧❡t ❣ ✑ ♣ ✭ ❛❀ ❳❀ ❣ ✭ ✖ ❳❀ ❚ ✮✮ ❛♥❞ ✚ ❂ ❢ ❳ ✌✊ ✶ ❀ ❚ ✌✊ ✷ ❣ ✱ t❀❡♥ ❝♊❞❡ ● ❣ ✚ ❡♠✐ts t❀❡ ❝♊❞❡✿ mark A putref 1 call p/3 ❆✿ ✳ ✳ ✳ putatom a putvar 2 putvar 1 putstruct g/2

  2. ❚r❛♥s❧❛t✐♊♥ ♊❢ ●♩❛❧s ❙tr✉❝t✉r❡ ♊❢ ❛ ❢r❛♠❡✿ ❙P ❧♩❝❛❧ st❛❝❩ ❛r❣✉♠❡♥ts ❋P P♩s❈♊♥t ✵ ❋P♩❧❞ ✲✶ ✲✷ ♩r❣❛♥✐③❛t✐♊♥❛❧ ❝❡❧❧s ✲✞ ✲✹ ✲✺

  3. ❚r❛♥s❧❛t✐♊♥ ♊❢ ●♩❛❧s ❘❡♠❛r❊s✿ ❚❀❡ ♣♊s✐t✐✈❡ ❝♊♥t✐♥✉❛t✐♊♥ ❛❞❞r❡ss PosCont r❡❝♊r❞s ✇❀❡r❡ t♩ ❝♊♥t✐♥✉❡ ❛❢t❡r s✉❝❝❡ss❢✉❧ tr❡❛t♠❡♥t ♊❢ t❀❡ ❣♊❛❧✳ ❆❞❞✐t✐♊♥❛❧ ♩r❣❛♥✐③❛t✐♊♥❛❧ ❝❡❧❧s ❛r❡ ♥❡❝❡ss❛r② ❢♊r ❜❛❝❩tr❛❝❊✐♥❣ ✳

  4. ❚r❛♥s❧❛t✐♊♥ ♊❢ ●♩❛❧s ❆ ✻ ♠❛r❊ ❆ ❋P ❋P SP = SP + 6; S[SP] = A; S[SP-1] = FP;

  5. ❚r❛♥s❧❛t✐♊♥ ♊❢ ●♩❛❧s P❈ ♣✎♥ ❝❛❧❧ ♣✎♥ ♥ ❋P FP = SP - n; PC = p/n;

  6. ❯♥✐☞❝❛t✐♊♥ ❲❡ ❞❡♥♊t❡ ♩❝❝✉rr❡♥❝❡s ♊❢ ❛ ✈❛r✐❛❜❧❡ ❳ ❜② ⑩ ❳ ✳ ■t ✇✐❧❧ ❜❡ tr❛♥s❧❛t❡❞ ❞✐☛❡r❡♥t❧② ❞❡♣❡♥❞✐♥❣ ✇❀❡t❀❡r ✐t✬s ✐♥✐t✐❛❧✐③❡❞ ♩r ♥♊t✳ ❲❡ ✐♥tr♊❞✉❝❡ t❀❡ ♠❛❝r♩ ♣✉t ⑩ ❳ ✚ ✿ ♣✉t ❳ ✚ ❂ putvar ✭ ✚❳ ✮ ♣✉t ✖ ❳ ✚ ❂ putref ✭ ✚❳ ✮ ♣✉t ✚ ❂ putanon

  7. ❯♥✐☞❝❛t✐♊♥ ❚r❛♥s❧❛t✐♊♥ ♊❢ t❀❡ ✉♥✐☞❝❛t✐♊♥ ⑩ ❳ ❂ t ✿ ♣✉s❀ ❛ r❡❢❡r❡♥❝❡ t♩ ❳ ♊♥t♩ t❀❡ st❛❝❩❀ ❝♊♥str✉❝t t❀❡ t❡r♠ t ✐♥ t❀❡ ❀❡❛♣❀ ✐♥tr♊❞✉❝❡ ❛ ♥❡✇ ✐♥str✉❝t✐♊♥ ✇❀✐❝❀ ✐♠♣❧❡♠❡♥ts t❀❡ ✉♥✐☞❝❛t✐♊♥✳ ❝♊❞❡ ● ✭ ⑩ ♣✉t ⑩ ❳ ❂ t ✮ ✚ ❂ ❳ ✚ ❝♊❞❡ ❆ t ✚ unify

  8. ❯♥✐☞❝❛t✐♊♥ ❊①❛♠♣❧❡✿ ❝♊♥s✐❞❡r t❀❡ ❡q✉❛t✐♊♥ ❯ ❂ ❢ ✭ ❣ ✭ ✖ ✖ ❳❀ ❚ ✮ ❀ ❛❀ ❩ ✮ ❚❀❡♥✱ ❣✐✈❡♥ ❛♥ ❛❞❞r❡ss ❡♥✈✐r♊♥♠❡♥t ✚ ❂ ❢ ❳ ✌✊ ✶ ❀ ❚ ✌✊ ✷ ❀ ❩ ✌✊ ✾ ❀ ❯ ✌✊ ✹ ❣ t❀❡ ❢♊❧❧♊✇✐♥❣ ❝♊❞❡ ✐s ❣❡♥❡r❛t❡❞✿ putref 4 putatom a putref 1 putvar 3 putvar 2 putstruct f/3 putstruct g/2 unify

  9. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ unify ❛♣♣❧✐❡s t❀❡ r✉♥✲t✐♠❡ ❢✉♥❝t✐♊♥ unify() t♩ t❀❡ t♊♣♠♊st t✇♩ r❡❢❡r❡♥❝❡s✿ ✉♥✐❢② unify (S[SP-1], S[SP-2]); SP = SP - 2;

  10. ❯♥✐☞❝❛t✐♊♥ ❋✉♥❝t✐♊♥ unify() ✳ ✳ ✳ t❛❊❡s t✇♩ ❀❡❛♣ ❛❞❞r❡ss❡s✳ ❋♩r ❡❛❝❀ ❝❛❧❧ ✇❡ ❣✉❛r❛♥t❡❡ t❀❛t t❀❡s❡ ❛r❡ ♠❛①✐♠❛❧❧② ❞❡r❡❢❡r❡♥❝❡❞ ✳ ✳ ✳ ✳ ❝❀❡❝❊s ✇❀❡t❀❡r t❀❡ t✇♩ ❛❞❞r❡ss❡s ❛r❡ ❛❧r❡❛❞② ✐❞❡♥t✐❝❛❧ ✳ ■♥ t❀❛t ❝❛s❡ ❞♊❡s ♥♊t❀✐♥❣ ❛♥❞ t❀❡ ✉♥✐☞❝❛t✐♊♥ s✉❝❝❡❡❞❡❞✳ ✳ ✳ ✳ ❜✐♥❞s ②♊✉♥❣❡r ✈❛r✐❛❜❧❡s ✭❧❛r❣❡r ❛❞❞r❡ss❡s✮ t♩ ♊❧❞❡r ✈❛r✐❛❜❧❡s ✭s♠❛❧❧❡r ❛❞❞r❡ss❡s✮✳ ✳ ✳ ✳ ✇❀❡♥ ❜✐♥❞✐♥❣ ❛ ✈❛r✐❛❜❧❡ t♩ ❛ t❡r♠✱ ❝❀❡❝❊s ✇❀❡t❀❡r t❀❡ ✈❛r✐❛❜❧❡ ♩❝❝✉rs ✐♥s✐❞❡ t❀❡ t❡r♠ ✭ ♩❝❝✉r✲❝❀❡❝❊ ✮✳ ✳ ✳ ✳ r❡❝♊r❞s ♥❡✇❧② ❝r❡❛t❡❞ ❜✐♥❞✐♥❣s✳ ✳ ✳ ✳ ♠❛② ❢❛✐❧✱ ✐♥ ✇❀✐❝❀ ❝❛s❡ ✐♥✐t✐❛t❡s ❜❛❝❩tr❛❝❊✐♥❣ ✳

  11. ❯♥✐☞❝❛t✐♊♥ bool unify (ref u, ref v) { if (u == v) return true; if (H[u] == (R, )) { if (H[v] == (R, )) { if (u > v) { H[u] = (R,v); trail(u); return true; } else { H[v] = (R,u); trail(v); return true; } } else if (check (u,v)) { H[u] = (R,v); trail(u); return true; } else { backtrack(); return false; } } ...

  12. ❯♥✐☞❝❛t✐♊♥ ... if (H[v] == (R, )) { if (check (v,u)) { H[v] = (R,u); trail(v); return true; } else { backtrack(); return false; } } if (H[u] == (A,a) && H[v] == (A,a)) return true; if (H[u] == (S,f/n) && H[v] == (S,f/n)) { for (int i=1; i<=n; i++) if (!unify (deref(H[u+i]), deref(H[v+i]))) return false; return true; } backtrack(); return false; }

  13. ❯♥✐☞❝❛t✐♊♥ ❘ ❛ ❆ ❙ ❢✎✷ ❘ ❘ ❘ ❙ ❢✎✷

  14. ❯♥✐☞❝❛t✐♊♥ ❘ ❛ ❆ ❙ ❢✎✷ ❘ ❘ ❘ ❙ ❢✎✷

  15. ❯♥✐☞❝❛t✐♊♥ ❘ ❛ ❆ ❙ ❢✎✷ ❘ ❘ ❘ ❙ ❢✎✷

  16. ❯♥✐☞❝❛t✐♊♥ ❘ ❛ ❆ ❙ ❢✎✷ ❘ ❘ ❘ ❙ ❢✎✷

  17. ❯♥✐☞❝❛t✐♊♥ ❘ ❛ ❆ ❙ ❢✎✷ ❘ ❘ ❘ ❙ ❢✎✷

  18. ❯♥✐☞❝❛t✐♊♥ ❚❀❡ ❢✉♥❝t✐♊♥ trail() r❡❝♊r❞s ♥❡✇ ❜✐♥❞✐♥❣s✳ ❚❀❡ ❢✉♥❝t✐♊♥ backtrack() ✐♥✐t✐❛t❡s ❜❛❝❩tr❛❝❊✐♥❣✳ ❚❀❡ ❢✉♥❝t✐♊♥ check() ♣❡r❢♊r♠s t❀❡ ♩❝❝✉r✲❝❀❡❝❊❀ ✐❡✳ t❡sts ✇❀❡t❀❡r ❛ ✈❛r✐❛❜❧❡ ✭✐ts ☞rst ❛r❣✉♠❡♥t✮ ♩❝❝✉rs ✐♥s✐❞❡ ❛ t❡r♠ ✭✐ts s❡❝♊♥❞ ❛r❣✉♠❡♥t✮✳ ❖❢t❡♥✱ t❀✐s ❝❀❡❝❊ ✐s s❊✐♣♣❡❞✿ bool check (ref u, ref v) { return true; }

  19. ❯♥✐☞❝❛t✐♊♥ ❖t❀❡r✇✐s❡✱ ✇❡ ❝♩✉❧❞ ✐♠♣❧❡♠❡♥t check() ❛s ❢♊❧❧♊✇s✿ bool check (ref u, ref v) { if (u == v) return false; if (H[v] == (S,f/n)) for (int i=1; i<=n; i++) if (!check (u, deref (H[v+i]))) return false; return true; }

  20. ❯♥✐☞❝❛t✐♊♥ ❚❀❡ tr❛♥s❧❛t✐♊♥ ♊❢ ❛♥ ❡q✉❛t✐♊♥ ⑩ ❳ ❂ t ✐s ✈❡r② s✐♠♣❧❡✱ ❜✉t ❛❧❧ t❀❡ ♊❜❥❡❝ts ❝♊♥str✉❝t❡❞ t♩ r❡♣r❡s❡♥t t ✇❀✐❝❀ ❀❛✈❡ ❝♩rr❡s♣♊♥❞✐♥❣ ♠❛t❝❀✐♥❣ ♊❜❥❡❝t r❡❛❝❀❛❜❧❡ ❢r♩♠ ❳ ❜❡❝♊♠❡s ✐♠♠❡❞✐❛t❡❧② ❣❛r❜❛❣❡ ✳ ■❞❡❛✿ ④ P✉s❀ ❛ r❡❢❡r❡♥❝❡ t♩ t❀❡ r✉♥✲t✐♠❡ ❜✐♥❞✐♥❣ ♊❢ ⑩ ❳ ♊♥t♩ t❀❡ st❛❝❊✳ ④ ❆✈♩✐❞ ❝♊♥str✉❝t✐♊♥ ♊❢ s✉❜t❡r♠s ♊❢ t ❛s ❧♊♥❣ ❛s ♣♊ss✐❜❧❡✳ ④ ■♥st❡❛❞✱ tr❛♥s❧❛t❡ ❡❛❝❀ ♥♊❞❡ ♊❢ t ✐♥t♩ ❛♥ ✐♥str✉❝t✐♊♥ ✇❀✐❝❀ ♣❡r❢♊r♠s t❀❡ ✉♥✐☞❝❛t✐♊♥ ✇✐t❀ t❀✐s ♥♊❞❡✊ ❝♊❞❡ ● ✭ ⑩ ♣✉t ⑩ ❳ ❂ t ✮ ✚ ❂ ❳ ✚ ❝♊❞❡ ❯ t ✚

  21. ❯♥✐☞❝❛t✐♊♥ ❯♥✐☞❝❛t✐♊♥ ♊❢ ❛t♩♠s ❛♥❞ ✈❛r✐❛❜❧❡s✿ ❝♊❞❡ ❯ ❛ ✚ ❂ uatom a ❝♊❞❡ ❯ ❳ ✚ ❂ uvar ✭ ✚❳ ✮ ❝♊❞❡ ❯ ✖ ❳ ✚ ❂ uref ✭ ✚❳ ✮ ❝♊❞❡ ❯ ✚ ❂ pop

  22. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ uatom a ✐♠♣❧❡♠❡♥ts t❀❡ ✉♥✐☞❝❛t✐♊♥ ✇✐t❀ ❛♥ ❛t♊♠✿ ❛ ❘ ❘ ❆ ✉❛t♩♠ ❛ v = S[SP]; SP--; switch (H[v]) { case (A,a): break; case (R, ): H[v] = (R, new(A,a)); trail(v); break; default: backtrack(); }

  23. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ uvar i ✐♠♣❧❡♠❡♥ts t❀❡ ✉♥✐☞❝❛t✐♊♥ ✇✐t❀ ❛♥ ✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡✿ ✐ ✐ ❋P ❋P ✉✈❛r ✐ S[FP+i] = S[SP]; SP--;

  24. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ pop ✐♠♣❧❡♠❡♥ts t❀❡ ✉♥✐☞❝❛t✐♊♥ ✇✐t❀ ❛♥ ❛♥♊♥②♠♊✉s ✈❛r✐❛❜❧❡✿ ♣♊♣ SP--;

  25. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ uref i ✐♠♣❧❡♠❡♥ts t❀❡ ✉♥✐☞❝❛t✐♊♥ ✇✐t❀ ❛♥ ✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡✿ ❳ ❚ ✒ ✐ ✐ ❋P ❋P ✒ ❂ ♠❣✉✭ ❳❀ ❚ ✮ ✉r❡❢ ✐ unify (S[SP], deref(S[FP+i])); SP--; ❚❀❡ ♊♥❧② ♣❧❛❝❡✱ ✇❀❡r❡ t❀❡ r✉♥✲t✐♠❡ ❢✉♥❝t✐♊♥ unify() ✐s ❝❛❧❧❡❞✊

  26. ❯♥✐☞❝❛t✐♊♥ ❯♥✐☞❝❛t✐♊♥ ♊❢ ❝♊♥str✉❝t♩r ❛♣♣❧✐❝❛t✐♊♥s✿ ❚❀❡ ✉♥✐☞❝❛t✐♊♥ ❝♊❞❡ ♣❡r❢♊r♠s ❛ ♣r❡✲♊r❞❡r tr❛✈❡rs❛❧ ♊✈❡r t ✳ ❋✐rst ✐t ❝❀❡❝❊s ✇❀❡t❀❡r t❀❡ r♩♩t ♥♊❞❡ ✐s ✉♥✐☞❛❜❧❡✳ ■❢ ❜♩t❀ t❡r♠s ❀❛✈❡ t❀❡ s❛♠❡ t♊♣♠♊st ❝♊♥str✉❝t♩r✱ t❀❡♥ r❡❝✉rs✐✈❡❧② ❝❀❡❝❊s ❢♊r s✉❜t❡r♠s✳ ■♥ t❀❡ ❝❛s❡ ♊❢ ❛♥ ✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡ s✇✐t❝❀❡s ❢r♩♠ ❝❀❡❝❊✐♥❣ t♩ ❜✉✐❧❞✐♥❣✳

  27. ❯♥✐☞❝❛t✐♊♥ ❯♥✐☞❝❛t✐♊♥ ♊❢ ❝♊♥str✉❝t♩r ❛♣♣❧✐❝❛t✐♊♥s✿ ❝♊❞❡ ❯ ✭ ❢ ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ♥ ✮✮ ✚ ❂ ustruct f/n A up B ❆✿ ❝❀❡❝❊ ✐✈❛rs✭ ❢ ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ♥ ✮✮ ✚ son 1 ❝♊❞❡ ❯ t ✶ ✚ ❝♊❞❡ ❆ ✭ ❢ ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ♥ ✮✮ ✚ ✳ ✳ ✳ bind son n ❇✿ ✳ ✳ ✳ ❝♊❞❡ ❯ t ♥ ✚

  28. ❯♥✐☞❝❛t✐♊♥ ❙ ❢✎♥ ❙ ❢✎♥ ✉str✉❝t ❢✎♥ ❆ ❘ ❘ ✉str✉❝t ❢✎♥ ❆ P❈ ❆ switch (H[S[SP]]) { case (S,f/n): break; case (R, ): PC = A; break; default: backtrack(); }

  29. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ son i ♣✉s❀❡s t❀❡ r❡❢❡r❡♥❝❡ ♊❢ t❀❡ ✐ ✲t❀ s✉❜t❡r♠ ♊♥t♩ t❀❡ st❛❝❊✿ ✐ ✐ ❢✎♥ ❢✎♥ ❙ ❙ s♊♥ ✐ S[SP+1] = deref (H[S[SP]]+i); SP++;

  30. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ up A ♣♊♣s ❛ r❡❢❡r❡♥❝❡ ❢r♩♠ t❀❡ st❛❝❩ ❛♥❞ ❥✉♠♣s t♩ t❀❡ ❝♊♥t✐♥✉❛t✐♊♥ ❛❞❞r❡ss✿ ✉♣ ❆ P❈ ❆ SP--; PC = A;

  31. ❯♥✐☞❝❛t✐♊♥ ■♥ t❀❡ ❝❛s❡ ♊❢ ❛♥ ✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡ ✇❡ ♥❡❡❞ t♩ s✇✐t❝❀ ❢r♩♠ ❝❀❡❝❊✐♥❣ t♩ ❜✉✐❧❞✐♥❣✳ ❇❡❢♊r❡ ❝♊♥str✉❝t✐♥❣ t❀❡ ♥❡✇ t❡r♠ ✇❡ ♥❡❡❞ t♩ ❡①❝❧✉❞❡ t❀❛t ✐t ❝♊♥t❛✐♥s t❀❡ ✈❛r✐❛❜❧❡ ♊♥ t♊♣ ♊❢ t❀❡ st❛❝❊✿ ④ t❀❡ ❢✉♥❝t✐♊♥ ✐✈❛rs✭ t ✮ r❡t✉r♥s t❀❡ s❡t ♊❢ ✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡s ♊❢ t ❀ ④ t❀❡ ♠❛❝r♩ ❝❀❡❝❊ ❢ ❚ ✶ ❀ ✿ ✿ ✿ ❀ ❚ ❞ ❣ ✚ ❣❡♥❡r❛t❡s t❀❡ ♥❡❝❡ss❛r② t❡sts✿ ❝❀❡❝❊ ❢ ❚ ✶ ❀ ✿ ✿ ✿ ❀ ❚ ❞ ❣ ✚ ❂ check ✭ ✚ ❚ ✶ ✮ ✳ ✳ ✳ check ✭ ✚ ❚ ❞ ✮

  32. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ check i t❡sts ✇❀❡t❀❡r t❀❡ ✭✉♥✐♥✐t✐❛❧✐③❡❞✮ ✈❛r✐❛❜❧❡ ♊♥ t♊♣ ♊❢ t❀❡ st❛❝❩ ♩❝❝✉rs ✐♥s✐❞❡ t❀❡ t❡r♠ ❜♊✉♥❞ t♩ t❀❡ ✐ ✲t❀ ✈❛r✐❛❜❧❡✿ ❘ ❘ ✐ ✐ ❋P ❋P ❝❀❡❝❊ ✐ if (!check (S[SP], deref(S[FP+i]))) backtrack();

  33. ❯♥✐☞❝❛t✐♊♥ ■♥str✉❝t✐♊♥ bind ❜✐♥❞s t❀❡ ✭✉♥✐♥✐t✐❛❧✐③❡❞✮ ✈❛r✐❛❜❧❡ t♩ t❀❡ ❝♊♥str✉❝t❡❞ t❡r♠✿ ❘ ❘ ❜✐♥❞ H[S[SP-1]] = (R, S[SP]); trail (S[SP-1]); SP = SP - 2;

  34. ❯♥✐☞❝❛t✐♊♥ ❊①❛♠♣❧❡✿ ▲❡t t ✑ ❢ ✭ ❣ ✭ ✖ ❳❀ ❚ ✮ ❀ ❛❀ ❩ ✮ ✇✐t❀ ❡♥✈✐r♊♥♠❡♥t ✚ ❂ ❢ ❳ ✌✊ ✶ ❀ ❚ ✌✊ ✷ ❀ ❩ ✌✊ ✾ ❣ ✳ ❚❀❡♥ ❝♊❞❡ ❯ t ✚ ❣❡♥❡r❛t❡s t❀❡ ❝♊❞❡✿ ❆ ✶ ✿ check 1 ustruct f/3 A ✶ putref 1 son 1 putvar 2 putref 1 ustruct g/2 A ✷ putstruct g/2 putvar 2 son 1 bind putstruct g/2 ❇ ✷ ✿ son 2 uref 1 putatom a son 2 uatom a putvar 3 uvar 2 son 3 putstruct f/3 up B ✷ uvar 3 bind ❆ ✷ ✿ check 1 ❇ ✶ ✿ ✳ ✳ ✳ up B ✶

  35. ❈❧❛✉s❡s ❚❀❡ ❝♊❞❡ ❢♊r ❝❧❛✉s❡s ✇✐❧❧✿ ❛❧❧♩❝❛t❡ st❛❝❩ s♣❛❝❡ ❢♊r ❧♩❝❛❧s❀ ❡✈❛❧✉❛t❡ t❀❡ ❜♊❞②❀ ❢r❡❡ t❀❡ st❛❝❩ ❢r❛♠❡ ✭✐❢ ♣♊ss✐❜❧❡✮✳ ❲❡ ❞❡♥♊t❡ ❧♩❝❛❧ ✈❛r✐❛❜❧❡s ❜② ❢ ❳ ✶ ❀ ✿ ✿ ✿ ❀ ❳ ♠ ❣ ✱ ✇❀❡r❡ t❀❡ ☞rst ❊ ♊♥❡s ❛r❡ ❢♊r♠❛❧ ♣❛r❛♠❡t❡rs✳ ❝♊❞❡ ❈ ✭ ♣ ✭ ❳ ✶ ❀ ✿ ✿ ✿ ❀ ❳ ❊ ✮ ✥ ❣ ✶ ❀ ✿ ✿ ✿ ❀ ❣ ♥ ✮ ❂ pushenv m ❝♊❞❡ ● ❣ ✶ ✚ ✳ ✳ ✳ ❝♊❞❡ ● ❣ ♥ ✚ popenv

  36. ❈❧❛✉s❡s ■♥str✉❝t✐♊♥ pushenv m ❛❧❧♩❝❛t❡s st❛❝❩ s♣❛❝❡ ❢♊r ❧♩❝❛❧ ✈❛r✐❛❜❧❡s✿ ♠ ❋P ❋P ♣✉s❀❡♥✈ ♠ SP = FP + m;

  37. ❈❧❛✉s❡s ❊①❛♠♣❧❡✿ ▲❡t r ✑ a ✭ ❳❀ ❚ ✮ ✥ f ✭ ✖ ❳❀ ❳ ✶ ✮ ❀ a ✭ ✖ ❳ ✶ ❀ ✖ ❚ ✮ ❚❀❡♥ ❝♊❞❡ ❈ r ❣❡♥❡r❛t❡s t❀❡ ❝♊❞❡✿ pushenv 3 call f/2 putref 2 ❆✿ mark B mark A call a/2 putref 1 putref 3 ❇✿ popenv putvar 3

  38. Pr❡❞✐❝❛t❡s ❆ ♣r❡❞✐❝❛t❡ q/k ✐s ❞❡☞♥❡❞ ❜② ❛ s❡q✉❡♥❝❡ ♊❢ ❝❧❛✉s❡s rr ✑ r ✶ ✿ ✿ ✿ r ❢ ✳ ❚❀❡ tr❛♥s❧❛t✐♊♥ ♊❢ ♣r❡❞✐❝❛t❡s ✐s ♣❡r❢♊r♠❡❞ ❜② t❀❡ ❢✉♥❝t✐♊♥ ❝♊❞❡ P ✳ ■❢ ❛ ♣r❡❞✐❝❛t❡ ❀❛s ❥✉st ❛ s✐♥❣❧❡ ❝❧❛✉s❡ ✭✐❡✳ ❢ ❂ ✶✮✱ ✇❡ ❀❛✈❡✿ ❝♊❞❡ P r ❂ ❝♊❞❡ ❈ r ■❢ ❛ ♣r❡❞✐❝❛t❡ ❀❛s s❡✈❡r❛❧ ❝❧❛✉s❡s✱ t❀❡♥✿ ④ ✇❡ ☞rst ✧tr②✧ t❀❡ ☞rst ❝❧❛✉s❡❀ ④ ✐❢ ✐t ❢❛✐❧s✱ t❀❡♥ ✧tr②✧ t❀❡ s❡❝♊♥❞ ♊♥❡❀ ❡t❝✳

  39. Pr❡❞✐❝❛t❡s ■❢ ✉♥✐☞❝❛t✐♊♥ ❢❛✐❧s✱ ✇❡ ❝❛❧❧ t❀❡ r✉♥✲t✐♠❡ ❢✉♥❝t✐♊♥ backtrack() ✳ ❚❀❡ ❣♊❛❧ ✐s t♩ r♩❧❧ ❜❛❝❩ t❀❡ ✇❀♊❧❡ ❝♊♠♣✉t❛t✐♊♥ t♩ t❀❡ ❜❛❝❩tr❛❝❩ ♣♊✐♥t ❀ ✐❡✳ t♩ t❀❡ ✭❞②♥❛♠✐❝❛❧❧②✮ ❧❛t❡st ❣♊❛❧ ✇❀❡r❡ t❀❡r❡ ✐s ❛♥♊t❀❡r ❝❧❛✉s❡ t♩ ✧tr②✧✳ ■♥ ♩r❞❡r t♩ r❡st♩r❡ ♣r❡✈✐♊✉s❧② ✈❛❧✐❞ ❜✐♥❞✐♥❣s✱ ✇❡ ❀❛✈❡ ✉s❡❞ t❀❡ r✉♥✲t✐♠❡ ❢✉♥❝t✐♊♥ trail() ✇❀✐❝❀ st♩r❡s ♥❡✇ ❜✐♥❞✐♥❣s ✐♥ ❛ s♣❡❝✐❛❧ ♠❡♠♊r② ❛r❡❛✳

  40. Pr❡❞✐❝❛t❡s ❚r❛✐❧✿ ❚ ✵ ✶ ❚P ❚ ❂ ❚r❛✐❧ â‘€ ♠❡♠♊r② ❛r❡❛ ❢♊r st♩r✐♥❣ ♥❡✇ ❜✐♥❞✐♥❣s❀ ❚P ❂ ❚❛✐❧✲P♊✐♥t❡r â‘€ ♣♊✐♥ts t♩ t❀❡ t♊♣♠♊st ✉s❡❞ ❝❡❧❧✳

  41. Pr❡❞✐❝❛t❡s ❚❀❡r❡ ✐s ❛❧s♩ ❛ s♣❡❝✐❛❧ r❡❣✐st❡r ❇P ✇❀✐❝❀ ♣♊✐♥ts t♩ t❀❡ ❝✉rr❡♥t ❜❛❝❩tr❛❝❩ ♣♊✐♥t✳ ❙ ✵ ✶ ❙P ❋P ❇P

  42. Pr❡❞✐❝❛t❡s ❆ ❜❛❝❩tr❛❝❩ ♣♊✐♥t ✐s ❛ st❛❝❩ ❢r❛♠❡ t♩ ✇❀✐❝❀ ♣r♊❣r❛♠ ❡①❡❝✉t✐♊♥ ♣♊ss✐❜❧② r❡t✉r♥s✿ ❋P P♩s❈♊♥t ✵ ❋P♩❧❞ ✲✶ ❍P♩❧❞ ✲✷ ❚P♩❧❞ ✲✞ ❇P♩❧❞ ✲✹ ◆❡❣❈♊♥t ✲✺ ❲❡ ✇✐❧❧ ✉s❡ ❢♊❧❧♊✇✐♥❣ ♠❛❝r♩s t♩ ❞❡♥♊t❡ ♩r❣❛♥✐③❛t✐♊♥❛❧ ❝❡❧❧s✿ ✑ ✑ S[FP ï¿œ ✾ ] PosCont S[FP] TPold FPold ✑ S[FP ï¿œ ✶ ] BPold ✑ S[FP ï¿œ ✹ ] ✑ S[FP ï¿œ ✷ ] ✑ S[FP ï¿œ ✺ ] HPold NegCont

  43. Pr❡❞✐❝❛t❡s ❚❀❡ r✉♥✲t✐♠❡ ❢✉♥❝t✐♊♥ backtrack() r❡st♩r❡s r❡❣✐st❡rs ❛❝❝♩r❞✐♥❣ t♩ t❀❡ ❢r❛♠❡ ❝♩rr❡s♣♊♥❞✐♥❣ t♩ ❜❛❝❩tr❛❝❩ ♣♊✐♥t✿ void backtrack() { FP = BP; HP = HPold; reset (TPold,TP); TP = TPold; PC = NegCont; } ❚❀❡ ❢✉♥❝t✐♊♥ reset() r❡st♩r❡s ✈❛r✐❛❜❧❡ ❜✐♥❞✐♥❣s❀ ✐❡✳ ✉♥❞♊❡s ❛❧❧ ❜✐♥❞✐♥❣s ❝r❡❛t❡❞ ❛❢t❡r t❀❡ ❜❛❝❩tr❛❝❩ ♣♊✐♥t✳

  44. Pr❡❞✐❝❛t❡s ❋P ❋P ❜❛❝❩tr❛❝❊✭✮ ❍P ❍P ✹✷ ✹✷ ✹✷ ❚P ❚P ✶✌ ✶✌ ✶✌ ❇P ❇P P❈ P❈ ✶✞ ✶✞ ✶✞

  45. Pr❡❞✐❝❛t❡s ❚❀❡ ✈❛r✐❛❜❧❡s ✇❀✐❝❀ ❛r❡ ❝r❡❛t❡❞ s✐♥❝❡ t❀❡ ❧❛st ❜❛❝❩tr❛❝❩ ♣♊✐♥t ❝❛♥ ❜❡ r❡♠♊✈❡❞ t♊❣❡t❀❡r ✇✐t❀ t❀❡✐r ❜✐♥❞✐♥❣s s✐♠♣❧② ❜② r❡st♩r✐♥❣ t❀❡ ♩❧❞ ✈❛❧✉❡ ♊❢ t❀❡ r❡❣✐st❡r ❍P✳ ❚❀✐s ✇♩r❊s ☞♥❡ ✐❢ ②♊✉♥❣❡r ✈❛r✐❛❜❧❡s ❛❧✇❛②s ♣♊✐♥t t♩ ♊❧❞❡r ♊❜❥❡❝ts✳ ❇✐♥❞✐♥❣s ✇❀❡r❡ ♊❧❞❡r ✈❛r✐❛❜❧❡s ♣♊✐♥t t♩ ②♊✉♥❣❡r ♊❜❥❡❝ts ♠✉st ❜❡ r❡s❡t ✧♠❛♥✉❛❧❧②✧✳ ❚❀❡s❡ ❜✐♥❞✐♥❣s ❛r❡ r❡❝♊r❞❡❞ ✐♥ t❀❡ tr❛✐❧ ✳

  46. Pr❡❞✐❝❛t❡s ❚❀❡ ❢✉♥❝t✐♊♥ trail() r❡❝♊r❞s ❛ ❜✐♥❞✐♥❣ ✐❢ t❀❡ ❛r❣✉♠❡♥t ♣♊✐♥ts t♩ ❛ ②♊✉♥❣❡r ♊❜❥❡❝t✿ void trail (ref u) { if (u < S[BP-2]) { TP = TP+1; T[TP] = u; } } ❚❀❡ ❝❡❧❧ S[BP-2] ❝♊♥t❛✐♥s t❀❡ ✈❛❧✉❡ ♊❢ ❍P ❜❡❢♊r❡ t❀❡ ❝r❡❛t✐♊♥ ♊❢ ❜❛❝❩tr❛❝❩ ♣♊✐♥t✳ ❚❀❡ ❢✉♥❝t✐♊♥ reset() r❡♠♊✈❡s ❛❧❧ ❜✐♥❞✐♥❣s ❝r❡❛t❡❞ ❛❢t❡r t❀❡ ❧❛st ❜❛❝❩tr❛❝❩ ♣♊✐♥t✿ void reset (ref x, ref y) { for (ref u=y; x<u; u--) H[T[u]] = (R,T[u]); }

  47. Pr❡❞✐❝❛t❡s ❚r❛♥s❧❛t✐♊♥ ♊❢ ❛ ♣r❡❞✐❝❛t❡ q/k ✱ ✇❀✐❝❀ ✐s ❞❡☞♥❡❞ ❜② ❝❧❛✉s❡s r ✶ ❀ ✿ ✿ ✿ ❀ r ❢ ✭ ❢ ❃ ✶✮✱ ❣❡♥❡r❛t❡s ❛ ❝♊❞❡ ✇❀✐❝❀✿ ❝r❡❛t❡s ❛ ❜❛❝❩tr❛❝❩ ♣♊✐♥t❀ s✉❝❝❡ss✐✈❡❧② ✧tr✐❡s✧ t❀❡ ❛❧t❡r♥❛t✐✈❡s❀ ❞❡❧❡t❡s t❀❡ ❜❛❝❩tr❛❝❩ ♣♊✐♥t✳

  48. Pr❡❞✐❝❛t❡s ❝♊❞❡ P ✭ r ✶ ❀ ✿ ✿ ✿ ❀ r ❢ ✮ ❂ q✎❊✿ setbtp jump A ❢ ❆ ✶ ✿ ❝♊❞❡ ❈ r ✶ try A ✶ ✳ ✳ ✳ ✳ ✳ ✳ try A ❢ ï¿œ ✶ ❆ ❢ ✿ ❝♊❞❡ ❈ r ❢ delbtp ◆❇✩ ❚❀❡ ❜❛❝❩tr❛❝❩ ♣♊✐♥t ✐s ❞❡❧❡t❡❞ ❜❡❢♊r❡ t❀❡ ❧❛st ❛❧t❡r♥❛t✐✈❡ ✐s ✧tr✐❡❞✧✳ ❋♩r t❀❡ ✧❧❛st tr②✧✱ t❀❡ ❝♊❞❡ ❥✉♠♣s ❞✐r❡❝t❧② t♩ t❀❡ ❛❧t❡r♥❛t✐✈❡ ❛♥❞ ♥❡✈❡r r❡t✉r♥s t♩ t❀❡ ♣r❡s❡♥t ❢r❛♠❡✳

  49. Pr❡❞✐❝❛t❡s ❊①❛♠♣❧❡✿ t ✭ ✖ s ✭ ❳ ✮ ✥ ❳ ✮ ✖ s ✭ ❳ ✮ ✥ ❳ ❂ ❛ ❚r❛♥s❧❛t✐♊♥ ♊❢ t❀❡ ♣r❡❞✐❝❛t❡ s ❂ 1 r❡s✉❧ts✿ s✎✶✿ setbtp ❆✿ pushenv 1 ❇✿ pushenv 1 try A mark C putref 1 delbtp putref 1 uatom a jump B call t/1 popenv ❈✿ popenv

  50. Pr❡❞✐❝❛t❡s ■♥str✉❝t✐♊♥ setbtp s❛✈❡s r❡❣✐st❡rs ❍P✱ ❚P✱ ❇P✿ ❋P ❋P ✹✷ s❡t❜t♣ ✶✌ ❍P ❍P ✹✷ ✹✷ ❚P ❚P ✶✌ ✶✌ ❇P ❇P HPold = HP; TPold = TP; BPold = BP; BP = FP;

  51. Pr❡❞✐❝❛t❡s ■♥str✉❝t✐♊♥ try A s❛✈❡s t❀❡ ❝✉rr❡♥t P❈ ❛s t❀❡ ♥❡❣❛t✐✈❡ ❝♊♥t✐♥✉❛t✐♊♥ ❛❞❞r❡ss ❛♥❞ ❥✉♠♣s t♩ t❀❡ ❛❧t❡r♥❛t✐✈❡ t♩ ❜❡ ✧tr✐❡❞✧ ❛t ❛❞❞r❡ss ❆✿ ❋P ❋P ❍P ❍P tr② ❆ ❚P ❚P ❇P ❇P P❈ P❈ ✷✟ ❆ ✷✟ NegCont = PC; PC = A;

  52. Pr❡❞✐❝❛t❡s ■♥str✉❝t✐♊♥ delbtp r❡st♩r❡s t❀❡ ✈❛❧✉❡ ♊❢ ❇P✿ ❋P ❋P ❞❡❧❜t♣ ❍P ❍P ❚P ❚P ❇P ❇P BP = BPold;

  53. Pr❡❞✐❝❛t❡s ■♥str✉❝t✐♊♥ popenv r❡st♩r❡s r❡❣✐st❡rs ❋P ❛♥❞ P❈✱ ❛♥❞ ✐❢ ♣♊ss✐❜❧❡ ♣♊♣s t❀❡ st❛❝❩ ❢r❛♠❡✿ ❋P ❋P ✹✷ ✻ ♣♊♣❡♥✈ ❇P ❇P P❈ P❈ ✹✷ if (FP ❃ BP) SP = FP - 6; PC = PosCont; FP = FPold;

  54. Pr❡❞✐❝❛t❡s ■❢ ❋P ✔ ❇P t❀❡ ❢r❛♠❡ ✐s ♥♊t ❞❡❛❧❧♊❝❛t❡❞✿ ❋P ❋P ✹✷ ✹✷ ♣♊♣❡♥✈ ✻ ✻ ❇P ❇P P❈ P❈ ✹✷ if (FP ❃ BP) SP = FP - 6; PC = PosCont; FP = FPold;

  55. ◗✉❡r✐❡s ❛♥❞ Pr♊❣r❛♠s ❚r❛♥s❧❛t✐♊♥ ♊❢ ❛ ♣r♊❣r❛♠ ♣ ✑ rr ✶ ✿ ✿ ✿ rr ❀ ❄ ❣ ❣❡♥❡r❛t❡s✿ ④ ❝♊❞❡ ❢♊r ❡✈❛❧✉❛t✐♥❣ t❀❡ q✉❡r② ❣ ❀ ④ ❝♊❞❡ ❢♊r t❀❡ ♣r❡❞✐❝❛t❡ ❞❡☞♥✐t✐♊♥s rr ✐ ✳ ◗✉❡r② ❡✈❛❧✉❛t✐♊♥ ✐s ♣r❡❝❡❞❡❞ ❜②✿ ④ ✐♥✐t✐❛❧✐③❛t✐♊♥ ♊❢ r❡❣✐st❡rs❀ ④ ❛❧❧♩❝❛t✐♊♥ ♊❢ s♣❛❝❡ ❢♊r ❣❧♊❜❛❧s✳ ◗✉❡r② ❡✈❛❧✉❛t✐♊♥ ✐s s✉❝❝❡❡❞❡❞ ❜②✿ ④ r❡t✉r♥✐♥❣ t❀❡ ✈❛❧✉❡s ♊❢ ❣❧♊❜❛❧s✳

  56. ◗✉❡r✐❡s ❛♥❞ Pr♊❣r❛♠s ❝♊❞❡ ✭ rr ✶ ✿ ✿ ✿ rr ❀ ❄ ❣ ✮ ❂ ❝♊❞❡ P rr ✶ init ✳ ✳ ✳ pushenv d ❝♊❞❡ ● ❣ ✚ ❝♊❞❡ P rr ❀ halt d ✇❀❡r❡ ❢r❡❡ ✭ ❣ ✮ ❂ ❢ ❳ ✶ ❀ ✿ ✿ ✿ ❀ ❳ ❞ ❣ ❛♥❞ ✚ ❂ ❢ ❳ ✐ ✌✊ ✐ ❥ ✐ ❂ ✶ ✿ ✿ ✿ ❞ ❣ ✳ ■♥str✉❝t✐♊♥ halt d ✳ ✳ ✳ ✳ ✳ ✳ t❡r♠✐♥❛t❡s t❀❡ ♣r♊❣r❛♠ ❡①❡❝✉t✐♊♥❀ ✳ ✳ ✳ r❡t✉r♥s t❀❡ ✈❛❧✉❡s ♊❢ ❞ ❣❧♊❜❛❧s❀ ✳ ✳ ✳ ✐❢ ✉s❡r r❡q✉❡sts✱ ♣❡r❢♊r♠s ❜❛❝❩tr❛❝❊✐♥❣✳

  57. ◗✉❡r✐❡s ❛♥❞ Pr♊❣r❛♠s ■♥str✉❝t✐♊♥ init ❝r❡❛t❡s t❀❡ ✐♥✐t✐❛❧ ❜❛❝❩tr❛❝❩ ♣♊✐♥t✿ ❋P ❋P ✲✶ ❍P ❍P ✵ ✵ ❚P ✐♥✐t ❚P ✲✶ ✲✶ ✵ ❇P ❇P ✲✶ ✲✶ ✲✶ BP = FP = SP = 5; S[0] = f; ❢ S[1] = S[2] = -1; S[3] = 0; BP = FP; ■❢ t❀❡ q✉❡r② ❣ ❢❛✐❧s✱ t❀❡ ❝♊❞❡ ❛t ❛❞❞r❡ss ❢ ✇✐❧❧ ❜❡ ❡①❡❝✉t❡❞ ✭❡❣✳ ♣r✐♥ts ❛ ♠❡ss❛❣❡ t❡❧❧✐♥❣ ❛❜♩✉t t❀❡ ❢❛✐❧✉r❡✮✳

  58. ◗✉❡r✐❡s ❛♥❞ Pr♊❣r❛♠s ❊①❛♠♣❧❡✿ t ✭ ❳ ✮ ✥ ✖ q ✭ ❳ ✮ ✥ s ✭ ✖ s ✭ ❳ ✮ ✥ ✖ ❳ ❂ ❜ ❳ ✮ ❳ ❂ ❛ p ✥ q ✭ ❳ ✮ ❀ t ✭ ✖ s ✭ ❳ ✮ ✥ t ✭ ✖ ❳ ✮ ❳ ✮ ❄ p init ♣✎✵✿ pushenv 1 q✎✶✿ pushenv 1 ❊✿ pushenv 1 pushenv 0 mark B mark D mark G mark A putvar 1 putref 1 putref 1 call p/0 call q/1 call s/1 call t/1 ❆✿ halt 0 ❇✿ mark C ❉✿ popenv ●✿ popenv t✎✶✿ pushenv 1 s✎✶✿ setbtp ❋✿ pushenv 1 putref 1 putref 1 call t/1 try E putref 1 ❈✿ popenv uatom b delbtp uatom a popenv jump F popenv

  59. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❈♊♥s✐❞❡r t❀❡ ♣r❡❞✐❝❛t❡ app/3 ❞❡☞♥❡❞ ❛s ❢♊❧❧♊✇s✿ app ✭ ❳❀ ❹❀ ❩ ✮ ✥ ❳ ❂ ❬ ❪ ❀ ❚ ❂ ❩ app ✭ ❳❀ ❹❀ ❩ ✮ ✥ ❳ ❂ ❬ ❍ ❥ ❳ ✵ ❪ ❀ ❩ ❂ ❬ ❍ ❥ ❩ ✵ ❪ ❀ app ✭ ❳ ✵ ❀ ❹❀ ❩ ✵ ✮ ❚❀❡ ❧❛st ❣♊❛❧ ♊❢ t❀❡ s❡❝♊♥❞ ❝❧❛✉s❡ ✐s ❛ r❡❝✉rs✐✈❡ ❝❛❧❧✿ ✇❡ ❝❛♥ ❡✈❛❧✉❛t❡ ✐t ✐♥ t❀❡ ❝✉rr❡♥t st❛❝❩ ❢r❛♠❡❀ ❛❢t❡r ✭s✉❝❝❡ss❢✉❧✮ ❝♊♠♣❧❡t✐♊♥✱ ✇❡ ✇✐❧❧ ♥♊t r❡t✉r♥ t♩ t❀❡ ❝✉rr❡♥t ❢r❛♠❡ ❜✉t ❣♊ ❞✐r❡❝t❧② ❜❛❝❩ t♩ t❀❡ ✧♣r❡❞❡❝❡ss♩r✧ ❢r❛♠❡✳

  60. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❈♊♥s✐❞❡r ❛ ❝❧❛✉s❡ r ✑ p ✭ ❳ ✶ ❀ ✿ ✿ ✿ ❀ ❳ ❊ ✮ ✥ ❣ ✶ ❀ ✿ ✿ ✿ ❀ ❣ ♥ ✱ ✇❀✐❝❀ ❀❛s ♠ ❧♩❝❛❧ ✈❛r✐❛❜❧❡s ❛♥❞ ✇❀❡r❡ ❣ ♥ ✑ q ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ❀ ✮✳ ❝♊❞❡ ❈ r ❂ pushenv m ❝♊❞❡ ❆ t ✶ ✚ ❝♊❞❡ ● ❣ ✶ ✚ ✳ ✳ ✳ ✳ ✳ ✳ ❝♊❞❡ ❆ t ❀ ✚ ❝♊❞❡ ● ❣ ♥ ï¿œ ✶ ✚ call q/h ❇✿ popenv mark B

  61. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❈♊♥s✐❞❡r ❛ ❝❧❛✉s❡ r ✑ p ✭ ❳ ✶ ❀ ✿ ✿ ✿ ❀ ❳ ❊ ✮ ✥ ❣ ✶ ❀ ✿ ✿ ✿ ❀ ❣ ♥ ✱ ✇❀✐❝❀ ❀❛s ♠ ❧♩❝❛❧ ✈❛r✐❛❜❧❡s ❛♥❞ ✇❀❡r❡ ❣ ♥ ✑ q ✭ t ✶ ❀ ✿ ✿ ✿ ❀ t ❀ ✮✳ ❝♊❞❡ ❈ r ❂ pushenv m ❝♊❞❡ ❆ t ✶ ✚ ❝♊❞❡ ● ❣ ✶ ✚ ✳ ✳ ✳ ✳ ✳ ✳ ❝♊❞❡ ❆ t ❀ ✚ ❝♊❞❡ ● ❣ ♥ ï¿œ ✶ ✚ lastcall (q/h,m) lastmark

  62. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ■❢ t❀❡ ❝✉rr❡♥t ❝❧❛✉s❡ ✐s ♥♊t ❧❛st ♩r ❣♊❛❧s ❣ ✶ ❀ ✿ ✿ ✿ ❀ ❣ ♥ ï¿œ ✶ ❀❛✈❡ ❝r❡❛t❡❞ ❜❛❝❩tr❛❝❩ ♣♊✐♥ts✱ t❀❡♥ ❋P ✔ ❇P✳ ❚❀❡♥ t❀❡ ✐♥str✉❝t✐♊♥ lastmark ❝r❡❛t❡s ❛ ♥❡✇ ❢r❛♠❡ ❜✉t st♩r❡s ❛ r❡❢❡r❡♥❝❡ t♩ t❀❡ ♣r❡❞❡❝❡ss♩r ❢r❛♠❡✳ ❖t❀❡r✇✐s❡ ✭✐❡✳ ✐❢ ❋P ❃ ❇P✮✱ ✐t ❞♊❡s ♥♊t❀✐♥❣✳

  63. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❆ ✻ ❇P ❇P ❧❛st♠❛r❊ ❋P ❋P ❆ ❆ if (FP ✔ BP) { SP = SP + 6; S[SP] = PosCont; S[SP-1] = FPold; }

  64. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ■❢ ❋P ✔ ❇P✱ t❀❡♥ t❀❡ ✐♥str✉❝t✐♊♥ lastcall (q/h,m) ❜❡❀❛✈❡s ❧✐❊❡ call q/h ✳ ❖t❀❡r✇✐s❡✱ t❀❡ ❝✉rr❡♥t st❛❝❩ ❢r❛♠❡ ✐s r❡✉s❡❞✿ ④ t❀❡ ❝❡❧❧s S[FP+1] ✱ ✳ ✳ ✳ ✱ S[FP+h] ❣❡t ♥❡✇ ✈❛❧✉❡s❀ ④ ❛♥❞ t❀❡♥ ❞✐r❡❝t❧② ❥✉♠♣s t♩ t❀❡ ♣r❡❞✐❝❛t❡ q/h ✳ lastcall (q/h,m) ❂ if (FP ✔ BP) call q/h; else { move (m,h); jump q/h; }

  65. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❀ ♠ ❧❛st❝❛❧❧✭q✎❀✱♠✮ ❋P ❋P ❇P ❇P q✎❀ P❈

  66. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❈♊♥s✐❞❡r t❀❡ ❝❧❛✉s❡ a ✭ ❳❀ ❚ ✮ ✥ f ✭ ✖ ❳❀ ❳ ✶ ✮ ❀ a ✭ ✖ ❳ ✶ ❀ ✖ ❚ ✮ ❚❀❡ ❧❛st ❝❛❧❧ ♊♣t✐♠✐③❛t✐♊♥ ②✐❡❧❞s✿ pushenv 3 putvar 3 putref 3 mark A call f/2 putref 2 putref 1 ❆✿ lastmark lastcall(a/2,3) ◆❇✩ ■❢ t❀❡ ❝❧❛✉s❡ ✐s ❧❛st ❛♥❞ ✐ts ❧❛st ❣♊❛❧ ✐s t❀❡ ♊♥❧② ♊♥❡✱ t❀❡♥ ✇❡ ❝❛♥ ♩♠✐t lastmark ❛♥❞ r❡♣❧❛❝❡ lastcall(q/h,m) ✇✐t❀ ✐♥str✉❝t✐♊♥s move(m,h) ❛♥❞ jump q/h ✳

  67. ▲❛st ❈❛❧❧ ❖♣t✐♠✐③❛t✐♊♥ ❚❀❡ ❧❛st ❝❛❧❧ ♊♣t✐♠✐③❛t✐♊♥ ❢♊r t❀❡ s❡❝♊♥❞ ❝❧❛✉s❡ ♊❢ app/3 ②✐❡❧❞s✿ ❆✿ pushenv 6 putstruct [|]/2 ❉✿ check 4 putref 1 bind putref 4 ustruct [|]/2 B ❈✿ putref 3 putvar 6 son 1 ustruct [|]/2 D putstruct [|]/2 uvar 4 son 1 bind ❊✿ putref 5 son 2 uref 4 uvar 5 son 2 putref 2 up C uvar 6 putref 6 ❇✿ putvar 4 up E move(6,3) putvar 5 jump app/3

  68. ❙t❛❝❩ ❋r❛♠❡ ❚r✐♠♠✐♥❣ ❖r❞❡r ❧♩❝❛❧ ✈❛r✐❛❜❧❡s ❛❝❝♩r❞✐♥❣ t♩ t❀❡✐r ❧✐❢❡ t✐♠❡ ✳ ■❢ ♣♊ss✐❜❧❡✱ r❡♠♊✈❡ ❞❡❛❞ ✈❛r✐❛❜❧❡s✳ ❊①❛♠♣❧❡✿ a ✭ ❳❀ ❩ ✮ ✥ p ✶ ✭ ✖ ❳❀ ❳ ✶ ✮ ❀ p ✷ ✭ ✖ ❳ ✶ ❀ ❳ ✷ ✮ ❀ p ✾ ✭ ✖ ❳ ✷ ❀ ❳ ✾ ✮ ❀ p ✹ ✭ ✖ ❳ ✾ ❀ ❩ ✮ ④ ❛❢t❡r t❀❡ ❣♊❛❧ p ✷ ✭ ✖ ❳ ✶ ❀ ❳ ✷ ✮ t❀❡ ✈❛r✐❛❜❧❡ ❳ ✶ ✐s ❞❡❛❞❀ ④ ❛❢t❡r t❀❡ ❣♊❛❧ p ✾ ✭ ✖ ❳ ✷ ❀ ❳ ✾ ✮ t❀❡ ✈❛r✐❛❜❧❡ ❳ ✷ ✐s ❞❡❛❞✳

  69. ❙t❛❝❩ ❋r❛♠❡ ❚r✐♠♠✐♥❣ ❆❢t❡r ❡✈❡r② ♥♊♥✲❧❛st ❣♊❛❧ ✇❀✐❝❀ ❀❛s ❞❡❛❞ ✈❛r✐❛❜❧❡s ✐♥s❡rt ❛♥ ✐♥str✉❝t✐♊♥ trim ✿ ♠ tr✐♠ ♠ ❋P ❋P if (FP ✕ BP) SP = FP + m; ◆❇✩ ❲❡ ❝❛♥ r❡♠♊✈❡ ❞❡❛❞ ❧♩❝❛❧s ♊♥❧② ✐❢ t❀❡r❡ ❛r❡ ♥♊ ♥❡✇ ❜❛❝❩tr❛❝❩ ♣♊✐♥ts ❝r❡❛t❡❞✳

  70. ❙t❛❝❩ ❋r❛♠❡ ❚r✐♠♠✐♥❣ ❊①❛♠♣❧❡✿ a ✭ ❳❀ ❩ ✮ ✥ p ✶ ✭ ✖ ❳❀ ❳ ✶ ✮ ❀ p ✷ ✭ ✖ ❳ ✶ ❀ ❳ ✷ ✮ ❀ p ✾ ✭ ✖ ❳ ✷ ❀ ❳ ✾ ✮ ❀ p ✹ ✭ ✖ ❳ ✾ ❀ ❩ ✮ ❖r❞❡r✐♥❣ ♊❢ t❀❡ ✈❛r✐❛❜❧❡s✿ ✚ ❂ ❢ ❳ ✌✊ ✶ ❀ ❩ ✌✊ ✷ ❀ ❳ ✾ ✌✊ ✾ ❀ ❳ ✷ ✌✊ ✹ ❀ ❳ ✶ ✌✊ ✺ ❣ pushenv 5 putvar 4 ❈✿ trim 3 mark A call p ✷ /2 lastmark putref 1 ❇✿ trim 4 putref 3 putvar 5 mark C putref 2 call p ✶ /2 putref 4 lastcall (p ✹ /2,3) ❆✿ mark B putvar 3 putref 5 call p ✾ /2

  71. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ❖❢t❡♥✱ ♣r❡❞✐❝❛t❡s ❛r❡ ✐♠♣❧❡♠❡♥t❡❞ ❜② ❝❛s❡ ❞✐st✐♥❝t✐♊♥ ♊♥ t❀❡ ☞rst ❛r❣✉♠❡♥t✳ ❍❡♥❝❡✱ ❜② ✐♥s♣❡❝t✐♥❣ t❀❡ ☞rst ❛r❣✉♠❡♥t✱ ♠❛♥② ❛❧t❡r♥❛t✐✈❡s ❝❛♥ ❜❡ ❡①❝❧✉❞❡❞✳ ④ ❋❛✐❧✉r❡ ✐s ❞❡t❡❝t❡❞ ❡❛r❧✐❡r✳ ④ ❇❛❝❩tr❛❝❩ ♣♊✐♥ts ❛r❡ r❡♠♊✈❡❞ ❡❛r❧✐❡r✳ ④ ❙t❛❝❩ ❢r❛♠❡s ❛r❡ r❡♠♊✈❡❞ ❡❛r❧✐❡r✳

  72. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ❊①❛♠♣❧❡✿ app ✭ ❳❀ ❹❀ ❩ ✮ ✥ ❳ ❂ ❬ ❪ ❀ ❚ ❂ ❩ app ✭ ❳❀ ❹❀ ❩ ✮ ✥ ❳ ❂ ❬ ❍ ❥ ❳ ✵ ❪ ❀ ❩ ❂ ❬ ❍ ❥ ❩ ✵ ❪ ❀ app ✭ ❳ ✵ ❀ ❹❀ ❩ ✵ ✮ ■❢ t❀❡ ☞rst ❛r❣✉♠❡♥t ✐s [] ✱ t❀❡♥ ♊♥❧② t❀❡ ☞rst ❝❧❛✉s❡ ✐s ❛♣♣❧✐❝❛❜❧❡✳ ■❢ t❀❡ ☞rst ❛r❣✉♠❡♥t ❀❛s [|] ❛s ✐ts r♩♩t ❝♊♥str✉❝t♩r✱ t❀❡♥ ♊♥❧② t❀❡ s❡❝♊♥❞ ❝❧❛✉s❡ ✐s ❛♣♣❧✐❝❛❜❧❡✳ ❊✈❡r② ♩t❀❡r r♩♩t ❝♊♥str✉❝t♩r ♊❢ t❀❡ ☞rst ❛r❣✉♠❡♥t ✇✐❧❧ ❢❛✐❧✳ ❇♩t❀ ❛❧t❡r♥❛t✐✈❡s s❀♊✉❧❞ ❜❡ tr✐❡❞ ♊♥❧② ✐❢ t❀❡ ☞rst ❛r❣✉♠❡♥t ✐s ✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡✳

  73. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ■♥tr♊❞✉❝❡ ❛ s❡♣❛r❛t❡ tr② ❝❀❛✐♥ ❢♊r ❡✈❡r② ♣♊ss✐❜❧❡ ❝♊♥str✉❝t♩r✳ ■♥s♣❡❝t t❀❡ r♩♩t ♥♊❞❡ ♊❢ t❀❡ ☞rst ❛r❣✉♠❡♥t✳ ❉❡♣❡♥❞✐♥❣ ♊♥ t❀❡ r❡s✉❧t✱ ♣❡r❢♊r♠ ❛♥ ✐♥❞❡①❡❞ ❥✉♠♣ t♩ t❀❡ ❛♣♣r♊♣r✐❛t❡ tr② ❝❀❛✐♥✳ ▲❡t t❀❡ ♣r❡❞✐❝❛t❡ p/k ❞❡☞♥❡❞ ❜② t❀❡ s❡q✉❡♥❝❡ ♊❢ ❝❧❛✉s❡s rr ✑ r ✶ ✿ ✿ ✿ r ♠ ✳ ❚❀❡ ♠❛❝r♩ t❝❀❛✐♥s rr ❞❡♥♊t❡s t❀❡ s❡q✉❡♥❝❡ ♊❢ tr② ❝❀❛✐♥s ✇❀✐❝❀ ❝♩rr❡s♣♊♥❞ t♩ t❀❡ r♩♩t ❝♊♥str✉❝t♩rs ♩❝❝✉rr✐♥❣ ✐♥ ✉♥✐☞❝❛t✐♊♥s ❳ ✶ ❂ t ✳

  74. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ❊①❛♠♣❧❡✿ ❈♊♥s✐❞❡r t❀❡ ♣r❡❞✐❝❛t❡ app/3 ✳ ▲❡t t❀❡ ❝♊❞❡ ❢♊r ✐ts t✇♩ ❝❧❛✉s❡s st❛rt ❛t ❛❞❞r❡ss❡s ❆ ✶ ❛♥❞ ❆ ✷ ✳ ❚❀❡♥ ✇❡ ❣❡t t❀❡ ❢♊❧❧♊✇✐♥❣ ❢♊✉r tr② ❝❀❛✐♥s✿ ❱❆❘✿ setbtb // variables ◆■▲✿ jump A ✶ // [] ❈❖◆❙✿ jump A ✷ // [|] try A ✶ delbtp ❊▲❙❊✿ fail // default jump A ✷ ■♥str✉❝t✐♊♥ fail ❀❛♥❞❧❡s ❛❧❧ ❝♊♥str✉❝t♩rs ❜❡s✐❞❡s [] ❛♥❞ [|] ✳ ❂ fail backtrack()

  75. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ❚❀❡♥ ✇❡ ❣❡♥❡r❛t❡ ❢♊r ❛ ♣r❡❞✐❝❛t❡ p/k ✿ ❝♊❞❡ P rr ❂ putref 1 getNode index p/k t❝❀❛✐♥s rr ❆ ✶ ✿ ❝♊❞❡ ❈ r ✶ ✳ ✳ ✳ ❆ ♠ ✿ ❝♊❞❡ ❈ r ♠

  76. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ❙ ❢✎♥ ❢✎♥ ❣❡t◆♊❞❡ ❘ ❘ ❣❡t◆♊❞❡ switch (H[S[SP]]) { case (S,f/n): S[SP] = f/n; break; case (A,a): S[SP] = a; break; case (R, ): S[SP] = R; }

  77. ❈❧❛✉s❡ ■♥❞❡①✐♥❣ ■♥str✉❝t✐♊♥ index p/k ♣❡r❢♊r♠s ❛♥ ✐♥❞❡①❡❞ ❥✉♠♣ t♩ t❀❡ ❛♣♣r♊♣r✐❛t❡ tr② ❝❀❛✐♥✿ ❛ ❆ ❂ ♠❛♣✭♣✎❊✱❛✮ ✐♥❞❡① ♣✎❊ ❆ P❈ PC = map(p/k,S[SP]); SP = SP - 1; ❚❀❡ ❢✉♥❝t✐♊♥ map() r❡t✉r♥s t❀❡ st❛rt ❛❞❞r❡ss ♊❢ t❀❡ ❛♣♣r♊♣r✐❛t❡ tr② ❝❀❛✐♥✳ ❈❛♥ ❜❡ ❞❡☞♥❡❞ ❡❣✳ t❀r♊✉❣❀ s♊♠❡ ❀❛s❀ t❛❜❧❡✳

  78. ❈✉t ❖♣❡r❛t♩r ❲❡ ❡①t❡♥❞ t❀❡ ❧❛♥❣✉❛❣❡ Pr♩❧❧ ✇✐t❀ t❀❡ ❝✉t ♊♣❡r❛t♩r ✧✩✧ ✇❀✐❝❀ ❡①♣❧✐❝✐t❧② ❛❧❧♩✇s t♩ ♣r✉♥❡ t❀❡ s❡❛r❝❀ s♣❛❝❡ ♊❢ ❜❛❝❩tr❛❝❊✐♥❣✳ ❊①❛♠♣❧❡✿ branch ✭ ❳❀ ❚ ✮ ✥ p ✭ ❳ ✮ ❀ ✩ ❀ q ✶ ✭ ❳❀ ❚ ✮ branch ✭ ❳❀ ❚ ✮ ✥ q ✷ ✭ ❳❀ ❚ ✮ ■❢ ❛❧❧ t❀❡ q✉❡r✐❡s ❜❡❢♊r❡ t❀❡ ❝✉t ❀❛✈❡ s✉❝❝❡❡❞❡❞✱ t❀❡♥ t❀❡ ❝❀♊✐❝❡ ✐s ❝♩♠♠✐tt❡❞ ✿ ❜❛❝❩tr❛❝❊✐♥❣ ✇✐❧❧ r❡t✉r♥ ♊♥❧② t♩ ❜❛❝❩tr❛❝❩ ♣♊✐♥ts ♣r❡❝❡❞✐♥❣ t❀❡ ❝❛❧❧ t♩ t❀❡ ♣r❡❞✐❝❛t❡✳

  79. ❈✉t ❖♣❡r❛t♩r ❚❀❡ ❝✉t ♊♣❡r❛t♩r s❀♊✉❧❞✿ r❡st♩r❡ t❀❡ r❡❣✐st❡r ❇P ❜② ❛ss✐❣♥✐♥❣ t♩ ✐t ❇P♩❧❞ ❢r♩♠ t❀❡ ❝✉rr❡♥t ❢r❛♠❡❀ r❡♠♊✈❡ ❛❧❧ ❢r❛♠❡s ✇❀✐❝❀ ❛r❡ ♊♥ t♊♣ ♊❢ t❀❡ ❧♩❝❛❧ ✈❛r✐❛❜❧❡s✳ ❆❝❝♩r❞✐♥❣❧②✱ ✇❡ tr❛♥s❧❛t❡ t❀❡ ❝✉t ✐♥t♩ t❀❡ s❡q✉❡♥❝❡✿ prune pushenv m ✇❀❡r❡ ♠ ✐s t❀❡ ♥✉♠❜❡r ♊❢ ✭st✐❧❧ ❛❧✐✈❡✮ ❧♩❝❛❧ ✈❛r✐❛❜❧❡s ♊❢ t❀❡ ❝❧❛✉s❡✳

  80. ❈✉t ❖♣❡r❛t♩r ❊①❛♠♣❧❡✿ branch ✭ ❳❀ ❚ ✮ ✥ p ✭ ❳ ✮ ❀ ✩ ❀ q ✶ ✭ ❳❀ ❚ ✮ branch ✭ ❳❀ ❚ ✮ ✥ q ✷ ✭ ❳❀ ❚ ✮ ❲❡ ♩❜t❛✐♥✿ setbtp ❆✿ pushenv 2 ❈✿ prune ❇✿ pushenv 2 try A mark C pushenv 2 putref 1 delbtp putref 1 lastmark putref 2 jump B call p/1 putref 1 move(2,2) putref 2 jump q ✷ /2 lastcall(q ✶ /2,2)

  81. ❈✉t ❖♣❡r❛t♩r ❊①❛♠♣❧❡✿ branch ✭ ❳❀ ❚ ✮ ✥ p ✭ ❳ ✮ ❀ ✩ ❀ q ✶ ✭ ❳❀ ❚ ✮ branch ✭ ❳❀ ❚ ✮ ✥ q ✷ ✭ ❳❀ ❚ ✮ ✳ ✳ ✳ ♩r✱ ✇❀❡♥ ✉s✐♥❣ ♊♣t✐♠✐③❛t✐♊♥s✿ setbtp ❆✿ pushenv 2 ❈✿ prune ❇✿ pushenv 2 try A mark C pushenv 2 putref 1 delbtp putref 1 putref 1 putref 2 jump B call p/1 putref 2 move(2,2) move(2,2) jump q ✷ /2 jump q ✶ /2

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