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CS 60

CS 60. 2012-09-26 Wednesday – Week 3. Prof Lewis’ world + child. parent(sleeping, swimming). parent(swimming, skittles). parent(skittles, spam). parent(42, spam). child(Kid, P) :- parent(P, Kid). 42. 10. 1. Kid = spam What = P. 9. 2. 7. 8. 6. 5. 3. 4. P = sleeping

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CS 60

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  1. CS 60 2012-09-26 Wednesday – Week 3

  2. Prof Lewis’ world + child • parent(sleeping, swimming). • parent(swimming, skittles). • parent(skittles, spam). • parent(42, spam). • child(Kid, P) :- parent(P, Kid). 42

  3. 10 1 Kid = spam What = P 9 2 7 8 6 5 3 4 P = sleeping Kid = swimming P = swimming Kid = skittles P = skittles Kid = spam P = 42 Kid = spam

  4. Ancestor (anc) 42

  5. Ancestor (anc) • anc(A, B) :- parent(A, B). • anc(X, Y) :- parent(X, Z), anc(Z, Y). 42

  6. A B This matched with the base case! 42

  7. X Z A Y B 42 42 We made a recursive call here. And then matched with the base case.

  8. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  9. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  10. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  11. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  12. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  13. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  14. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  15. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  16. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  17. R1 R2 F1 F1 F2 F2 R1 R2 R1 R2 F1 F1 F1 F1 F2 F2 F2 F2

  18. Negation (Summary) X = Y • X = Y succeeds if X can be unified with Y. X \= Y • X \= Y succeeds if X cannot be unified with Y. X == Y • X == Y succeeds if X and Y are identical, i.e., they unify with no variable bindings occurring. X \== Y • X \== Y succeeds if X and Y are not identical. http://www.amzi.com/manuals/amzi/pro/ref_manipulating_terms.htm#EqualityofTerms

  19. Negation Demo \= succeeds if they CANNOT be unified = succeeds if they CAN be unified == succeeds if they are ALREADY the same \== succeeds if they are NOT ALREADY the same

  20. simpsonSmall.pl • parent(homer, bart). • parent(homer, lisa). • parent(marge, bart). • parent(marge, lisa). • parent(homer, maggie). • parent(marge, maggie). • age(lisa, 8). • age(maggie, 1). • age(bart, 10). • age(marge, 35). • age(homer, 38). • person(marge). • person(homer). • person(lisa). • person(bart). • person(maggie).

  21. sib Demo (Big idea: Negation) This says that bart is his own sibling!

  22. sib Demo (Big idea: Negation) Works for specific cases. If X and Y are unbound, X \= Y returns false

  23. sib Demo (Big idea: Negation) REMEMBER: Put negation as late as possible so that variables already have known values! Why are there all of these duplicates?

  24. setof(format,query,Var). setof allows you to see only non-duplicates [X, Y] gives the format we want our answer in (as a list)

  25. notAparent Demo (Intro: \+ ) \+ means not Singleton variables: [Y]. _ is a variable that doesn’t need to match anything else. Doesn’t work with variables!

  26. Write: • eightYearsOld(X) :- • olderThan8(X) :- • not8(X) :- Hints: You can use > < and these can build upon each other

  27. Lists in Prolog Demo Length

  28. Expressing if in prolog L unifies with [] N unifies with 0 "The length of L is N" if and length(L,N) :- L = [], N = 0. Even simpler version of this: Prolog allows pattern-matching within the left-hand side of its rules! length([],0).

  29. Nonempty matching: The cons bar! length([],0). This matches only the empty list. This matches any NON-empty list – and names the first F and the rest R! length([F|R],N) :- This is read "F cons R" . It only binds to nonempty lists - and you can use F and R!

  30. Expressing if in prolog "F cons R" L unifies with [F|R] F = first of L "The length of L is N" R = rest of L if L is nonempty! length(L,N) :- L = [F|R], and length(R,M), and N is M+1. Even simpler version of this: length([F|R],N) :- length(R,M), N is M+1. pattern matching is cool!

  31. Inference on structure, instead of a database. More prolog lists, trees, graphs Test Generate member(E, [1,2,3,4,5]). E = 1 ; E = 2 ; E = 3 ; E = 4 ; E = 5 ; false member(3, [1,2,3,4,5]). true member(6, [1,2,3,4,5]). false both variable?

  32. don't cares Prolog let's you say "I don't care!" We never used R … it's a singleton. mem( E, [E|R] ). mem( E, [F|R] ) :- mem(E, R). Prolog will warn you about singletons! and we never used F in this rule! The underscore _ is just a place holder: mem( E, [E|_] ). mem( E, [_|R] ) :- mem(E, R). Let me underscore that _ has no value!

  33. Prolog patterns (1) Base case (usually no constraint clauses at all!) mem(E, [E|_]). mem(E, [_|R]) :- mem(E, R). (2) Recursion first! (when possible) an element a list (3) Arithmetic next (RHS must be bound) len([], 0). len([_|R], N) :- len(R, M), N is M+1. list its length (4) Negation last (all vars must be bound)

  34. true or false ? Name: ________________ For each line, determine if Prolog will find it true or false. What bindings will Prolog create? [F|R] = [42]. <-- [F|R] = []. <-- [Root,L,R] = [42,[],[]] <-- [Root,L,R] = [42,[]] <-- X = 5+2. <-- X \= Y. <-- X=3, Y=2, X \= Y. <-- Binding = tries to assign any two structures to one another… 1+2 == 1+2. <-- 1+2 == 2+1. <-- [1,X] == [1,X]. <-- [1,2] == [1,X]. <-- X \== Y. <-- X=3, Y=3, X \== Y. <-- Structure == compares any two structures to one another… Math X is 5+2. <-- X is Y+3. <-- Y = 6, X is Y*7. <-- 1+2 is 2+1. <-- X = 3, Y < X <-- is computes the right-hand side and binds to the left-hand side

  35. Not all equals are created equal! For each line, determine if Prolog will find it true or false. What bindings will Prolog create? [F|R] = [42]. <-- true, binds F to 42 and R to [] [F|R] = []. <-- false, [] does not have a first! [Root,L,R] = [42,[],[]] <-- true, binds Root=42, L=R=[] [Root,L,R] = [42,[]] <-- false, different # of elems. X = 5+2. <-- true, but X is 5+2, not 7 X \= Y. <-- false, X CAN unify with Y. X=3, Y=2, X \= Y. <-- true, they can not be unified Binding = tries to assign any two structures to one another… 1+2 == 1+2. <-- true, the same structure 1+2 == 2+1. <-- false, NOT the same structure! [1,X] == [1,X]. <-- true [1,2] == [1,X]. <-- false, no bindings are made X \== Y. <-- true, they have different names! X=3, Y=3, X \== Y. <-- false, it uses the values! Structure == compares any two structures to one another… Math X is 5+2. <-- true, now X is 7 X is Y+3. <-- error: Y is unbound Y = 6, X is Y*7. <-- true, X is bound to 42 1+2 is 2+1. <-- false: only evals the RHS X = 3, Y < X <-- error: Y is unbound is computes the right-hand side and binds to the left-hand side

  36. age Homework Reference age male female 93 92 97 99 uggette ug helga olf 65 76 101 78 59 62 matilda skug skugerina homericus john jackie 27 44 35 55 54 38 38 38 41 cher glum marge patty selma gemini esmerelda homer gomer 19 1 18 10 8 20 8 8 lachesis maggie atropos lisa terpsichore klotho bart millhouse

  37. Solutions

  38. CS 60 Survey 2012-09-26 (Turn this in, but don’t write your name on it) • What is at least one thing Prof. Lewis does during lecture that helps you learn? • What is at least one thing Prof. Lewis could do (or could stop doing) during lecture to help you learn? • What is one thing you’re having trouble understanding in CS60? • Other comments?

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