Logic Programming. Prolog : 3

Transcription

1 Logic Programming Prolog : 3

2 Review We don't write normal functions in Prolog. Instead we relate the input and the output e.g. factorial: factorial(0, 1). factorial(n, V) : N > 0, N1 is N 1, factorial(n1, V1), V is N * V1.

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4 3 > 0 N1 is 3 1 factorial(n1, V1) APPLY RULE

5 3 > 0 N1 is 3 1 factorial(n1, V1)

6 3 > 0 N1 is 3 1 factorial(n1, V1) SOLVE SUBGOALS (left to right)

7 3 > 0 N1 is 3 1 factorial(n1, V1)

8 3 > 0 N1 is 3 1 factorial(n1, V1) N1 ==> 2

9 3 > 0 2 is 3 1 factorial(2, V1) N1 ==> 2

10 3 > 0 2 is 3 1 factorial(2, V1)

11 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 N2 is 2 1 factorial(n2, V2) V1 is 2 * V2 APPLY RULE

12 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 N2 is 2 1 factorial(n2, V2) V1 is 2 * V2

13 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 N2 is 2 1 factorial(n2, V2) V1 is 2 * V2 SOLVE SUBGOALS (left to right)

14 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 N2 is 2 1 factorial(n2, V2) V1 is 2 * V2

15 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 N2 is 2 1 factorial(n2, V2) V1 is 2 * V2 N2 ==> 1

16 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, V2) V1 is 2 * V2 N2 ==> 1

17 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, V2) V1 is 2 * V2

18 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, V2) V1 is 2 * V2 factorial(0, 1) USE FACT

19 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, V2) V1 is 2 * V2 factorial(0, 1) V2 ==> 1

20 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, 1) V1 is 2 * 1 factorial(0, 1) V2 ==> 1

21 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, 1) V1 is 2 * 1 factorial(0, 1)

22 3 > 0 2 is 3 1 factorial(2, V1) 2 > 0 1 is 2 1 factorial(1, 1) V1 is 2 * 1 factorial(0, 1) V1 ==> 2

23 3 > 0 2 is 3 1 factorial(2, 2) V is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1) V1 ==> 2

24 3 > 0 2 is 3 1 factorial(2, 2) V is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1)

25 3 > 0 2 is 3 1 factorial(2, 2) V is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1) V ==> 6

26 factorial(3, F) 6) 3 > 0 2 is 3 1 factorial(2, 2) 6 is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1) V ==> 6

27 factorial(3, F) 6) 3 > 0 2 is 3 1 factorial(2, 2) 6 is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1)

28 Backtracking True. Search V = 6. factorial(3, F) 6) 3 > 0 2 is 3 1 factorial(2, 2) 6 is 3 * 2 2 > 0 1 is 2 1 factorial(1, 1) 2 is 2 * 1 factorial(0, 1)

29 Cuts : Control the Search Some control from ordering clauses and goals Cut : stop back tracking! Critical for efficient Prolog Allows us to short circuit evaluation Use carefully... cut breaks our simple logical model Prolog = controlled search

30 Style Exercise (10 min) Select: Write a function select(x, L, R) so that: X is in the list L R has all the other items of L Perm: Write a function perm(l, P) so that: P is some permutation of L (permutation = reordering) (hint: use select!)

31 Logic Puzzle I Towers of Hanoi N disks of increasing radius on a peg #1 Move all disks to peg #3, but... Move only one (top) disk at a time Never put a larger disk on top of a smaller disk.

32 Logic Puzzle II Farmer, Wolf, Goat, Cabbage All are on the east side of river. We want all on the west side of the river, ALIVE wolf and goat alone => wolf will eat goat goat and cabbage alone => goat will eat cabbage Can we get everyone across without being eaten?