Introduction (1A) Young Won Lim 9/12/13

Transcription

1 Introduction (1A)

2 Copyright (c) 2013 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to youngwlim@hotmail.com. This document was produced by using OpenOffice.

3 Goal Execution mortal(x) :- man(x). man(socrates).?- mortal(socrates). a rule a fact a query mortal(socrates) mortal(x) :- man(x). man(socrates). an initial goal try to match a first rule try to match a first fact socrates a variable instantitation X an atom mortal(socrates) :- man(socrates). man(socrates) mortal(x) :- man(x). man(socrates). extend the variable instantiation a new goal try to match a first rule try to match a first fact Introduction 3

4 Select Select (Element, List, Rest), ( List Element ) Rest If Element is in List, then remove Element from List and return Rest permutation([], []). permutation(list, [Element Result]) :- bind Element [Head Tail] select(element, List, Rest), permutation(rest, Result). Introduction 4

5 Permutation Recursive Call permutation([], []). permutation(list, [Element Result] ) :- select(element, List, Rest), permutation(rest, Result). bind Rest Introduction 5

6 Permutation Backtracking Permutation([], []). permutation(list, [Element Result]) :- select(element, List, Rest), permutation(rest, Result). X = [1, 2, 3] ; X = [1, 3, 2] ; X = [2, 1, 3] ; X = [2, 3, 1] ; X = [3, 1, 2] ; X = [3, 2, 1] ; No P([1,2,3], X). E=1 E=2 E=3 [1,2,3] [2,1,3] [3,1.2] [1,3,2] [2,3,1] [3,2,1] P([2,3], X). P([1,3], X). P([1,2], X). E=2 E=3 E=1 E=3 E=1 E=2 [2,3] [3,2] [1,3] [3,1] [1,2] [2,1] P([3], X). P([2], X). P([3], X). P([1], X). P([2], X). P([1], X). [3] [2] [3] [1] [2] [1] Introduction 6

7 Remove Duplicates remove_duplicates([], []). bind Head, Tail remove_duplicates([head Tail], Result) :- member(head, Tail), remove_duplicates(tail, Result). remove_duplicates([head Tail], [Head Result]) :- bind Head, Tail remove_duplicates(tail, Result). Introduction 7

8 remove_duplicates Backtracking remove_duplicates([], []). bind Head, Tail remove_duplicates([head Tail], Result) :- member(head, Tail), List = [b, c, a] ; (alternative List = [b, b, c, a] ; List = [a, b, c, a] ; List = [a, b, b, c, a] ; backtracking) remove_duplicates(tail, Result). No remove_duplicates([head Tail], [Head Result]) :- bind Head, Tail remove_duplicates(tail, Result). rd([h, T], List) List=[List] List=[H, List] rd([t], List) rd([t], List) Introduction 8

9 Backtracking (1) rd([a, b, b, c, a], List) List=[b,c,a] rd([a, b, b, c, a], List) List=[b,b,c,a] rd([b, b, c, a], List) List=[b,c,a] rd([b, b, c, a], List) List=[b,b,c,a] rd([b, c, a], List) List=[b,c,a] List=[b,b,c,a] rd([b, c, a], List) List=[b,c,a] rd([c, a], List) List=[c,a] rd([a], List) List=[b,c,a] rd([c, a], List) List=[c,a] rd([a], List) List=[a] rd([ ], List) List=[List] rd([h, T], List) List=[H, List] List=[a] rd([ ], List) rd([t], List) rd([t], List) Introduction 9

10 Backtracking (2) List=[a,b,c,a] rd([a, b, b, c, a], List) List=[a,b,c,a] rd([b, b, c, a], List) List=[a,b,b,c,a] rd([a, b, b, c, a], List) List=[a,b,b,c,a] rd([b, b, c, a], List) List=[b,c,a] List=[b.b,c,a] rd([b, c, a], List) rd([b, c, a], List) List=[b,c,a] rd([c, a], List) List=[c,a] rd([a], List) List=[b,c,a] rd([c, a], List) List=[c,a] rd([a], List) List=[a] rd([ ], List) List=[List] rd([h, T], List) List=[H, List] List=[a] rd([ ], List) rd([t], List) rd([t], List) Introduction 10

11 Backtracking (3) [b,c] [b] [ ] rd([b, c, a], List) rd([b, c, a], List) rd([b, c, a], List) List=[b,c] rd([c, a], List) List=[c] rd([a], List) List=[b] rd([c, a], List) List=[ ] rd([a], List) rd([a], List) rd([c, a], List) List=[ ] List=[ ] List=[ ] rd([ ], List) rd([ ], List) List=[ ] rd([ ], List) List=[ ] In the first solution, the first branch were rejected and the second were selected. No more branches are left to try for the alternative solutions. List=[List] rd([t], List) rd([h, T], List) List=[H, List] rd([t], List) In the first solution, the first branch were selected and the second are left to try for the alternative solutions. List=[List] rd([t], List) rd([h, T], List) List=[H, List] rd([t], List) During backtracking, however, also all other branches of the search tree will be visited. Even if the first rule would match, sometimes the second one will be picked instead and the duplicate head will remain in the list. Introduction 11

12 Cut! : cut, the predefined predicate can be anywhere in a rule s body can be a part of a sequence of subgoals in a query The subgoal! is always succeed backtracking into subgoals placed before the cut inside the same rule body is not possible anymore Whenever a cut is encountered in a rule s body, all choices made between the time that rule s head has been matched with the parent goal and the time the cut is passed are final, i.e. any choicepoints are being discarded. Introduction 12

13 A Cut Example bride(girl) :- beautiful(girl),!, intelligent(girl). Bound variable before the cut are final Cannot change the first choice Considered as True regardless of the possible failure of the subgoals after the cut?- bride(x). No The first choice X=a is final cannot try other alternatives bride(x) X=a beautiful(a) intelligent(a) beautiful(b) intelligent(b) beautiful(z) intelligent(z) No match after the cut Result: No Without the cut Result: X=b Introduction 13

14 remove_duplicates with a cut remove_duplicates([], []). bind Head, Tail remove_duplicates([head Tail], Result) :- member(head, Tail),!, When this part is matched, that match is final Therefore, during backtracking the second rule will not be tried List = [b, c, a] ; No remove_duplicates(tail, Result). remove_duplicates([head Tail], [Head Result]) :- bind Head, Tail remove_duplicates(tail, Result). Introduction 14

15 Member member(x, [X T]). bind Head & Tail Returns Yes if X is equal to Head member(x, [H T]) :- bind Head & Tail Else try the recursive calls member(x, T) Introduction 15

16 Recursing Down Lists a2b([], []). a2b([a Ta], [b Tb]) :-?- a2b([a, a, a], [b, b, b]). Yes?- a2b([a, 8, 9], [b, b, b]). No a2b(ta, Tb) Introduction 16

17 Append Append([], L, L). Append( [H T], L2, [H L3]) :- append(t, L2, L3). Introduction 17

18 Naïve Reversing with Append Naiverev ([], []). Naiverev ([H T], R):- Naiverev (T, RevT), append(revt, [H], R). Introduction 18

19 Reversing with an Accumulator accrev( [H T], A, R ):- accrev( T, [H A], R). accrev( [], A, A ). Introduction 19

20 References [1] U. Endriss, Lecture Notes : Introduction to Prolog Programming [2] Learn Prolog Now!