zebra puzzle continued recap Prolog concepts family relations

Transcription

1 zebra puzzle continued recap Prolog concepts family relations 1 recapping the Zebra puzzle 2

2 ****** the facts ****** There are 5 houses, occupied by politicallyincorrect gentlemen of 5 different nationalities, who all have different coloured houses, keep different pets, drink different drinks, and smoke different (now-extinct) brands of cigarettes.... specific constraints... 3 translating constraints to Prolog % Who owns the zebra and who drinks water? find(zebraowner,waterdrinker) :- makehouses(5, List), % The Englishman lives in a red house. house( red, englishman, _, _, _) on List, % The Spaniard keeps a dog. house( _, spaniard, dog, _, _) on List,... Notice: this is a single clause contaning all the constraints 4

3 the empty houses?- makehouses(5, List). List = [house(_g233, _G234, _G235, _G236, _G237), house(_g245, _G246, _G247, _G248, _G249), house(_g257, _G258, _G259, _G260, _G261), house(_g269, _G270, _G271, _G272, _G273), house(_g281, _G282, _G283, _G284, _G285)] 5 special predicates "just to the left of"? "lives next to"? define sublist2(s, L) sublist2([s1, S2], [S1, S2 L]). % why do we get a warning here? sublist2(s, [_ T]) :- sublist2(s, T). define nextto predicate nextto(h1, H2, L) :- sublist2([h1, H2], L). nextto(h1, H2,L) :- sublist2([h2, H1], L). 6

4 translate constraints The ivory house is just to the left of the green house. sublist2( [house(ivory, _, _, _, _), house(green, _, _, _, _)], List),... The horse owner lives next to the Kools smoker. nextto(house( _, _, _, _, kools), house( _, _, horse, _, _), List),... 7 so far so good after 1st 9 rules: the subgoal house(yellow, _G430, _G431, _G432, kools) on [house(red, englishman, snail, _G384, old_gold), house(green, spaniard, dog, coffee, _G397), house(ivory, ukrainian, _G407, tea, _G409), house(green, _G418, _G419, _G420, _G421), house(yellow, _G430, _G431, _G432, kools)] succeeds, but... 8

5 if at first you don't succeed.. constraint 10 says % A Norwegian owns the first house. List = [house(_, norwegian, _, _, _) _], this fails because List = [house(red, englishman,... so this binding is undone and a search begins for another alternative backtracking eventually finds a solution. see Chapter 26 9 looking for the zebra Who owns the zebra and who drinks water? find(zebraowner,waterdrinker) :- makehouses(5, List), house( red, englishman, _, _, _) on List, %... assert all the constraints... house( _, WaterDrinker, _, water, _) on List, house( _, ZebraOwner, zebra, _, _) on List. solution is generated and then queried in the same clause. notice that neither water nor zebra occur anywhere in the constraints! 10

6 solving the puzzle?- ['/cs/course/3401/zebra.pl'].?- find(zebraowner, WaterDrinker). ZebraOwner = japanese WaterDrinker = norwegian ; No 11 Prolog concepts: a recap 12

7 classification procedural/operational vs. denotational Java, C, etc. Lisp, Prolog denotational functional vs. declarative Lisp Prolog denotation = denotation = expression statement 13 clauses facts and rules are called clauses. A fact is a clause with no condition. Prolog uses a particular form of logic called clause logic special form of first-order logic (FOL) 14

8 queries a query is one or more terms input, as a conjunction, to the Prolog interpreter answer to the query is yes if all terms succeed. each term in the query succeeds if it can be shown to: match a fact in the database, or match the goal of a clause whose body succeeds 15 clarification text, p. 141:?- relation [, relation]... non-standard usage of the word "relation" a relation in the book's sense is not a relation in the mathematical sense. name(me, 'Peter') is a proposition stating an instance of the name relation. 16

9 terminology the mathematical denotation of a functor is a relation, but more common terminology for Prolog: functors denote predicates with 0 or more arguments. "predicates" : the ingredients of predicate logic "first-order predicate logic" "first-order logic" or just "FOL" 17 example of is to illustrate the is predicate length([], 0). length([h T], L) :- length(t, L1), L is 1 + L1. notice: two clauses define the predicate one fact and one (recursive) rule 18

10 family relations 19 a simple disjunction Ch. 18, p. 154 parent(parent, Child) :- mother(parent, Child). parent(parent, Child) :- father(parent, Child). what's the logical meaning of 2 rules with same predicate? what's the database to support queries such as?- parent(parent, 'Elizabeth').?- parent('mary', Child).? 20

11 family relations the database parent(parent, Child) :- mother(parent, Child). parent(parent, Child) :- father(parent, Child). father('george', 'Elizabeth'). father('george', 'Margaret'). mother('mary', 'Elizabeth'). mother('mary', 'Margaret'). consulting the clauses?- [p154]. % p154 compiled 0.01 sec, 1,220 bytes Yes?- 21 explicit searching?- parent(parent, Child). Parent = 'Mary' Child = 'Elizabeth' ; Parent = 'Mary' Child = 'Margaret' ; Parent = 'George' Child = 'Elizabeth' ; Parent = 'George' Child = 'Margaret' ; no 22

12 implicit search [trace]?- parent(parent, Child1), parent(parent, Child2), not(child1 = Child2). T Call: (8) parent(_g313, _G314) Call: (8) parent(_g313, _G314)? creep Call: (9) mother(_g313, _G314)? creep Exit: (9) mother('mary', 'Elizabeth')? creep T Exit: (8) parent('mary', 'Elizabeth') Exit: (8) parent('mary', 'Elizabeth')? creep T Call: (8) parent('mary', _G317) Call: (8) parent('mary', _G317)? creep Call: (9) mother('mary', _G317)? creep Exit: (9) mother('mary', 'Elizabeth')? creep T Exit: (8) parent('mary', 'Elizabeth') Exit: (8) parent('mary', 'Elizabeth')? creep Redo: (9) mother('mary', _G317)? creep Exit: (9) mother('mary', 'Margaret')? creep T Exit: (8) parent('mary', 'Margaret') Exit: (8) parent('mary', 'Margaret')? creep Parent = 'Mary' Child1 = 'Elizabeth' Child2 = 'Margaret' 23