Basic Prolog

1. Basic Prolog

2. Structure of Programs • Programs consist of procedures. • Procedures consist of clauses. • Each clause is a fact or a rule. • Programs are executed by posing queries.

3. Clauses: Facts and Rules "if" "provided that" "turnstile" Head :- Body. This is a rule. Head. This is a fact. Full stop at the end.

4. Body of a (Rule) Clause Contains Goals Head Body likes(mary, X) human(X), honest(X). :- Goals

5. Example Program Predicate Procedure for elephant Facts • elephant(george). • elephant(mary). • elephant(X) :- grey(X), mammal(X), • hasTrunk(X). Clauses Rule

6. Interpretation of Clauses Clauses can be interpreted in a declarative or a procedural way H :- G1, G2, …, Gn. That H is provable follows from goals G1, G2, …, Gn being provable To execute procedure H, the procedures called by goals G1, G2, …, Gn are executed first Clause: Declarative reading: Procedural reading:

7. Interpretation of Clauses • Clauses can be interpreted • in a declarative, or • in a procedural way Clause: Declarative reading: Procedural reading: H :- G1, G2, …, Gn. That H is provable follows from goals G1, G2, …, Gn being provable To execute procedure H, the procedures called by goals G1, G2, …, Gn are executed first

8. Clauses • Clauses provide a convenient way to express case analysis and non-determinism. • Program clauses and data have the same form. • A Prolog program can also be seen as a relational database containing rules and facts. • The relational form of procedures makes it possible to define ‘reversible’ procedures.

9. Unification • Term-manipulation that • passes parameters, • returns results, • selects and constructs data structures • Basic control flow model is backtracking • Sometimes it is necessary to use control features that are not part of ‘logic’

10. Computation via Queries • Facts and rules are stored in a database • They can be queried ?- likes(joe, fish). yes ?- likes(joe, chocolate) no • Important: • no • means “I know it’s false, or I don’t know” • yes • means “I can prove it” • asymmetric

11. Example Queries • ?- elephant(george). • Yes • ?- elephant(jane). • no Queries Replies

12. Prolog’s Style • State the facts and rules • Pose queries • Prolog finds the answers by • searching the facts • deducing new facts from the rules • Answers depend on the search algorithm

13. Imperative/Functional/Declarative Styles –Example - Concatenate lists a and b list procedure concat(list a, list b) { list t = list u = copylist(a); while (t.tail != nil) t = t.tail; t.tail = b; return u; } In an imperative PL cat(a,b) ≡ if b = nil then a else cons(head(a), concat(tail(a),b)) In a functional PL concat([], Z, Z). concat([H|T], L, [H|Z]) :- concat(T, L, Z). In a declarative PL

14. Example: Zoo /* Facts */ elephant(gigi). elephant(mary). elephant(joe). panda(chi_chi). panda(ming_ming). stripey(tigger). stripey(mrED). big_teeth(tigger). isaCat(tigger). isaHorse(mrED). venomous(rattler). venomous(grass_snake). /* Rules */ dangerous(X) :- big_teeth(X). dangerous(X) :- venomous(X). swims(Y) :- isaFish(Y). guess(X, tiger) :- stripey(X), big_teeth(X), isaCat(X). guess(X, koala) :- arboreal(X), sleepy(X). guess(X, zebra) :- stripey(X), isaHorse(X). /* Sample Queries */ ?- dangerous(ming_ming). ?- dangerous(X). ?- guess(X,Y). • www2.hawaii.edu/~janst/313/prolog/zoo.pl

15. Colored ball problem • Find the correct sequence of colored balls to satisfy the given rules: • One red, one black and one white ball • Solution will be a permutation of {red,black,white} • white is just to the right of black • If black is in pos1, white is in pos2, • If black is in pos2, white is in pos3 • black is not in the center • Black can’t be in pos2 • www2.hawaii.edu/~janst/313/prolog/colors.pl

16. Cryptarithmatic Problem • Find the unique digit that will replace each character to solve a puzzle S E N D + M O R E --------- M O N E Y • www2.hawaii.edu/~janst/313/prolog/crypto.pl

17. Eight Queens Problem • Given an 8-by-8 chessboard, place 8 queens so that they do not threaten each other along a row, column, or a diagonal • Mathematically determine diagonal • two queens are on the same / (UR->BL) diagonal iff the sum of the row and the column is the same for each • two queens are on the same \ (UL->BR) diagonal iff the difference between the row and the column are the same for each • Generalize: N queens (N >=4) www2.hawaii.edu/~janst/313/prolog/queens.pl

18. N-Queens Without Searching • A solution to the N-Queens problem for any N >= 4 • Placing queens takes constant time per queen, O(N) • Drawing the board takes O(N^2) time • Published in ACM SIGART Bulletin, 2(2), page 7 • See example at • www.apl.jhu.edu/~hall/NQueens.html • now unfortunately broken