Prolog Fundamentals

1. Prolog Fundamentals

2. Review Last Lecture A Prolog program consists of a database of facts and rules, and queries (questions). Fact: ... . Rule: ... :- ... . Query: ?- ... . Variables: must begin with an upper case letter or underscore. Nora, _nora. Constants (atoms): begin with lowercase letter, or enclosed in single quotes. uncle_ali, nora, year2007, . numbers3, 6, 2957, 8.34, ... complex termsAn atom (the functor) is followed by a comma separated sequence of Prolog terms enclosed in parenthesis (the arguments). likes(lama,apples), likes(amy,X). 2

3. Outline Predicate Definitions Matching Backtracking Recursion 3

4. Predicate Definitions Both facts and rules are predicate definitions. Predicate:is the name given to the word occurring before the bracket in a fact or rule: parent(ali,samir). By defining a predicate you are specifying which information needs to be known for the property denoted by the predicate to be true. Predicate name 4

5. Prolog Matching (unification) Two atoms match if they are the same atom. Ex.: nora = nora, but nora ≠ ’Nora’. A variable matches any other Prolog term. The variable gets instantiated with the other term. Ex.: X = teacher(jacky) Ex.: X = Y Two complex terms match if they have the same functorand the same number of arguments and if all pairs of parallel arguments match. Ex.: like(sara,basma) = like(sara,X) Ex.: like(sara,basma) ≠ like(X,X) 5

6. Prolog Execution When Prolog tries to answer a query, it does so by trying to match the goal to the head of the rule. This might result in some variables getting bound. Example: KB:cleaner(nancey).Query: cleaner (mary). cleaner (shona). nurse(sister_jacky). ?- cleaner(X). X = nancey ; X = mary ; X = shona ; No • Prolog checks for facts that match the query. (There are three.) • Prolog starts from the top of the knowledge base and, therefore, finds cleaner(nancey) first. • Typing ; forces Prolog to check whether there are other possibilities. 6

7. Example likes(huda, X) :- fresh(X), sweet(X). fresh(Y) :- juicy(Y). juicy(orange). sweet(orange). ?- likes(huda, orange). MATCHES likes(huda, orange) to head of rule 1, with X=orange. Sets fresh(orange), sweet(orange) as new goals. Tries to prove fresh(orange). MATCHES head of rule 2. Y=orange. Tries to prove juicy(orange). MATCHES a fact. So proved. Tries to prove sweet(orange). MATCHES a fact, So proved. 7

8. Proof tree. Likes (huda, orange) Using rule 1 sweet(orange) fresh(orange) Using rule 2 True fact juicy(orange) True fact likes(huda, X) :- fresh(X), sweet(X). fresh(Y) :- juicy(Y). juicy(orange). sweet(orange). ?- likes(huda, orange). 8

9. Backtracking Prolog goes through facts/rules top to bottom looking for facts or rule heads which match the goal. If a rule fails as can’t prove body, Prolog will try next rule/fact matching current goal. If can’t find ANY way to prove current goal, Prolog will retrythe previous goal, to see if it can be solved another way. Example: facts only teacher(saleh). teacher(nora). teacher('Aunt Laura'). father( saleh, jaber). teacher(X). X = saleh ; X = nora ; X = 'Aunt Laura' ; No Note: Here we use “;” to ask it to look for other solutions, which forces backtracking. 9

10. Example using facts & rules (1) likes(huda, X) :- fresh(X), sweet(X). fresh(apple). fresh(orange). sweet(orange). ?- likes(huda, What). Matches head of rule with X=What (binding two variables to same value). Tries to satisfy fresh(What). fresh(apple) succeeds. Tries to satisfy sweet(apple). This fails. So backtracks and retries fresh(What). Succeeds with What=orange etc. 10

11. Example using facts & rules (2) female(lara). female(hana). female(sara). female(dia). haschildren(sara). haschildren(dia). mother(X) :-female(X), haschildren(X). mother(aisha). • ?- mother(X). • Matches with head of first rule. • Tries to satisfy female(X). • Matches female(lara). • Tries to satisfy haschildren(lara). • FAILS, so GOES BACK to try • female(X) again. • Maches femal(sara). • Tries haschildrens(sara). • Succeeds, so mother(X) succeeds/ • X = sara ; • Going back and trying later femalfacts: • X = dia; • And trying later “mother” fact: • X = aisha. 11

12. Recursion in any language is a function that can call itself until the goal has been succeed. In Prolog, when a predicate contain a goal that refers to itself. Example. parent(noha,jaber). parent(jaber,salim). parent(salim,reda). ancestor(X,Y) :- parent(X,Y). /* If X is a parent of Y, then X is an ancestor of Y */ ancestor(X,Z) :- parent(X,Y), ancestor(Y,Z). /* if Y is an ancestor of Z and X is a parent of Y, then X is an ancestor of Z */ recursion 12

13. Recursion (Cont.) KB: Query: ?- ancestor(jaber,reda). • parent(noha,jaber). • parent(jaber,salim). • parent(salim,reda). • ancestor(X,Y) :- parent(X,Y). • ancestor(X,Z) :- parent(X,Y), ancestor(Y,Z). 1.Prolog will first try the goal parent(jaber,reda). and it will fail. 2. then try the second clause of ancestor. The new query is parent(jaber,Y). 3.Prolog will find Y=salim and try ancestor(salim,reda) wich will conduct to check parent(salim,reda). This is succesfull. As a result the goal ancestor(salim,reda) succeeds. Then ancestor(jaber,reda) can succeed. 13

14. Summary Matching: Prolog tries to prove goals by matching them with rules/facts. Tries to find variable bindings making expressions identical. SEARCHING the whole activity of the Prolog system is to search through various options to find a combination that succeeds. Main search tools are backtracking and recursion Backtracking Prolog goes through facts/rules from top to bottom to try to find matching rules or facts. when the system fails during its search, it returns to previous choices to see if making a different choice would allow success. Recursion when a predicate contain a goal that refers to itself. 14