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,. numbers 3, 6, 2957, 8.34,... –complex terms An atom (the functor) is followed by a comma separated sequence of Prolog terms enclosed in parenthesis (the arguments). likes(lama,apples), likes(amy,X).

3 Outline Predicate Definitions Matching Backtracking Recursion

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

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 functor and 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)

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.

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.

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

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 retry the 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.

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.

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 femal facts: X = dia; And trying later “mother” fact: X = aisha.

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

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.

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.