CSEN403 Concepts of Programming Languages. Topics: Logic Programming Paradigm: PROLOG Search Tree Recursion Arithmetic

Transcription

1 CSEN403 Concepts of Programming Languages Topics: Logic Programming Paradigm: PROLOG Search Tree Recursion Arithmetic Prof. Dr. Slim Abdennadher c S. Abdennadher 1

2 Logic Programming versus Prolog Logic Programming: Nondeterministic Arbitrary choose rule to expand first Arbitrary choose subgoal to explore first Results do not depend on rule and subgoal ordering Prolog: Deterministic Expand first rule first Explore first subgoal first Results may depend on rule and subgoal ordering c S. Abdennadher 2

3 How Prolog Answers Queries Example 1 Knowledge Base: parent(alex,julia). parent(alex,rosa). parent(lina,julia). male(alex). Query:?- parent(x,y). X = alex X = alex X = lina Y = julia?; Y = rosa?; Y = julia?; The query parent(x,y) matches the fact parent(alex,julia). This instantiates the variable X with alex and the variable Y with julia. The query parent(x,y) also matches parent(alex,rosa) and parent(lina,julia). c S. Abdennadher 3

4 Matching Two atoms match if they are the same atoms, e.g a = a. a \= b. A variable matches any other Prolog term. The variable gets instantiated with the other term. X = mother(lina). 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. loves(romeo,julia) = loves(romeo,x). loves(romeo,julia) = loves(x,y). loves(romeo,julia) \= loves(x,x). c S. Abdennadher 4

5 Back to Example 1 Knowledge Base: parent(alex,julia). parent(alex,rosa). parent(lina,julia). male(alex). Query:?- parent(x,y). X = alex X = alex X = lina Y = julia?; Y = rosa?; Y = julia?; Prolog checks for fact that matches the query, here there are three. Prolog starts form the top of the knowledge base and, therefore finds parent(alex,julia). Typing ; forces Prolog to check whether there are other possibilities. c S. Abdennadher 5

6 Search Tree: Example 1 Knowledge Base: parent(alex,julia). parent(alex,rosa). parent(lina,julia). male(alex). Query: parent(x, Y) X = alex, Y = julia X = alex, Y = rosa X = lina, Y = julia c S. Abdennadher 6

7 How Prolog Answers Queries Example 2 Knowledge Base: parent(alex,julia). parent(alex,rosa). parent(lina,julia). male(alex). father(x,y) :- parent(x,y), male(x). Query:?- father(alex,julia). Check for a fact or head of a rule that matches the query. If you find a fact you are done. If you find a rule, prove all goals specified in the body of the rule. c S. Abdennadher 7

8 Search Tree: Example 2 parent(alex,julia). parent(alex,rosa). parent(lina,julia). male(alex). father(x,y) :- parent(x,y), male(x). father(alex, julia) parent(alex, julia), male(alex) male(alex) No No Yes c S. Abdennadher 8

9 Recursion is Power Common in Prolog to use recursive rules, where the predicate in head occurs in the body. Example: X is an ancestor of Y if X is a parent of Y or X is a parent of Z and Z is a ancestor of Y ancestor(x,y) :- parent(x,y). ancestor(x,y) :- parent(x,z), ancestor(z,y). The order of the rules and the subgoals in the body is of critical importance. As the rules are tested in the given order using a depth-first search, the non-recursive rule has to be given first. c S. Abdennadher 9

10 Search Tree: Example 3 a c b d e Prolog Program: edge(a,b). %e1 edge(a,c). %e2 edge(b,d). %e3 edge(c,d). %e4 edge(d,e). %e5 path(start,end) :- edge(start,end). path(start,end):- edge(start,node), path(node,end) Query: path(b,y). c S. Abdennadher 10

11 Search Tree: Example 3 path(b, Y) p1 p2 edge(b, Y) edge(b, N),path(N, Y) e1... e5 e2 e1 e3 e2 e3 e4 No No Y = d No No path(d, Y) No p1 p2 edge(d, Y) edge(d, N1), path(n1, Y)... Y = e No Selection strategy: textual order of rules and atoms in a program. (Chronological) backtracking: backtrack search Left-to-right, depth-first exploration of the search tree c S. Abdennadher 11

12 Arithmetic Arithmetic expressions are represented in form of nested lists which give a list structure: 2 * is equivalent to +(*(2,3),7). Arithmetic expressions are evaluated only on request using the is operator.?- Area is 3.14 * 5 * 5. Area = 78.5?- Area = 3.14 * 5 * 5. Area = 3.14 * 5 * 5 Don t be tempted to write predicate(n1+n2), if you liked to pass a sum instead of a little tree. Instead you need N is N1 + N2, predicate(n). Variables within expressions that are to be evaluated must be bound. c S. Abdennadher 12

13 Arithmetic and Logical Operations Arithmetic X + Y, X - Y, X * Y, X / Y (float division), X // Y (integer division), X mod Y (remainder) Logical Operations X < Y, X =< Y, X >= Y, X > Y X = Y: succeeds if X matches with Y X \= Y: if X = Y would fail, this succeeds X == Y: compares only, does not match X \== Y: negation of X == Y X =:= Y: evaluates both sides and compares them numerically X =\= Y: similar to =:= but tests for inequality c S. Abdennadher 13

14 Examples of Using Arithmetic Remember: Prolog s rules define predicates, not functions. Thus in general, a function which takes n arguments is transformed into a predicates which takes n+1. Factorial Example fact(0,1). fact(x,f) :- X>0, X1 is X-1, fact(x1,f1), F is X*F1. Greatest common divisor Example gcd(x,x,x). gcd(x,y,z) :- X<Y, Y1 is Y-X, gcd(x,y1,z). gcd(x,y,z) :- X>Y, X1 is X-Y, gcd(x1,y,z). c S. Abdennadher 14