CSE240 Lecture 26

Introduction to Programming Languages
Recursion in Prolog
(202204)

Transcript

1. jgs CSE 240 Introduction to Programming Languages Lecture 26: Recursion in Prolog Dr. Javier Gonzalez-Sanchez javiergs@asu.edu javiergs.engineering.asu.edu | javiergs.com PERALTA 230U Office Hours: By appointment
2. jgs Previously
3. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 3 jgs Arithmetic Queries ?- X is 10+5. X = 15 ?- 6 is 10+5. false ?- 15 is 10+5. true ?- 10+5 is X. Error: Arguments are not sufficiently instantiated ?- 10+5 is 10+5. false
4. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 4 jgs Arithmetic Queries § X is 5 /3, X = 1. false § X is 5 /3, Y = 1. X=1.666666667, Y=1 § X is 5 /3; X = 1. X = 1.6666666667 X = 1
5. jgs Rules and Recursion
6. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 6 jgs Rules as functions § doSomething(A,B,P) :- P is A + B. ?-doSomething(3,2,P). ?-doSomething(3,2,10).
7. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 7 jgs Recursion | Factorial % this is fact factorial(0, 1). % this is a rule % the factorial of F is N*F1 % if N>0 and % N1 is N-1 and % the factorial of N1 is F1 factorial(N, F) :- N>0, N1 is N - 1, factorial(N1, F1), F is N * F1. ?- factorial (3, W). W=6 1. factorial(3, W) apply rule 2 2. 3>0, N1 is 3-1, factorial (N1, F1), F is 3 *F1 solve the individual parts true, 2 is 3-1, factorial (2, F1), F is 3*F1 apply rule 2 again 3. 2>0, N2 is 2-1, factorial (N2, F2), F1 is 2 * F2 solve the individual parts true, 1 is 2-1, factorial (1, F1), F1 is 2*F2 apply rule 2 again 4. 1>0, N3 is 1-1, factorial (N3, F3), F2 is 2 * F3 solve the individual parts true, 0 is 1-1, factorial (0, F3), F2 is 1*F3 apply rule 1 5. factorial (0, 1) F3 is 1 6. Go back, replace F3 to get F2, then F2 to get F1, then F1 to get F.
8. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 8 jgs Recursion | Factorial
9. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 9 jgs Recursion | Fibonacci fib(0, 0). fib(1, 1). fib(X, Y) :- X > 1, X2 is X – 2, fib(X2, Y2), X1 is X – 1, fib(X1, Y1), Y is Y1 + Y2.
10. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 10 jgs Recursion | Fibonacci
11. jgs Test Yourselves C/C++
12. Javier Gonzalez-Sanchez | CSE240 | Spring 2020 | 12 jgs Test Yourselves § A recursive function rec is defined as follows Write a set of rules in Prolog to define the solution to this function. ï î ï í ì ³ - - + - = £ = 3 ) 3 ( * ) 2 ( ) 1 ( 2 1 1 0 ) ( n n rec n rec n rec n n n rec
13. jgs CSE 240 Introduction to Programming Languages Javier Gonzalez-Sanchez, Ph.D. javiergs@asu.edu Fall 2021 Copyright. These slides can only be used as study material for the class CSE240 at Arizona State University. They cannot be distributed or used for another purpose.