LING 388: Language and Computers

LING 388: Language and Computers Sandiway Fong Lecture 7 9/15

Administrivia • Reminder • Homework 3 • due next Monday by midnight

Today’s Topic • Practice makes perfect… • more practice writing programs

Infinite set: N = {1,2,3,4,5,..} Base case nn(1). “1 is a natural number” Recursive case nn(N) :- nn(M), N is M+1. “N is a natural number if M is a natural number and N is M+1” ?-nn(X). X = 1 ; X = 2 ; X = 3 ; X = 4 ; X = 5 ; X = 6 ; X = 7 ; X = 8 ; X = 9 Natural Numbers (NN)

Suppose even numbers are natural numbers that are divisible by 2 Set: N = {1,2,3,4,5,..} E = {2,4,..} Task: Write a predicate even/1 that generates the even numbers Method 1 Base Case even(2). Recursive Case even(N) :- even(M), N is M+2. Query: ?- e(X). X = 2 ; X = 4 ; X = 6 ; X = 8 Even Numbers

Suppose even numbers are natural numbers that are divisible by 2 Set: N = {1,2,3,4,5,..} E = {2,4,..} Task: Write a predicate even/1 that generates the even numbers Method 2 Use the natural number definition and permit only the even ones Modify: nn(1). nn(N) :- nn(M), N is M+1. into even(N) :- nn(N), is_even(N). where is_even(N) tests N to see if it’s an even number Even Numbers

Method 2 Use the natural number definition and permit only the even ones Modify: nn(1). nn(N) :- nn(M), N is M+1. into even(N) :- nn(N), is_even(N). where is_even(N) tests N to see if it’s an even number Suppose even numbers are natural numbers that are divisible by 2 Let’s use Prolog’s built-in arithmetic evaluation predicate is/2 ?- Y is 3/2. produces a floating point number Y=1.5 ?- Y is 4/2. produces an integer Y=2 ?- Y is round(3/2). rounds up to the nearest integer Y=2 Even Numbers

Suppose even numbers are natural numbers that are divisible by 2 Let’s use Prolog’s built-in arithmetic evaluation predicate is/2 ?- Y is 3/2. produces a floating point number Y=1.5 ?- Y is 4/2. produces an integer Y=2 ?- Y is round(3/2). rounds up to the nearest integer Y=2 Definition so far even(N) :- nn(N), is_even(N). where is_even(N) tests N to see if it’s an even number Simple Idea: to test whether a number X is even divide it by 2, call this number Y divide it by 2 and round it, call this number Z X is even if Y=Z. Define is_even(X) :- Y is X/2, Z is round(X/2), Y = Z. Even Numbers

Even numbers Idea: to test whether a number X is even divide it by 2, call this number Y divide it by 2 and round it, call this number Z X is even if Y=Z. Define is_even(X) :- Y is X/2, Z is round(X/2), Y = Z. Odd numbers Define is_odd(X) :- Y is X/2, Z is round(X/2), \+ Y = Z. or define is_odd(X) :- \+ is_even(X). Odd Numbers

You can use built-in predicates write/1 and nl/1 to print values of variables etc. Example if X = the ?- write(X), nl. prints the [newline] Sometimes useful for debugging is_odd(X) :- Y is X/2, write(Y), nl, Z is round(X/2), write(Z), nl, \+ Y = Z. Examples: ?- is_odd(7). 3.5 4 Yes ?- is_odd(6). 3 3 No Output

Template: <test> -> <then-part> ; <else-part> <test> <then-part> <else-part> are all Prolog goals (queries) Example: test(N) :- is_even(N) -> write(N), write(‘ is even’), nl ; write(N), write(‘ is odd’), nl. Queries: ?- test(3). 3 is odd Yes ?- test(4). 4 is even Yes If-Then-Else

An Aside http://en.wikipedia.org/wiki/Parity_of_zero • Zero is considered to be an even number • Integer multiple of 2 (definition) • shares all properties of even numbers

Template: <test> -> <then-part> ; (<test> -> <then-part> ; <else-part>) <test> <then-part> <else-part> are all Prolog goals (queries) ( ... ) indicate nesting Example: test(N) :- N = 0 -> write(‘Zero is tricky’), nl ; (is_even(N) ->write(N), write(‘ is even’), nl ; write(N), write(‘ is odd’), nl). Queries: ?- test(0). Zero is tricky Nested If-Then-Else

Exercise (Ungraded homework exercise) Write a Prolog program toenumerate the integer line i.e. a program that would print out all and only the numbers on the integer line (given enough time…) Where would you start?

LING 388: Language and Computers