COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 1

Computing Fibonacci Numbers

fib(n)

0,

1,

fib(n-2) + fib(n-1),

if n = 0

if n > 1

if n = 1=

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 2

Recursive Fibonacci Program

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.

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 3

Running the Fibonacci Program

fib(4)

fib(2)

10 fib(2)

10

1

fib(3)fib(2)

10

1

fib(3)

fib(5)

+

+ +

+ + +

+

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 4

Efficient Fibonacci Programfib(0, 0).fib(X, Y) :- X > 0, fib(X, Y, _).

fib(1, 1, 0).fib(X, Y1, Y2) :-● X > 1,● X1 is X - 1,● fib(X1, Y2, Y3),● Y1 is Y2 + Y3.

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 5

Collecting all Solutions

Getting all answers to a question …

➢ Through backtracking we can get all answers toa question one by one.

➢ Using setof we can collect all answers to a questionin a list.

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 6

Collecting all Solutions

age(peter, 7).age(ann, 5).age(pat, 8).age(tom, 5).

?- setof(Child, age(Child, 5), List).

List = [ann, tom]

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 7

Collecting all Solutions?- setof(Child, age(Child, Age), List).

Age = 7List = [peter] ;

Age = 5List = [ann, tom] ;

Age = 8List = [pat] ;No

?- setof(Child, Age ^ age(Child, Age), List).

List = [ann, pat, peter, tom]

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 8

Collecting all Solutions

age(peter, 7).age(ann, 5).age(pat, 8).age(tom, 5).

?- setof(Child, age(Child, 3), List).

No

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 9

Testing Prolog Code

➢ Easy because all “state” accessible inparameters

➢ Need to check both number and values ofall answers to calls (failure is same as noanswers)

➢ We will ignore the order of the answers

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 10

Test Example - fibonaccitest(fib(0, 0)).test(fib(1, 1)).test(fib(2, 1)).test(fib(3, 2)).test(fib(4, 3)).test(fib(5, 5)).test(fib(6, 8)).test(fib(7, 13)).

testFail(fib(-1,_)).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 11

Test Example - fibonacci?- [fib,fibTest,test].

Yes?- testRun.

starting testing++++++++-end of testing

Yes

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 12

Quick Sorting

quicksort([], []).quicksort([X | Tail], Sorted) :-split(X, Tail, Small, Big),

quicksort(Small, SSmall),

quicksort(Big, SBig),

append(SSmall, [X | SBig], Sorted).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 13

Quick Sorting

split(_X, [], [], []).

split(X, [Y|Tail], [Y|Small], Big) :-X >= Y, split(X, Tail, Small, Big).

split(X, [Y|Tail], Small, [Y|Big]) :-X < Y, split(X, Tail, Small, Big).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 14

Testing sortDifferent ways of saying the same thing:

test(quicksort([3,1,2], [1,2,3])).

test(quicksort([3,1,2], S), [quicksort([3,1,2], [1,2,3])]).

test(quicksort([3,1,2], S), S, [[1,2,3]]).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 15

Testing sortA handy way that shows you can write testing rules.

test(quicksort(L,X), X, [S]) :- test_sort(L, S).

test_sort([], []).test_sort([1], [1]).test_sort([2,1], [1,2]).test_sort([1,2], [1,2]).test_sort([3,1,2], [1,2,3]).test_sort([5,6,1,3,4,7,2],

[1,2,3,4,5,6,7]).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 16

Testing splittest(split(X,L,Sn,Bn), [Sn,Bn], [[S,B]]) :-test_split(X,L,S,B).

test_split(3, [3,2,1,4,5,1,7],[3,2,1,1], [4,5,7]).

test_split(0, [3,2,1,4,5,1,7],[], [3,2,1,4,5,1,7]).

test_split(1, [], [], []).test_split(1, [1], [1], []).test_split(0, [1], [], [1]).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 17

Implementing Test

check(G, Re, Ex) :-setof(Re, G, Res)-> soln(G, Ex, Res); failed(G, Ex).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 18

Implementing Test

soln(G, Ex, Res) :- sort(Ex, Exs),(Res = Exs-> (Ex = [] -> print('-') ; print('+')); error(G, Exs, Res))).

failed(G, Ex) :-(Ex = []-> print('-'); error(G, Ex, []))).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 19

Implementing Test

testRun :- nl, print('starting testing'), nl, fail.testRun :- test, fail.testRun :- nl, print('end of testing'), nl.

test :- test(G, Re, Ex), check(G, Re, Ex).test :- test(G, Ex), check(G, G, Ex).test :- test(G), check(G, G, [G]).test :- testFail(G), check(G, G, []).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 20

Testing sorttest :- test_sort(L, S),

check(quicksort(L,X), [S], X).

test_sort([], []).test_sort([1], [1]).test_sort([2,1], [1,2]).test_sort([1,2], [1,2]).test_sort([3,1,2], [1,2,3]).test_sort([5,6,1,3,4,7,2],

[1,2,3,4,5,6,7]).

COMP 222 Logic and Programming Module B — Prolog Chapter 7, Slide 21

Merge Sortmerge_pass([], []).

merge_pass([L], [L]).

merge_pass([L1, L2 | L], [M | Ln]) :- merge(L1, L2, M),merge_pass(L, Ln).