Script started on Mon Mar 30 20:21:47 1998

xavier[12]% cat Hmwk8.pp
/* Webber Assignment 8
   Dan J. Fraser (1219229) */
   
list_of_k_integers(X, List) :- 
   counter(X,0,List).

counter(Size, Count, List) :-
 list_of_k_integers_that_sum_to_S(Size,Count,List).

counter(Size,Count,List) :-
 plus(Count,1,New_Count),
 counter(Size,New_Count,List).

an_integer_less_than_or_equal_to(X, X) :- .

an_integer_less_than_or_equal_to(Int, X) :- 
  plus(Z, 1, Int), an_integer_less_than_or_equal_to(Z,X).

list_of_k_integers_that_sum_to_S(0, 0, nil) :- .

list_of_k_integers_that_sum_to_S(Size, 0, 0:Tail) :- 
  not Size = 0,
  plus(New_Size,1,Size),
  list_of_k_integers_that_sum_to_S(New_Size, 0, Tail).

list_of_k_integers_that_sum_to_S(Size, Sum, Y:X ) :- 
  not Size = 0,
  not Sum = 0,
  an_integer_less_than_or_equal_to(Sum,Y),
  plus(New_Size,1,Size),
  plus(New_Sum,Y,Sum),
  list_of_k_integers_that_sum_to_S(New_Size, New_Sum, X).

xavier[13]% cat Hmwk8.Given.pp 

pythagorean_triples(X, Y, Z) :-
       list_of_k_integers(3, X:Y:Z:nil),
       plus(2, Something, X), /* X >= 2 */
       plus(X, SomethingElse, Y), /* Y >= X */
       times(X,X,Xsquared),
       times(Y,Y,Ysquared),
       times(Z,Z,Zsquared),
       plus(Xsquared,Ysquared,Zsquared).

sum_of_four_squares(S, W, X, Y, Z) :-
       list_of_k_integers(4, W:X:Y:Z:nil),
       times(W,W,Wsquared),
       times(X,X,Xsquared),
       times(Y,Y,Ysquared),
       times(Z,Z,Zsquared),
       plus(Wsquared, Xsquared, FirstSubTotal),
       plus(Ysquared,Zsquared, SecondSubTotal),
       plus(FirstSubTotal, SecondSubTotal, S).



xavier[14]% pprolog Hmwk8.pp Hmwk8.Given.pp
Welcome to picoProlog
Reading Hmwk8.pp
Reading Hmwk8.Given.pp

# :- sum_of_four_squares(159, W, X, Y, Z).

W = 11
X = 6
Y = 1
Z = 1 ? .

yes

# :- pythagorean_triples(X, Y, Z).

X = 3
Y = 4
Z = 5 ? 

X = 6
Y = 8
Z = 10 ? 

X = 5
Y = 12
Z = 13 ? 

X = 9
Y = 12
Z = 15 ? 

X = 8
Y = 15
Z = 17 ? 

X = 12
Y = 16
Z = 20 ? 

X = 7
Y = 24
Z = 25 ? 

X = 15
Y = 20
Z = 25 ? 

X = 10
Y = 24
Z = 26 ? .

yes

# :- list_of_k_integers(5, X).

X = 0:0:0:0:0:nil ? 

X = 1:0:0:0:0:nil ? 

X = 0:1:0:0:0:nil ? 

X = 0:0:1:0:0:nil ? 

X = 0:0:0:1:0:nil ? 

X = 0:0:0:0:1:nil ? 

X = 2:0:0:0:0:nil ? 

X = 1:1:0:0:0:nil ? 

X = 1:0:1:0:0:nil ? 

X = 1:0:0:1:0:nil ? 

X = 1:0:0:0:1:nil ? 

X = 0:2:0:0:0:nil ? 

X = 0:1:1:0:0:nil ? 

X = 0:1:0:1:0:nil ? 

X = 0:1:0:0:1:nil ? 

X = 0:0:2:0:0:nil ? 

X = 0:0:1:1:0:nil ? 

X = 0:0:1:0:1:nil ? 

X = 0:0:0:2:0:nil ? 

X = 0:0:0:1:1:nil ? 

X = 0:0:0:0:2:nil ? 

X = 3:0:0:0:0:nil ? .

yes

# :- ^D

xavier[15]% exit

script done on Mon Mar 30 20:32:15 1998