HOMEWORK 3.


1. Write a program for factorial computation using accumulator.

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2. Write a program sum_and_squaresum that from a given list of numbers
finds the sum of its elements and the sum of their squares. Use
accumulators. Sample run:

?- sum_and_squaresum([1,-3,2,0],Sum,SQS).

Sum = 0
SQS = 14 ;

No


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3. Define the relation flatten_list(InputList, FlatList) where
InputList can be a list with nested occurrences of lists, and
FlatList is InputList "flattened" so that the elements of
InputList's sublists (or sub-lists, sub-sub-lists, etc) are
reorganized as one plain list. Use difference structures.

A sample session should look something like:
?- flatten_list([1,[a,[b,c]],2,[d],[]],X).

X=[1,a,b,c,2,d];

No
?- flatten_list([[]],X).

X=[];

No
?- flatten_list([1,[a,[b,c]],2,[d],[]],[1, a, b, c, 2, d]).

Yes
?- flatten_list([1,2], X).

X = [1, 2] ;

No

Make sure that the program does not return multiple solutions. For
instance, you should NOT get something like:


?- flatten_list([1,[a,[b,c]],2,[d],[]],X).

X = [1, a, b, c, 2, d] ;

X = [1, a, b, c, 2, d, []] ;

X = [1, a, b, c, 2, d, []] ;

X = [1, a, b, c, 2, d, [], []] ;

X = [1, a, b, c, 2, d, [[]]]

...

You can use 'cut' to prevent such cases.



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4. Write a predicate twice_as_long(L1,L2) that succeeds
if the list L2 is twice as long as the list L1. Do NOT
compute the lengths of the lists. Sample run:

?- twice_as_long([],[]).

Yes.

?- twice_as_long([a],[1,2]).

Yes.

?- twice_as_long([a,b],X).

X = [_G328, _G331, _G334, _G337] ;

No


?- twice_as_long(X,[_,_]).

X = [_G328] ;

No

?- twice_as_long([_],X).

X = [_G313, _G316] ;

No


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