Re: Prolog Programming for AI, problem 7.1
- From: "growe" <orders@xxxxxxxxxxxxx>
- Date: 31 Aug 2006 09:29:14 -0700
Lash Rambo wrote:
I'm soldiering through "Prolog Programming for Artifical Intelligence" by
Bratko, but have run into a nasty exercise. It's 7.1, and reads:
"
Write a procedure 'simplify' to symbolically simplify summation
expressions with numbers and symbols (lower-case letters). Let the
procedure rearrange the expressions so that all the symbols precede
numbers. These are examples of its use:
?- simplify(1 + 1 + a, E).
E = a + 2
?- simplify(1 + a + 4 + 2 + b + c, E).
E = a + b + c + 7
?- simplify(3 + x + x, E).
E = 2*x + 3
"
I hit the same exercise today, and eventually came up with the
following. It doesn't use anything that Bratko hasn't covered in his
book up to that point. The only outside functions it uses are the count
procedure from his book (which appears in the same section as the
exercise so I suspect you're supposed to use it) and the delete
procedure that comes with SWI Prolog (but Bratko does a delete earlier
in the book on page 69).
The only thing I couldn't get rid of were the parentheses in the answer
(maybe this is an artifact of SWI?). The output it gives for the
examples in Bratko's question are:
134 ?- simplify(1+1+a,E).
E = a+2
Yes
135 ?- simplify(1+a+4+2+b+c,E).
E = a+ (b+ (c+7))
Yes
136 ?- simplify(3+x+x,E).
E = 2*x+3
=====================
% Ex 7.1. simplify additions
% X is compound expression, A is simplied expression
% The idea is to calculate the numeric sum, and build
% a list of the atoms in the compound expression, then
% convert the list of atoms into the correct format
simplify(X, A) :-
simplify(X, Sum, Atoms),
atomSums(A, Sum, Atoms).
% If X is an atom, there are no numbers so Sum is 0
% Atom list contains the atom
simplify(X, Sum, [X]) :-
atom(X),
Sum is 0, !.
% If X is a number, then Sum is X, and the atom list
% is empty
simplify(X, Sum, []) :-
integer(X),
Sum is X, !.
% Recursive case
simplify(X, Sum, Atoms) :-
X = Y + Z, % Split compound expression
simplify(Z, SumZ, AtomsZ), % Simplify each part
simplify(Y, SumY, AtomsY),
Sum is SumY + SumZ, % Add the subsums together
append(AtomsY, AtomsZ, Atoms),!. % Join the sub-lists of atoms
% Convert the list of atoms to the simplified format
atomSums(A, A, []). % If no atoms, expression is just
the sum
% Recursive case
atomSums(A, Sum, [T|Atoms]) :- % Get first atom T in list
count(T, [T|Atoms], CountT), % Count number of times it occurs
in list
delete(Atoms, T, NewAtoms), % Delete it from list so you don't
count it again
atomSums(B, Sum, NewAtoms), % Convert remainder of list
buildExp(A, B, T, CountT), !. % Build the expression
% Only print out the count for an atom if it's > 1
buildExp(A, B, T, CountT) :-
CountT > 1,
A = CountT * T + B, !
;
A = T + B, !.
% count procedure from Bratko's book, page 150.
count(_,[],0).
count(A, [B|L],N) :-
atom(A), A = B, !,
count(A,L,N1),
N is N1 + 1
;
count(A,L,N).
.
- References:
- Prolog Programming for AI, problem 7.1
- From: Lash Rambo
- Prolog Programming for AI, problem 7.1
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