PROLOG

Question :

Implement PROLOG program for plus, times, and greater than using the successor representation of natural numbers.

And use the definition of plus and times to implement the factorial function. Will the factorial function work in the opposite direction?

Fill these code:

%Peano Arithmetic

% Peano Numbers

num(0).

num(s(X)) :- num(X).

% Helper func, converts decimal repr of peano num and back.

peano_to_decimal_rec(0, 0).

peano_to_decimal_rec(s(X), Y) :- peano_to_decimal_rec(X, N), Y is N + 1.

peano_to_decimal(X, Y) :- once(peano_to_decimal_rec(X, Y)).

% Comparison

% equal

equal(X, X).

% less than (add base cases when needed)

less_than(X, Y) :-

write("Error: Not Implemented"), false.

% greater than (add base cases when needed)

greater_than(X, Y) :-

write("Error: Not Implemented"), false.

% addition (add base cases when needed)

add(Addend, Augend, Sum) :-

write("Error: Not Implemented"), false.

% multiplication (add base cases when needed)

multiply(Multiplicand, Multiplier, Product) :-

write("Error: Not Implemented"), false.

% Peano Factorial

% Try to make it reversible.

% HINT: See the implementation of `peano_to_decimal`.

% There are multiple ways of making the function reversible, the hint is one way.

factorial(Number, Value) :-

write("Error: Not Implemented"), false.