Recursive Arithmetic

Consider the definition of check numbers from a previous lecture. Another important definition, is of the factorial function :

0! = 1
n! = n*(n-1)!

factorial(0,1).

factorial(N,F) :-
   N > 0,
   N1 is N-1,
   factorial(N1, F1),
   F is N * F1.

• Again, the boundary condition is given first, followed by the definition of the rule
• The first check is on the input arguments, and validates the calling arguments
• the repeated call to factorial is then made with a slightly smaller parameter

Possible to extend the definition of our racers with the use of a third argument, which encapsulates time - therefore

better(X,Y,T) :-
  before(X,Y,T).

better(X,Y,T) :-
 before(X, Z, T1),
 better(Z, Y, T2),
 T is T1 + T2.

• Ordering in the 3rd goal above is important, because T cannot be evaluated before T1 and T2 have been instantiated
• We can also perform other arithmetic operations to achieve more statistics about the race, done in the same way as the second definition of better