Summary of Results

      The only two examples Foil came with that had test data were the Crx and Member examples. They achieved an accuracy of 79.5% and 75.0%, respectively. The rules produced for each example follows.

Ackermann

  Ackermann(0,B,C) :- succ(B,C).
  Ackermann(A,0,C) :- succ(0,D), succ(E,A), Ackermann(E,D,C).
  Ackermann(A,B,C) :- succ(D,A), succ(E,B), Ackermann(A,E,F), 
			Ackermann(D,F,C).
    

Crx - ( 79.5% )

  is_+(A,B,C,D,E,F,G,H,Ft,J,K,L,M,N,O) :- O>500.
  is_+(A,B,C,D,Dg,F,G,H,Ft,J,K,L,M,N,O) :- N<=100, H>0.375.
  is_+(A,B,C,D,E,F,G,H,I,J,K,L,Gg,N,O) :- K>3, O<=0.
  is_+(A,B,C,D,E,F,G,H,Ft,J,K,L,M,N,O) :- O>5, C>1.75, H>0.375.
  is_+(A,B,C,D,E,F,Eh,H,Ft,J,K,L,M,N,O) :- H<=4.165, F<>Ec.
  is_+(A,B,C,D,E,F,G,H,Ft,J,K,L,Gg,N,O) :- N>200, C<=3.165, F<>Ek.
  is_+(A,B,C,D,E,F,G,H,Ft,J,K,L,M,N,O) :- B<=26.67, N<=100, B>18.67.
  is_+(A,B,C,D,E,F,G,H,Ft,J,K,L,M,N,O) :- C>2.25, B>38.58, C<=12.54.
  is_+(Ab,B,C,D,E,F,G,H,I,Ff,K,L,M,N,O) :- C<=H, B>34.83, H<=3.5.
  is_+(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) :- M<>Gg, B<=20.17, N>280.
  is_+(A,B,C,D,E,F,G,H,Ft,Ff,K,L,M,N,O) :- C>2.25, C<=5.625, H<=2.5, 
						F<>Ei.
  is_+(Aa,B,C,D,E,F,G,H,I,J,K,L,Gp,N,O).
  is_+(A,B,C,D,Dg,F,G,C,I,J,K,Ff,M,N,O).
  is_+(A,B,C,D,E,Ex,G,H,I,J,K,L,M,N,O) :- C>2.25, H<>K.
  is_+(A,B,C,D,E,Ej,G,H,Ft,J,K,Ff,M,N,O).
  is_+(A,B,C,D,E,F,En,H,I,J,K,Ff,M,N,O).
  is_+(A,B,C,D,Dg,Ec,G,H,I,Ff,K,L,M,N,O) :- C<=0.83, C>0.585.
  is_+(Ab,B,C,D,E,Ecc,G,H,I,J,K,Ft,Gg,N,O).
  is_+(A,B,C,D,E,Ek,G,H,I,J,K,L,M,N,O) :- O>2100.
    

Member - ( 75.0% )

  member(A,B) :- components(B,A,C).
  member(A,B) :- components(B,C,D), member(A,D).
    

Ncm

  choose(A,B,C) :- dec(C,D), mult(A,B,E), mult(B,C,F), 
			mult(B,D,D), mult(B,F,E).
  choose(A,B,C) :- dec(A,D), dec(B,E), mult(B,C,F), choose(D,E,G), 
			mult(A,G,F).
    

Qs44

  sort([],[]).
  sort(A,B) :- components(A,C,D), partition(C,D,E,F), sort(E,G), 
		sort(F,H), components(I,C,H), append(G,I,B).