/* 

  Mutual recursion (Rosetta code) in Picat.

  http://rosettacode.org/wiki/Mutual_recursion
  """
  Two functions are said to be mutually recursive if the first calls 
  the second, and in turn the second calls the first.

  Write two mutually recursive functions that compute members of the Hofstadter 
  Female and Male sequences defined as:

     F(0) = 1 ; M(0)=0 
     F(n) = n-M(F(n-1)), n>0 
     M(n) = n-F(M(n-1)), n>0

  (If a language does not allow for a solution using mutually recursive functions 
  then state this rather than give a solution by other means).
  """

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


main => go.

% For small values table is not needed
go =>
  N = 30,
  println(func),
  test_func(N),
  println(pred),
  test_pred(N),
  nl.

% the predicate version is a little faster than the function version
% N=1_000_000
% func: 1.829s
% pred: 1.407s
%
go2 =>
  N = 1_000_000,
  println(func),
  time(test_func(N)),
  println(pred),
  time(test_pred(N)),
  nl.


test_func(N) =>
  println([M : I in 0..N, male(I,M)]),
  println([F : I in 0..N, female(I,F)]),
  nl.

test_pred(N) => 
  println([M : I in 0..N, male(I,M)]),
  println([F : I in 0..N, female(I,F)]),
  nl.
  

table
f(0) = 1.
f(N) = N - m(f(N-1)), N > 0 => true. 

table
m(0) = 0.
m(N) = N - f(m(N-1)), N > 0 => true.


% translation of the Prolog solution
table
female(0,1).
female(N,F) :-
  N>0, 
  N1 = N-1, 
  female(N1,R),
  male(R, R1),
  F = N-R1.
 
table
male(0,0).
male(N,F) :-
  N>0, 
  N1 = N-1, 
  male(N1,R),
  female(R, R1),
  F = N-R1.