/* 

  forall/2 and forany/2 in Picat.

  Testing forall/2 and forany/2 predicate.

  Inspired by B-Prolog's and SWI Prolog's forall/2 (and forany/2):
     http://www.probp.com/manual/node35.html
     http://www.swi-prolog.org/pldoc/man?predicate=forall/2

  Note: These are also defined in v3_utils.pi

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

*/


main => go.

go =>

   % All numbers satisfy p/1
   if forall($member(X,[1,2,3]),$p(X)) then
      println(ok1)
   else
     println(not_ok1)
   end,

   % Not all numbers satisfy p/1.
   if not forall($member(X,[1,2,3,20]),$p(X)) then
      println(ok2)
   else
     println(not_ok2)
   end,

   % All numbers satisfy q/1
   if forall($member(X,[1,2,3]),$q(X)) then
      println(ok3)
   else
     println(not_ok3)
   end,

   % Not all numbers satisfy q/1
   if not forall($member(X,[1,2,3,20]),$q(X)) then
      println(ok4)
   else
     println(not_ok4)
   end,

   % Not all numbers satisfy p/1
   if not forall($q2(X),$p(X)) then
      println(ok5)
   else
     println(not_ok5)
   end,


   % This works as well where 
   %     $(X < 10) 
   % is a lambda like expression
   % All numbers satisfies the condition
   if forall($member(X,[1,2,3,4]),$(X < 10)) then
      println(ok6)
   else
     println(not_ok6)
   end,

   % Not all numbers satisfies the expression
   if not forall($member(X,[1,2,3,4,20]),$(X < 10)) then
      println(ok7)
   else
     println(not_ok7)
   end,

   % All numbers satisfy p/1
   if forall($member(X,[1,2,3]),$(p(X),println(x=X))) then
      println(ok8)
   else
     println(not_ok8)
   end,

   nl.


% The example from SWI Prolog 
% http://www.swi-prolog.org/pldoc/man?predicate=forall/2
% 
%   forall($member(Result = Formula, [2 = 1 + 1, 4 = 2 * 2]),(Result == Formula)),
%   nl.
%
% Note that we must use $() to escape the expressions and use 
%    Result =:= Formula
% to force arithmetic comparison.
% 
go2 => 

   if forall($member(Result = Formula, $[2 = 1 + 1, 4 = 2 * 2]), $(Result =:= Formula)) then
       println(ok1)
   else
       print(not_ok1)
   end,

   if forall($member(Result = Formula, $[2=1 + 1, 4=2 * 2]), $z(Result,Formula)) then
       println(ok2)
   else
       print(not_ok2)
   end,

   % Failure test.
   if not forall($member(Result = Formula, $[2 = 1 + 1, 4 = 2 * 2, 6 = 3*3]), $(Result =:= Formula)) then
       println(ok3)
   else
       print(not_ok3)
   end,

   if not forall($member(Result = Formula, $[2=1 + 1, 4=2 * 2, 6=3*3]), $z(Result,Formula)) then
       println(ok4)
   else
       print(not_ok4)
   end,


   nl.

%
% Testing forany/2
%
go3 :-
   if forany($member(X,[1,2,3]),$p(X)) then
      println(ok1)
   else
     println(not_ok1)
   end,

   if forany($member(X,[1,2,3,20,23]),$(p(X),writeln(X))) then
      println(ok2)
   else
     println(not_ok2)
   end,

   % All numbers satisfy q/1
   if forany($member(X,[1,2,3]),$q(X)) then
      println(ok3)
   else
     println(not_ok3)
   end,

   % No number satisfy q/1
   if not forany($member(X,[20,21,22,23]),$q(X)) then
      println(ok4)
   else
     println(not_ok4)
   end,

   % Not all numbers satisfy p/1
   if forany($q2(X),$p(X)) then
      println(ok5)
   else
     println(not_ok5)
   end,


   % This works as well where 
   %     $(X < 10) 
   % is a lambda like expression
   if forany($member(X,[1,2,3,4]),$(X < 10)) then
      println(ok6)
   else
     println(not_ok6)
   end,

   % No number is < 10
   if not forany($member(X,[10,20,21,22,23]),$(X < 10)) then
      println(ok7)
   else
     println(not_ok7)
   end,

   if forany($member(X,[1,2,3]),$(p(X),println(x=X))) then
      println(ok8)
   else
     println(not_ok8)
   end,
   nl.

%
% Test of prime_n/1
%
go4 :-
  Map = get_global_map(),
  Max = 1_000_000,
  Map.put(count,0),
  Map.put(max,Max),
  between(1,Max,N),
  (prime_n(N) -> Map.put(count,Map.get(count)+1),println(N) ; true),
  fail,
  nl.
go4 :-
  Map = get_global_map(),
  Count=Map.get(count),
  println(count=Count),
  Max = Map.get(max),
  % Checking the result
  println(count=count_all((between(1,Max,N),prime(N)))).

% 
% From
% https://mvolkmann.github.io/blog/topics/#/blog/prolog/
% ->
% maisey is a treeing_walker_coonhound.
% oscar is a german_shorthaired_pointer.
% ramsay is a native_american_indian_dog.
%
go5 :-
  forall(
    ($dog(Name, Breed), Name != comet),
    $printf("%w is a %w.%n", Name, Breed)
  ).
  


% predicate to test
p(X) => X < 10.

q(X) => member(X,[1,2,3]).

q2(X) => member(X,[1,2,13]).

z(X,Y) => X =:= Y.

%
% From B-Prolog: http://www.probp.com/manual/node35.html
%
forall(Generate, Test) => not (call(Generate), not call(Test)).

% From https://www.swi-prolog.org/pldoc/man?predicate=forall/2
forany(Cond,Action) :-
  \+forall(Cond,\+Action).


% From https://www.swi-prolog.org/pldoc/man?predicate=forall/2
% """
% From http://rosettacode.org/wiki/Primality_by_trial_division#Prolog
% """
prime_n(2).
prime_n(N) :-
  % between(3, 10000000, N),
  N >= 3,
  1 = N mod 2,             % odd
  M = floor(sqrt(N+1)),    % round-off paranoia
  Max = (M-1) // 2,        % integer division
  % Note the escaping of between/3 and N mod ...
  forall( $between(1, Max, I), $(N mod (2*I+1) > 0) ).


% From https://mvolkmann.github.io/blog/topics/#/blog/prolog/
% Used in go5/0
dog(comet, whippet).
dog(maisey, treeing_walker_coonhound).
dog(oscar, german_shorthaired_pointer).
dog(ramsay, native_american_indian_dog).