/* 

  Substring primes (Rosetta code) in Picat.

  http://rosettacode.org/wiki/Substring_primes
  """
  Task

  Find all primes in which all substrings (in base ten) are also primes.

  This can be achieved by filtering all primes below 500 (there are 95 of them), but 
  there are better ways.

  Advanced

  Solve by testing at most 15 numbers for primality. Show a list of all numbers tested that were not prime.

  """

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

*/

main => go.


% loop approach

% get all substrings of a number
subs(N) = findall(S, (append(_Pre,S,_Post,N.to_string), S.len > 0) ).

go =>
  Ps = [],
  foreach(Prime in primes(500))
    (foreach(N in subs(Prime)) prime(N.to_int) end -> Ps := Ps ++ [Prime] ; true)
  end,
  println(Ps),
  nl.

% Picat does not have have a return statement (it's a logic programming language)
% We must use cut (!) to ensure that the test does not continue. This is a "red cut"
% which should be avoided if possible...
t(N,false) :-
  not prime(N),!.
t(N,true) :-
  N < 10,!.
t(N,false) :-
  not prime(N mod 100), !.
t(N,false) :-
  not prime(N mod 10),!.
t(N,false) :-
  not prime(N // 10),!.
t(N,true) :-
  N < 100,!.
t(N,false) :-
  not prime(N // 100),!.
t(N,false) :-
  not prime((N mod 100) // 10),!.
t(_N,true).

go2 =>
  println(findall(N,(member(N,1..500),t(N,Status), Status == true))).


% 2 3 5 7 23 37 53 73 373
go3 ?=>
  % is_substring_prime(731),
  P = [],
  foreach(I in 1..500)
    if is_substring_prime(I) then
      println(I),
      P := P ++ [I]
    end
  end,
  println(ps=P),
  nl.
go3 => true.


% {{trans|BASIC256}}
% Picat doesn't not have have a return statement (it's a logic programming language)
is_substring_prime(N) =>
    /*
    (not prime(N) return False),
    (N < 10  return True
    if not prime(N mod 100) then return False
    if not prime(N mod 10)  then return False
    if not prime(N // 10)   then return False
    if n < 100              then return True
    if not prime(N // 100)  then return False
    if not prime((N mod 100) // 10) then return False
    */
    println([cond(prime(N),true,false), N < 10, N mod 100, N mod 10, N // 10, N < 100, N // 100, (N mod 100) // 10]),
    println([cond(not prime(N),true,false),
             cond(N < 10,true,false),
             cond(not prime(N mod 100),true,false),
             cond(not prime(N mod 10),true,false),
             cond(not prime(N // 10),true,false),
             cond(N < 100,true,false),
             cond(not prime(N // 100),true,false),
             cond(not prime((N mod 100) // 10),true,false)]),    
    % Checks = $[
    % [not prime(N), false],
    % [N < 10, true],
    % [not prime(N mod 100), false],
    % [not prime(N mod 10), false],
    % [not prime(N // 10), false],
    % [N < 100, true],
    % [not prime(N // 100), false],
    % [not prime((N mod 100) // 10),false]],
    % foreach([Check,Status] in Checks)
    %   println([check=Check,status=Status]),
    %   Cond = cond(Check,true,false),
    %   println(cond=Cond),
    %   Cond == Status,
    %   println(ok)
    % end,
       
    Return = true,
    if not prime(N)         then Return = false end,
    println(N=check1=Return),
    if Return, N < 10               then Return = true end,
    println(N=check2=Return),
    
    if Return, not prime(N mod 100) then Return = false end,
    println(N=check3=Return),
    
    if Return, not prime(N mod 10)  then Return = false end,
    println(N=check4=Return),
    
    if Return, not prime(N // 10)   then Return = false end,
    println(N=check5=Return),
    
    if Return, N < 100              then Return = true end,
    println(N=check6=Return),
    
    if Return, not prime(N // 100)  then Return = true end,
    println(N=check7=Return),
    
    if Return,not prime((N mod 100) // 10) then Return = false end,
    println(N=check8=Return),
    println(N=ok).