module Logic.Board;

open import Stdlib.Prelude;
open import Stdlib.Debug.Fail;
open import Logic.Square public;
open import Logic.Symbol public;
open import Logic.Extra;

--- A 3x3 grid of ;Square;s
type Board :=
  | board : List (List Square) → Board;

--- Returns the list of numbers corresponding to the empty ;Square;s
possibleMoves : List Square → List Nat;
possibleMoves nil := nil;
possibleMoves (empty n :: xs) := n :: possibleMoves xs;
possibleMoves (_ :: xs) := possibleMoves xs;

--- ;true; if all the ;Square;s in the list are equal
full : List Square → Bool;
full (a :: b :: c :: nil) := ==Square a b && ==Square b c;
full _ := fail "full";

diagonals : List (List Square) → List (List Square);
diagonals ((a1 :: _ :: b1 :: nil)
  :: (_ :: c :: _ :: nil)
  :: (b2 :: _ :: a2 :: nil)
  :: nil) := (a1 :: c :: a2 :: nil) :: (b1 :: c :: b2 :: nil) :: nil;
diagonals _ := fail "diagonals";

columns : List (List Square) → List (List Square);
columns := transpose;

rows : List (List Square) → List (List Square);
rows := id;

--- Textual representation of a ;List Square;
showRow : List Square → String;
showRow xs := concat (surround "|" (map showSquare xs));

showBoard : Board → String;
showBoard (board squares) :=
  unlines (surround "+---+---+---+" (map showRow squares));