How to abstract a mancala board in lisp - common-lisp

Question

I'm trying to make a Mancala game in Lisp. It's going to have an AI to play against a human player, but I'm stuck. I can't find the way to represent the board as list; the major issue in my mind is how to move the tokens. Here are the references of how to play mancala
I'm thinking about a circular list, but I can't find any clear documentation on how to do that in Lisp.
Sorry about my grammar; English is not my native language.

Answer 1

Now I havent read the rules (sorry!) so this is just to address the idea of using a circular data structure.
A data structure doesnt have to be circular. As long as you pretend it is it will work!
Have a read of the mod function.
;; a1 a6 b1 b6
(defparameter *board* '(nil nil nil nil nil nil nil nil nil nil nil nil))
(defun wrap-position (pos)
(mod pos (length *board*)))
(defun push-token (position)
(push t (nth (wrap-position position) *board*)))
(defun pull-token (position)
(let ((contents (nth (wrap-position position) *board*)))
(setf (nth (wrap-position position) *board*) (rest contents))))
(defun print-board ()
(format t "| ~{~10<~a~>~} |~%| ~{~10<~a~>~} |" (reverse (subseq *board* 6))
(subseq *board* 0 6))
*board*)
Now the technique above is destructive. If you don't know yet what that is in lisp have a google or search here on stackoveflow, there are some good descriptions. It is worth looking into as you may find that your AI want to 'try out' lots of potential moves with 'damaging' the actual game board, a non destructive approach can help with this. The phenomenal book land of lisp has some great info on this.
Here is a simple usage example
CL-USER> *board*
(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL)
CL-USER> (push-token 5)
(T)
CL-USER> *board*
(NIL NIL NIL NIL NIL (T) NIL NIL NIL NIL NIL NIL)
CL-USER> (push-token 5)
(T T)
CL-USER> *board*
(NIL NIL NIL NIL NIL (T T) NIL NIL NIL NIL NIL NIL)
CL-USER> (PULL-token 5)
(T)
CL-USER> *board*
(NIL NIL NIL NIL NIL (T) NIL NIL NIL NIL NIL NIL)
...I change the board before doing the next bit...
CL-USER> (print-board)
| NIL NIL NIL NIL NIL NIL |
| NIL NIL NIL NIL NIL (T T T T) |
Now have a look at Sylwester's answer and see that you can replace the sublists with just a number of stones. You will need to change the print-board obviously but that gives you a very simple model you can manipulate very easily (almost can be the big step you need to make this non-destructive). Have a go!

Answer 2

I would have used an array of 14 fixnums. index 0-5 are pits for A, 6 is A's basket. 7-12 are pits for player B and 13 is B's basket. You do minimax with copy-array.
If you want lists I would have either had A and B's lists individually or interleaved them. You could also just have a list of 14 cons.

Answer 3

Sorry, I couldn't really understand how to play the game, but here's something I could think about w/r to how to go about the board:
(defstruct (mancala-cell
(:print-object
(lambda (cell stream)
(format stream "<stones: ~d>"
(length (mancala-cell-stones cell))))))
(stones nil :type list)
(next nil))
(defun make-cells ()
(labels ((%make-cells (head count)
(let ((next (make-mancala-cell)))
(setf (mancala-cell-next head) next)
(if (> count 0) (%make-cells next (1- count)) next))))
(let* ((first (make-mancala-cell))
(last (%make-cells first 12)))
(setf (mancala-cell-next last) first))))
(defstruct (mancala-board
(:print-object
(lambda (board stream)
(loop :for i :from 0 :below 12
:for cell := (mancala-board-cells board)
:then (mancala-cell-next cell)
:do (princ (case i
(6 #\Newline) (0 "") (otherwise #\-))
stream)
(princ cell stream)))))
(cells (make-cells) :type mancala-cell))
(print (make-mancala-board))
;; <stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>
;; <stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>-<stones: 0>
Then here's one more example:
(defstruct (mancala-cell
(:print-object
(lambda (cell stream)
(format stream "<stones: ~d>"
(mancala-cell-stones cell)))))
(stones 4 :type fixnum))
(defconstant +null-cell+ (make-mancala-cell))
(deftype mancala-grid () '(array mancala-cell (12)))
(defun make-cells ()
(loop
:for i :from 0 :below 12
:with result := (make-array
12 :element-type 'mancala-cell
:initial-element +null-cell+)
:do (setf (aref result i) (make-mancala-cell))
:finally (return result)))
(defstruct (mancala-board
(:print-object
(lambda (board stream)
(loop :for i :from 0 :below 12
:for cell :across (mancala-board-cells board)
:do (princ (case i
(6 #\Newline) (0 "") (otherwise #\-))
stream)
(princ cell stream)))))
(cells (make-cells) :type mancala-grid))
(defun map-cells-in-range (function board &key (start 0) (end 12))
(loop
:for i :from start :below end
:with board := (mancala-board-cells board)
:collect (funcall function (aref board (mod i 12)))))
(defun fold-cells-in-range (function board &key (start 0) (end 12))
(loop
:for i :from start :below (1- end)
:with board := (mancala-board-cells board)
:for cell := (aref board (mod i 12))
:for result := (funcall
function
(aref board (mod i 12))
(aref board (mod (1+ i) 12)))
:then (funcall function result (aref board (mod (1+ i) 12)))
:finally (return result)))
(fold-cells-in-range
(lambda (a b)
(+ (mancala-cell-stones b)
(if (integerp a) a (mancala-cell-stones a))))
(make-mancala-board)) ; 48