(defun crisp (x a b crisp)
  "Return a point in a sigmoid function centered ar (a - b)/2"
  (labels ((as100 (x min max)
	     (+ -50 (* 100 (/ (- x min) (- max min))))))
    (/ 1 (+ 1 (exp (* -1 (as100 x a b) crisp))))))
  
(defun fuzzy-grade (x &optional (a 0) (b 1) (slope 0.1))
  (crisp x a b slope))

(defun fuzzy-triangle (x a b c) 
  (max 0 (min (/ (- x a) (- b a))
	      (/ (- c x) (- c b)))))

(defun fuzzy-trapezoid (x a b c d)
  (max 0 (min (/ (- x a) (- b a))
	      1
	      (/ (- d x) (- d c)))))

(defun dist (d what)  
  (case what
    (range    '(close medium far))
    (close     (fuzzy-triangle d -30 0 30))
    (medium    (fuzzy-trapezoid  d 10 30  50 70))
    (far       (fuzzy-grade      d 0.3  50 100))
    (t         (warn "~a not known to dist" what))))

(defun size (s what)
  (case what
    (range    '(tiny small moderate large))
    (tiny      (fuzzy-triangle  s -10 0 10))
    (small     (fuzzy-trapezoid s 2.5 10 15 20))
    (moderate  (fuzzy-trapezoid s 15 20 25 30))
    (large     (fuzzy-grade     s 0.3 25 40))
    (t          (warn "~a not known to size " what))))


(defmacro $and (&rest l) `(min ,@l))
(defmacro $or  (&rest l) `(max ,@l))
(defun    $not (x)       (- 1 x))

(defun fuzzy-deploy (d s what)
  (macrolet (($if (x y) `($and (dist d ',x) (size s ',y))))
    (case what
      (range  '(low medum high))
      (low    ($or ($if medium tiny)
		   ($if far    tiny)
		   ($if medium small)
		   ($if far    small)))
      (medium ($or ($if close  tiny)
		   ($if medium moderate)))
      (high   ($or ($if close  small)
		   ($if close  moderate)
		   ($if close  large)
		   ($if medium moderate)))
      (t      (warn "~a not known to fuzzy-deploy" what)))))

(defun defuzzy-deploy (&key distance size)
  "Return how many marines to deply"
  (let ((low    (fuzzy-deploy distance size 'low))
	(medium (fuzzy-deploy distance size 'medium))
	(high   (fuzzy-deploy distance size 'high)))
    (round 
     (/ (+ (* 10 low) (* 30 medium) (* 50 high))
	(+ low medium high)))))

(defun demo1 ()
  "how many maries to call out?"
  (defuzzy-deploy :distance 25 :size 8))