fix traffic jam

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

examples/python/trafficjam.py

@@ -0,0 +1,128 @@
+from z3 import *
+
+class Car():
+    def __init__(self, is_vertical, base_pos, length, start, color):
+        self.is_vertical = is_vertical          
+        self.base = base_pos
+        self.length = length
+        self.start = start
+        self.color = color
+
+    def __eq__(self, other):
+        return self.color == other.color
+
+    def __ne__(self, other):
+        return self.color != other.color
+
+dimension = 6
+
+red_car = Car(False, 2, 2, 3, "red")
+cars = [
+    Car(True, 0, 3, 0, 'yellow'),
+    Car(False, 3, 3, 0, 'blue'),
+    Car(False, 5, 2, 0, "brown"),
+    Car(False, 0, 2, 1, "lgreen"),
+    Car(True,  1, 2, 1, "light blue"),
+    Car(True,  2, 2, 1, "pink"),
+    Car(True,  2, 2, 4, "dark green"),
+    red_car,
+    Car(True,  3, 2, 3, "purple"),
+    Car(False, 5, 2, 3, "light yellow"),
+    Car(True,  4, 2, 0, "orange"),
+    Car(False, 4, 2, 4, "black"),
+    Car(True,  5, 3, 1, "light purple")
+    ]
+
+num_cars = len(cars)
+B = BoolSort()
+bv3 = BitVecSort(3)
+
+
+state = Function('state', [ bv3 for c in cars] + [B])
+
+def num(i):
+    return BitVecVal(i,bv3)
+
+def bound(i):
+    return Const(cars[i].color, bv3)
+
+fp = Fixedpoint()
+fp.set("fp.engine","datalog")
+fp.set("datalog.generate_explanations",True)
+fp.declare_var([bound(i) for i in range(num_cars)])
+fp.register_relation(state)
+
+def mk_state(car, value):
+    return state([ (num(value) if (cars[i] == car) else bound(i)) for i in range(num_cars)])
+
+def mk_transition(row, col, i0, j, car0):
+    body = [mk_state(car0, i0)]
+    for index in range(num_cars):
+        car = cars[index]
+        if car0 != car:
+            if car.is_vertical and car.base == col:
+                for i in range(dimension):
+                    if i <= row and row < i + car.length and i + car.length <= dimension:
+                        body += [bound(index) != num(i)]
+            if car.base == row and not car.is_vertical:
+                for i in range(dimension):
+                    if i <= col and col < i + car.length and i + car.length <= dimension:
+                        body += [bound(index) != num(i)]
+
+    s = "%s %d->%d" % (car0.color, i0, j)
+    fp.rule(mk_state(car0, j), body, s)
+    
+
+def move_down(i, car):
+    free_row = i + car.length
+    if free_row < dimension:
+        mk_transition(free_row, car.base, i, i + 1, car)
+            
+
+def move_up(i, car):
+    free_row = i  - 1
+    if 0 <= free_row and i + car.length <= dimension:
+        mk_transition(free_row, car.base, i, i - 1, car)
+
+def move_left(i, car):
+    free_col = i - 1;
+    if 0 <= free_col and i + car.length <= dimension:
+        mk_transition(car.base, free_col, i, i - 1, car)
+
+
+def move_right(i, car):
+    free_col = car.length + i
+    if free_col < dimension:
+        mk_transition(car.base, free_col, i, i + 1, car)
+
+
+# Initial state:
+fp.fact(state([num(cars[i].start) for i in range(num_cars)]))
+
+# Transitions:
+for car in cars:
+    for i in range(dimension):
+        if car.is_vertical:
+            move_down(i, car)
+            move_up(i, car)
+        else:
+            move_left(i, car)
+            move_right(i, car)
+    
+
+def get_instructions(ans):
+    lastAnd = ans.arg(0).children()[-1]
+    trace = lastAnd.children()[1]
+    while trace.num_args() > 0:
+        print(trace.decl())
+        trace = trace.children()[-1]
+
+
+goal = state([ (num(4) if cars[i] == red_car else bound(i)) for i in range(num_cars)])
+fp.query(goal)
+get_instructions(fp.get_answer())
+
+del goal
+del state
+del fp
+