Create bubble_sort.py (#4976)

examples/python/bounded model checking/bubble_sort.py

@@ -0,0 +1,69 @@
+# BUBBLESORT  -  Copyright (c) June, 2020 - Matteo Nicoli
+
+from z3 import Solver, Int, Array, IntSort, And, Not, If, Select, Store, sat
+
+def init(i,j) :
+    return And(i == 0, j == 0)
+
+def invert(A0, A1, tmp, i0, i1) :
+    return If(Select(A0, i0) > Select(A0, i0 + 1),  \
+                And(tmp == Select(A0, i0),  \
+                    A1 == Store(A0, i0, Select(A0, i0 + 1)),  \
+                    A1 == Store(A0, i0 + 1, tmp)), \
+                A1 == A0)
+
+def bsort_step(A0, A1, tmp, i0, j0, i1, j1, dim) :
+    return If( j0 < dim - 1, \
+                And(         \
+                    If( i0 < dim - 1, \
+                    And(invert(A0, A1, tmp, i0, i1),i1 == i0 + 1), \
+                    i1 == i0 + 1), \
+                    j1 == j0 + 1), \
+                And(j1 == j0 + 1, A1 == A0))
+
+def mk_tran_condition(A, i, j, tmp, dim) :
+    condition = []
+    for _ in range(dim) :
+        condition.append(bsort_step(A[0],A[1],tmp[0],i[0],j[0],i[1],j[1],dim))
+        A = A[1:]
+        i = i[1:]
+        j = j[1:]
+        tmp = tmp[1:]
+    return condition
+
+def check(variables, Ar, dim) :
+    for e in range(dim) :
+        yield variables[e] == Select(Ar,e)
+
+def mk_post_condition(values) :
+    condition = []
+    for v1,v2 in zip(values,values[1:]) :
+        condition.append(v1 <= v2)
+    return And(*condition)
+
+dim = int(input("size of the array: "))
+
+i = [Int(f"i_{x}") for x in range(dim + 1)]
+j = [Int(f"j_{x}") for x in range(dim + 1)]
+A = [Array(f"A_{x}",IntSort(),IntSort()) for x in range(dim + 1)]
+tmp = [Int(f"tmp_{x}") for x in range(dim)]
+
+s = Solver()
+
+init_condition = init(i[0],j[0])
+s.add(init_condition)
+
+tran_condition= mk_tran_condition(A, i, j, tmp, dim)
+s.add(And(*tran_condition))
+
+values = [Int(f"n_{x}") for x in range(dim)]
+init_check_condition = check(values,A[-1],dim)
+s.add(And(*init_check_condition))
+
+post_condition = mk_post_condition(values)
+s.add(Not(post_condition))
+
+if s.check() == sat :
+    print(f"counterexample:\n{s.model()}")
+else :
+    print("valid")