mirror of
https://github.com/Z3Prover/z3
synced 2025-04-05 17:14:07 +00:00
169 lines
3.8 KiB
Plaintext
169 lines
3.8 KiB
Plaintext
; File name: bubble_sort.smt2
|
|
;
|
|
; BUBBLESORT - Copyright (c) March, 2021 - Matteo Nicoli
|
|
;
|
|
; An example of bounded model checking of the classic bubble sort algorithm.
|
|
; we will copy the array values into a list in order to check whether the
|
|
; array is ordered or not. That's because:
|
|
; - it's easier to walk recursively through a list
|
|
; - it gives an example of how list and sequences work in Z3
|
|
;
|
|
|
|
|
|
; size of the array
|
|
(declare-const dim Int)
|
|
|
|
; arrays declaration
|
|
(declare-const A0 (Array Int Int))
|
|
(declare-const A1 (Array Int Int))
|
|
(declare-const A2 (Array Int Int))
|
|
(declare-const A3 (Array Int Int))
|
|
|
|
; indexes declaration
|
|
(declare-const i0 Int)
|
|
(declare-const i1 Int)
|
|
(declare-const i2 Int)
|
|
(declare-const i3 Int)
|
|
|
|
(declare-const j0 Int)
|
|
(declare-const j1 Int)
|
|
(declare-const j2 Int)
|
|
(declare-const j3 Int)
|
|
|
|
(declare-const tmp0 Int)
|
|
(declare-const tmp1 Int)
|
|
(declare-const tmp2 Int)
|
|
|
|
; lists declaration (for post condition)
|
|
(declare-const l0 (List Int))
|
|
(declare-const l1 (List Int))
|
|
(declare-const l2 (List Int))
|
|
(declare-const l3 (List Int))
|
|
(declare-const l4 (List Int))
|
|
|
|
(define-fun init_indexes ((_i Int) (_j Int)) Bool
|
|
(and
|
|
(= _i 0)
|
|
(= _j 0)
|
|
)
|
|
)
|
|
|
|
(define-fun inner_loop
|
|
(
|
|
(_A0 (Array Int Int))
|
|
(_A1 (Array Int Int))
|
|
(tmp Int)
|
|
(_i0 Int)
|
|
(_dim Int)
|
|
) Bool
|
|
(ite
|
|
(> (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)
|
|
)
|
|
)
|
|
|
|
; the body of the bubblesort algorithm
|
|
(define-fun bsort_step
|
|
(
|
|
(_A0 (Array Int Int))
|
|
(_A1 (Array Int Int))
|
|
(tmp Int)
|
|
(_i0 Int)
|
|
(_j0 Int)
|
|
(_i1 Int)
|
|
(_j1 Int)
|
|
(_dim Int)
|
|
) Bool
|
|
(ite
|
|
(< _j0 (- _dim 1))
|
|
(and
|
|
(ite
|
|
(< _i0 (- _dim 1))
|
|
(and
|
|
(inner_loop _A0 _A1 tmp _i0 _dim)
|
|
(= _i1 (+ _i0 1))
|
|
)
|
|
(= _j1 (+ _j0 1))
|
|
)
|
|
(= _j1 (+ _j0 1))
|
|
)
|
|
(and
|
|
(= _j1 (+ _j0 1))
|
|
(= _A1 _A0)
|
|
)
|
|
)
|
|
)
|
|
|
|
; the function by which we check whether the list is ordered
|
|
(define-fun-rec check ((_l (List Int))) Bool
|
|
(ite
|
|
(= _l nil)
|
|
true
|
|
(ite
|
|
(not (= (tail _l) nil))
|
|
(and
|
|
(>= (head _l) (head (tail _l)))
|
|
(check (tail _l))
|
|
)
|
|
true
|
|
)
|
|
)
|
|
)
|
|
|
|
; sets the size of the array
|
|
(assert (= dim 4))
|
|
|
|
; initialization of the counters
|
|
(assert (init_indexes i0 j0))
|
|
|
|
; the first step of the sorting algorithm
|
|
(assert (bsort_step A0 A1 tmp0 i0 j0 i1 j1 dim))
|
|
(assert (bsort_step A1 A2 tmp1 i1 j1 i2 j2 dim))
|
|
(assert (bsort_step A2 A3 tmp2 i2 j2 i3 j3 dim))
|
|
|
|
; filling the list for test
|
|
(assert
|
|
(and
|
|
(= l0 nil)
|
|
(= l1 (insert (select A3 0) l0))
|
|
(= l2 (insert (select A3 1) l1))
|
|
(= l3 (insert (select A3 2) l2))
|
|
(= l4 (insert (select A3 3) l3))
|
|
)
|
|
)
|
|
|
|
(echo "BUBBLE SORT")
|
|
|
|
(push)
|
|
|
|
; (negated) post-condition
|
|
(assert (not (check l4)))
|
|
|
|
(echo "Testing the validity of the algorithm; `unsat` expected: ")
|
|
|
|
; `unsat` expected
|
|
(check-sat)
|
|
|
|
(echo "---------------------")
|
|
|
|
(pop)
|
|
|
|
; post-condition
|
|
(assert (check l4))
|
|
|
|
(echo "Getting a model; `sat` expected: ")
|
|
|
|
; `sat` expected
|
|
(check-sat)
|
|
|
|
(echo "---------------------")
|
|
|
|
(echo "Model: ")
|
|
(get-value (A3))
|
|
(exit)
|