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three smt2 examples added and one python example updated (#5690)

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Matteo Nicoli 2021-12-02 01:21:12 +01:00 • committed by GitHub
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; File name: loop_unrolling_bitvec.smt2
;
; Copyright (c) March, 2021 - Matteo Nicoli
;
;
; Let's start considering a simple C program involving an iteration:
;
; #define DIM 2
;
; /* uninterpreted functions */
; long get_number();
; void fill_array(long *A);
;
; int main()
; {
; long x = get_number();
; long A[DIM];
; long i = 0;
; long found = 0;
;
; fill_array(A);
;
; while(i < DIM) {
; if(x == A[i])
; found = 1;
; i++;
; }
; }
;
; Below, we can see its SSA representation in SMT-LIB2.
; Our goal is to verify that, at the end of the program, the variable `found`
; is equal to 1 if, and only if, `x` is an element of the array.
; We define our custom sort `IntValue` that represents a 32-bit integer value.
(define-sort IntValue () (_ BitVec 32))
(declare-const x IntValue)
(declare-const A (Array IntValue IntValue))
(declare-const i_0 IntValue)
(declare-const found_0 IntValue)
(declare-const found_1 IntValue)
(declare-const found_2 IntValue)
(declare-const i_1 IntValue)
(declare-const i_2 IntValue)
; Pre-condition: variables initialization
(assert
(and
(= i_0 #x00000000)
(= found_0 #x00000000)
)
)
; Transition funcion
(define-fun body ((f_0 IntValue) (f IntValue) (i_0 IntValue) (i_1 IntValue)(_A (Array IntValue IntValue)) (_x IntValue)) Bool
(and
(= f (ite (= _x (select _A i_0)) #x00000001 f_0))
(= i_1 (bvadd i_0 #x00000001))
)
)
; Post-condition function
(define-fun post ((_f IntValue) (_i IntValue) (_x IntValue) (_A (Array IntValue IntValue))) Bool
(=
(= _f #x00000001)
(= _x (select _A _i))
)
)
; Transition function is called DIM times:
; for practical reasons, we are considering here DIM = 2
(assert (body found_0 found_1 i_0 i_1 A x))
(assert (body found_1 found_2 i_1 i_2 A x))
(push)
(echo "Bounded model checking with loop unrolling")
(echo "------------------------------------------")
; Post-condition (negated) is called DIM times
(assert
(not
(or
(post found_2 i_0 x A)
(post found_2 i_1 x A)
)
)
)
(echo "Testing the validity of the post-condition: `unsat expected`")
; `unsat` expected
(check-sat)
(pop)
; Post-condition (called DIM times)
(assert
(or
(post found_2 i_0 x A)
(post found_2 i_1 x A)
)
)
(echo "Getting a model; `sat` expected: ")
; `sat` expected
(check-sat)
(echo "------------------------------------------")
(echo "Model: ")
(get-value (x A found_2))
(exit)