src/HOL/Boogie/Examples/Boogie_Max.thy
author hoelzl
Thu Sep 02 10:14:32 2010 +0200 (2010-09-02)
changeset 39072 1030b1a166ef
parent 36081 70deefb6c093
child 40163 a462d5207aa6
permissions -rw-r--r--
Add lessThan_Suc_eq_insert_0
     1 (*  Title:      HOL/Boogie/Examples/Boogie_Max.thy
     2     Author:     Sascha Boehme, TU Muenchen
     3 *)
     4 
     5 header {* Boogie example: get the greatest element of a list *}
     6 
     7 theory Boogie_Max
     8 imports Boogie
     9 begin
    10 
    11 text {*
    12 We prove correct the verification condition generated from the following
    13 Boogie code:
    14 
    15 \begin{verbatim}
    16 procedure max(array : [int]int, length : int)
    17   returns (max : int);
    18   requires (0 < length);
    19   ensures (forall i: int :: 0 <= i && i < length ==> array[i] <= max);
    20   ensures (exists i: int :: 0 <= i && i < length ==> array[i] == max);
    21 
    22 implementation max(array : [int]int, length : int) returns (max : int)
    23 {
    24   var p : int, k : int;
    25   max := array[0];
    26   k := 0;
    27   p := 1;
    28   while (p < length)
    29     invariant (forall i: int :: 0 <= i && i < p ==> array[i] <= max);
    30     invariant (array[k] == max);
    31   {
    32     if (array[p] > max) { max := array[p]; k := p; }
    33     p := p + 1;
    34   }
    35 }
    36 \end{verbatim}
    37 *}
    38 
    39 boogie_open "~~/src/HOL/Boogie/Examples/Boogie_Max"
    40 
    41 declare [[smt_certificates="~~/src/HOL/Boogie/Examples/Boogie_Max.certs"]]
    42 declare [[smt_fixed=true]]
    43 
    44 boogie_vc max
    45   using [[z3_proofs=true]]
    46   by boogie
    47 
    48 boogie_end
    49 
    50 end