Proof of a if statement total correctness

Asked Nov 26 '19 at 11:07

Active Nov 27 '19 at 15:48

Viewed 242 times

The program I need to prove is

if(x>y){
   z=x;
}else{
   z=y;
}

And I need to show that (where the P here should be the program above) is vaild, what I can do is to prove its partial correctness, but how to prove its total correctness?

Here is my proof of the partial correctness:

    {T}
    {(x>y -> x=max(x,y) ) ∧ (\neg(x>y) -> y=max(x,y) ) }  
    if (x>y)
        {T∧x>y}   If-statement
        {x=max(x,y)}   Implied
   z=x
        {z=max(x,y)}  Assignment
   else
        {T∧¬(x>y)}  If-statement
        {y=max(x,y)}  Implied
    z=y
        {z=max(x,y)}  Assignment
    fi  
        {z=max(x,y)}  If-statement

edited Nov 27 '19 at 15:48

asked Nov 26 '19 at 11:07

Roy Shell

1

Can u kindly explain what partial correctness and total correctness is? – Deepak Tatyaji Ahire Nov 26 '19 at 11:40
Show us the 'partial correctness'-proof. This may help. – MrSmith42 Nov 26 '19 at 11:45
1

@DeepakTatyajiAhire Partial correctness is to show that an algorithm yields the correct result (if any), total correctness is to also show that it always terminates. – Emily Nov 27 '19 at 14:51
Ok,I edit my question and add the partial correctness proof to it. @MrSmith42 – Roy Shell Nov 27 '19 at 15:45
@DeepakTatyajiAhire What Emily try to explain is what I want to say – Roy Shell Nov 27 '19 at 15:52
1

The program always does one comparison, one conditional jump forwards and one assignment; how could it not terminate? – kaya3 Dec 01 '19 at 17:02

Proof of a if statement total correctness

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