Hoares Method Exercise Consider the following program (written in pseudo-code) begin x:= 0; y:= 1; z:= 1; while y =0} Post: {sqrt2

Hoares Method

Exercise Consider the following program (written in pseudo-code)

begin

x:= 0;

y:= 1;

z:= 1;

while y <= n do

x:= x+1;

z:= z+2;

y:= y+z;

od

sqrt := x;

end

Prove the partial correctness of the program w.r.t. the following predicates:

Pre: {n>=0}

Post: {sqrt2 <= n and n < (sqrt+1)^2 )

That is,

{Pre}

begin

x:= 0;

y:= 1;

z:= 1;

while y <= n do

x:= x+1;

z:= z+2;

y:= y+z;

od

sqrt := x;

end

{Post}