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|
class Cube0 {
method compute(n)
requires n >= 0;
{
var v [v == n*n*n];
}
}
class Cube1 refines Cube0 {
transforms compute(n)
{
replaces v by {
var i := 0;
var v := 0;
while (i < n)
invariant i <= n
invariant v == i * i * i
{
i := i + 1;
var v [v == i * i * i];
}
}
}
}
class Cube2 refines Cube1 {
transforms compute(n)
{
_
var w := 1;
while
invariant w == (i+1)*(i+1)*(i+1) - i*i*i
{
_
replaces v by {
v := v + w;
var w [w == (i+1)*(i+1)*(i+1) - i*i*i];
}
}
_
}
}
class Cube3 refines Cube2 {
transforms compute(n)
{
_
var x := 0;
while
invariant x == i*i
{
_
replaces w by {
x := x + 2*i - 1;
w := 3*x + 3*i + 1;
}
}
_
}
}
|
