blob: 1a971aed655551d6d4fe09ab70c1e3ee1f4877dd (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
|
// Example of a program computing cube using only addition.
// Step-wise refinement using specification statement.
// Chalice does not have termination metric for recursive methods.
class Cube0 {
method compute(n) returns (v)
requires n >= 0;
ensures v == n*n*n;
{
var v [v == n*n*n]
}
}
class Cube1 refines Cube0 {
transforms compute(n) returns (v, w)
// strengthen post-condition based on new output variables
ensures w == (n+1)*(n+1)*(n+1)-n*n*n;
{
replaces v by {
if (n == 0) {
v := 0;
w := 1;
} else {
call v1,w1 := compute(n-1); // rely on stronger post-condition
v := v1 + w1;
// simplified form: aha! we need n*n to compute with addition
var w [w == 3*n*n + 3*n + 1];
}
}
}
}
class Cube2 refines Cube1 {
transforms compute(n) returns (v, w, x)
ensures x == (n+1)*(n+1);
{
if {
_
x := 1;
} else {
replaces v1, w1 by {
call v1,w1,x1 := compute(n-1);
}
_
replaces w by {
w := 3*x1 + 3*n + 1;
x := x1 + 2*n + 1;
}
}
}
}
|
