kmc7468/cs220
1
0
Fork 0
mirror of https://github.com/kmc7468/cs220.git synced 2025-12-14 22:18:46 +00:00
Code Issues Packages Projects Releases Wiki Activity

why3 assignment: add one-line comment, fixed max spec

Browse Source
This commit is contained in:
AnHaechan
2023-08-29 07:29:56 +00:00
committed by Jeehoon Kang
parent be4fc57edb
commit e5b80e7365
2 changed files with 24 additions and 14 deletions
Download Patch File Download Diff File Expand all files Collapse all files

32
assets/why3/assignment05/max.mlw
View File

@@ -1,9 +1,14 @@
(* Max
Given an array `a` of natural numbers with length `n`,
return the maximum element of the array.
Given an array `a` of integers with length `n` greater than `0`,
return `max_idx`, the index of the maximum element of that array.
You should stengthen the loop invariant.
E.g. `max_idx [5, 12, 34, 10] 4` will return `2`
E.g. `max_idx [4, 3, 2] 3` will return `0`
E.g. `max_idx [1, 2, 3, 4] 4` will return `3`
Prove the below program indeed follows the given specification,
by giving an appropriate invariant.
*)
module Max
@@ -12,18 +17,21 @@ module Max
use ref.Ref
use array.Array
let max (a: array int) (n: int) : (max: int)
let max_idx (a: array int) (n: int) : (max_idx: int)
requires { length a > 0 }
requires { n = length a }
requires { forall i. 0 <= i < n -> a[i] >= 0 }
ensures { forall i. 0 <= i < n -> a[i] <= max }
ensures { exists i. 0 <= i < n -> a[i] = max }
= let ref max = 0 in
for i = 0 to n - 1 do
ensures { 0 <= max_idx <= n-1 }
ensures { forall i. 0 <= i <= n-1 -> a[i] <= a[max_idx] }
=
let ref max_idx = 0 in
for i = 0 to n-1 do
invariant { 0 <= max_idx <= n-1 }
(* IMPORTANT: DON'T MODIFY THE ABOVE LINES *)
invariant { true (* TODO: Replace `true` with your solution *) }
invariant { true (* TODO: Replace `true` with your solution. Your solution MUST be a single line, at line number 30. DON'T add another line of codes. *) }
(* IMPORTANT: DON'T MODIFY THE BELOW LINES *)
if max < a[i] then max <- a[i];
if a[max_idx] < a[i] then max_idx <- i;
done;
max
max_idx
end