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This commit is contained in:
Janggun Lee
2024-07-30 15:26:33 +09:00
parent d34f586e4d
commit af889722bc
64 changed files with 452 additions and 384 deletions
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11
assets/why3/assignment05/pascal.mlw
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@@ -17,9 +17,9 @@ module Pascal
ensures { result >= 1 }
= if k = 0 || k = n then 1 else comb (n-1) k + comb (n-1) (k-1)
(* Computes the Pascal's triangle and returns the `n`th row of it. *)
(* Computes Pascal's triangle and returns the `n`th row of it. *)
(* Insert an appropriate invariant so that Why3 can verify this function. *)
(* You SHOULD understand the Pascal's triangle first to find good invariants. *)
(* You should understand Pascal's triangle first to find good invariants. *)
let chooses (n : int) : array int
requires { n > 0 }
ensures { forall i: int.
@@ -28,16 +28,17 @@ module Pascal
let ref row = Array.make 1 1 in
for r = 1 to n do
invariant { length row = r }
invariant { forall c: int. 0 <= c < r -> row[c] = comb (r-1) c }
invariant { forall c: int. 0 <= c < r -> row[c] = comb (r-1) c }
let new_row = Array.make (r+1) 1 in
for c = 1 to r-1 do
(* IMPORTANT: DON'T MODIFY THE ABOVE LINES *)
invariant { true (* TODO: Replace `true` with your solution. Your solution MUST be a single line, at line number 35. DON'T add another lines. *) }
(* TODO: Replace `true` with your solution. Your solution MUST be a single line, at line 36. DON'T add more code above or below. *)
invariant { true }
(* IMPORTANT: DON'T MODIFY THE BELOW LINES *)
new_row[c] <- row[c-1] + row[c]
done;
row <- new_row
done;
row
end