Add why3 files

assets/why3/ex1_eucl_div.mlw

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+(* Euclidean division
+
+   1. Prove soundness, i.e. (division a b) returns an integer q such that
+      a = bq+r and 0 <= r < b for some r.
+      (You have to strengthen the precondition.)
+
+      Do you have to require b <> 0? Why?
+
+   2. Prove termination.
+      (You may have to strengthen the precondition even further.)
+*)
+
+module Division
+
+  use int.Int
+
+  let division (a b: int) : int
+    requires { a > 0 /\ b > 0 }
+    ensures  { exists r: int. a = b * result + r /\ 0 <= r < b }
+  =
+    let ref q = 0 in
+    let ref r = a in
+    while r >= b do
+      invariant { a = b * q + r /\ r >= 0 }
+      variant { r }
+      q <- q + 1;
+      r <- r - b
+    done;
+    q
+
+  let main () =
+    division 1000 42
+
+end