assignment 1~5: fixes

- assignment05/pascal.mlw: lowered the difficulty (one more invariant given)
- assignment02, 03: minor fixes & divide into sub-problems

assets/why3/assignment05/binary_search.mlw

@@ -0,0 +1,22 @@
+(* Binary search
+
+   A classical example. Searches a sorted array for a given value v.
+   Consult <https://gitlab.inria.fr/why3/why3/-/blob/master/examples/binary_search.mlw>.
+ *)
+
+module BinarySearch
+
+  use int.Int
+  use int.ComputerDivision
+  use ref.Ref
+  use array.Array
+
+  let binary_search (a : array int) (v : int) : int
+    requires { forall i1 i2 : int. 0 <= i1 < i2 < length a -> a[i1] <= a[i2] }
+    ensures  { 0 <= result <= length a }
+    ensures  { forall i: int. 0 <= i < result -> a[i] < v }
+    ensures  { forall i: int. result <= i < length a -> v <= a[i] }
+  =
+    (* IMPORTANT: DON'T MODIFY THE ABOVE LINES *)
+    0 (* TODO *)
+end