• API
• FAQ
• Tools
• Archive
daily pastebin goal
31%
SHARE
TWEET

# Untitled

a guest Jan 19th, 2019 50 Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
1. function sum( n :Z) : Z
2.     precondition n_ge_one : n >=1
3.     postcondition sum=n*(n+1)/2
4.     var x : Z
5.         y : Z
6. begin
7.     { x = x /\ n >= 1 }
8.     x := 1
9.     { x = 1 /\ n >= 1 }
10.     { y = y /\ x = 1 /\ n>=1 }
11.     y := 0
12.     { y = 0 /\ x = 1 /\ n>=1 }
13.     while x <= n do
14.     invariant y = (x-1)*x/2 /\ n>=1 /\ x <= n + 1
15.     begin
16.         { y + x = (x-1)*x/2 + x /\ n>=1 /\ x < n + 1 }
17.         y := y + x
18.         { y = (x-1)*x/2 + x /\ n>=1 }
19.         { y = (x + 1 - 2)*(x + 1 - 1)/2 + x + 1 - 1 /\ n>=1 /\ x < n + 1}
20.         x := x + 1
21.         { y = (x-2)*(x-1)/2 + x-1 /\ n>=1 /\ x <= n + 1}
22.     end
23.     { y = n*(n+1)/2}
24.     sum := y
25.     { sum = n*(n+1)/2}
26. end
RAW Paste Data
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.

Top