Presburger Arithmetic and Its Use in Verification

Appendix B
Source code of experiments
B.1 Utilities.fs
module Utilities
open System
open System.Threading.Tasks
open System.Collections.Concurrent
type System.Threading.Tasks.Task with
static member WaitAll(ts) =
Task.WaitAll [| for t in ts −> t :> Task |]
let (%|)ab=(b % a =0)
let rec gcd(l1, l2) =
if l2 =0then l1 else gcd(l2, l1 % l2)
// Calculate gcd of a list of postive integer.
// Rewrite to use tail recursion.
let gcds ls =
let rec recGcds ls res =
match ls with
|[]−> res
| l::ls’ −> recGcds ls’ (gcd(res, abs(l)))
match ls with
|[]−> 1
|[l]−> abs(l)
| l::ls’ −> recGcds ls’ l
let gcda ls =
Array.fold(fun acc l −> gcd(abs(l), acc)) 1 ls
let lcm(l1, l2) =
(l1 / gcd(l1, l2)) ∗ l2
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