Presburger Arithmetic and Its Use in Verification

APPENDIX B. SOURCE CODE OF EXPERIMENTS
acc2.Add(c1)
merge(n1−1, n2, l1, l2, t1, t2, acc1, acc2)
else
if c2 0 then
acc1.Add(v2)
acc2.Add(c2)
merge(n1, n2−1, l1, l2, t1, t2, acc1, acc2)
let (++) (t1: Term) (t2:Term) =
let l1 = t1.vars.Length
let l2 = t2.vars.Length
let acc1 = new ResizeArray(l1 + l2)
let acc2 = new ResizeArray(l1 + l2)
merge(l1, l2, l1, l2, t1, t2, acc1, acc2)
Term(t1.constant + t2.constant, acc1.ToArray(), acc2.ToArray())
let (~~) (t: Term) =
Term(−t.constant, t.vars, Array.map (fun c −> −c) t.coeffs)
let (−−) t1 t2 = t1 ++ ( ~~ t2)
let (∗∗)a (t: Term) =
if a =0then Zero
elif a =1then t
else
Term(a∗t.constant, t.vars, Array.map (fun c −> a∗c) t.coeffs)
let (∗/∗)(t: Term) a =
if a =0then invalidArg "Term" "Division␣by␣zero"
elif a =1then t
else
Term(t.constant/a, t.vars, Array.map (fun c −> c/a) t.coeffs)
let rec findIndex f xs i =
if i >= Array.length xs then −1
elif fxs.[i] then i
else findIndex f xs (i+1)
// Find coefficient of variable x in term t
let findCoeff (t: Term, x) =
try
let i = Array.findIndex (fun v −> v = x) t.vars
t.coeffs.[i]
with
|:?System.Collections.Generic.KeyNotFoundException −> 0
// Filter out variable x in term t
let filterOut (t: Term, x): Term =
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