Presburger Arithmetic and Its Use in Verification

B.2.
TERM.FS
B.2 Term.fs
module Term
open Microsoft.FSharp.Collections
open Utilities
type Term = struct
val constant: int
val coeffs: int [] // Order of fields matters
val vars: string []
new(c, vs, cs) ={constant = c; vars = vs; coeffs = cs}
override t.ToString() = "(" + string t.constant + ",␣[" + Array.fold2 (fun acc
vc−> acc + "(" + string v + "," + string c + ")" + ",␣" ) "" t.vars t.
coeffs + "])"
end
let newTerm (c, xs, cs) =Term(c, xs, cs)
let term(c, x) =Term(0, [|x|], [|c|])
let var x = term(1, x)
let constTerm i = Term(i, [||],[||])
let Zero = constTerm 0
let One = constTerm 1
let MinusOne = constTerm −1
let rec merge(n1, n2, l1, l2, t1: Term, t2: Term, acc1: ResizeArray, acc2:
ResizeArray) =
if n1 =0then
for i = l2−n2 to l2−1 do
acc1.Add(t2.vars.[i])
acc2.Add(t2.coeffs.[i])
elif n2 =0then
for i = l1−n1 to l1−1 do
acc1.Add(t1.vars.[i])
acc2.Add(t1.coeffs.[i])
else
let v1 = t1.vars.[l1−n1]
let c1 = t1.coeffs.[l1−n1]
let v2 = t2.vars.[l2−n2]
let c2 = t2.coeffs.[l2−n2]
if v1 = v2 then
if c1 + c2 0 then
acc1.Add(v1)
acc2.Add(c1+c2)
merge(n1−1, n2−1, l1, l2, t1, t2, acc1, acc2)
elif v1 < v2 then
if c1 0 then
acc1.Add(v1)
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