Presburger Arithmetic and Its Use in Verification

B.2.
TERM.FS
Term(t.constant, t.vars, Array.map2(fun vc−> if v=x then 0 else c) t.vars t.
coeffs) // Not removing for better performance.
// Substitute variable c∗x in term t by a new term tx
let substitute (c, x, tx, t): Term =
let c0 = findCoeff (t, x)
if c0 =0then t
else
let lcm = lcm(abs(c0), abs(c))
let d = lcm/abs(c0)
let t’ =filterOut (d∗∗t, x)
t’ ++(d∗c0/abs(c)) ∗∗ tx
let rec subst (t: Term, xts) =
match xts with
|[]−> t
|(x, tx)::xts’ −> subst (substitute (1, x, constTerm tx, t), xts’)
let getCoeffsWithoutConst (t: Term) =
List.ofArray t.coeffs
let getCoeffs (t: Term) =
t.constant::getCoeffsWithoutConst(t)
// Note: may change for optimization
let redCoeffs (t: Term) =
let vars =[|for i=0 to t.vars.Length−1 do
if t.coeffs.[i] 0then yield t.vars.[i]
|]
let coeffs = Array.filter(fun c −> c 0) t.coeffs
let t’ =Term(t.constant, vars, coeffs)
let g = getCoeffs t’ |>gcds
if g =0||g =1then t’ else t’ ∗/∗g
let isConstTerm (t: Term) =
Array.isEmpty t.vars || Array.forall (fun c −> c =0)t.coeffs
let getConst (t: Term) =t.constant
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