Presburger Arithmetic and Its Use in Verification

APPENDIX B. SOURCE CODE OF EXPERIMENTS
// The formula is quantifier−free.
let rec elimQuantifier x formula =
match formula with
| SAnd(f, vr) −> (f |> elimQuantifier x, vr) |>SAnd
| SOr(f, vr) −> (f |> elimQuantifier x, vr) |>SOr
| Or fs −> fs |> List.map (elimQuantifier x) |>Or
| _ −> formula |> reduce |> elimVariable x
// Eliminate all quantifiers, one by one.
let rec cooper formula =
match formula with
| Not f −> f |> cooper |> Not
| And fs −> fs |> List.map cooper |> And
| Or fs −> fs |> List.map cooper |> Or
| SAnd(f, vr) −> (f |> cooper, vr) |>SAnd
| SOr(f, vr) −> (f |> cooper, vr) |>SOr
| E(xs, SOr(f, vr))
−> SOr(cooper (E(xs, f)), vr)
| E(xs, Or fs) −> fs |> List.map (fun f −> cooper (E(xs, f))) |> Or
| E(xs, f) −> List.fold (fun acc x −> (elimQuantifier x acc)) (nnf (cooper f))
xs
| A(xs, SAnd(f, vr))
−> SAnd(cooper (A(xs, f)), vr)
| A(xs, And fs) −> fs |> List.map (fun f −> cooper (A(xs, f))) |> And
| A(xs, f) −> Not (List.fold (fun acc x −> (elimQuantifier x acc)) (nnf (cooper
(Not f))) xs)
| _ −> formula
let parMap func fs =
let fs’ =List.map (fun f −> Task.Factory.StartNew(fun() −> func f)) fs
Task.WaitAll(fs’)
List.map (fun (t’: Task) −> t’.Result) fs’
let rec elimQuantifierParallel x formula =
//printfn "var0=%s" x
match formula with
| SAnd(f, vr) −> (f |> elimQuantifierParallel x, vr) |>SAnd
| SOr(f, vr) −> (f |> elimQuantifierParallel x, vr) |>SOr
| Or fs −> //printfn "elim.var=%s, fs=%i" x fs.Length
fs |> parMap (elimQuantifier x) |>Or
| _ −> formula |> reduce |> elimVariable x
// Eliminate all quantifiers, one by one.
let rec cooperParallel formula =
match formula with
| Not f −> f |> cooperParallel |> Not
| And fs −> fs |> List.map cooperParallel |> And
| Or fs −> fs |> List.map cooperParallel |> Or
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