Presburger Arithmetic and Its Use in Verification

APPENDIX B. SOURCE CODE OF EXPERIMENTS
B.6 OmegaTest.fs
module OmegaTest
open Microsoft.FSharp.Collections
open Utilities
open Term
// Input: a list of conjunctions and a list of disjunction pairs.
// Output: do cartesian products on the input.
let cartesian (cons, diss) =
let rec cartesianUtil = function
|[]−> [cons]
| L::Ls −> cartesianUtil Ls |> List.collect (fun C −> L |> List.map (fun x
−> x::C))
cartesianUtil diss
exception OmegaTestFail
type CoeffTerm = struct
val coeff: int
val term: Term
new (c, t) ={coeff = c; term = t}
end
// Product all pairs of opposite literals
let merge(outs, lowers: CoeffTerm list, uppers: CoeffTerm list) =
let ins =[for l in lowers do
for u in uppers do
if l.coeff =1||u.coeff =1then
yield ((l.coeff ∗∗ u.term ++ u.coeff ∗∗ l.term) −− One)
else raise OmegaTestFail]
ins@outs
let project(x, fs) =
let outs = List.filter (fun t −> findCoeff(t, x) =0)fs
let lowers =[
for t in fs do
let c = findCoeff(t, x)
if c >0then yield CoeffTerm(c, t)
]
let uppers =[
for t in fs do
let c = findCoeff(t, x)
if c