Presburger Arithmetic and Its Use in Verification

APPENDIX B. SOURCE CODE OF EXPERIMENTS
B.7 OmegaTestArray.fs
module OmegaTestArray
open System.Threading.Tasks
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 klls=[|for x in l do
for xs in ls −> Array.append [|x|] xs |]
Array.foldBack k diss [|cons|]
exception OmegaTestFail
type CoeffTerm = struct
val coeff: int
val term: Term
new (c, t) ={coeff = c; term = t}
end
let merge(outs, lowers: CoeffTerm [], uppers: CoeffTerm []) =
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|]
Array.append ins outs
let project(x, fs) =
let outs =[|
for t in fs do
let c = findCoeff(t, x)
if c =0then yield t
|]
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