Presburger Arithmetic and Its Use in Verification

APPENDIX B. SOURCE CODE OF EXPERIMENTS
| f::fs’−> let f’ =func f
if f’ =condVal then condVal else mapUntil(func, condVal, combFunc,
fs’, f’::acc)
let rec genInfFormula (x, leftProjection, lcm) form =
match form with
| C(t, ct) −> match ct with
| EQ −> if findCoeff (t, x) 0then FF
else
if lcm =1then C(filterOut(t, x), ct) else form
| UEQ −> if findCoeff (t, x) 0then TT
else
if lcm =1then C(filterOut(t, x), ct) else form
| GT −> let c = findCoeff (t, x)
if c >0&&leftProjection then FF
elif c if lcm =1then C(filterOut(t, x), ct) else form
| D(i, t) −> if lcm =1then D(i, filterOut(t, x)) else form
| And fs −> mapUntil(genInfFormula (x, leftProjection, lcm), FF, And, fs, [])
| Or fs −> mapUntil(genInfFormula (x, leftProjection, lcm), TT, Or, fs, [])
| Not f −> match genInfFormula (x, leftProjection, lcm) f with
| TT −> FF
| FF −> TT
| f’ −> Not f’
| SAnd(f, vr) −> match genInfFormula (x, leftProjection, lcm) f with
| TT −> TT
| FF −> FF
| SAnd(f’, vr’) −> SAnd(f’, vr’@vr)
| f’ −> SAnd(f’, vr)
| SOr(f, vr) −> match genInfFormula (x, leftProjection, lcm) f with
| TT −> TT
| FF −> FF
| SOr(f’, vr’) −> SOr(f’, vr’@vr)
| f’ −> SOr(f’, vr)
| _ −> form
let rec substituteFormula (c, x, tx) formula =
match formula with
| C(t, ct) −> C(substitute (c, x, tx, t), ct)
| D(i, t) −> D(i, substitute (c, x, tx, t))
| And fs −> fs |> List.map (substituteFormula (c, x, tx)) |> And
| Or fs −> fs |> List.map (substituteFormula (c, x, tx)) |> Or
| SAnd(f, vr) −> (substituteFormula (c, x, tx) f, vr) |>SAnd
| SOr(f, vr) −> (substituteFormula (c, x, tx) f, vr) |>SOr
| Not f −> substituteFormula (c, x, tx) f |> Not
| _ −> formula
80