Presburger Arithmetic and Its Use in Verification

B.5.
COOPER.FS (EXCERPT)
let rec genTermFormula (x, leftProjection, aLits, bLits, lcm, form) =
let newX = if lcm =1then One else var x
if leftProjection then
bLits |> List.map (fun (c, b) −> match substituteFormula (c, x, b ++ newX)
form with
| And fs −> if c =1then And fs else And ((
D(c, b ++ newX))::fs)
| f −> if c =1then f else And [f; D(c, b
++ newX)]
)
else
aLits |> List.map (fun (c, a) −> match substituteFormula (c, x, a −− newX)
form with
| And fs −> if c =1then And fs else And ((
D(c, a −− newX))::fs)
| f −> if c =1then f else And [f; D(c, a
−− newX)]
)
let elimVariable x formula =
// Choice of left projection or right projection depends on the number of literals.
let divCoeffs, aLits, bLits = retrieveInfo (x, formula)
let leftProjection = aLits.Length >= bLits.Length
//let _ = if leftProjection then bLits.Length |>printfn"Leftprojection:%i"elseaLits
.Length |> printfn "Right projection:%i"
let lcm = divCoeffs |> lcms
match formula with
| SOr(f’, vr) −> match genInfFormula (x, leftProjection, lcm) f’,
genTermFormula (x, leftProjection, aLits, bLits, lcm, f’) with
| TT, _ −> TT
| FF, []−> FF
| FF, fs−> if lcm =1then (fs |> Or, vr) |>SOr else (fs |> Or,
(x, lcm)::vr) |>SOr
| f, []−> if lcm =1then (f, vr) |>SOr else (f, (x, lcm)::vr) |>
SOr
| f, fs −> if lcm =1then (f::fs |> Or, vr) |>SOr else (f::fs
|> Or, (x, lcm)::vr) |>SOr
| _ −> match genInfFormula (x, leftProjection, lcm) formula, genTermFormula (
x, leftProjection, aLits, bLits, lcm, formula) with
| TT, _ −> TT
| FF, []−> FF
| FF, fs−> if lcm =1then fs |> Or else (fs |> Or, [(x, lcm)])
|> SOr
| f, []−> if lcm =1then f else (f, [(x, lcm)]) |> SOr
| f, fs −> if lcm =1then f::fs |> Or else (f::fs |> Or, [(x, lcm
)]) |> SOr
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