godelian-toolkit.fsx

////////////////////////////////////////////////////////////////////////
///  The Gödelian Toolkit
////////////////////////////////////////////////////////////////////////

module GodelianTooklit

let sqrt (z: bigint) : bigint =
    if z < 0I then
        invalidArg "z" "Cannot compute the square root of a negative number"
    elif z = 0I then
        0I
    else
        let rec newtonRaphson (x: bigint) : bigint =
            let nextX = (x + z / x) / 2I
            if nextX >= x then x else newtonRaphson nextX

        newtonRaphson z

let encodePair (z: bigint) : bigint * bigint =
    let m = sqrt (z)
    let m2 = m * m
    if z - m2 < m then (z - m2, m) else (m, m2 + 2I * m - z)

let (|Pair|) = encodePair

let decodePair (p: bigint * bigint) : bigint =
    let (x, y) = p
    let m = max x y
    m * m + m + x - y


let combineChoices functionList =
    let length = bigint (List.length functionList)

    let rec chooseFunction n =
        let (d, r) = bigint.DivRem(n, length)
        let f = functionList.[int (r)]
        f chooseFunction d

    chooseFunction