MinPlus semi-ring (http://d.hatena.ne.jp/m-hiyama/20151202/1449016930)

fstropical.fs

namespace fstropical

type MinPlus = 
    struct
        val value: float
        new(x: float) = { value = x }
        override this.ToString() =
            if this.value = System.Double.PositiveInfinity then "∞" else string this.value
        static member Zero = new MinPlus(System.Double.PositiveInfinity)
        static member One = new MinPlus(0.0)
        static member (+) (x: MinPlus, y: MinPlus) = new MinPlus(min x.value y.value)
        static member (*) (x: MinPlus, y: MinPlus) = new MinPlus(x.value + y.value)
        static member op_Explicit (x: float) = new MinPlus(x)
    end

module NumericLiteralQ =
    let FromZero() = new MinPlus(0.0)
    let FromOne() = new MinPlus(1.0)
    let FromInt32 (i: int) = new MinPlus(float i)

Program.fs

open System
open LanguagePrimitives
open fstropical

[<EntryPoint>]
let main argv = 
    printfn "%s" "Custom Numeric Literal Prefix"
    printf "(0Q, 1Q, 15Q) = "
    printfn "%A" (0Q, 1Q, 15Q) // (0, 1, 15)
    printfn ""

    printfn "%s" "Explicit Type Conversion"
    printf "(MinPlus 0.0, MinPlus 1.0, MinPlus Double.PositiveInfinity) = "
    printfn "%A" (MinPlus 0.0, MinPlus 1.0, MinPlus Double.PositiveInfinity) // (0, 1, ∞)
    printfn ""

    printfn "%s" "Tropical Identity Elements"
    printf "(MinPlus.Zero, MinPlus.One) = "
    printfn "%A" (MinPlus.Zero, MinPlus.One) // (∞, 0)
    printfn ""

    printfn "%s" "Tropical Identity Elements (Generic)"
    let (generic0: MinPlus, generic1: MinPlus) = (GenericZero, GenericOne)
    printf "(GenericZero, GenericOne) = "
    printfn "%A" (generic0, generic1) // (∞, 0)
    printfn ""

    let inf = MinPlus Double.PositiveInfinity
    printfn "1 + 1 = %A" (1Q + 1Q) // 1
    printfn "2 + 3 = %A" (2Q + 3Q) // 2
    printfn "2 * 3 = %A" (2Q * 3Q) // 5
    printfn "2 * 0 = %A" (2Q * 0Q) // 2
    printfn "3 + ∞ = %A" (3Q + inf) // 3
    printfn "3 * ∞ = %A" (3Q * inf) // ∞

    0

result.png