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Simple type arithmetic with Peano numbers.

Simple type arithmetic with Peano numbers, using a recursive type and pattern matching over it.

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type Peano = Zero | Succ of Peano
    with
        static member op_Explicit(source: Peano) : int =
            let rec desugar = 
                function
                | Zero   -> 0
                | Succ x -> 1 + desugar x
            desugar source
        override this.ToString() =       
            sprintf "%d" (int this)

let rec add a b =
    match a, b with
    | Zero, b   -> b
    | Succ x, b -> Succ (add x b)

let rec mult a b =
    match a, b with
    | a, Zero   -> Zero
    | a, Succ x -> add a (mult a x)

(*
 * Examples:
*)
let five = add (Succ(Succ(Succ(Zero)))) (Succ(Succ(Zero)))
let fiveAsInt = int five
let report = sprintf "the result is %s" (five.ToString())
let ten =  mult (Succ(Succ(Zero))) (Succ(Succ(Succ(Succ(Succ(Zero))))))
let report' = sprintf "the result is %d" (int ten)
union case Peano.Zero: Peano
union case Peano.Succ: Peano -> Peano
type Peano =
  | Zero
  | Succ of Peano
  override ToString : unit -> string
  static member op_Explicit : source:Peano -> int

Full name: Script.Peano
static member Peano.op_Explicit : source:Peano -> int

Full name: Script.Peano.op_Explicit
val source : Peano
Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>
val desugar : (Peano -> int)
val x : Peano
val this : Peano
override Peano.ToString : unit -> string

Full name: Script.Peano.ToString
val sprintf : format:Printf.StringFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.sprintf
val add : a:Peano -> b:Peano -> Peano

Full name: Script.add
val a : Peano
val b : Peano
val mult : a:Peano -> b:Peano -> Peano

Full name: Script.mult
val five : Peano

Full name: Script.five
val fiveAsInt : int

Full name: Script.fiveAsInt
val report : string

Full name: Script.report
override Peano.ToString : unit -> string
val ten : Peano

Full name: Script.ten
val report' : string

Full name: Script.report'

More information

Link:http://fssnip.net/sq
Posted:4 years ago
Author:Giacomo Stelluti Scala
Tags: types