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Staged Ackermann

Partial evaluating the Ackermann function.

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// http://lambda-the-ultimate.org/node/4039#comment-61431

open Microsoft.FSharp.Quotations

// <@ fun x -> (% <@ x @> ) @> ~ lambda (fun x -> x)
let lambda (f : Expr<'T> -> Expr<'R>) : Expr<'T -> 'R> =
    let var = new Var("__temp__", typeof<'T>)
    Expr.Cast<_>(Expr.Lambda(var,  f (Expr.Cast<_>(Expr.Var var))))

// Staged fixed-point combinator
let fix : (Expr<'T -> 'R> -> Expr<'T -> 'R>) -> Expr<'T -> 'R> = fun f ->
    <@ fun x -> let rec loop x = (% lambda (fun f' -> f f') ) loop x in loop x @>

let rec ack (m : int) : Expr<int -> int> = 
    fix (fun f -> lambda (fun (n : Expr<int>) ->
        if m = 0 then <@ %n + 1 @>
        else <@ if %n = 0 then (% ack (m - 1)) 1
                else (% ack (m - 1)) ((%f) (%n - 1)) @>)) 

// Example 
let ack2 = ack 2 // m=2
namespace Microsoft
namespace Microsoft.FSharp
namespace Microsoft.FSharp.Quotations
val lambda : f:(Expr<'T> -> Expr<'R>) -> Expr<('T -> 'R)>

Full name: Script.lambda
val f : (Expr<'T> -> Expr<'R>)
Multiple items
type Expr =
  override Equals : obj:obj -> bool
  member GetFreeVars : unit -> seq<Var>
  member Substitute : substitution:(Var -> Expr option) -> Expr
  member ToString : full:bool -> string
  member CustomAttributes : Expr list
  member Type : Type
  static member AddressOf : target:Expr -> Expr
  static member AddressSet : target:Expr * value:Expr -> Expr
  static member Application : functionExpr:Expr * argument:Expr -> Expr
  static member Applications : functionExpr:Expr * arguments:Expr list list -> Expr
  ...

Full name: Microsoft.FSharp.Quotations.Expr

--------------------
type Expr<'T> =
  inherit Expr
  member Raw : Expr

Full name: Microsoft.FSharp.Quotations.Expr<_>
val var : Var
Multiple items
type Var =
  interface IComparable
  new : name:string * typ:Type * ?isMutable:bool -> Var
  member IsMutable : bool
  member Name : string
  member Type : Type
  static member Global : name:string * typ:Type -> Var

Full name: Microsoft.FSharp.Quotations.Var

--------------------
new : name:string * typ:System.Type * ?isMutable:bool -> Var
val typeof<'T> : System.Type

Full name: Microsoft.FSharp.Core.Operators.typeof
static member Expr.Cast : source:Expr -> Expr<'T>
static member Expr.Lambda : parameter:Var * body:Expr -> Expr
static member Expr.Var : variable:Var -> Expr
val fix : f:(Expr<('T -> 'R)> -> Expr<('T -> 'R)>) -> Expr<('T -> 'R)>

Full name: Script.fix
val f : (Expr<('T -> 'R)> -> Expr<('T -> 'R)>)
val x : 'T
val loop : ('T -> 'R)
val f' : Expr<('T -> 'R)>
val ack : m:int -> Expr<(int -> int)>

Full name: Script.ack
val m : int
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 f : Expr<(int -> int)>
val n : Expr<int>
val ack2 : Expr<(int -> int)>

Full name: Script.ack2
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More information

Link:http://fssnip.net/tx
Posted:1 year ago
Author:Nick Palladinos
Tags: staging , ackermann