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HLists, Peano & Type-level computations

An experiment on type-level computations.

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type HList = interface end
and HNil = HNil with
    static member inline (|*|) (f, HNil) = f $ HNil
    interface HList
and HCons<'a, 'b when 'b :> HList> = HCons of 'a * 'b with
    static member inline (|*|) (f, HCons(x, xs)) = f $ HCons(x, xs) 
    interface HList 

type Peano = interface end
and Zero = Zero with
    static member inline (|*|) (f, Zero) = f $ Zero
    interface Peano
and Succ<'a when 'a :> Peano> = Succ of 'a  with
    static member inline (|*|) (f, Succ(x)) = f $ Succ(x) 
    interface Peano 

type Bool = interface end
and True = True with
    interface Bool
and False = False with
    interface Bool

let inline (^+^) head tail = HCons(head, tail)

// Examples

type Append = Append with
    static member ($) (Append, HNil) = id
    static member inline ($) (Append, HCons(x, xs)) = fun list ->
        HCons (x, (Append |*| xs) list)

type Length = Length with
    static member ($) (Length, HNil) = Zero
    static member inline ($) (Length, HCons(x, xs)) = Succ (Length |*| xs) 

type Even = Even with
    static member ($) (Even, Zero) = True
    static member inline ($) (Even, Succ (x)) = Odd |*| x 
and Odd = Odd with
    static member ($) (Odd, Zero) = False
    static member inline ($) (Odd, Succ (x)) = Even |*| x 

let first = 1 ^+^ '1' ^+^ HNil
let second =  "1" ^+^ true ^+^ HNil

// result : HCons<int,HCons<char,HCons<string,HCons<bool,HNil>>>>
let result = (Append $ first) second // HCons (1,HCons ('1',HCons ("1",HCons (true,HNil))))
// length : Succ<Succ<Succ<Succ<Zero>>>>
let length = Length $ result // Succ (Succ (Succ (Succ Zero)))
let _ : True = Even $ length // ok
let _ : False = Even $ length // type error
let _ : True = Odd $ length // type error
let _ : False = Odd $ length // ok
Multiple items
union case HNil.HNil: HNil

--------------------
type HNil =
  | HNil
  interface HList
  static member ( |*| ) : f:'a * HNil:HNil -> '_arg5 (requires member ( $ ))

Full name: Script.HNil
val f : 'a (requires member ( $ ))
type HList

Full name: Script.HList
Multiple items
union case HCons.HCons: 'a * 'b -> HCons<'a,'b>

--------------------
type HCons<'a,'b (requires 'b :> HList)> =
  | HCons of 'a * 'b
  interface HList
  static member ( |*| ) : f:'a0 * HCons<'b1,'c> -> '_arg8 (requires member ( $ ) and 'c :> HList)

Full name: Script.HCons<_,_>
val f : 'a (requires member ( $ ) and 'c :> HList)
val x : 'b
val xs : #HList
type Peano

Full name: Script.Peano
Multiple items
union case Zero.Zero: Zero

--------------------
type Zero =
  | Zero
  interface Peano
  static member ( |*| ) : f:'a * Zero:Zero -> '_arg5 (requires member ( $ ))

Full name: Script.Zero
Multiple items
union case Succ.Succ: 'a -> Succ<'a>

--------------------
type Succ<'a (requires 'a :> Peano)> =
  | Succ of 'a
  interface Peano
  static member ( |*| ) : f:'a0 * Succ<'b> -> '_arg8 (requires member ( $ ) and 'b :> Peano)

Full name: Script.Succ<_>
val f : 'a (requires member ( $ ) and 'b :> Peano)
val x : #Peano
type Bool

Full name: Script.Bool
Multiple items
union case True.True: True

--------------------
type True =
  | True
  interface Bool

Full name: Script.True
type False =
  | False
  interface Bool

Full name: Script.False
Multiple items
union case False.False: False

--------------------
type False =
  | False
  interface Bool

Full name: Script.False
val head : 'a
val tail : #HList
Multiple items
union case Append.Append: Append

--------------------
type Append =
  | Append
  static member ( $ ) : Append:Append * HNil:HNil -> ('a -> 'a)
  static member ( $ ) : Append:Append * HCons<'a,'b> -> ('c -> HCons<'a,'d>) (requires 'b :> HList and member ( |*| ) and 'd :> HList)

Full name: Script.Append
val id : x:'T -> 'T

Full name: Microsoft.FSharp.Core.Operators.id
val x : 'a
val xs : 'b (requires 'b :> HList and member ( |*| ) and 'd :> HList)
Multiple items
val list : 'c

--------------------
type 'T list = List<'T>

Full name: Microsoft.FSharp.Collections.list<_>
Multiple items
union case Length.Length: Length

--------------------
type Length =
  | Length
  static member ( $ ) : Length:Length * HNil:HNil -> Zero
  static member ( $ ) : Length:Length * HCons<'a,'b> -> Succ<'_arg7> (requires 'b :> HList and member ( |*| ) and '_arg7 :> Peano)

Full name: Script.Length
val xs : 'b (requires 'b :> HList and member ( |*| ) and '_arg7 :> Peano)
Multiple items
union case Even.Even: Even

--------------------
type Even =
  | Even
  static member ( $ ) : Even:Even * Zero:Zero -> True
  static member ( $ ) : Even:Even * Succ<'b> -> '_arg11 (requires 'b :> Peano and member ( |*| ))

Full name: Script.Even
val x : 'b (requires 'b :> Peano and member ( |*| ))
Multiple items
union case Odd.Odd: Odd

--------------------
type Odd =
  | Odd
  static member ( $ ) : Odd:Odd * Zero:Zero -> False
  static member ( $ ) : Odd:Odd * Succ<'a> -> '_arg14 (requires 'a :> Peano and member ( |*| ))

Full name: Script.Odd
val x : 'a (requires 'a :> Peano and member ( |*| ))
val first : HCons<int,HCons<char,HNil>>

Full name: Script.first
val second : HCons<string,HCons<bool,HNil>>

Full name: Script.second
val result : HCons<int,HCons<char,HCons<string,HCons<bool,HNil>>>>

Full name: Script.result
val length : Succ<Succ<Succ<Succ<Zero>>>>

Full name: Script.length
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More information

Link:http://fssnip.net/d2
Posted:5 years ago
Author:Nick Palladinos
Tags: hlist , type-level computations