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Normalisation by evaluation

Normalisation of "F# quotations" by evaluation.

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open System
open Microsoft.FSharp.Quotations
open Microsoft.FSharp.Quotations.Patterns


// Helper active patters for System.Type
let (|Arrow|_|) (t : Type) = 
    if t.IsGenericType && t.GetGenericTypeDefinition() = typedefof<_ -> _> then
        let args = t.GetGenericArguments()
        Some (args.[0], args.[1])
    else
        None

let (|Base|_|) (t : Type) =
    if t = typeof<obj> then
        Some t
    else
        None


// Semantic Domain
type Sem = 
    | Lam of (Sem -> Sem)
    | Expr of Expr

// reflect : Expr -> Sem
let rec reflect (expr : Expr) = 
    match expr.Type with
    | Arrow (a, b) -> 
        Lam (fun sem -> reflect <| Expr.Application(expr, reify a sem)) 
    | Base _ -> Expr expr 
    | t -> failwithf "Not supported, type: %s" t.Name

// reify : Type -> Sem -> Expr
and reify (t : Type) (sem : Sem) = 
    match t, sem with
    | Arrow (a, b), Lam f -> 
        let var = new Var("var", a) // fresh var
        Expr.Lambda(var, reify b (f (reflect (Expr.Var(var)))))
    | Base _, Expr expr -> expr
    | _ -> failwith "Invalid state"

// meaning : Map<Var, Sem> -> Expr -> Sem
let rec meaning (ctx : Map<Var, Sem>) (expr : Expr) = 
    match expr with
    | Var var -> ctx.[var]
    | Lambda (var, body) -> 
        Lam (fun sem -> meaning (Map.add var sem ctx) body)
    | Application (f, s) -> 
        match meaning ctx f with
        | Lam f' -> f' (meaning ctx s)
        | _ -> failwith "Invalid state"
    | _ -> failwithf "Not supported, expr: %A" expr

// nbe : Expr -> Expr
let nbe (expr : Expr) = 
    reify expr.Type (meaning Map.empty expr)

// Example
let K () = <@ fun x y -> x @>
let S () = <@ fun x y z -> x z (y z) @>
let SKK () = <@ (%S ()) (%K ()) (%K ()) @>

nbe <| SKK () // Lambda (var, var)
namespace System
namespace Microsoft
namespace Microsoft.FSharp
namespace Microsoft.FSharp.Quotations
module Patterns

from Microsoft.FSharp.Quotations
val t : Type
type Type =
  inherit MemberInfo
  member Assembly : Assembly
  member AssemblyQualifiedName : string
  member Attributes : TypeAttributes
  member BaseType : Type
  member ContainsGenericParameters : bool
  member DeclaringMethod : MethodBase
  member DeclaringType : Type
  member Equals : o:obj -> bool + 1 overload
  member FindInterfaces : filter:TypeFilter * filterCriteria:obj -> Type[]
  member FindMembers : memberType:MemberTypes * bindingAttr:BindingFlags * filter:MemberFilter * filterCriteria:obj -> MemberInfo[]
  ...

Full name: System.Type
property Type.IsGenericType: bool
Type.GetGenericTypeDefinition() : Type
val typedefof<'T> : Type

Full name: Microsoft.FSharp.Core.Operators.typedefof
val args : Type []
Type.GetGenericArguments() : Type []
union case Option.Some: Value: 'T -> Option<'T>
union case Option.None: Option<'T>
val typeof<'T> : Type

Full name: Microsoft.FSharp.Core.Operators.typeof
type obj = Object

Full name: Microsoft.FSharp.Core.obj
type Sem =
  | Lam of (Sem -> Sem)
  | Expr of Expr

Full name: Script.Sem
union case Sem.Lam: (Sem -> Sem) -> Sem
Multiple items
union case Sem.Expr: Expr -> Sem

--------------------
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 reflect : expr:Expr -> Sem

Full name: Script.reflect
val expr : Expr
property Expr.Type: Type
active recognizer Arrow: Type -> (Type * Type) option

Full name: Script.( |Arrow|_| )
val a : Type
val b : Type
val sem : Sem
static member Expr.Application : functionExpr:Expr * argument:Expr -> Expr
val reify : t:Type -> sem:Sem -> Expr

Full name: Script.reify
active recognizer Base: Type -> Type option

Full name: Script.( |Base|_| )
val failwithf : format:Printf.StringFormat<'T,'Result> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.failwithf
property Reflection.MemberInfo.Name: string
val f : (Sem -> Sem)
val var : Var
Multiple items
active recognizer Var: Expr -> Var option

Full name: Microsoft.FSharp.Quotations.Patterns.( |Var|_| )

--------------------
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:Type * ?isMutable:bool -> Var
static member Expr.Lambda : parameter:Var * body:Expr -> Expr
static member Expr.Var : variable:Var -> Expr
val failwith : message:string -> 'T

Full name: Microsoft.FSharp.Core.Operators.failwith
val meaning : ctx:Map<Var,Sem> -> expr:Expr -> Sem

Full name: Script.meaning
val ctx : Map<Var,Sem>
Multiple items
module Map

from Microsoft.FSharp.Collections

--------------------
type Map<'Key,'Value (requires comparison)> =
  interface IEnumerable
  interface IComparable
  interface IEnumerable<KeyValuePair<'Key,'Value>>
  interface ICollection<KeyValuePair<'Key,'Value>>
  interface IDictionary<'Key,'Value>
  new : elements:seq<'Key * 'Value> -> Map<'Key,'Value>
  member Add : key:'Key * value:'Value -> Map<'Key,'Value>
  member ContainsKey : key:'Key -> bool
  override Equals : obj -> bool
  member Remove : key:'Key -> Map<'Key,'Value>
  ...

Full name: Microsoft.FSharp.Collections.Map<_,_>

--------------------
new : elements:seq<'Key * 'Value> -> Map<'Key,'Value>
active recognizer Lambda: Expr -> (Var * Expr) option

Full name: Microsoft.FSharp.Quotations.Patterns.( |Lambda|_| )
val body : Expr
val add : key:'Key -> value:'T -> table:Map<'Key,'T> -> Map<'Key,'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Map.add
active recognizer Application: Expr -> (Expr * Expr) option

Full name: Microsoft.FSharp.Quotations.Patterns.( |Application|_| )
val f : Expr
val s : Expr
val f' : (Sem -> Sem)
val nbe : expr:Expr -> Expr

Full name: Script.nbe
val empty<'Key,'T (requires comparison)> : Map<'Key,'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Map.empty
val K : unit -> Expr<('a -> 'b -> 'a)>

Full name: Script.K
val x : 'a
val y : 'b
val S : unit -> Expr<(('a -> 'b -> 'c) -> ('a -> 'b) -> 'a -> 'c)>

Full name: Script.S
val x : ('a -> 'b -> 'c)
val y : ('a -> 'b)
val z : 'a
val SKK : unit -> Expr<('a -> 'a)>

Full name: Script.SKK
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More information

Link:http://fssnip.net/q1
Posted:2 years ago
Author:Nick Palladinos
Tags: quotations