// Typed Lambda Calculus in C#

using System;
using System.Collections.Generic;

public class lambdacalc
{
   public static a I<a>(a x) => x;  // type of I is a -> a
   public static Func<b,a> K<a,b>(a x) => (b y) => x; // a->b->a
   public static Func<Func<a,b>,Func<a,c>> S<a,b,c>(Func<a,Func<b,c>> x) =>
      (y) => (z) => x(z)(y(z)); //(a->b->c)->(a->b)->a->c

   public static Func<b,b> ZERO<a,b>(a x) => (y) => y; // KI a->b->b
   public static Func<b,a> ONE<a,b>(a x) => (b y) => x; // a->b->a

   public static Func<a,Func<a,a>> IFELSE<a>(Func<a,Func<a,a>> c) =>
     (x) => (y) => c(x)(y);

   // recursion must be defined as a separate constant in typed lamb. calc.
   public static a FIX<a>(Func<a,a> M) => M(FIX(M));
   
   public static void Main()
   {
      Func<int,int> i = S<int,int,int>(K<int,int>)(I<int>);  // choke!

      int t1 = IFELSE<int>(ONE<int,int>)(1)(2);
      int t2 = IFELSE<int>(ZERO<int,int>)(1)(2);
      Console.WriteLine(t1+" and "+t2);
   }//main
}

// C# is not the right language to do this with: need F#!