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Implementing Programming Languages Using C# 4.0

, 12 Jul 2012
An introduction to creating programming language tools using C# 4.0.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Diggins.Jigsaw 
{
    /// <summary>
    /// This class demonstrates the embedding of the un-typed LambdaCalculus in C#. 
    /// There is only type of term in the untyped lambda calculus: a function that returns a function. 
    /// The definitions are taken from: http://en.wikipedia.org/wiki/Lambda_calculus. 
    /// </summary>
    public class LambdaCalculus
    {
        public delegate Lambda Lambda(Lambda x);

        public static Lambda Id         = x => x;
        public static Lambda Zero       = f => x => x;
        public static Lambda True       = x => y => x;
        public static Lambda False      = x => y => y;
        public static Lambda One        = f => x => f(x);
        public static Lambda Two        = f => x => f(f(x));
        public static Lambda Succ       = n => f => x => f(n(f)(x));
        public static Lambda Three      = Succ(Two);
        public static Lambda Pred       = n => f => x => n(g => h => h(g(f)))(u => x)(Id);
        public static Lambda Plus       = m => n => f => x => m(f)(n(f)(x));
        public static Lambda Sub        = m => n => n (Pred) (m);
        public static Lambda And        = p => q => p(q)(p);
        public static Lambda Or         = p => q => p(p)(q);
        public static Lambda Not        = p => a => b => p(b)(a);
        public static Lambda IfThenElse = p => a => b => p(a)(b);
        public static Lambda IsZero     = n => n(x => False)(True);
        public static Lambda IsLtEqOne  = n => IsZero(Pred(n));
        public static Lambda Pair       = x => y => f => f(x)(y);
        public static Lambda First      = pair => pair(True);
        public static Lambda Second     = pair => pair(False);
        public static Lambda Nil        = x => True;
        public static Lambda Null       = p => p(x => y => False);
        public static Lambda LtEq       = x => y => IsZero(Sub(x)(y));
        public static Lambda Gt         = x => y => LtEq(y)(x);
        public static Lambda Eq         = x => y => And(LtEq(x)(y))(LtEq(y)(x));
        
        /// <summary>
        /// Self-application combinator (Mockingbird)
        /// </summary>
        public static Lambda M          = x => x(x);

        /// <summary>
        /// Fixed-point combinator appropriate only for lazy or call-by-name evaluation 
        /// </summary>
        public static Lambda Y          = f => M(x => f(M(x)));

        /// <summary>
        /// Fixed-point combinator appropriate for call by value evaluation (e.g. the one used by C#).
        /// </summary>
        public static Lambda Z          = f => M(x => f(y => M(x)(y)));

        public static Lambda Write(string s) { return (x) => { Console.WriteLine(s); return x; }; }

        public static Lambda SampleList = Pair(Write("I'm first"))(Write("I'm second"));

        public static void Test()
        {
            Console.WriteLine("Expect true");
            True(Write("True"))(Write("False"))(Id);

            Console.WriteLine("Expect false");
            False(Write("True"))(Write("False"))(Id);

            Console.WriteLine("Expect zero");
            IsZero(Zero)(Write("is zero"))(Write("is not zero"))(Id);

            Console.WriteLine("Expect zero");
            IsZero(Pred(One))(Write("is zero"))(Write("is not zero"))(Id);

            Console.WriteLine("Expect not zero");
            IsZero(One)(Write("is zero"))(Write("is not zero"))(Id);

            Console.WriteLine("Expect not zero");
            IsZero(Two)(Write("is zero"))(Write("is not zero"))(Id);

            Console.WriteLine("Expect not zero");
            IsZero(Succ(Zero))(Write("is zero"))(Write("is not zero"))(Id);
            
            Console.WriteLine("Expect <= one");
            IsLtEqOne(One)(Write("is <= one"))(Write("is > one"))(Id);

            Console.WriteLine("Expect <= one");
            IsLtEqOne(Zero)(Write("is <= one"))(Write("is > one"))(Id);

            Console.WriteLine("Expect > one");
            IsLtEqOne(Two)(Write("is <= one"))(Write("is > one"))(Id);

            Console.WriteLine("Expect I'm first");
            First(SampleList)(Id);

            Console.WriteLine("Expect I'm second");
            Second(SampleList)(Id);
        }
    }
}

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This article, along with any associated source code and files, is licensed under The MIT License

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About the Author

Christopher Diggins
Software Developer Autodesk
Canada Canada
This article was written by Christopher Diggins, a computer science nerd who currently works at Autodesk as an SDK specialist.
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