I’ve just recently discovered the functional programming style […]
Well, recently I was given a chance to give a talk on how to reduce
software development efforts, and I
wanted to introduce the concept of
functional programming.
If you’ve only just discovered functional programming, I do not recommend trying to speak authoritatively on the subject. I know for the first 6 months while I was learnig F#, all of my code was just C# with a little more awkward syntax. However, after that period of time, I was able to write consistently good code in an idiomatic, functional style.
I recommend that you do the same: wait for 6 months or so until functional programming style comes more naturally, then give your presentation.
I’m trying to
illustrate the benefits of functional
programming, and I had the idea of
showing people 2 set of code that does
the same thing, one coded in a very
imperative way, and the other in a
very functional way, to show that
functional programming can made code
way shorter, easier to understand and
thus maintain. Is there such example,
beside the famous sum of squares
example by Luca Bolognese?
I gave an F# presentation to the .NET users group in my area, and many people in my group were impressed by F#’s pattern matching. Specifically, I showed how to traverse an abstract syntax tree in C# and F#:
using System;
namespace ConsoleApplication1
{
public interface IExprVisitor<t>
{
t Visit(TrueExpr expr);
t Visit(And expr);
t Visit(Nand expr);
t Visit(Or expr);
t Visit(Xor expr);
t Visit(Not expr);
}
public abstract class Expr
{
public abstract t Accept<t>(IExprVisitor<t> visitor);
}
public abstract class UnaryOp : Expr
{
public Expr First { get; private set; }
public UnaryOp(Expr first)
{
this.First = first;
}
}
public abstract class BinExpr : Expr
{
public Expr First { get; private set; }
public Expr Second { get; private set; }
public BinExpr(Expr first, Expr second)
{
this.First = first;
this.Second = second;
}
}
public class TrueExpr : Expr
{
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class And : BinExpr
{
public And(Expr first, Expr second) : base(first, second) { }
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class Nand : BinExpr
{
public Nand(Expr first, Expr second) : base(first, second) { }
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class Or : BinExpr
{
public Or(Expr first, Expr second) : base(first, second) { }
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class Xor : BinExpr
{
public Xor(Expr first, Expr second) : base(first, second) { }
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class Not : UnaryOp
{
public Not(Expr first) : base(first) { }
public override t Accept<t>(IExprVisitor<t> visitor)
{
return visitor.Visit(this);
}
}
public class EvalVisitor : IExprVisitor<bool>
{
public bool Visit(TrueExpr expr)
{
return true;
}
public bool Visit(And expr)
{
return Eval(expr.First) && Eval(expr.Second);
}
public bool Visit(Nand expr)
{
return !(Eval(expr.First) && Eval(expr.Second));
}
public bool Visit(Or expr)
{
return Eval(expr.First) || Eval(expr.Second);
}
public bool Visit(Xor expr)
{
return Eval(expr.First) ^ Eval(expr.Second);
}
public bool Visit(Not expr)
{
return !Eval(expr.First);
}
public bool Eval(Expr expr)
{
return expr.Accept(this);
}
}
public class PrettyPrintVisitor : IExprVisitor<string>
{
public string Visit(TrueExpr expr)
{
return "True";
}
public string Visit(And expr)
{
return string.Format("({0}) AND ({1})", expr.First.Accept(this), expr.Second.Accept(this));
}
public string Visit(Nand expr)
{
return string.Format("({0}) NAND ({1})", expr.First.Accept(this), expr.Second.Accept(this));
}
public string Visit(Or expr)
{
return string.Format("({0}) OR ({1})", expr.First.Accept(this), expr.Second.Accept(this));
}
public string Visit(Xor expr)
{
return string.Format("({0}) XOR ({1})", expr.First.Accept(this), expr.Second.Accept(this));
}
public string Visit(Not expr)
{
return string.Format("Not ({0})", expr.First.Accept(this));
}
public string Pretty(Expr expr)
{
return expr.Accept(this).Replace("(True)", "True");
}
}
class Program
{
static void TestLogicalEquivalence(Expr first, Expr second)
{
var prettyPrinter = new PrettyPrintVisitor();
var eval = new EvalVisitor();
var evalFirst = eval.Eval(first);
var evalSecond = eval.Eval(second);
Console.WriteLine("Testing expressions:");
Console.WriteLine(" First = {0}", prettyPrinter.Pretty(first));
Console.WriteLine(" Eval(First): {0}", evalFirst);
Console.WriteLine(" Second = {0}", prettyPrinter.Pretty(second));
Console.WriteLine(" Eval(Second): {0}", evalSecond);;
Console.WriteLine(" Equivalent? {0}", evalFirst == evalSecond);
Console.WriteLine();
}
static void Main(string[] args)
{
var P = new TrueExpr();
var Q = new Not(new TrueExpr());
TestLogicalEquivalence(P, Q);
TestLogicalEquivalence(
new Not(P),
new Nand(P, P));
TestLogicalEquivalence(
new And(P, Q),
new Nand(new Nand(P, Q), new Nand(P, Q)));
TestLogicalEquivalence(
new Or(P, Q),
new Nand(new Nand(P, P), new Nand(Q, Q)));
TestLogicalEquivalence(
new Xor(P, Q),
new Nand(
new Nand(P, new Nand(P, Q)),
new Nand(Q, new Nand(P, Q)))
);
Console.ReadKey(true);
}
}
}
The code above is written in an idiomatic C# style. It uses the visitor pattern rather than type-testing to guarantee type safety. This is about 218 LOC.
Here’s the F# version:
#light
open System
type expr =
| True
| And of expr * expr
| Nand of expr * expr
| Or of expr * expr
| Xor of expr * expr
| Not of expr
let (^^) p q = not(p && q) && (p || q) // makeshift xor operator
let rec eval = function
| True -> true
| And(e1, e2) -> eval(e1) && eval(e2)
| Nand(e1, e2) -> not(eval(e1) && eval(e2))
| Or(e1, e2) -> eval(e1) || eval(e2)
| Xor(e1, e2) -> eval(e1) ^^ eval(e2)
| Not(e1) -> not(eval(e1))
let rec prettyPrint e =
let rec loop = function
| True -> "True"
| And(e1, e2) -> sprintf "(%s) AND (%s)" (loop e1) (loop e2)
| Nand(e1, e2) -> sprintf "(%s) NAND (%s)" (loop e1) (loop e2)
| Or(e1, e2) -> sprintf "(%s) OR (%s)" (loop e1) (loop e2)
| Xor(e1, e2) -> sprintf "(%s) XOR (%s)" (loop e1) (loop e2)
| Not(e1) -> sprintf "NOT (%s)" (loop e1)
(loop e).Replace("(True)", "True")
let testLogicalEquivalence e1 e2 =
let eval1, eval2 = eval e1, eval e2
printfn "Testing expressions:"
printfn " First = %s" (prettyPrint e1)
printfn " eval(e1): %b" eval1
printfn " Second = %s" (prettyPrint e2)
printfn " eval(e2): %b" eval2
printfn " Equilalent? %b" (eval1 = eval2)
printfn ""
let p, q = True, Not True
let tests =
[
p, q;
Not(p), Nand(p, p);
And(p, q),
Nand(Nand(p, q), Nand(p, q));
Or(p, q),
Nand(Nand(p, p), Nand(q, q));
Xor(p, q),
Nand(
Nand(p, Nand(p, q)),
Nand(q, Nand(p, q))
)
]
tests |> Seq.iter (fun (e1, e2) -> testLogicalEquivalence e1 e2)
Console.WriteLine("(press any key)")
Console.ReadKey(true) |> ignore
This is 65 LOC. Since it uses pattern matching rather than the visitor pattern, we don’t lose any type-safety, and the code is very easy to read.
Any kind of symbolic processing is orders of magnitude easier to write in F# than C#.
[Edit to add:] Oh, and pattern matching isn’t just a replacement for the visitor pattern, it also allows you to match against the shape of data. For example, here’s a function which converts Nand’s to their equivalents:
let rec simplify = function
| Nand(p, q) when p = q -> Not(simplify p)
| Nand(Nand(p1, q1), Nand(p2, q2))
when equivalent [p1; p2] && equivalent [q1; q2]
-> And(simplify p1, simplify q1)
| Nand(Nand(p1, p2), Nand(q1, q2))
when equivalent [p1; p2] && equivalent [q1; q2]
-> Or(simplify p1, simplify q1)
| Nand(Nand(p1, Nand(p2, q1)), Nand(q2, Nand(p3, q3)))
when equivalent [p1; p2; p3] && equivalent [q1; q2; q3]
-> Xor(simplify p1, simplify q1)
| Nand(p, q) -> Nand(simplify p, simplify q)
| True -> True
| And(p, q) -> And(simplify p, simplify q)
| Or(p, q) -> Or(simplify p, simplify q)
| Xor(p, q) -> Xor(simplify p, simplify q)
| Not(Not p) -> simplify p
| Not(p) -> Not(simplify p)
Its not possible to write this code concisely at all in C#.