How to best to represent a programming language's grammar?

I've been looking at Haskell and I'd quite like to write a compiler (as a learning exercise) in it, since a lot of it's innate features can be readily applied to a compiler (particularly a recursive decent compiler).

What I can't quite get my head around is how to represent a language's grammar in a Haskell-ian way. My first thought was to use recursive data type definitions, but I can't see how I use them to match against keywords in the language ("if") for example.

Thoughts and suggestions greatly appreciated,

Pete

A recursive data type is fine for this. For example, given the language:

expr ::= var
      |  "true"
      |  "false"
      |  "if" expr "then" expr "else" expr
      |  "(" expr ")"

an example expression in this language would be:

if true then x else (if false then y else true)

Your Haskell data type would look something like this:

data Expr = Var String
          | Lit Bool
          | If Expr Expr Expr

Your parser then takes care to translate, eg, x into Var "x" , and true into Lit True , etc. Ie:

parse "if x then false else true" 
  ==  If (Var "x") (Lit False) (Lit True)

For writing parsers you can roll your own using the techniques mentioned in Norman's answer, or using Parsec or use parser generators like Happy.

You represent programs using mutually recursive algebraic data types, and to parse programs you use parsing combinators . There are a million flavors; you will find three helpful tutorial papers on the schedule for my class for Monday, March 23, 2009. They are