# recursive descent parser and functional programming

Answer derived from this blog article:

So my question is what would a more traditional functional approach to parsing (i.e. few side effects) look like?

Sounds like you need to separate functional (as in Lisp, Scheme, Standard ML, CAML, OCaml, F#) from purity (absence of side effects, as in Haskell) and incidental language features (algebraic datatypes, pattern matching).

Thanks to algebraic datatypes, pattern matching and higher-order functions, F# is a good for parsing and great for transformations and code generation but most production parsers written in F# are not pure. Historically, the family of languages F# is mostly derived from (the MetaLanguages, or MLs) were bred specifically for this kind of metaprogramming.

Here is a very simple set of mutually-recursive active patterns that parse and evaluate mathematical expressions composed of single digits, `+ - *` operators and bracketed subexpressions:

``````> let rec (|Term|_|) = function
| Factor(e1, t) ->
let rec aux e1 = function
| '+'::Factor(e2, t) -> aux (e1 + e2) t
| '-'::Factor(e2, t) -> aux (e1 - e2) t
| t -> Some(e1, t)
aux e1 t
| _ -> None
and (|Factor|_|) = function
| '-'::Factor(e, t) -> Some(-e, t)
| Atom(e1, '*'::Factor(e2, t)) -> Some(e1 * e2, t)
| Atom(e, t) -> Some(e, t)
| _ -> None
and (|Atom|_|) = function
| c::t when '0'<=c && c<='9' -> Some(int(string c), t)
| '('::Term(e, ')'::t) -> Some(e, t)
| _ -> None;;
val ( |Term|_| ) : char list -> (int * char list) option
val ( |Factor|_| ) : char list -> (int * char list) option
val ( |Atom|_| ) : char list -> (int * char list) option
``````

Here is an example of it being used to parse and evaluate an expression:

``````> let (Term e) = List.ofSeq "1+2*(3-4)*-5";;
val e : int * char list = (11, [])
``````

That’s a pure solution that’s using pattern matching over lists with F#’s active patterns. In reality, you’ll want to define a type for your abstract syntax tree and return a value of that type. This is really easy in F#:

``````type expr =
| Int of int
| Neg of expr
| Add of expr * expr
| Sub of expr * expr
| Mul of expr * expr

static member (~-) f = Neg f
static member (+) (f, g) = Add(f, g)
static member (-) (f, g) = Sub(f, g)
static member (*) (f, g) = Mul(f, g)

let rec (|Term|_|) = function
| Factor(e1, t) ->
let rec aux e1 = function
| '+'::Factor(e2, t) -> aux (e1 + e2) t
| '-'::Factor(e2, t) -> aux (e1 - e2) t
| t -> Some(e1, t)
aux e1 t
| _ -> None
and (|Factor|_|) = function
| '-'::Factor(e, t) -> Some(-e, t)
| Atom(e1, '*'::Factor(e2, t)) -> Some(e1 * e2, t)
| Atom(e, t) -> Some(e, t)
| _ -> None
and (|Atom|_|) = function
| c::t when '0'<=c && c<='9' -> Some(Int(int(string c)), t)
| '('::Term(e, ')'::t) -> Some(e, t)
| _ -> None

let (Term e) = List.ofSeq "1+2*(3-4)*-5"
``````

Note that only one minor change to the parser was required because the AST can also be constructed using the `+`, `-` and `*` operators.

Second, is it worthwhile to try and adopt a functional approach to parsing, or is it really on optimizations to intermediate code that functional languages shine and I just haven’t gotten there yet?

You’re talking about purity, not functional programming. Purity is not particularly useful in the context of parsing text and, in fact, can be a real hindrance (e.g. interning symbols is a nightmare in Haskell). However, F# has many other benefits that make it good for this set of problems. In particular, although other languages like OCaml have much better tools for parsing, I think F# is the best .NET language in this context.

That is, should I fuddle through the parsing in F# using an imperative style and switch to a more functional approach later on?

Depends entirely upon what you want to make functional. I’d use fslex and fsyacc with pure code to construct ASTs in the actions but impurities for anything like hash consing or generating unique IDs.

You may appreciate the following articles I have written on this subject at this blog (note paywall):

• “Parsing text with Lex and Yacc” (30th September 2007).
• “Optimizing a simple bytecode interpreter” (31st October 2007).
• “Parser combinators” (30th November 2007).
• “Language-oriented programming: The Term-level Interpreter” (31st December 2007).
• “Language-oriented programming: Term Rewriting” (16th August 2008).
• “Run-time code generation using `System.Reflection.Emit`” (31st August 2008).
• “Parsing and visualizing binary Geographic Information System data” (30th November 2009).