F# Monadically label n-ary tree

// F# Monadically label n-ary tree
let MMap f xs = 
            let rec MMap' (f, xs', out) = 
                state {
                        match xs' with
                        | h :: t -> let! h' = f(h)
                                    return! MMap'(f, t, List.append out [h'])
                        | [] -> return out
                      }
            MMap' (f, xs, [])

type 'a ntree = | NLeaf of 'a
                | NNode of 'a ntree list


let rec private MNNode (x) =
    match x with
    | NLeaf(c) -> state { let! x = GetState
                          do! SetState (x + 1)
                          return NLeaf(c,x) }
                         
    | NNode(xs) -> state { let! xs' = MMap MNNode xs
                           return NNode(xs')  } 
                    
let MNLabel x = Execute(MNNode(x))    

F# State Monad

//F# State Monad

type State<'state, 'a> = State of ('state ->'a * 'state)

type StateMonad() = 
        member b.Bind(m, f) = State (fun s -> let r = match m with
                                                      | State f -> f s
                                              match r with
                                              | (v,s) -> match f v with
                                                         | State f -> f s)    
        member b.Return(x) = State (fun s -> x, s)

let state = StateMonad()

let GetState = State (fun s -> s, s)
let SetState s = State (fun _ -> (), s)  

let Execute m s = match m with
                  | State f -> let r = f s
                               match r with
                               |(x,_) -> x

F# Monadic tree labeller

open StateMonad

type 'a tree = | Leaf of 'a
               | Node of 'a tree * 'a tree
            
          
// F# Monadic tree labeller 

let rec private mNode x =
    match x with
    | Leaf(c) -> state { let! x = GetState
                         do! SetState (x + 1)
                         return Leaf(c,x) }
                         
    | Node(l,r) -> state { let! l = mNode(l)
                           let! r = mNode(r)
                           return Node(l,r) }
                    
let mLabel x = Execute(mNode(x))


// F# Non-Monadic manual state passing tree labeller

let Label a s = 
     let rec Lab' a s = 
                match a with 
                |Leaf(c) -> (Leaf(c,s), s + 1) 
                
                |Node(l,r) -> let l' = Lab' l s 
                              let r' = Lab' r (snd l')
                              (Node(fst l', fst r'), (snd r')) 
     fst (Lab' a s) 

The List Monad in F#

// The List Monad in F#

type ListMonad() =
   member o.Bind(  (m:'a list), (f: 'a -> 'b list) ) = List.concat( List.map (fun x -> f x) m )
   member o.Return(x) = [x]

let list = ListMonad()

let cartesian = list { let! x = [1..3]
                       let! y = [4..6]
                       return (x,y) }

printf "%A" cartesian

F# Monadic Parser - Calculator Example.

//F# Monadic Parser - Calculator Example :))) 

// Grammar
//expr ::= expr addop term j term
//term ::= term mulop factor j factor
//factor ::= digit j ( expr )
//digit ::= 0 j 1 j : : : j 9
//addop ::= + j -
//mulop ::= * j /

let addOp = parser { let! _ = symb "+" 
                     return (+) } +++ parser { let! _ = symb "-" 
                                               return (-) } 
let mulOp = parser { let! _ = symb "*" 
                     return (*) } +++ parser { let! _ = symb "/" 
                                               return (/) }  
let digit = parser { let! x = token (sat (fun ch -> Char.IsDigit(ch)))
                     return Char.GetNumericValue(x) - Char.GetNumericValue('0') }

let rec expr   = chainl1 term addOp
and     term   = chainl1 factor mulOp
and     factor = digit +++ parser { let! _ = symb "("
                                    let! n = expr
                                    let! _ = symb ")"
                                    return n }
                                    
let parse s = match apply expr s  with
              | [] -> failwith "failed to parse"
              | (ret, _)::xs -> ret 
              
parse "5 * (3 + 4)"              
|> printf "%A" 

F# Parsers combinators.

// F# Parsers combinators :))

open System

//A parser which successfully consumes the first character
//if the argument string is non-empty, and fails otherwise.
let item = Parser (fun cs -> match cs with
                             | "" -> []
                             | cs -> [cs.[0], cs.Substring(1)])
                            
//A combinator sat that takes a predicate, and yields a parser that
//consumes a single character if it satisfies the predicate, and fails otherwise.
let sat p = parser { let! c = item
                     if p c then
                      return c }
                      
//A parser for specific characters
let char c = sat (fun s -> c = s)
                                            
//Parse a specific string
let rec stringp s = match s with
                    | "" -> parser { return [] }
                    | xs -> parser { let! c = char xs.[0]
                                     let! cs = stringp (xs.Substring(1))
                                     return c::cs }                        
                                                          
//The many combinator permits zero
//or more applications of p, while many1 permits one or more.
let rec many1 p = parser { let! x = p
                           let! xs = many p
                           return (x::xs) }
and many p = (many1 p) +++ parser { return [] }

                            
//Parse repeated applications of a parser p, separated by applications of a parser
//op whose result value is an operator that is assumed to associate to the left,
//and which is used to combine the results from the p parsers.
and chainl1 p op = 
    let rec rest a = parser { let! f = op
                              let! b = p
                              return! rest (f a b) } +++ parser { return a }
    parser { let! a = p
             return! rest a } 
           
//Parse a string of spaces.
let space = many (sat (fun s -> Char.IsWhiteSpace s))

//Parse a token using a parser p, throwing away any trailing space.
let token p = parser { let! a = p
                       let! _ = space
                       return a }

//Parse a symbolic token:
let symb cs = token (stringp cs)

//Apply a parser p, throwing away any leading space:
let apply p = extract (parser { let! _ = space
                                let! r = p
                                return r })

F# Parser Monad (http://www.cs.nott.ac.uk/~gmh/pearl.pdf)

// F# Parser Monad (http://www.cs.nott.ac.uk/~gmh/pearl.pdf)

type Parser<'a> = Parser of (string ->('a * string) list)

let extract(Parser(f)) = f

type ParserMonad() =
    member b.Bind(p, f) = Parser (fun cs ->
                                            let r = extract(p) cs
                                            let r' = List.map (fun (a,cs') -> extract(f a) cs') r
                                            List.concat r')
    member b.Return(x) = Parser (fun cs -> [x,cs])
    member b.Zero() = Parser (fun cs -> [])


let (++) p q = Parser(fun cs -> List.append (extract p cs) (extract q cs))
let (+++) p q = Parser(fun cs -> match (extract(p ++ q) cs) with
                                 | [] -> []
                                 | x::xs -> [x])

let parser = ParserMonad()