Confusion as to how to integrate OperatorPrecedenceParser with mine - fparsec

Question

The only thing I have left for my parser is to successfully make operator precedence work and my parser will be done. But I don't know how I should integrate it with my current parser.
First, here is the language representation:
module MiniML
(* Structures de donnees a exporter *)
type Exp =
| C of Cst
| Id of Id
| Lam of Id * Exp
| App of Exp * Exp
| Let of Id * Exp * Exp
| Pair of Exp * Exp
| If of Exp * Exp * Exp
and Cst = I of int | B of bool | Unit | Nil
and Id = string;;
let op = ["+";
"-";
"*";
"/";
"=";
"<";
">";
"#";
"and";
"or";
",";
"::"
]
(* Fonction permettant de transformer une exp en string *)
let rec exp2str e = match e with
| C (I i) -> string i
| C (B b) -> string b
| C Unit -> "()"
| C Nil -> "nil"
| Id x -> x
| Lam(x,e) -> "lam " + x + "." + (exp2str e)
| App(Id x,Id y) -> x + " " + y
| App(Id x,((C _) as e')) -> x + " " + (exp2str e')
| App(Id x,Pair(e1,e2)) when List.contains x op -> (exp2str e1) + " " + x + " " + (exp2str e2)
| App(Id x,((Pair _) as e')) -> x + (exp2str e')
| App(Id x, e') -> x + " (" + (exp2str e') + ")"
| App(e, Id x) -> "(" + (exp2str e) + ") " + x
| App(e', ((C _) as e'')) -> "(" + (exp2str e') + ") " + (exp2str e'')
| App(e,e') -> "(" + (exp2str e) + ") (" + (exp2str e') + ")"
| Let(x,e,e') ->
"let " + x + " = " + (exp2str e) + " in " + (exp2str e') + " end"
(* entensions *)
| Pair(e1,e2) -> "(" + (exp2str e1) + "," + (exp2str e2) + ")"
| If(e,e1,e2) -> "if " + (exp2str e) + " then " + (exp2str e1) + " else " + (exp2str e2)
Here is the current state of the parser code (I've left the french comment for completness sake.):
module FPParse
open MiniML
open FParsec
(* Raccourcis pour spaces. ws veux dire whitespace *)
let ws = spaces
let operator : Parser<MiniML.Id,unit> = op |> List.map pstring |> choice
(* Liste des mots cles du langage *)
let keyword : Parser<string,unit> = ["false";"true";"let";"end";"in";"if";"then";"else";"lam"] |> List.map pstring |> choice
(* Parse la premiere lettre d'un identifiant *)
let fstId = asciiLetter <|> pchar '_'
(* Parse les lettres autres que la premiere d'un identifiant *)
let restId = fstId <|> digit <|> pchar '''
(* Genere un parseur pour des valeurs entre parenthese *)
let betweenPar p = between (pchar '(' .>> ws) (pchar ')' .>> ws) p
(* Parse une constante boolean *)
let cstB = (stringReturn "true" (B true)) <|> (stringReturn "false" (B false))
(* Parse une valeur entiere *)
let cstI = puint32 |>> (int >> I)
(*
Parse Unit
*)
let cstU = stringReturn "()" Unit
(*
Parse Nil
*)
let cstN = stringReturn "[]" Nil
(* Parse une expression constante *)
let expC : Parser<Exp,unit> = cstB <|> cstI <|> cstU <|> cstN |>> C
(* Parse un string d'identifiant avec un parseur qui lorsqu'il reussis indique la fin du parsing de l'identifiant *)
let expIdStr = notFollowedByL keyword "Cannot use keyword as variable" >>.
notFollowedByL operator "Cannot use operator as variable" >>.
many1CharsTill2 fstId restId (notFollowedBy restId)
(* Parse un identifiant *)
let expId : Parser<Exp,unit> = expIdStr |>> (MiniML.Exp.Id)
(* Comme exp est recursif on doit le declarer avec une valeur indefinie pour l'utiliser *)
let exp, expRef = createParserForwardedToRef<Exp, unit>()
(* Comme expApp est recursif on doit le declarer avec une valeur indefinie pour l'utiliser *)
let expApp, expAppRef = createParserForwardedToRef<Exp, unit>()
(*
Parse une expression lambda de la forme: lam( )*expId( )*.( )*exp
*)
let expLam : Parser<Exp,unit> = (pstring "lam" >>. ws >>. expIdStr .>> ws .>> pchar '.') .>> ws .>>. exp |>> Lam
(*
Parse une expression let de la forme: let( )*expId( )*=( )*exp( )*in( )*exp( )*end
*)
let expLet = tuple3 (pstring "let" >>. ws >>. expIdStr .>> ws .>> pchar '=' .>> ws) (exp .>> ws .>> pstring "in" .>> ws) (exp .>> ws .>> pstring "end") |>> Let
(*
Parse une expression if de la forme: if( )*exp( )*then( )*exp( )*else( )*exp
*)
let expIf = tuple3 (pstring "if" >>. ws >>. exp .>> ws) (pstring "then" >>. ws >>. exp .>> ws) (pstring "else" >>. ws >>. exp) |>> If
(* Comme closeEXP est recursif on doit le declarer avec une valeur indefinie pour l'utiliser *)
let closeEXP, closeEXPRef = createParserForwardedToRef<Exp, unit>()
(*
Parse un operateur ! de la forme: !exp
*)
let expBang = (pstring "!" >>% MiniML.Id "!") .>>. closeEXP |>> App
let buildList (el,ef) =
let rec go l = match l with
| (e::es) -> App(MiniML.Id "cons", Pair(e,go es))
| [] -> C Nil
go (el # [ef])
let expList = between (pchar '[' .>> ws) (pchar ']') (many (exp .>>? (ws .>> pchar ';' .>> ws)) .>>. exp .>> ws
|>> buildList )
let opOpp : InfixOperator<Exp,unit,unit> list =
[
InfixOperator("*", ws, 7, Associativity.Left, fun x y -> App(MiniML.Id "*",Pair(x,y)));
InfixOperator("/", ws, 7, Associativity.Left, fun x y -> App(MiniML.Id "/",Pair(x,y)));
InfixOperator("+", ws, 6, Associativity.Left, fun x y -> App(MiniML.Id "+",Pair(x,y)));
InfixOperator("-", ws, 6, Associativity.Left, fun x y -> App(MiniML.Id "-",Pair(x,y)));
InfixOperator("::", ws,5, Associativity.Right, fun x y -> App(MiniML.Id "cons",Pair(x,y)));
InfixOperator("=", ws, 4, Associativity.Left, fun x y -> App(MiniML.Id "=",Pair(x,y)));
InfixOperator("<", ws, 4, Associativity.Left, fun x y -> App(MiniML.Id "<",Pair(x,y)));
InfixOperator(">", ws, 4, Associativity.Left, fun x y -> App(MiniML.Id ">",Pair(x,y)));
InfixOperator("and", ws, 3, Associativity.Right, fun x y -> App(MiniML.Id "and",Pair(x,y)));
InfixOperator("or", ws, 2, Associativity.Right, fun x y -> App(MiniML.Id "or",Pair(x,y)));
InfixOperator(",", ws,1, Associativity.None, fun x y -> Pair(x,y) )
]
let opp = new OperatorPrecedenceParser<Exp,unit,unit>()
let expOp = opp.ExpressionParser
let term = exp <|> betweenPar expOp
opp.TermParser <- term
List.iter (fun x -> opp.AddOperator(x)) opOpp
(*
Parse une expression close de la forme: expC | expId | (exp)( )* | [exp]
*)
do closeEXPRef := choice [expC ; expId ; expBang ; betweenPar exp ; expList] .>> ws
(*
Assigne le parseur d'application en lambda-calcul. Le parseur parse autant d'expression close que possible.
Il est impossible que la liste soit vide, du a l'utilisation de many1 qui echoue et retourne s'il n'y a pas
au moins une valeur.
*)
do expAppRef := many1 closeEXP |>> (function (x::xs) -> List.fold (fun x y -> App(x,y)) x xs | [] -> failwith "Impossible")
(*
Assigne le parseur d'expression en lambda-calcul. L'ordre des expressions represente leur priorite
*)
do expRef := [expLam;expIf;expLet;expApp] |> choice
(*
Parse une expression lambda-calcul au complet. Le eof s'assure qu'il ne reste pas de caractere non parse
*)
let mainExp = expOp .>> eof
(*
Prends un string et retourne un Exp. Peut leve un message d'erreur en exception si le parsing echoue
*)
let str2exp s = match run mainExp s with
| Success(result, _, _) -> result
| Failure(errorMsg, _, _) -> failwith errorMsg
I've tried to add it in the list of choice after the expApp parser but it's just ignored. If I put it before the expApp on in the closedExp, it throws exception because, I think, of infinite recursion. I really don't know how to mix it in. I don't want to be just given the solution, I'd like to know why. Also, is there any non-trivial exemple of big language being parse by FParsec?