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Parsing expressions

To conclude, the parse function can be defined as follow.
Next, all the functions defined on the (syntax) tree can be used (eval, print, simplify, etc.).

open System;;

let parse s = 
  match exp s with
  | [(r,"")] -> r
  | _        -> failwith "Bad syntax";;

parse "(12+23)*45";;

Nb. It is possible to summarize the elements presented as follow:

type Parser<'t> = string -> (('t * string) list);;

sym  : Parser<char>;;
(&&) : Parser<'t1> -> ('t1-> Parser<'t2>) -> Parser<'t2>;;
(||) : Parser<'t>->Parser<'t>->Parser<'t>
rep  : Parser<'t> -> Parser<'t list>;;

num' : Parser<int>
exp  : Parser<Exp>

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