package pratter

Pratter: A parser for terms with operators and applications

Pratter is a library that provides a parser that transforms streams of terms to applied terms. Terms may contain infix, prefix or postfix operators and applications. The parser is an extension of the Pratt parsing algorithm.

Examples can be seen in tests inside the t/ folder.

Example: simple terms

Terms are made of symbols and applications and some symbol can be declared to be operators.

Start by defining the terms,

type term = Appl of term * term | Symb of string

and the data structure that maps symbols identifiers to operators properties,

type table = {
    prefix  : (string * Pratter.priority) list
  ; infix : (string * (Pratter.priority * Pratter.associativity)) list
  ; postfix : (string * Pratter.priority) list
}

Next, define a module to pack these two types, and two functions:

• get that is able to retrieve the properties of a symbol if it is declared as an operator,

• make_appl that creates an application out of two terms.

module Terms : Pratter.SUPPORT with type term = term and type table = table =
struct
  type nonrec term = term
  type nonrec table = table
  let get { prefix; infix; postfix } (t: term) =
  match t with
  | Symb id -> (
      try Some (Pratter.Prefix, List.assoc id prefix)
      with Not_found -> (
        try
          let bp, assoc = List.assoc id infix in
          Some (Pratter.Infix assoc, bp)
        with Not_found -> (
          try Some (Pratter.Postfix, List.assoc id postfix)
          with Not_found -> None) ) )
  | _ -> None

  let make_appl t u = Appl (t, u)
end

module Parser = Pratter.Make (Terms)

Then that's it, we can parse streams of terms with operators. For instance, assume that we want to parse x ! + y * -z where

• + and * are infix operators, with * having a higher binding power than +;

• - is a prefix operator having a higher binding power than + and *,

• ! is a postfix operator.

Create a table holding these operators:

let tbl =
  { prefix = [ "-", 1.0 ]
  ; infix = [ ("+", (0.5, Pratter.Left)) ; ("*", (0.6, Pratter.Left)) ]
  ; postfix = [ "!", 1.0 ] }

Priority (also called binding power) can be any float, and associativity may be Pratter.Left, Pratter.Right or Pratter.Neither.

Finally parse the input using Parser.expression:

let input = [ Symb "x"; Symb "!"; Symb "+"; Symb "y"; Symb "*"; Symb "-"; Symb "z"]
Parser.expression tbl (Stream.of_list input)

we obtain the term (x !) + (y * (-z)) (wrapped into a result) represented by

Appl (Appl (Symb "+", Appl (Symb "!", Symb "x")),
 Appl (Appl (Symb "*", Symb "y"), Appl (Symb "-", Symb "z")))