Lightweight Regular Expressions
 Christian Lindig
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Date:   (:) 
From:  Christian Lindig <lindig@i...> 
Subject:  Lightweight Regular Expressions 
OCamls regular expression module Str is expressive and fast but requires custom linking. An algorithm by Mark Hopkins (once posted to comp.compilers) permits to implement regular expression matching in about 100 lines of code; the OCaml module is appended below in the hope that is useful. Someone mentioned this algorithm in comp.text.xml for checking XML DTDs and provided a Haskell source. The module below is mostly a port to OCaml. + no precompiling of regexp's  they are interpreted directly + small OCaml module, no custom linking, no C runtime + can match any sequence of symbols, not just characters  only regexp matching, no subexpression matching, no substitution  not as efficient as an automaton based approach  Christian  Christian Lindig Gaertner Datensysteme GbR, Braunschweig, Germany http://www.gaertner.de/~lindig lindig@gaertner.de (* $Id: rx.ml,v 1.1 1999/08/29 09:03:01 lindig Exp $ This module provides regular expression matching. Regular expressions don't need to be compiled before they can be matched against some input. Instead the automaton is build while the input is consumed. The drawback of this method is that no subexpression matching is possible to extract matching substrings. This algorithm used here is by Mark Hopkins who posted it once to comp.compiles. Search the comp.compilers archive for a detailed article and an implementation in C. 1999 Christian Lindig <lindig@gaertner.de> *) type 'a rx =  RXzero (* {} *)  RXunit (* "" *)  RXsym of 'a (* 'x' *)  RXmany of ('a rx) (* e* *)  RXsome of ('a rx) (* e+ *)  RXopt of ('a rx) (* e? *)  RXseq of ('a rx) * ('a rx) (* e1 e2 *)  RXalt of ('a rx) * ('a rx) (* e1  e2 *) let zero = RXzero let unit = RXunit let sym x = RXsym x let many = function  RXunit > RXunit  RXzero > RXunit  x > RXmany x let some = function  RXunit > RXunit  RXzero > RXzero  x > RXsome x let opt = function  RXunit > RXunit  RXzero > RXunit  x > RXopt x let seq x y = match (x,y) with  RXzero, x > RXzero  RXunit, x > x  x , RXzero> RXzero  x , RXunit> x  x , y > RXseq(x,y) let alt x y = match (x,y) with  RXzero, x > x  x , RXzero> x  x , y > RXalt(x,y) (* two convenience infix operators *) let (  ) = alt let ( *** ) = seq (* [nullable e] is true, iff the empty sequence (RXzero) is recognized by [e]. *) let rec nullable = function  RXzero > false  RXunit > true  RXsym x > false  RXmany e > true  RXsome e > nullable e  RXopt e > true  RXseq(e1,e2) > nullable e1 && nullable e2  RXalt(e1,e2) > nullable e1  nullable e2 (* [residual e x] returns a regular expression e' that recognizes the language L(e') = { w  xw \in L(e)}. *) let rec residual e' x = match e' with  RXzero > RXzero  RXunit > RXzero  RXsym x' > if x' = x then RXunit else RXzero  RXmany e > seq (residual e x) (many e)  RXsome e > seq (residual e x) (many e)  RXopt e > residual e x  RXseq(e1,e2) > if nullable e1 then alt (seq (residual e1 x) e2) (residual e2 x) else seq (residual e1 x) e2  RXalt(e1,e2) > alt (residual e1 x) (residual e2 x) (* [matches e syms] is true, iff the word [syms] is an element of L(e), i.e. [e] matches the symbols [syms]. *) let matches e syms = nullable (List.fold_left residual e syms) (* [matchstr e str] is true, iff string [str] is matched by regular expression [e] *) let matchstr e str = let len = String.length str in let rec loop e i = if i = len then nullable e else loop (residual e (String.get str i)) (i+1) in loop e 0 (* examples *) let e1 = many (sym 'a') *** some (sym 'b') let e2 = sym 'a' *** opt (sym 'b') *** some (sym 'a')