Execute a Markov algorithm

This page uses content from Wikipedia. The original article was at Markov_algorithm. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

Execute a Markov algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

Create an interpreter for a Markov Algorithm. Rules have the syntax:

<ruleset> ::= ((<comment> | <rule>) <newline>+)*
<comment> ::= # {<any character>}
<rule> ::= <pattern> <whitespace> -> <whitespace> [.] <replacement>
<whitespace> ::= (<tab> | <space>) [<whitespace>]

There is one rule per line. If there is a . present before the <replacement>, then this is a terminating rule in which case the interpreter must halt execution. A ruleset consists of a sequence of rules, with optional comments.

Rulesets

Use the following tests on entries:

Ruleset 1

# This rules file is extracted from Wikipedia:
# http://en.wikipedia.org/wiki/Markov_Algorithm
A -> apple
B -> bag
S -> shop
T -> the
the shop -> my brother
a never used -> .terminating rule

Sample text of:

I bought a B of As from T S.

Should generate the output:

I bought a bag of apples from my brother.

Ruleset 2

A test of the terminating rule

# Slightly modified from the rules on Wikipedia
A -> apple
B -> bag
S -> .shop
T -> the
the shop -> my brother
a never used -> .terminating rule

Sample text of:

I bought a B of As from T S.

Should generate:

I bought a bag of apples from T shop.

Ruleset 3

This tests for correct substitution order and may trap simple regexp based replacement routines if special regexp characters are not escaped.

# BNF Syntax testing rules
A -> apple
WWWW -> with
Bgage -> ->.*
B -> bag
->.* -> money
W -> WW
S -> .shop
T -> the
the shop -> my brother
a never used -> .terminating rule

Sample text of:

I bought a B of As W my Bgage from T S.

Should generate:

I bought a bag of apples with my money from T shop.

Ruleset 4

This tests for correct order of scanning of rules, and may trap replacement routines that scan in the wrong order. It implements a general unary multiplication engine. (Note that the input expression must be placed within underscores in this implementation.)

### Unary Multiplication Engine, for testing Markov Algorithm implementations
### By Donal Fellows.
# Unary addition engine
_+1 -> _1+
1+1 -> 11+
# Pass for converting from the splitting of multiplication into ordinary
# addition
1! -> !1
,! -> !+
_! -> _
# Unary multiplication by duplicating left side, right side times
1*1 -> x,@y
1x -> xX
X, -> 1,1
X1 -> 1X
_x -> _X
,x -> ,X
y1 -> 1y
y_ -> _
# Next phase of applying
1@1 -> x,@y
1@_ -> @_
,@_ -> !_
++ -> +
# Termination cleanup for addition
_1 -> 1
1+_ -> 1
_+_ -> 

Sample text of:

_1111*11111_

should generate the output:

11111111111111111111

Ruleset 5

A simple Turing machine, implementing a three-state busy beaver. The tape consists of 0s and 1s, the states are A, B, C and H (for Halt), and the head position is indicated by writing the state letter before the character where the head is. All parts of the initial tape the machine operates on have to be given in the input.

Besides demonstrating that the Markov algorithm is Turing-complete, it also made me catch a bug in the C++ implementation which wasn't caught by the first four rulesets.

# Turing machine: three-state busy beaver
#
# state A, symbol 0 => write 1, move right, new state B
A0 -> 1B
# state A, symbol 1 => write 1, move left, new state C
0A1 -> C01
1A1 -> C11
# state B, symbol 0 => write 1, move left, new state A
0B0 -> A01
1B0 -> A11
# state B, symbol 1 => write 1, move right, new state B
B1 -> 1B
# state C, symbol 0 => write 1, move left, new state B
0C0 -> B01
1C0 -> B11
# state C, symbol 1 => write 1, move left, halt
0C1 -> H01
1C1 -> H11

This ruleset should turn

000000A000000

into

00011H1111000

Examples

AutoHotkey

<lang ahk>;---------------------------------------------------------------------------

Markov Algorithm.ahk

by wolf_II

---------------------------------------------------------------------------

interpreter for a Markov Algorithm

---------------------------------------------------------------------------

---------------------------------------------------------------------------

AutoExecute: ; auto-execute section of the script

---------------------------------------------------------------------------

   #SingleInstance, Force          ; only one instance allowed
   #NoEnv                          ; don't check empty variables
   StartupDir := A_WorkingDir      ; remember startup directory
   SetWorkingDir, %A_ScriptDir%    ; change directoy
   StringCaseSense, On             ; case sensitive comparisons
   ;-----------------------------------------------------------------------
   AppName := "Markov Algorithm"
   Gosub, GuiCreate
   Gui, Show,, %AppName%

Return

---------------------------------------------------------------------------

GuiCreate: ; create the GUI

---------------------------------------------------------------------------

   ; GUI options
   Gui, -MinimizeBox
   Gui, Add, Edit, y0 h0 ; catch the focus

   ; Ruleset
   Gui, Add, GroupBox, w445 h145 Section, Ruleset
   Gui, Add, Edit, xs+15 ys+20 w300 r8 vRuleset
   Gui, Add, Button, x+15 w100, Load Ruleset
   Gui, Add, Button, wp, Save Ruleset
   Gui, Add, Button, w30, 1
   Gui, Add, Button, x+5 wp, 2
   Gui, Add, Button, x+5 wp, 3
   Gui, Add, Button, xs+330 y+6 wp, 4
   Gui, Add, Button, x+5 wp, 5

   ; String
   Gui, Add, GroupBox, xs w445 h75 Section, String
   Gui, Add, Edit, xs+15 ys+20 w300 vString
   Gui, Add, Button, x+15 w100, Apply Ruleset
   Gui, Add, Button, xp wp Hidden, Stop
   Gui, Add, CheckBox, xs+15 yp+30 vSingleStepping, Single Stepping?

   ; Output
   Gui, Add, GroupBox, xs w445 h235 Section, Output
   Gui, Add, Edit, xs+15 ys+20 w415 r15 ReadOnly vOutput HwndhOut

Return

---------------------------------------------------------------------------

GuiClose:

---------------------------------------------------------------------------

   ExitApp

Return

---------------------------------------------------------------------------

ButtonLoadRuleset: ; load ruleset from file

---------------------------------------------------------------------------

   Gui, +OwnDialogs
   FileSelectFile, RulesetFile,,, Load Ruleset, *.markov
   If Not SubStr(RulesetFile, -6) = ".markov"
       RulesetFile .= ".markov"
   If FileExist(RulesetFile) {
       FileRead, Ruleset, %RulesetFile%
       GuiControl,, Ruleset, %Ruleset%
   } Else
       MsgBox, 16, Error - %AppName%, File not found:`n`n"%RulesetFile%"

Return

---------------------------------------------------------------------------

ButtonSaveRuleset: ; save ruleset to file

---------------------------------------------------------------------------

   Gui, +OwnDialogs
   Gui, Submit, NoHide
   FileSelectFile, RulesetFile, S16,, Save Ruleset, *.markov
   If Not SubStr(RulesetFile, -6) = ".markov"
       RulesetFile .= ".markov"
   FileDelete, %RulesetFile%
   FileAppend, %Ruleset%, %RulesetFile%
   Gui, Show

Return

---------------------------------------------------------------------------

Button1: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm#Ruleset_1

---------------------------------------------------------------------------

   GuiControl,, Output ; clear output
   GuiControl,, String, I bought a B of As from T S.
   GuiControl,, Ruleset,
   (LTrim
   # This rules file is extracted from Wikipedia:
   # http://en.wikipedia.org/wiki/Markov_Algorithm
   A -> apple
   B -> bag
   S -> shop
   T -> the
   the shop -> my brother
   a never used -> .terminating rule
   )

Return

---------------------------------------------------------------------------

Button2: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm#Ruleset_2

---------------------------------------------------------------------------

   GuiControl,, Output ; clear output
   GuiControl,, String, I bought a B of As from T S.
   GuiControl,, Ruleset,
   (LTrim
   # Slightly modified from the rules on Wikipedia
   A -> apple
   B -> bag
   S -> .shop
   T -> the
   the shop -> my brother
   a never used -> .terminating rule
   )

Return

---------------------------------------------------------------------------

Button3: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm#Ruleset_3

---------------------------------------------------------------------------

   GuiControl,, Output ; clear output
   GuiControl,, String, I bought a B of As W my Bgage from T S.
   GuiControl,, Ruleset,
   (LTrim
   # BNF Syntax testing rules
   A -> apple
   WWWW -> with
   Bgage -> ->.*
   B -> bag
   ->.* -> money
   W -> WW
   S -> .shop
   T -> the
   the shop -> my brother
   a never used -> .terminating rule
   )

Return

---------------------------------------------------------------------------

Button4: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm#Ruleset_4

---------------------------------------------------------------------------

   GuiControl,, Output ; clear output
   GuiControl,, String, _1111*11111_
   GuiControl,, Ruleset,
   (LTrim
   ### Unary Multiplication Engine, for testing Markov Algorithm implementations
   ### By Donal Fellows.
   # Unary addition engine
   _+1 -> _1+
   1+1 -> 11+
   # Pass for converting from the splitting of multiplication into ordinary
   # addition
   1! -> !1
   ,! -> !+
   _! -> _
   # Unary multiplication by duplicating left side, right side times
   1*1 -> x,@y
   1x -> xX
   X, -> 1,1
   X1 -> 1X
   _x -> _X
   ,x -> ,X
   y1 -> 1y
   y_ -> _
   # Next phase of applying
   1@1 -> x,@y
   1@_ -> @_
   ,@_ -> !_
   ++ -> +
   # Termination cleanup for addition
   _1 -> 1
   1+_ -> 1
   _+_ ->
   )

Return

---------------------------------------------------------------------------

Button5: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm#Ruleset_5

---------------------------------------------------------------------------

   GuiControl,, Output ; clear output
   GuiControl,, String, 000000A000000
   GuiControl,, Ruleset,
   (LTrim
   # Turing machine: three-state busy beaver
   #
   # state A, symbol 0 => write 1, move right, new state B
   A0 -> 1B
   # state A, symbol 1 => write 1, move left, new state C
   0A1 -> C01
   1A1 -> C11
   # state B, symbol 0 => write 1, move left, new state A
   0B0 -> A01
   1B0 -> A11
   # state B, symbol 1 => write 1, move right, new state B
   B1 -> 1B
   # state C, symbol 0 => write 1, move left, new state B
   0C0 -> B01
   1C0 -> B11
   # state C, symbol 1 => write 1, move left, halt
   0C1 -> H01
   1C1 -> H11
   )

Return

---------------------------------------------------------------------------

ButtonApplyRuleset: ; flow control for Algorithm

---------------------------------------------------------------------------

   ; prepare
   Gui, Submit, NoHide
   GuiControl,, Output ; clear
   Controls(False) ; disable
   Count := 0
   Subst := True
   Stop  := False

   ; keep substituting for as long as necessary
   While, Subst {
       Subst := False ; reset control variable
       IfEqual, Stop, 1, Break
       Gosub, Algorithm
   }

   ; clean up
   Output("Substitution count: " Count)
   Controls(True) ; re-enable

Return

---------------------------------------------------------------------------

ButtonStop: ; this button is initially hidden

---------------------------------------------------------------------------

   Stop := True

Return

---------------------------------------------------------------------------

Algorithm: ; http://rosettacode.org/wiki/Execute_a_Markov_algorithm

---------------------------------------------------------------------------

   ; Parse the ruleset and apply each rule to the string. Whenever a rule
   ; has changed the string goto first rule. Continue until a encountering
   ; a terminating rule, or until no further changes to the strings are
   ; made.
   ;-----------------------------------------------------------------------
   Loop, Parse, Ruleset, `n, `r ; always start from the beginning
   {
       ; check for comment
       If SubStr(A_LoopField, 1, 1) = "#"
           Continue ; get next line

       ; split a rule into $Search, $Terminator and $Replace
       LookFor := "(?P<Search>.+) -> (?P<Terminator>\.?)(?P<Replace>.+)"
       RegExMatch(A_LoopField, LookFor, $)

       ; single stepping through possible substitutions
       If SingleStepping
           MsgBox,, %AppName%, % ""
           . "Rule = """ A_LoopField """`n`n"
           . "Search`t= """ $Search """`n"
           . "Replace`t= """ $Replace """`n"
           . "Termintor`t= """ ($Terminator ? "True" : "False") """`n"

       ; try to substitute
       StringReplace, String, String, %$Search%, %$Replace%, UseErrorLevel

       ; any success?
       If ErrorLevel {     ; yes, substitution done
           Count++         ; keep count
           Subst := True   ; set control variable
           Output(String)  ; write new string to output
       }

       ; terminate?
       If $Terminator {    ; yes, terminate
           Stop := True    ; set control variable
           Break           ; back to flow control
       }

       ; we are not yet terminated ...
       If Subst            ; but we just did a substitution
           Break           ; back to flow control
   }

Return

---------------------------------------------------------------------------

Controls(Bool) { ; [en|dis]able controls

---------------------------------------------------------------------------

   Enable  := Bool ? "+" : "-"
   Disable := Bool ? "-" : "+"
   Loop, 2
       GuiControl, %Disable%ReadOnly, % "Edit" A_Index + 1
   Loop, 7
       GuiControl, %Disable%Disabled, % "Button" A_Index + 1
   GuiControl, %Disable%Disabled, Edit4
   GuiControl, %Disable%Hidden, Button10
   GuiControl, %Enable%Hidden, Button11
   GuiControl, %Disable%Disabled, Button12

}

---------------------------------------------------------------------------

Output(Text) { ; append text to output

---------------------------------------------------------------------------

   static EM_REPLACESEL = 0xC2
   global hOut
   Sleep, 100
   Text .= "`r`n"
   SendMessage, EM_REPLACESEL,, &Text,, ahk_id %hOut%

}

---------- end of file ----------------------------------------------------</lang>

C

<lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <stdbool.h> // requires C99
3. include <string.h>
4. include <assert.h>

1. define MAX_RULE_LEN 1024
2. define MAX_STR_LEN 1024

typedef struct rulestruct {

 const char *trigger;
 const char *replacement;
 bool terminal;
 struct rulestruct *next;

} rule_t;

rule_t *free_rule(rule_t *r) {

 if ( r == NULL ) return NULL;
 if ( r->trigger != NULL ) free(r->trigger);
 if ( r->replacement != NULL ) free(r->replacement);
 rule_t *next = r->next;
 free(r);
 return next;

}

void free_rulelist(rule_t *head) {

 rule_t *n = head;
 while( n != NULL ) n = free_rule(n);

}

void readrules(FILE *f, rule_t **ruleset) {

 char buffer[MAX_RULE_LEN];
 rule_t *t, *prev;
 int i, j;
 size_t l;
 
 *ruleset = prev = NULL;
 for(l=1; fgets(buffer, MAX_RULE_LEN, f) != NULL; l++ )
 {
   if ( buffer[0] == '#' ) continue; // not a rule but a comment
   t = malloc(sizeof(rule_t)); assert( t != NULL );
   memset(t, 0, sizeof(rule_t)); // just to be sure, in case of failure, to avoid
                                 // freeing unallocated memory
   // skip blank lines (there cannot be leading spaces...!)
   if ( (buffer[0] == '\n') || (buffer[0] == '\r') ) continue;
   // it's a rule: let's move until the first " -> "
   char *map = strstr(buffer, " -> ");
   if ( map == NULL )
   {
     fprintf(stderr, "rule set syntax error line %d\n", l);
     free_rule(t); 
     return;
   }
   i = map - buffer + 4; // skip " -> "
   j = map - buffer - 1;
   while( (buffer[j] == ' ') || (buffer[j] == '\t') ) j--;
   buffer[j+1] = 0;
   t->trigger = strdup(buffer);   assert( t->trigger != NULL );
   //skip whitespaces after ->
   for( ; (buffer[i] == '\t') || (buffer[i] == ' '); i++) ;
   if ( buffer[i] == '.' ) 
   { 
     t->terminal = true; i++;  // terminal rule
   } else {
     t->terminal = false;      // or not
   }
   j = i; // store this position and let's find the end
   i += strlen(buffer+j);
   for( i--; (buffer[i] == '\n') || (buffer[i] == '\r') ; i--) ;
   buffer[i+1] = 0;
   t->replacement = strdup(buffer+j);   assert(t->replacement != NULL);
   if ( prev == NULL ) 
   {
     *ruleset = t;
   } else {
     prev->next = t;
   }
   prev = t;
 }

}

// each line of the file is a "string" void markov(FILE *f, rule_t *rule) {

 char buffer[2][MAX_STR_LEN]; // double to allow state changing and no overlapping
 int bi;
 rule_t *r;
 char *d;
 const char *p, *bp;
 bool repldone;
 size_t s;

 while( ( fgets(buffer[0], MAX_STR_LEN, f) != NULL ) )
 {
   bi = 0;

   do
   {
     repldone = false;
     for( r = rule; r != NULL; r = r->next, bi++)
     {

bp = buffer[bi%2]; d = buffer[(bi+1)%2]; if ( (p = strstr(bp, r->trigger)) != NULL ) { s = p - bp; memcpy(d, bp, s);

         d += s;

strcpy(d, r->replacement);

         d += strlen(r->replacement);

strcpy(d, bp + strlen(r->trigger) + s); if ( r->terminal ) { repldone = false; bi++; // let be bi the current (last) buffer break; } repldone = true; // a repl. was done r = rule; // since a repl. was done, let's "reset" r } else { bi--; // stay on the same buffer }

     }
   } while( repldone );
 }
 puts(buffer[(bi)%2]);

}

int main() {

 FILE *rulefile_h = NULL;
 FILE *stringfile_h = NULL;
 rule_t *rulelist;

 if ( argc < 3 ) {
   printf("Usage: %s rulefile stringfile\n", argv[0]);
   exit(EXIT_FAILURE);
 }
 
 rulefile_h = fopen(argv[1], "r");   assert( rulefile_h != NULL );
 stringfile_h = fopen(argv[2], "r"); assert( stringfile_h != NULL );

 readrules(rulefile_h, &rulelist);   assert( rulelist != NULL );
 markov(stringfile_h, rulelist);

 // dump rules

/*

   rule_t *h = rulelist;
   while( h != NULL )
   {
     printf("%s -> %s%s\n", h->trigger, h->replacement, h->terminal ? " [TERMINATING RULE]" : "");
     h = h->next;
   }

• /

 free_rulelist(rulelist);

 fclose(rulefile_h); fclose(stringfile_h);

 return EXIT_SUCCESS;

}</lang>

C++

Note: Non-use of iswhite is intentional, since depending on the locale, other chars besides space and tab might be detected by that function. <lang cpp>

1. include <cstdlib>
2. include <iostream>
3. include <fstream>
4. include <vector>
5. include <string>

struct rule {

 std::string pattern;
 std::string replacement;
 bool terminal;
 rule(std::string pat, std::string rep, bool term):
   pattern(pat),
   replacement(rep),
   terminal(term)
 {
 }

};

std::string const whitespace = " \t"; std::string::size_type const npos = std::string::npos;

bool is_whitespace(char c) {

 return whitespace.find(c) != npos;

}

std::vector<rule> read_rules(std::ifstream& rulefile) {

 std::vector<rule> rules;
 std::string line;
 while (std::getline(rulefile, line))
 {
   std::string::size_type pos;

   // remove comments
   pos = line.find('#');
   if (pos != npos)
     line.resize(pos);

   // ignore lines consisting only of whitespace
   if (line.find_first_not_of(whitespace) == npos)
     continue;

   // find "->" surrounded by whitespace
   pos = line.find("->");
   while (pos != npos && (pos == 0 || !is_whitespace(line[pos-1])))
     pos = line.find("->", pos+1);

   if (pos == npos || line.length() < pos+3 || !is_whitespace(line[pos+2]))
   {
     std::cerr << "invalid rule: " << line << "\n";
     std::exit(EXIT_FAILURE);
   }

   std::string pattern = line.substr(0, pos-1);
   std::string replacement = line.substr(pos+3);

   // remove additional separating whitespace
   pattern.erase(pattern.find_last_not_of(whitespace)+1);
   replacement.erase(0, replacement.find_first_not_of(whitespace));

   // test for terminal rule
   bool terminal = !replacement.empty() && replacement[0] == '.';
   if (terminal)
     replacement.erase(0,1);

   rules.push_back(rule(pattern, replacement, terminal));
 }

 return rules;

}

std::string markov(std::vector<rule> rules, std::string input) {

 std::string& output = input;
 std::vector<rule>::iterator iter = rules.begin();

 // Loop through each rule, transforming our current version
 // with each rule.
 while (iter != rules.end())
 {
   std::string::size_type pos = output.find(iter->pattern);
   if (pos != npos)
   {
     output.replace(pos, iter->pattern.length(), iter->replacement);
     if (iter->terminal)
       break;
     iter = rules.begin();
   }
   else
     ++iter;
 }

 return output;

}

int main(int argc, char* argv[]) {

 if (argc != 3)
 {
   std::cout << "usage:\n " << argv[0] << " rulefile text\n";
   return EXIT_FAILURE;
 }

 std::ifstream rulefile(argv[1]);
 std::vector<rule> rules = read_rules(rulefile);

 std::string input(argv[2]);
 std::string output = markov(rules, input);

 std::cout << output << "\n";

} </lang>

Haskell

This program expects a source file as an argument and uses the standard input and output devices for the algorithm's I/O.

<lang haskell>import Data.List (isPrefixOf) import Data.Maybe (catMaybes) import Control.Monad import Text.ParserCombinators.Parsec import System.IO import System.Environment (getArgs)

main = do

  args <- getArgs
  unless (length args == 1) $
      fail "Please provide exactly one source file as an argument."
  let sourcePath = head args
  source <- readFile sourcePath
  input <- getContents
  case parse markovParser sourcePath source of
      Right rules -> putStr $ runMarkov rules input
      Left  err   -> hPutStrLn stderr $ "Parse error at " ++ show err

data Rule = Rule

  {from :: String, terminating :: Bool, to :: String}

markovParser :: Parser [Rule] markovParser = liftM catMaybes $

   (comment <|> rule) `sepEndBy` many1 newline
 where comment = char '#' >> skipMany nonnl >> return Nothing
       rule = liftM Just $ liftM3 Rule
           (manyTill (nonnl <?> "pattern character") $ try arrow)
           (succeeds $ char '.')
           (many nonnl)
       arrow = ws >> string "->" >> ws <?> "whitespace-delimited arrow"
       nonnl = noneOf "\n"
       ws = many1 $ oneOf " \t"
       succeeds p = option False $ p >> return True

runMarkov :: [Rule] -> String -> String runMarkov rules s = f rules s

 where f []                              s = s
       f (Rule from terminating to : rs) s = g "" s
         where g _      ""    = f rs s
               g before ahead@(a : as) = if from `isPrefixOf` ahead
                 then let new = reverse before ++ to ++ drop (length from) ahead
                      in if terminating then new else f rules new
                 else g (a : before) as</lang>

J

Solution:<lang j>require'strings regex'

markovLexer =: verb define

 rules =.  LF cut TAB&=`(,:&' ')}y
 rules =.  a: -.~ (dltb@:{.~ i:&'#')&.> rules
 rules =.  0 _1 {"1 '\s+->\s+' (rxmatch rxcut ])S:0 rules
 (,. ] (}.&.>~ ,. ]) ('.'={.)&.>)/ |: rules

)

replace =: dyad define

 'index patternLength replacement'=.  x
 'head tail' =.  index split y
 head, replacement, patternLength }. tail

)

matches =: E. i. 1:

markov =: dyad define

 ruleIdx =. 0 [ rules =.  markovLexer x
 while. ruleIdx < #rules do.
   'pattern replacement terminating' =. ruleIdx { rules
   ruleIdx =. 1 + ruleIdx
   if. (#y) > index =. pattern matches y do.
     y =. (index ; (#pattern) ; replacement) replace y
     ruleIdx =. _ * terminating
   end.
 end.
 y

)</lang>

Example:<lang j> m1 =. noun define # This rules file is extracted from Wikipedia: # http://en.wikipedia.org/wiki/Markov_Algorithm A -> apple B -> bag S -> shop T -> the the shop -> my brother a never used -> .terminating rule )

  m1 markov 'I bought a B of As from T S.' 

I bought a bag of apples from my brother. </lang> Discussion: The J implementation correctly processes all the rulesets. More details are available on the the talk page.

Perl

This program expects a source file as an argument and uses the standard input and output devices for the algorithm's I/O.

<lang perl>@ARGV == 1 or die "Please provide exactly one source file as an argument.\n"; open my $source, '<', $ARGV[0] or die "I couldn't open \"$ARGV[0]\" for reading. ($!.)\n"; my @rules; while (<$source>)

  {/\A#/ and next;
   my @a = /(.*?)\s+->\s+(\.?)(.*)/ or die "Syntax error: $_";
   push @rules, \@a;}

close $source;

my $input = do {local $/; <STDIN>;};

OUTER:

  {foreach (@rules)
      {my ($from, $terminating, $to) = @$_;
       $input =~ s/\Q$from\E/$to/
           and ($terminating ? last OUTER : redo OUTER);}}

print $input;</lang>

Python

The example uses a regexp to parse the syntax of the grammar. This regexp is multi-line and verbose, and uses named groups to aid in understanding the regexp and to allow more meaningful group names to be used when extracting the replacement data from the grammars in function extractreplacements.

The example gains flexibility by not being tied to specific files. The functions may be imported into other programs which then can provide textual input from their sources without the need to pass 'file handles' around. <lang python>import re

def extractreplacements(grammar):

   return [ (matchobj.group('pat'), matchobj.group('repl'), bool(matchobj.group('term')))
               for matchobj in re.finditer(syntaxre, grammar)
               if matchobj.group('rule')]

def replace(text, replacements):

   while True:
       for pat, repl, term in replacements:
           if pat in text:
               text = text.replace(pat, repl, 1)
               if term:
                   return text
               break
       else:
           return text

syntaxre = r"""(?mx) ^(?:

 (?: (?P<comment> \# .* ) ) |
 (?: (?P<blank>   \s*  ) (?: \n | $ )  ) |
 (?: (?P<rule>    (?P<pat> .+? ) \s+ -> \s+ (?P<term> \.)? (?P<repl> .+) ) )

)$ """

grammar1 = """\

1. This rules file is extracted from Wikipedia:
2. http://en.wikipedia.org/wiki/Markov_Algorithm

A -> apple B -> bag S -> shop T -> the the shop -> my brother a never used -> .terminating rule """

grammar2 = \

1. Slightly modified from the rules on Wikipedia

A -> apple B -> bag S -> .shop T -> the the shop -> my brother a never used -> .terminating rule

grammar3 = \

1. BNF Syntax testing rules

A -> apple WWWW -> with Bgage -> ->.* B -> bag ->.* -> money W -> WW S -> .shop T -> the the shop -> my brother a never used -> .terminating rule

grammar4 = \

1. 1. 1. Unary Multiplication Engine, for testing Markov Algorithm implementations
      2. By Donal Fellows.
2. Unary addition engine

_+1 -> _1+ 1+1 -> 11+

1. Pass for converting from the splitting of multiplication into ordinary
2. addition

1! -> !1 ,! -> !+ _! -> _

1. Unary multiplication by duplicating left side, right side times

1*1 -> x,@y 1x -> xX X, -> 1,1 X1 -> 1X _x -> _X ,x -> ,X y1 -> 1y y_ -> _

1. Next phase of applying

1@1 -> x,@y 1@_ -> @_ ,@_ -> !_ ++ -> +

1. Termination cleanup for addition

_1 -> 1 1+_ -> 1 _+_ ->

grammar5 = \

1. Turing machine: three-state busy beaver
3. state A, symbol 0 => write 1, move right, new state B

A0 -> 1B

1. state A, symbol 1 => write 1, move left, new state C

0A1 -> C01 1A1 -> C11

1. state B, symbol 0 => write 1, move left, new state A

0B0 -> A01 1B0 -> A11

1. state B, symbol 1 => write 1, move right, new state B

B1 -> 1B

1. state C, symbol 0 => write 1, move left, new state B

0C0 -> B01 1C0 -> B11

1. state C, symbol 1 => write 1, move left, halt

0C1 -> H01 1C1 -> H11

text1 = "I bought a B of As from T S."

text2 = "I bought a B of As W my Bgage from T S."

text3 = '_1111*11111_'

text4 = '000000A000000'

if __name__ == '__main__':

   assert replace(text1, extractreplacements(grammar1)) \
          == 'I bought a bag of apples from my brother.'
   assert replace(text1, extractreplacements(grammar2)) \
          == 'I bought a bag of apples from T shop.'
   # Stretch goals
   assert replace(text2, extractreplacements(grammar3)) \
          == 'I bought a bag of apples with my money from T shop.'
   assert replace(text3, extractreplacements(grammar4)) \
          == '11111111111111111111'
   assert replace(text4, extractreplacements(grammar5)) \
          == '00011H1111000'</lang>

Ruby

Works with: Ruby version 1.8.7

<lang Ruby>raise "Please input an input code file, an input data file, and an output file." if ARGV.size < 3

rules = File.readlines(ARGV[0]).inject([]) do |rules, line|

 if line =~ /^\s*#/
   rules
 elsif line =~ /^(.+)\s+->\s+(\.?)(.*)$/
   rules << [$1, $3, $2 != ""]
 else
   raise "Syntax error: #{line}"
 end

end

File.open(ARGV[2], "w") do |file|

 file.write(File.read(ARGV[1]).tap { |input_data|
   while (matched = rules.find { |match, replace, term|
     input_data[match] and input_data.sub!(match, replace)
   }) and !matched[2]
   end
 })

end</lang>

Scala

Works with: Scala version 2.8

<lang scala>import scala.io.Source

object MarkovAlgorithm {

 val RulePattern = """(.*?)\s+->\s+(\.?)(.*)""".r
 val CommentPattern = """#.*|\s*""".r
 
 def rule(line: String) = line match {
   case CommentPattern() => None
   case RulePattern(pattern, terminal, replacement) => Some(pattern, replacement, terminal == ".")
   case _ => error("Syntax error on line "+line)
 }
 
 def main(args: Array[String]) {
   if (args.size != 2 ) {
     println("Syntax: MarkovAlgorithm inputFile inputPattern")
     exit(1)
   }
   
   val rules = (Source fromPath args(0) getLines () map rule).toList.flatten
   
   def algorithm(input: String): String = rules find (input contains _._1) match {
     case Some((pattern, replacement, true)) => input replaceFirst ("\\Q"+pattern+"\\E", replacement)
     case Some((pattern, replacement, false)) => algorithm(input replaceFirst ("\\Q"+pattern+"\\E", replacement))
     case None => input
   }

   println(args(1))
   println(algorithm(args(1)))
 }

}</lang>

Script-style, and more concise:

<lang scala>import scala.io.Source

if (argv.size != 2 ) error("Syntax: MarkovAlgorithm inputFile inputPattern")

val rulePattern = """(.*?)\s+->\s+(\.?)(.*)""".r val isComment = (_: String) matches "#.*|\\s*" val rules = Source fromPath args(0) getLines () filterNot isComment map (rulePattern unapplySeq _ get) toList;

def algorithm(input: String): String = rules find (input contains _.head) match {

 case Some(Seq(pattern, ".", replacement)) => input replaceFirst ("\\Q"+pattern+"\\E", replacement)
 case Some(Seq(pattern, "", replacement)) => algorithm(input replaceFirst ("\\Q"+pattern+"\\E", replacement))
 case None => input

}

println(argv(1)) println(algorithm(argv(1)))</lang>

Sample outputs:

C:\>scala MarkovAlgorithm ruleset1.txt "I bought a B of As from T S."
I bought a B of As from T S.
I bought a bag of apples from my brother.

C:\>scala MarkovAlgorithm ruleset2.txt "I bought a B of As from T S."
I bought a B of As from T S.
I bought a bag of apples from T shop.

C:\>scala MarkovAlgorithm ruleset3.txt "I bought a B of As W my Bgage from T S."
I bought a B of As W my Bgage from T S.
I bought a bag of apples with my money from T shop.

C:\>scala MarkovAlgorithm ruleset4.txt "_1111*11111_"
_1111*11111_
11111111111111111111

The script is called much in the same way, but with the ".scala" extension added.

Tcl

Works with: Tcl version 8.5

<lang tcl>package require Tcl 8.5 if {$argc < 3} {error "usage: $argv0 ruleFile inputFile outputFile"} lassign $argv ruleFile inputFile outputFile

1. Read the file of rules

set rules {} set f [open $ruleFile] foreach line [split [read $f] \n[close $f]] {

   if {[string match "#*" $line] || $line eq ""} continue
   if {[regexp {^(.+)\s+->\s+(\.?)(.*)$} $line -> from final to]} {

lappend rules $from $to [string compare "." $final] [string length $from]

   } else {

error "Syntax error: \"$line\""

   }

}

1. Apply the rules

set f [open $inputFile] set out [open $outputFile w] foreach line [split [read $f] \n[close $f]] {

   set any 1
   while {$any} {

set any 0 foreach {from to more fl} $rules { # If we match the 'from' pattern... if {[set idx [string first $from $line]] >= 0} { # Change for the 'to' replacement set line [string replace $line $idx [expr {$idx+$fl-1}] $to]

# Stop if we terminate, otherwise note that we've more work to do

       	set any $more

break; # Restart search for rules to apply } }

       #DEBUG# puts $line
   }

   # Output the processed line
   puts $out $line

} close $out</lang> In the case where there are no terminating rules and no overlapping issues, the following is an alternative: <lang tcl>package require Tcl 8.5 if {$argc < 3} {error "usage: $argv0 ruleFile inputFile outputFile"} lassign $argv ruleFile inputFile outputFile

1. Read the file of rules

set rules {} set f [open $ruleFile] foreach line [split [read $f] \n[close $f]] {

   if {[string match "#*" $line] || $line eq ""} continue
   if {[regexp {^(.+)\s+->\s+(.*)$} $line -> from to]} {
       dict set rules $from $to
   } else {

error "Syntax error: \"$line\""

   }

}

1. Apply the rules in a simplistic manner

set in [open $inputFile] set out [open $outputFile w] set data [read $in] close $in while 1 {

   set newData [string map $rules $data]
   if {$newData eq $data} break
   set data $newData

} puts $out $data close $out</lang>

VBScript

Implementation

<lang vb> class markovparser

dim aRules public property let ruleset( sBlock ) dim i aRules = split( sBlock, vbNewLine ) '~ remove blank lines from end of array do while aRules( ubound( aRules ) ) = vbnullstring redim preserve aRules( ubound( aRules ) - 1 ) loop '~ parse array for i = lbound( aRules ) to ubound( aRules ) if left( aRules( i ), 1 ) = "#" then aRules( i ) = Array( vbnullstring, aRules(i)) else aRules( i ) = Split( aRules( i ), " -> ", 2 ) end if next end property

public function apply( sArg ) dim ruleapplied dim terminator dim was dim i dim repl dim changes

ruleapplied = true terminator = false

do while ruleapplied and (not terminator) changes = 0 was = sArg for i = lbound( aRules ) to ubound( aRules ) repl = aRules(i)(1) if left( repl, 1 ) = "." then terminator = true repl = mid( repl, 2 ) end if sArg = replace( sArg, aRules(i)(0), repl) if was <> sArg then changes = changes + 1 if changes = 1 then exit for end if end if if terminator then exit for end if next if changes = 0 then ruleapplied = false end if loop apply = sArg end function

sub dump dim i for i = lbound( aRules ) to ubound( aRules ) wscript.echo eef(aRules(i)(0)=vbnullstring,aRules(i)(1),aRules(i)(0)& " -> " & aRules(i)(1)) & eef( left( aRules(i)(1), 1 ) = ".", " #terminator", "" ) next end sub

private function eef( bCond, sExp1, sExp2 ) if bCond then eef = sExp1 else eef = sExp2 end if end function end class </lang>

Invocation

<lang vb> dim m1 set m1 = new markovparser m1.ruleset = "# This rules file is extracted from Wikipedia:" & vbNewLine & _ "# http://en.wikipedia.org/wiki/Markov_Algorithm" & vbNewLine & _ "A -> apple" & vbNewLine & _ "B -> bag" & vbNewLine & _ "S -> shop" & vbNewLine & _ "T -> the" & vbNewLine & _ "the shop -> my brother" & vbNewLine & _ "a never used -> .terminating rule" wscript.echo m1.apply( "I bought a B of As from T S.")

dim m2 set m2 = new markovparser m2.ruleset = replace( "# Slightly modified from the rules on Wikipedia\nA -> apple\nB -> bag\nS -> .shop\nT -> the\nthe shop -> my brother\na never used -> .terminating rule", "\n", vbNewLine ) '~ m1.dump wscript.echo m2.apply( "I bought a B of As from T S.")

dim m3 set m3 = new markovparser m3.ruleset = replace("# BNF Syntax testing rules\nA -> apple\nWWWW -> with\nBgage -> ->.*\nB -> bag" & vbNewLine & _ "->.* -> money\nW -> WW\nS -> .shop\nT -> the\nthe shop -> my brother\na never used -> .terminating rule", "\n", vbNewLine ) wscript.echo m3.apply("I bought a B of As W my Bgage from T S.")

set m4 = new markovparser m4.ruleset = "### Unary Multiplication Engine, for testing Markov Algorithm implementations" & vbNewLine & _ "### By Donal Fellows." & vbNewLine & _ "# Unary addition engine" & vbNewLine & _ "_+1 -> _1+" & vbNewLine & _ "1+1 -> 11+" & vbNewLine & _ "# Pass for converting from the splitting of multiplication into ordinary" & vbNewLine & _ "# addition" & vbNewLine & _ "1! -> !1" & vbNewLine & _ ",! -> !+" & vbNewLine & _ "_! -> _" & vbNewLine & _ "# Unary multiplication by duplicating left side, right side times" & vbNewLine & _ "1*1 -> x,@y" & vbNewLine & _ "1x -> xX" & vbNewLine & _ "X, -> 1,1" & vbNewLine & _ "X1 -> 1X" & vbNewLine & _ "_x -> _X" & vbNewLine & _ ",x -> ,X" & vbNewLine & _ "y1 -> 1y" & vbNewLine & _ "y_ -> _" & vbNewLine & _ "# Next phase of applying" & vbNewLine & _ "1@1 -> x,@y" & vbNewLine & _ "1@_ -> @_" & vbNewLine & _ ",@_ -> !_" & vbNewLine & _ "++ -> +" & vbNewLine & _ "# Termination cleanup for addition" & vbNewLine & _ "_1 -> 1" & vbNewLine & _ "1+_ -> 1" & vbNewLine & _ "_+_ -> " '~ m4.dump wscript.echo m4.apply( "_1111*11111_")

set fso = createobject("scripting.filesystemobject") set m5 = new markovparser m5.ruleset = fso.opentextfile("busybeaver.tur").readall wscript.echo m5.apply("000000A000000") </lang>

Output

<lang vb> I bought a bag of apples from my brother. I bought a bag of apples from T shop. I bought a bag of apples with my money from T shop. 11111111111111111111 00011H1111000 </lang>