Execute a Markov algorithm

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


Task

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   .   (period)   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 


markov = cluster is make, run
    rule = struct[from, to: string, term: bool]
    rep = array[rule]
 
    % Remove leading and trailing whitespace from a string
    trim = proc (s: string) returns (string)
        ac = array[char]
        sc = sequence[char]
        own ws: string := "\n\t "
        a: ac := string$s2ac(s) 
        while ~ac$empty(a) cand string$indexc(ac$bottom(a), ws) ~= 0 do 
            ac$reml(a)
        end
        while ~ac$empty(a) cand string$indexc(ac$top(a), ws) ~= 0 do
            ac$remh(a)
        end
        return(string$sc2s(sc$a2s(a)))
    end trim
 
    % Parse a single Markov rule
    parse = proc (s: string) returns (rule) signals (comment, invalid(string))
        if string$empty(s) cor s[1]='#' then signal comment end
        arrow: int := string$indexs(" -> ", s)
        if arrow=0 then signal invalid(s) end
        left: string := trim(string$substr(s, 1, arrow-1))
        right: string := trim(string$rest(s, arrow+4))
 
        if ~string$empty(right) cand right[1] = '.' then
            right := string$rest(right, 2)
            return(rule${from: left, to: right, term: true})
        else
            return(rule${from: left, to: right, term: false})
        end
    end parse
 
    % Add a rule to the list
    add_rule = proc (m: cvt, s: string) signals (invalid(string))
        rep$addh(m, parse(s)) resignal invalid
        except when comment: end
    end add_rule
 
    % Read rules in sequence from a stream
    add_rules = proc (m: cvt, s: stream) signals (invalid(string))
        while true do
            add_rule(up(m), stream$getl(s)) resignal invalid
            except when end_of_file: break end
        end
    end add_rules
 
    make = proc (s: stream) returns (cvt) signals (invalid(string))
        a: rep := rep$new()
        add_rules(up(a), s)
        return(a)
    end make
 
    % Apply a rule to a string
    apply_rule = proc (r: rule, s: string) returns (string) signals (no_match)
        match: int := string$indexs(r.from, s)
        if match = 0 then signal no_match end
        new: string := string$substr(s, 1, match-1)
                    || r.to 
                    || string$rest(s, match+string$size(r.from))
        return(new)
    end apply_rule
 
    % Apply all rules to a string repeatedly
    run = proc (c: cvt, s: string) returns (string)
        i: int := 1 
        while i <= rep$high(c) do
            r: rule := c[i]
            begin
                s := apply_rule(r, s)
                i := 1
                if r.term then break end
            end except when no_match: 
                i := i+1 
            end
        end
        return(s)
    end run
end markov
 
start_up = proc ()
    po: stream := stream$primary_output()
    eo: stream := stream$error_output()
 
    begin
        args: sequence[string] := get_argv()
        file: string := args[1]
        input: string := args[2]
        fs: stream := stream$open(file_name$parse(file), "read")
        mkv: markov := markov$make(fs)
        stream$close(fs)
        stream$putl(po, markov$run(mkv, input))
    end except 
        when bounds: stream$putl(eo, "Arguments: markov [filename] [string]")
        when not_possible(s: string): stream$putl(eo, "File error: " || s)
        when invalid(s: string): stream$putl(eo, "Parse error: " || s)
    end
end start_up