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 


module MarkovAlgos
 
struct MarkovRule{F,T}
    patt::F
    repl::T
    term::Bool
end
 
isterminating(r::MarkovRule) = r.term
Base.show(io::IO, rule::MarkovRule) =
    print(io, rule.patt, " → ", isterminating(rule) ? "." : "", rule.repl)
function Base.convert(::Type{MarkovRule}, s::AbstractString)
    rmatch = match(r"^(.+)\s+->\s*(\.)?(.*)?$", s)
    if rmatch ≡ nothing || isempty(rmatch.captures)
        throw(ParseError("not valid rule: " * s))
    end
    patt, term, repl = rmatch.captures
    return MarkovRule(patt, repl ≢ nothing ? repl : "", term ≢ nothing)
end
 
function ruleset(file::Union{AbstractString,IO})
    ruleset = Vector{MarkovRule}(0)
    for line in eachline(file)
        ismatch(r"(^#|^\s*$)", line) || push!(ruleset, MarkovRule(line))
    end
    return ruleset
end
 
apply(text::AbstractString, rule::MarkovRule) = replace(text, rule.patt, rule.repl)
function apply(file::Union{AbstractString,IO}, ruleset::AbstractVector{<:MarkovRule})
    text = readstring(file)
    redo = !isempty(text)
    while redo
        matchrule = false
        for rule in ruleset
            if contains(text, rule.patt)
                matchrule = true
                text = apply(text, rule)
                redo = !isterminating(rule)
                break
            end
        end
        redo = redo && matchrule
    end
    return text
end
 
end  # module MarkovAlgos