How to resolve the algorithm Execute a Markov algorithm step by step in the Python programming language

Problem Statement
Step by Step Solution
Sourcecode

Problem Statement

Create an interpreter for a Markov Algorithm. Rules have the syntax: There is one rule per line. If there is a . (period) present before the , 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:

Sample text of: Should generate the output:

A test of the terminating rule Sample text of: Should generate:

This tests for correct substitution order and may trap simple regexp based replacement routines if special regexp characters are not escaped. Sample text of: Should generate:

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.) Sample text of: should generate the output:

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. This ruleset should turn into

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Execute a Markov algorithm step by step in the Python programming language

This Python code is based on the Markov Algorithm, which is a type of grammar-based text rewrite system. The code defines a set of rules for rewriting text, and then uses these rules to transform input text.

Here is a detailed explanation of the code:

The extractreplacements function takes a string of grammar rules as input and returns a list of replacement rules. Each replacement rule consists of a pattern, a replacement string, and a boolean flag indicating whether the rule is a terminating rule.
The replace function takes a string of text and a list of replacement rules as input. It repeatedly applies the replacement rules to the input text until no more rules can be applied.
The syntaxre regular expression defines the format of the grammar rules. The rules consist of three parts: a pattern, a replacement string, and a terminating rule flag.
The grammar1, grammar2, grammar3, grammar4, and grammar5 strings contain different sets of grammar rules.
The text1, text2, text3, and text4 strings contain different input texts.

The following example shows how the code can be used to rewrite text:

>>> text = "I bought a B of As from T S."
>>> replacements = extractreplacements(grammar1)
>>> replace(text, replacements)
'I bought a bag of apples from my brother.'

In this example, the input text is "I bought a B of As from T S.", and the grammar rules are defined in the grammar1 string. The extractreplacements function is used to extract the replacement rules from the grammar, and the replace function is used to apply the rules to the input text. The output text is "I bought a bag of apples from my brother.", which is the result of applying the following replacement rules:

"B -> bag"
"A -> apple"
"T -> the"
"the shop -> my brother"

The code can be used to rewrite text in a variety of ways, depending on the grammar rules that are used. The example above shows how the code can be used to rewrite text into a more natural language form. However, the code could also be used to rewrite text into a different language, or to generate new text based on a set of rules.

Source code in the python programming language

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 = """\
# 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
"""
 
grammar2 = '''\
# 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 = '''\
# 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 = '''\
### 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
_+_ -> 
'''

grammar5 = '''\
# 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
'''

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'

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How to resolve the algorithm Execute a Markov algorithm step by step in the Python programming language

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Problem Statement

Step by Step solution about How to resolve the algorithm Execute a Markov algorithm step by step in the Python programming language

Source code in the python programming language