Figuring out how to expand a grammar (Python)

Question

Im trying to write code that will return an expanding grammar. so in this example I will specify a length of 3, N = N D will expand it self to N = N D D and then it will expand again to N = N D D D but then exit the program, any advice for making this happen? I currently tried to do the replace method in printGrammar but as you can see when you run it for some reason NT (the non terminal being replaced, in this example N), and item (the value from the dictionary, in this case N D and D) wont replace and I am left with a list with 'N' instead of what I want which is N D D, can someone please help me?

Binary.txt is:

N = N D
N = D
D = 0
D = 1

Code is

import sys
import string
from collections import defaultdict

#default length of 3
stringLength = 3

#get last argument of command line(file)
if len(sys.argv) == 1:
    #get a length from user
    try:
        stringLength = int(input('Length? '))
        filename = input('Filename: ')
    except ValueError:
        print("Not a number")

elif len(sys.argv) == 2:
    #get a length from user
    try:
        stringLength = int(input('Length? '))
        filename = sys.argv[1]
    except ValueError:
        print("Not a number")

elif len(sys.argv) == 3:
    filename = sys.argv[2]
    stringLength  = sys.argv[1].split('l')[1]
else:
    print("Invalid input!")


#get start symbol
with open(filename, "r") as grammar:
    #read file 
    lines = grammar.readlines()
    start = lines[0].split('=')[0]
    start = start.replace(" ", "")


#checks

#print(stringLength)
#print(filename)
#print(start)
def str2dict(filename):
    result = defaultdict(list)
    with open(filename, "r") as grammar:
        #read file 
        lines = grammar.readlines()
        count = 0

        #loop through
        for line in lines:
            #append info 
            line = line.rstrip()

            result[line[0]].append(line.split('=')[1])

    return result


workingDict = str2dict("Binary.txt")
print(workingDict)


def strings(grammar, start):
    queue = [start]
    while len(queue):
        current = queue.pop(0)
        # for each symbol in the current string
        for n, sym in enumerate(current):
            # if this symbol is a non-terminal
            if sym in grammar:
                # for each rule for this symbol...
                for rhs in grammar[sym]:
                    # replace it with the right part
                    new = current[:n] + rhs + current[n+1:]
                    # does the result contain non-terminals
                    if any(s in grammar for s in new):
                        # yes, place it into the queue
                        queue.append(new)
                    else:
                        # no, return it
                        yield new

for x in strings(workingDict, stringLength):
    print (x)
    if len(x) > 4:
        break

Answer 1

Assuming your grammar is in the form

grammar = {
    'N': ['ND', 'D'],
    'D': ['0', '1']
}

the algorithm looks straightforward:

• iterate over the current string (which is initially just one symbol)
• if the symbol is a non-terminal, replace it with its production
• if the result contains non-terminals, place it in a queue for further processing
• otherwise, return the result (which is a string of terminals)
• pick the next "current" string from the top of the queue and continue

:

def strings(grammar, start):
    queue = [start]
    while len(queue):
        current = queue.pop(0)
        # for each symbol in the current string
        for n, sym in enumerate(current):
            # if this symbol is a non-terminal
            if sym in grammar:
                # for each rule for this symbol...
                for rhs in grammar[sym]:
                    # replace it with the right part
                    new = current[:n] + rhs + current[n+1:]
                    # does the result contain non-terminals
                    if any(s in grammar for s in new):
                        # yes, place it into the queue
                        queue.append(new)
                    else:
                        # no, return it
                        yield new

Usage:

for x in strings(grammar, 'N'):
    print x
    if len(x) > 4:
        break