This program implements a recursive descent parser for grammar rules 5, 6, 7 below.

Please implement rules 1, 2, 3, 4 for this parser.

Relational operators in Rule 4 have spaces in front of and after each operator. The True and False literals in rule 3 also have spaces in front of and after each operator.

'|' means the | is a terminal symbol.

| alone is a meta-symbol separating different rewriting rules.

1 { '|' }

2 { '&' }

3 ( ) | '~' | ' True ' | ' False ' |

4 ' < ' | ' > ' | ' <= ' | ' >= ' | ' == '

5 { '+' | '-' }

6 { '*' | '/' }

7 () | | 'e'

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import math

class ParseError(Exception): pass

i = 0

err = None

def texpression(): #implement rule 1

def tterm(): #implement rule 2

def tfact(): #implement rule 3

def relational(): #implement rule 4

def expression():

global i, err

val = term()

while True:

if s[i] == '+':

i += 1

val = operations('+', val, term())

elif s[i] == '-':

i += 1

val = operations('-', val, term())

else:

break

return val

def term():

global i, err

val = factor()

while True:

if s[i] == '*':

i += 1

val = operations('*', val, factor())

elif s[i] == '/':

i += 1

val = operations('/', val, factor())

else:

break

return val

def factor():

global i, err

val = None

if s[i] == '(':

i += 1

val = expression()

if s[i] == ')':

i += 1

return val

else:

print('missing )')

raise ParseError

elif s[i] == 'e':

i += 1

return math.e

else:

try:

val = float(s[i])

i += 1

except ValueError:

print('number expected')

val = None

#print('factor returning', val)

if val == None: raise ParseError

return val

def operations(op, left, right):

if op == '+': return left + right

elif op == '-': return left - right

elif op == '*': return left * right

elif op == '/': return left / right

else: return None

def float(x):

return float(x)

s = input(' Expression: ')

while s != '':

for c in '()+-*/':

s = s.replace(c, ' '+c+' ')

s = s.split()

s.append('$') # EOF marker

print(' Token Stream: ', end = '')

for t in s: print(t, end = ' ')

print(' ')

i = 0

try:

print('val: ', bexpression())

except:

print('parse error')

print()

if s[i] != '$': print('Syntax error:')

print('read | did not read: ', end = '')

for c in s[:i]: print(c, end = ' ')

print(' | ', end = '')

for c in s[i:]: print(c, end = ' ')

print()

s = input(' Expression: ')

'''

Example:

Expression: 2*(3 + 4) < 15 & 1 + 2 == 3

Token Stream: 2 * ( 3 + 4 ) < 15 & 1 + 2 == 3 $

val: True

read : did not read: 2 * ( 3 + 4 ) < 15 & 1 + 2 == 3 : $

Expression: ~ 2*(3 + 4) < 15 & 1 + 2 == 3

Token Stream: ~ 2 * ( 3 + 4 ) < 15 & 1 + 2 == 3 $

val: False

read : did not read: ~ 2 * ( 3 + 4 ) < 15 & 1 + 2 == 3 : $

'''