|
| 1 | +TOKENS = { |
| 2 | + 'AND': 'AND', |
| 3 | + '.': 'AND', |
| 4 | + 'OR': 'OR', |
| 5 | + '+': 'OR', |
| 6 | + 'NOT': 'NOT', |
| 7 | + '!': 'NOT', |
| 8 | + '^': 'NOT', |
| 9 | + '¬': 'NOT', |
| 10 | + '(': 'OPEN_PAREN', |
| 11 | + ')': 'CLOSE_PAREN', |
| 12 | +} |
| 13 | + |
| 14 | +OPERATORS = ['AND', 'OR', 'NOT'] |
| 15 | + |
| 16 | +DEBUG_LOGGING = False |
| 17 | + |
| 18 | + |
| 19 | +Table = list[list[bool | None]] |
| 20 | +Expression = tuple[list[str], list[str]] |
| 21 | + |
| 22 | + |
| 23 | +def debug_print(*values): |
| 24 | + if DEBUG_LOGGING: |
| 25 | + print(*values) |
| 26 | + |
| 27 | + |
| 28 | +def print_table(expr: Expression, table: Table) -> None: |
| 29 | + '''Prints a table in a nice format.''' |
| 30 | + |
| 31 | + header = ' '.join(expr[1]) + ' | Result' |
| 32 | + print(header) |
| 33 | + print('-' * len(header)) |
| 34 | + |
| 35 | + for row in table: |
| 36 | + print(' '.join([ ('1' if x else '0') for x in row[:-1] ]), '|', '1' if row[-1] else '0') |
| 37 | + |
| 38 | + |
| 39 | + |
| 40 | +def tokenise(text: str) -> Expression: |
| 41 | + '''Converts a boolean expression string into a list of tokens.''' |
| 42 | + |
| 43 | + tokens: list[str] = [] |
| 44 | + variables: list[str] = [] |
| 45 | + text = text.upper() |
| 46 | + |
| 47 | + i: int = 0 |
| 48 | + while True: |
| 49 | + if i >= len(text): |
| 50 | + break |
| 51 | + |
| 52 | + char = text[i] |
| 53 | + |
| 54 | + if char == ' ': |
| 55 | + i += 1 |
| 56 | + continue |
| 57 | + |
| 58 | + if ' ' in text[i:]: |
| 59 | + next_word_index = text.index(' ', i) |
| 60 | + else: |
| 61 | + next_word_index = len(text) - 1 |
| 62 | + |
| 63 | + word = text[i:next_word_index] |
| 64 | + |
| 65 | + debug_print(f'{char} {next_word_index} {word}') |
| 66 | + |
| 67 | + if word in TOKENS: |
| 68 | + tokens.append(TOKENS[word]) |
| 69 | + i = next_word_index |
| 70 | + continue |
| 71 | + |
| 72 | + if char in TOKENS: |
| 73 | + tokens.append(TOKENS[char]) |
| 74 | + i += 1 |
| 75 | + continue |
| 76 | + |
| 77 | + if char not in variables: |
| 78 | + variables.append(char) |
| 79 | + |
| 80 | + tokens.append(f'VAR_{char}') |
| 81 | + |
| 82 | + i += 1 |
| 83 | + |
| 84 | + variables.sort() |
| 85 | + |
| 86 | + return tokens, variables |
| 87 | + |
| 88 | + |
| 89 | + |
| 90 | +def prepare_table(expr: Expression): |
| 91 | + variables = { x[0]: 0 for x in expr[1] } |
| 92 | + |
| 93 | + num_rows = 2 ** len(variables) |
| 94 | + table: Table = [] |
| 95 | + |
| 96 | + for row in range(num_rows): |
| 97 | + bin_str = bin(row)[2:].zfill(len(variables)) # Remove 0b prefix |
| 98 | + table.append([ bool(int(x)) for x in bin_str ]) |
| 99 | + table[row].append(None) |
| 100 | + |
| 101 | + return table |
| 102 | + |
| 103 | + |
| 104 | + |
| 105 | +def simulate(expr: Expression, table: Table): |
| 106 | + |
| 107 | + tokens = expr[0] |
| 108 | + variables = expr[1] |
| 109 | + |
| 110 | + for row in table: |
| 111 | + for i, token in enumerate(tokens): |
| 112 | + if token in OPERATORS: |
| 113 | + result: bool | None = None |
| 114 | + |
| 115 | + match token: |
| 116 | + case 'AND': |
| 117 | + operand1_token = tokens[i - 1] |
| 118 | + operand2_token = tokens[i + 1] |
| 119 | + operand1 = row[variables.index(operand1_token.replace('VAR_', ''))] |
| 120 | + operand2 = row[variables.index(operand2_token.replace('VAR_', ''))] |
| 121 | + result = operand1 and operand2 |
| 122 | + case 'OR': |
| 123 | + operand1_token = tokens[i - 1] |
| 124 | + operand2_token = tokens[i + 1] |
| 125 | + operand1 = row[variables.index(operand1_token.replace('VAR_', ''))] |
| 126 | + operand2 = row[variables.index(operand2_token.replace('VAR_', ''))] |
| 127 | + result = operand1 or operand2 |
| 128 | + case 'NOT': |
| 129 | + operand1_token = tokens[i + 1] |
| 130 | + operand1 = row[variables.index(operand1_token.replace('VAR_', ''))] |
| 131 | + result = not operand1 |
| 132 | + |
| 133 | + row[-1] = result |
| 134 | + |
| 135 | + return table |
| 136 | + |
| 137 | + |
| 138 | + |
| 139 | + |
| 140 | + |
| 141 | +def main(): |
| 142 | + '''Main program loop.''' |
| 143 | + |
| 144 | + print('Basic information:') |
| 145 | + print(' - inputs should be letters, case insensitive (i.e. a=A)') |
| 146 | + print(' - allowed gates: AND (.), OR (+), NOT (!,¬,^)') |
| 147 | + print(' - allowed punctuation: (, )') |
| 148 | + print(' - enter \'q\' to quit') |
| 149 | + |
| 150 | + stop = False |
| 151 | + while not stop: |
| 152 | + |
| 153 | + expr1 = tokenise('A AND B . C OR A') |
| 154 | + debug_print(f'Tokens: {",".join(expr1[0])}') |
| 155 | + debug_print(f'Variables: {",".join(expr1[1])}') |
| 156 | + |
| 157 | + table1 = prepare_table(expr1) |
| 158 | + table1 = simulate(expr1, table1) |
| 159 | + |
| 160 | + print_table(expr1, table1) |
| 161 | + |
| 162 | + |
| 163 | + stop = True |
| 164 | + |
| 165 | + |
| 166 | + |
| 167 | +if __name__ == '__main__': |
| 168 | + main() |
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