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This commit is contained in:
Alex Thannhauser
parent
dc8e79a9fa
commit
3feedab95c
1 changed files with 120 additions and 65 deletions
185
main.py
185
main.py
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@ -8,51 +8,68 @@ import sys;
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def parse_args(argv):
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parser = argparse.ArgumentParser(prog = '4-variable-simplifier');
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parser.add_argument('-c', '--command', help = '''
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Provide a boolean expression to simpliy on the command-line.
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Without this option, boolean expressions are read stdin.
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''')
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parser.add_argument('-e', '--extended-operators', action='store_true', help='''
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Use more than just the standard three boolean operators (not, or, and).
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This options allows use of: nor, nand, xor, nxor, andn, orn.
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''')
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parser.add_argument('-o', '--custom-operators', help='''
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Pick and choose which operators the simplifier can use. Comma seperated.
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You can refer to them using their names or their symbols.
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''')
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parser.add_argument('-E', '--experimental-operators', help='''
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For two boolean variables, there are four possible inputs into a
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binary operator. For each of those four an operator could return true
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or false. That would mean in theory there could exist up to 16
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theoretical operators with different behaviours. Even with the
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'extended operators' option, we're only introducing 9 possible
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operators, that's less that 60% of the possibilities!
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Some of these would of course be useless, like a binary operator that
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always produces 'false' regardless of the input, for instance, but
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other may be extremely useful for acting in place of much more complex
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trees of operators. In theory, the simplifier would produce the
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smallest most compact expression trees possible.
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Of course, no one would implement something like this and dare
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to anger the logic gods...
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''')
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parser.add_argument("-n", '--use-names', help='''
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Print the operator's names in the expression tree, rather than the
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symbols.
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''')
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parser.add_argument('-p', "--printout", action = 'store_true', help='''
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Print out all simplified expressions for the given expressions and
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quit.
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''')
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parser.add_argument("--simplifications-file", \
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default = ".simplifications.bin", help='''
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Path to pickle file that stores the cached simplifications.
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''')
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parser.add_argument("-y", "--yes", action = 'store_true', help='''
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Do not ask before generating simplification cache.
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''')
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parser.add_argument("-q", "--quiet", action = 'store_true', help='''
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Do not print anything but the simplification. Assumes '--yes'.
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''')
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parser.add_argument("-C", "--color", default = 'auto', \
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choices = ["off", "on", "auto"], help='''
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Select whether to use terminal colors. Default is to use if it is
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supported. use '--color=on' to force it on. '--color=off' otherwise.
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''')
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return parser.parse_args(argv[1:]);
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symbol_to_name = {
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@ -69,14 +86,32 @@ symbol_to_name = {
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def determine_available_operators(args):
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standard = ("!", "||", "&&");
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extended = ("!|", "!&", "!=", "==", "|!", "&!");
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experimental = (
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"<0000>",
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"<0001>",
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"<0010>",
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"<0011>",
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"<0100>",
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"<0101>",
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"<0110>",
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"<0111>",
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"<1000>",
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"<1001>",
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"<1010>",
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"<1011>",
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"<1100>",
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"<1101>",
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"<1110>",
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"<1111>");
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if args.extended_operators:
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return set(standard + extended);
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elif args.custom_operators:
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available_operators = set();
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for o in args.custom_operators.split(","):
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if o in symbol_to_name:
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available_operators.add(o);
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@ -86,8 +121,10 @@ def determine_available_operators(args):
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available_operators.add(k);
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else:
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raise BaseException(f"not an operator: '{o}'");
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return available_operators;
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elif args.experimental_operators:
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return set(experimental);
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else:
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return set(standard);
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@ -95,16 +132,16 @@ def pretty(exp):
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match exp:
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case ("literal", x):
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return str(x);
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case ("variable", x):
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return x
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case (op, inner):
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return f"({op}{pretty(inner)})"
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case (op, left, right):
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return f"({pretty(left)} {op} {pretty(right)})"
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case _:
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print(exp);
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assert(not "TODO");
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@ -122,16 +159,16 @@ def calculate_simplifications(args, available_operators):
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costs = dict() # truthtable -> cost
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todo = [set() for _ in range(100)] # indexed by cost, set of truthtables.
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todo_count = [0]; # I have to wrap in an array because python is dumb.
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def prequeue(truthtable, expression, cost):
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lookup[truthtable] = expression;
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costs[truthtable] = cost;
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todo[cost].add(truthtable);
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todo_count[0] += 1;
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# literals:
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# literals:
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prequeue(0b1111_1111_1111_1111, ("literal", 1), cost = 1);
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prequeue(0b0000_0000_0000_0000, ("literal", 0), cost = 1);
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@ -140,7 +177,7 @@ def calculate_simplifications(args, available_operators):
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prequeue(X, ("variable", "x"), cost = 0);
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prequeue(Y, ("variable", "y"), cost = 0);
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prequeue(Z, ("variable", "z"), cost = 0);
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# Completely unnecessary critera, alphabetical variables is more
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# aesthetically pleasing. Thanks Benson.
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def is_aesthetically_better(this, that):
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@ -165,32 +202,52 @@ def calculate_simplifications(args, available_operators):
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}
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binary_operators = {
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'||': lambda x, y: (x | y) & M,
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'&&': lambda x, y: (x & y) & M,
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'||': lambda x, y: (x | y) & M, # or
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'&&': lambda x, y: (x & y) & M, # and
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'!|': lambda x, y: ~(x | y) & M,
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'!&': lambda x, y: ~(x & y) & M,
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'!|': lambda x, y: ~(x | y) & M, # nor
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'!&': lambda x, y: ~(x & y) & M, # nand
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'&!': lambda x, y: (~x & y) & M,
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'|!': lambda x, y: (~x | y) & M,
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'&!': lambda x, y: (~x & y) & M, # andn
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'|!': lambda x, y: (~x | y) & M, # orn
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'!=': lambda x, y: (x ^ y) & M,
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'==': lambda x, y: (~(x ^ y)) & M,
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'!=': lambda x, y: (x ^ y) & M, # xor
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'==': lambda x, y: (~(x ^ y)) & M, # nxor
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# these were found by running the simplifier with -o xor,and,or,not
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# 1100 - x
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# 1010 - y
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"<0000>": lambda x, y: 0, # 0
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"<0001>": lambda x, y: 0, # ((x == 0) && (y == 0)) || 0
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"<0010>": lambda x, y: 0, # ((x == 0) && (y == 1)) || 0
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"<0011>": lambda x, y: 0, # ((x == 0) && (y == 1)) || ((x == 0) && (y == 0)) || 0
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"<0100>": lambda x, y: 0, # ((x == 1) && (y == 0)) || 0
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"<0101>": lambda x, y: 0, # ((x == 1) && (y == 0)) || ((x == 0) && (y == 0)) || 0
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"<0110>": lambda x, y: 0, # ((x == 1) && (y == 0)) || ((x == 0) && (y == 1)) || 0
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"<0111>": lambda x, y: 0, # ((x == 1) && (y == 0)) || ((x == 0) && (y == 1)) || ((x == 0) && (y == 0)) || 0
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"<1000>": lambda x, y: 0, # ((x == 1) && (y == 1)) || 0
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"<1001>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 0) && (y == 0)) || 0
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"<1010>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 0) && (y == 1)) || 0
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"<1011>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 0) && (y == 1)) || ((x == 0) && (y == 0)) || 0
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"<1100>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 1) && (y == 0)) || 0
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"<1101>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 1) && (y == 0)) || ((x == 0) && (y == 0)) || 0
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"<1110>": lambda x, y: 0, # ((x == 1) && (y == 1)) || ((x == 1) && (y == 0)) || ((x == 0) && (y == 1)) || 0
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"<1111>": lambda x, y: M, # ((x == 1) && (y == 1)) || ((x == 1) && (y == 0)) || ((x == 0) && (y == 1)) || ((x == 0) && (y == 0)) || 0
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}
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def print_status():
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numerator = 65536 - todo_count[0];
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denominator = 65536
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line = f'{numerator} of 65536';
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line += f' ({numerator / denominator * 100:.2f}%):'
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line += f' [{my_cost}]';
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line += f' {pretty(my_expression)}';
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print(line);
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min_cost = 0;
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while todo_count[0]:
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truthtables = todo[min_cost];
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@ -205,17 +262,17 @@ def calculate_simplifications(args, available_operators):
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my_cost = min_cost;
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my_expression = lookup[my_truthtable];
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todo_count[0] -= 1;
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if not args.quiet:
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print_status();
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def consider(new_truthtable, new_expression, new_cost):
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if new_truthtable not in costs:
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todo[new_cost].add(new_truthtable);
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costs[new_truthtable] = new_cost
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lookup[new_truthtable] = new_expression
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todo_count[0] += 1;
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elif new_cost < costs[new_truthtable] or \
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(new_cost == costs[new_truthtable] and \
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@ -266,13 +323,13 @@ pathname = "simplifications.bin"
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def get_simplifications(args, available_operators):
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available_operators = tuple(sorted(available_operators));
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try:
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with open(pathname, "rb") as stream:
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cache = pickle.load(stream);
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except FileNotFoundError:
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cache = dict();
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if available_operators not in cache:
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if not args.quiet:
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print("Oh! looks like you're running this for the first time");
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@ -284,24 +341,24 @@ def get_simplifications(args, available_operators):
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print();
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input("any input to start:");
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print();
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bundle = calculate_simplifications(args, available_operators);
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if not args.quiet:
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print();
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print("done!");
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print();
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cache[available_operators] = bundle;
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with open(pathname, "wb") as stream:
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pickle.dump(cache, stream);
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if not args.quiet:
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print();
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print("saved!");
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print();
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return cache[available_operators];
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def create_parser():
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@ -343,7 +400,7 @@ def create_parser():
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| logical_and_expression;
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root <<= logical_or_expression;
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return root;
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@ -396,35 +453,34 @@ def evaluate(expr):
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def repl(args, cost, lookup):
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import readline;
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print("Give a boolean expression using the variables 'w', 'x', 'y' and 'z'.");
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print("Operations: not ('!'), or ('||'), and ('&&').""");
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print();
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if args.extended_operators:
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print("Extended operations: nor ('!|'), orn ('|!'), nand ('!&'), ");
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print("andn ('&!'), xor ('!='), and nxor ('==')");
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print();
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# print(f'I can do anything in {max(cost.values())} operations.')
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# print();
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parser = create_parser();
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while True:
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try:
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line = input(">>> ");
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except EOFError:
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return;
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line = line.strip();
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if not line: continue;
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truthtable = evaluate(parse(parser, line));
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if truthtable in lookup:
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print(f'{cost[truthtable]}: {pretty(lookup[truthtable])}')
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else:
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@ -432,29 +488,28 @@ def repl(args, cost, lookup):
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def main(args):
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available_operators = determine_available_operators(args);
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match args.color:
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case 'off': args.color = False;
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case 'on': args.color = True;
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case 'auto': args.color = os.isatty(1);
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cost, lookup = get_simplifications(args, available_operators);
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if args.printout:
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for truthtable, exp in sorted(lookup.items()):
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print(f'{truthtable:016b}: {pretty(exp)}');
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elif args.command:
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truthtable = evaluate(parse(create_parser(), args.command));
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if truthtable in lookup:
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print(pretty(lookup[truthtable]));
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else:
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print('unreachable.')
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else:
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repl(args, cost, lookup);
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return 0;
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return 0;
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exit(main(parse_args(sys.argv)))
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