Completed HW2

hw2/ints/examples.py

@@ -0,0 +1,26 @@
+from logic import *
+
+
+# Sentence: "If it's rains, it's wet".
+def rain_wet():
+    Rain = Atom('Rain')  # whether it's raining
+    Wet = Atom('Wet')  # whether it's wet
+    return Implies(Rain, Wet)
+
+
+# Sentence: "There is a light that shines."
+def light_shines():
+    def Light(x): return Atom('Light', x)  # whether x is lit
+
+    def Shines(x): return Atom('Shines', x)  # whether x is shining
+
+    return Exists('$x', And(Light('$x'), Shines('$x')))
+
+
+# Defining Parent in terms of Child.
+def parent_child():
+    def Parent(x, y): return Atom('Parent', x, y)  # whether x has a parent y
+
+    def Child(x, y): return Atom('Child', x, y)  # whether x has a child y
+
+    return Forall('$x', Forall('$y', Equiv(Parent('$x', '$y'), Child('$y', '$x'))))

hw2/ints/grader.py

@@ -0,0 +1,109 @@
+#!/usr/bin/env python3
+
+from logic import *
+
+import pickle, gzip, os, random
+import grader_util
+
+grader = grader_util.Grader()
+submission = grader.load('submission')
+
+# name: name of this formula (used to load the models)
+# predForm: the formula predicted in the submission
+# preconditionForm: only consider models such that preconditionForm is true
+def checkFormula(name, predForm, preconditionForm=None, handle_grader=True):
+    filename = os.path.join('models', name + '.pklz')
+    objects, targetModels = pickle.load(gzip.open(filename))
+    # If preconditionion exists, change the formula to
+    preconditionPredForm = And(preconditionForm, predForm) if preconditionForm else predForm
+    predModels = performModelChecking([preconditionPredForm], findAll=True, objects=objects)
+    ok = True
+    def hashkey(model): return tuple(sorted(str(atom) for atom in model))
+    targetModelSet = set(hashkey(model) for model in targetModels)
+    predModelSet = set(hashkey(model) for model in predModels)
+    for model in targetModels:
+        if hashkey(model) not in predModelSet:
+            if handle_grader:
+                grader.fail("Your formula (%s) says the following model is FALSE, but it should be TRUE:" % predForm)
+            ok = False
+            printModel(model)
+            return ok
+    for model in predModels:
+        if hashkey(model) not in targetModelSet:
+            if handle_grader:
+                grader.fail("Your formula (%s) says the following model is TRUE, but it should be FALSE:" % predForm)
+            ok = False
+            printModel(model)
+            return ok
+    if handle_grader:
+        grader.add_message('You matched the %d models' % len(targetModels))
+        grader.add_message('Example model: %s' % rstr(random.choice(targetModels)))
+        grader.assign_full_credit()
+    return ok
+
+# name: name of this formula set (used to load the models)
+# predForms: formulas predicted in the submission
+# predQuery: query formula predicted in the submission
+def addParts(name, numForms, predictionFunc):
+    # part is either an individual formula (0:numForms), all (combine everything)
+    def check(part):
+        predForms, predQuery = predictionFunc()
+        if len(predForms) < numForms:
+            grader.fail("Wanted %d formulas, but got %d formulas:" % (numForms, len(predForms)))
+            for form in predForms: print(('-', form))
+            return
+        if part == 'all':
+            checkFormula(name + '-all', AndList(predForms))
+        elif part == 'run':
+            # Actually run it on a knowledge base
+            kb = createModelCheckingKB()
+
+            # Need to tell the KB about the objects to do model checking
+            filename = os.path.join('models', name + '-all.pklz')
+            objects, targetModels = pickle.load(gzip.open(filename))
+            for obj in objects:
+                kb.tell(Atom('Object', obj))
+
+            # Add the formulas
+            for predForm in predForms:
+                response = kb.tell(predForm)
+                showKBResponse(response)
+                grader.require_is_true(response.status in [CONTINGENT, ENTAILMENT])
+            response = kb.ask(predQuery)
+            showKBResponse(response)
+
+        else:  # Check the part-th formula
+            checkFormula(name + '-' + str(part), predForms[part])
+
+    def createCheck(part): return lambda : check(part)  # To create closure
+
+    # run part-all once first for combined correctness, if true, trivially assign full score for all subparts
+    # this is to account for student adding formulas to the list in different orders but still get
+    # the combined preds correct.
+    all_is_correct = False
+    try:
+        predForms, predQuery = predictionFunc()
+        all_is_correct = checkFormula(name + '-all', AndList(predForms), handle_grader=False)
+    except BaseException:
+        pass
+
+    for part in list(range(numForms)) + ['all', 'run']:
+        if part == 'all':
+            description = 'test implementation of %s for %s' % (part, name)
+        elif part == 'run':
+            description = 'test implementation of %s for %s' % (part, name)
+        else:
+            description = 'test implementation of statement %s for %s' % (part, name)
+        if all_is_correct and not part in ['all', 'run']:
+            grader.add_basic_part(name + '-' + str(part), lambda : grader.assign_full_credit(), max_points=1, max_seconds=10000, description=description)
+        else:
+            grader.add_basic_part(name + '-' + str(part), createCheck(part), max_points=1, max_seconds=10000, description=description)
+
+############################################################
+# Problem 4: odd and even integers
+
+# Add 5a-[0-5], 5a-all, 5a-run
+addParts('4a', 6, submission.ints)
+
+
+grader.grade()

hw2/ints/grader_util.py

@@ -0,0 +1,448 @@
+"""
+Library to do grading of Python programs.
+Usage (see grader.py):
+
+    # create a grader
+    grader = Grader("Name of assignment")
+
+    # add a basic test
+    grader.addBasicPart(number, grade_func, max_points, max_seconds, description="a basic test")
+
+    # add a hidden test
+    grader.addHiddenPart(number, grade_func, max_points, max_seconds, description="a hidden test")
+
+    # add a manual grading part
+    grader.addManualPart(number, grade_func, max_points, description="written problem")
+
+    # run grading
+    grader.grade()
+"""
+
+import argparse
+import datetime
+import gc
+import json
+import os
+import signal
+import sys
+import traceback
+
+default_max_seconds = 5  # 5 second
+TOLERANCE = 1e-4  # For measuring whether two floats are equal
+
+BASIC_MODE = 'basic'  # basic
+AUTO_MODE = 'auto'  # basic + hidden
+ALL_MODE = 'all'  # basic + hidden + manual
+
+
+# When reporting stack traces as feedback, ignore parts specific to the grading
+# system.
+def is_traceback_item_grader(item):
+    return item[0].endswith('graderUtil.py')
+
+
+def is_collection(x):
+    return isinstance(x, list) or isinstance(x, tuple)
+
+
+# Return whether two answers are equal.
+def is_equal(true_answer, pred_answer, tolerance=TOLERANCE):
+    # Handle floats specially
+    if isinstance(true_answer, float) or isinstance(pred_answer, float):
+        return abs(true_answer - pred_answer) < tolerance
+    # Recurse on collections to deal with floats inside them
+    if is_collection(true_answer) and is_collection(pred_answer) and len(true_answer) == len(pred_answer):
+        for a, b in zip(true_answer, pred_answer):
+            if not is_equal(a, b):
+                return False
+        return True
+    if isinstance(true_answer, dict) and isinstance(pred_answer, dict):
+        if len(true_answer) != len(pred_answer):
+            return False
+        for k, v in list(true_answer.items()):
+            if not is_equal(pred_answer.get(k), v):
+                return False
+        return True
+
+    # Numpy array comparison
+    if type(true_answer).__name__ == 'ndarray':
+        import numpy as np
+        if isinstance(true_answer, np.ndarray) and isinstance(pred_answer, np.ndarray):
+            if true_answer.shape != pred_answer.shape:
+                return False
+            for a, b in zip(true_answer, pred_answer):
+                if not is_equal(a, b):
+                    return False
+            return True
+
+    # Do normal comparison
+    return true_answer == pred_answer
+
+
+# Run a function, timing out after max_seconds.
+class TimeoutFunctionException(Exception):
+    pass
+
+
+class TimeoutFunction:
+    def __init__(self, function, max_seconds):
+        self.max_seconds = max_seconds
+        self.function = function
+
+    @staticmethod
+    def handle_max_seconds(signum, frame):
+        print('TIMEOUT!')
+        raise TimeoutFunctionException()
+
+    def __call__(self, *args):
+        if os.name == 'nt':
+            # Windows does not have signal.SIGALRM
+            # Will not stop after max_seconds second but can still throw an exception
+            time_start = datetime.datetime.now()
+            result = self.function(*args)
+            time_end = datetime.datetime.now()
+            if time_end - time_start > datetime.timedelta(seconds=self.max_seconds + 1):
+                raise TimeoutFunctionException()
+            return result
+            # End modification for Windows here
+        signal.signal(signal.SIGALRM, self.handle_max_seconds)
+        signal.alarm(self.max_seconds + 1)
+        result = self.function(*args)
+        signal.alarm(0)
+        return result
+
+
+class Part:
+    def __init__(self, number, grade_func, max_points, max_seconds, extra_credit, description, basic):
+        if not isinstance(number, str):
+            raise Exception("Invalid number: %s" % number)
+        if grade_func is not None and not callable(grade_func):
+            raise Exception("Invalid grade_func: %s" % grade_func)
+        if not isinstance(max_points, int) and not isinstance(max_points, float):
+            raise Exception("Invalid max_points: %s" % max_points)
+        if max_seconds is not None and not isinstance(max_seconds, int):
+            raise Exception("Invalid max_seconds: %s" % max_seconds)
+        if not description:
+            print('ERROR: description required for part {}'.format(number))
+        # Specification of part
+        self.number = number  # Unique identifier for this part.
+        self.description = description  # Description of this part
+        self.grade_func = grade_func  # Function to call to do grading
+        self.max_points = max_points  # Maximum number of points attainable on this part
+        self.max_seconds = max_seconds  # Maximum allowed time that the student's code can take (in seconds)
+        self.extra_credit = extra_credit  # Whether this is an extra credit problem
+        self.basic = basic
+        # Grading the part
+        self.points = 0
+        self.side = None  # Side information
+        self.seconds = 0
+        self.messages = []
+        self.failed = False
+
+    def fail(self):
+        self.failed = True
+
+    def is_basic(self):
+        return self.grade_func is not None and self.basic
+
+    def is_hidden(self):
+        return self.grade_func is not None and not self.basic
+
+    def is_auto(self):
+        return self.grade_func is not None
+
+    def is_manual(self):
+        return self.grade_func is None
+
+
+class Grader:
+    def __init__(self, args=None):
+        if args is None:
+            args = sys.argv
+        self.parts = []  # Parts (to be added)
+        self.useSolution = False  # Set to true if we are actually evaluating the hidden test cases
+
+        parser = argparse.ArgumentParser()
+        parser.add_argument('--js', action='store_true', help='Write JS file with information about this assignment')
+        parser.add_argument('--json', action='store_true',
+                            help='Write JSON file with information about this assignment')
+        parser.add_argument('--summary', action='store_true', help='Don\'t actually run code')
+        parser.add_argument('remainder', nargs=argparse.REMAINDER)
+        self.params = parser.parse_args(args[1:])
+
+        args = self.params.remainder
+        if len(args) < 1:
+            self.mode = AUTO_MODE
+            self.selectedPartName = None
+        else:
+            if args[0] in [BASIC_MODE, AUTO_MODE, ALL_MODE]:
+                self.mode = args[0]
+                self.selectedPartName = None
+            else:
+                self.mode = AUTO_MODE
+                self.selectedPartName = args[0]
+
+        self.messages = []  # General messages
+        self.currentPart = None  # Which part we're grading
+        self.fatalError = False  # Set this if we should just stop immediately
+
+    def add_basic_part(self, number, grade_func, max_points=1, max_seconds=default_max_seconds, extra_credit=False,
+                       description=""):
+        """Add a basic test case. The test will be visible to students."""
+        self.assert_new_number(number)
+        part = Part(number, grade_func, max_points, max_seconds, extra_credit, description, basic=True)
+        self.parts.append(part)
+
+    def add_hidden_part(self, number, grade_func, max_points=1, max_seconds=default_max_seconds, extra_credit=False,
+                        description=""):
+        """Add a hidden test case. The output should NOT be visible to students
+        and so should be inside a BEGIN_HIDE block."""
+        self.assert_new_number(number)
+        part = Part(number, grade_func, max_points, max_seconds, extra_credit, description, basic=False)
+        self.parts.append(part)
+
+    def add_manual_part(self, number, max_points, extra_credit=False, description=""):
+        """Add a manual part."""
+        self.assert_new_number(number)
+        part = Part(number, None, max_points, None, extra_credit, description, basic=False)
+        self.parts.append(part)
+
+    def assert_new_number(self, number):
+        if number in [part.number for part in self.parts]:
+            raise Exception("Part number %s already exists" % number)
+
+    # Try to load the module (submission from student).
+    def load(self, module_name):
+        try:
+            return __import__(module_name)
+        except Exception as e:
+            self.fail("Threw exception when importing '%s': %s" % (module_name, e))
+            self.fatalError = True
+            return None
+        except:
+            self.fail("Threw exception when importing '%s'" % module_name)
+            self.fatalError = True
+            return None
+
+    def grade_part(self, part):
+        print('----- START PART %s%s: %s' % (
+            part.number, ' (extra credit)' if part.extra_credit else '', part.description))
+        self.currentPart = part
+
+        start_time = datetime.datetime.now()
+        try:
+            TimeoutFunction(part.grade_func, part.max_seconds)()  # Call the part's function
+        except KeyboardInterrupt:
+            raise
+        except MemoryError:
+            signal.alarm(0)
+            gc.collect()
+            self.fail('Memory limit exceeded.')
+        except TimeoutFunctionException:
+            signal.alarm(0)
+            self.fail('Time limit (%s seconds) exceeded.' % part.max_seconds)
+        except Exception as e:
+            signal.alarm(0)
+            self.fail('Exception thrown: %s -- %s' % (str(type(e)), str(e)))
+            self.print_exception()
+        except SystemExit:
+            # Catch SystemExit raised by exit(), quit() or sys.exit()
+            # This class is not a subclass of Exception and we don't
+            # expect students to raise it.
+            self.fail('Unexpected exit.')
+            self.print_exception()
+        end_time = datetime.datetime.now()
+        part.seconds = (end_time - start_time).seconds
+        ###### quick fix to pacman problem 4 ######
+        if part.seconds > part.max_seconds:
+            signal.alarm(0)
+            self.fail('Time limit (%s seconds) exceeded.' % part.max_seconds)
+        ###### quick fix to pacman problem 4 ######
+        if part.is_hidden() and not self.useSolution:
+            display_points = '???/%s points (hidden test ungraded)' % part.max_points
+        else:
+            display_points = '%s/%s points' % (part.points, part.max_points)
+        print('----- END PART %s [%s]' % (
+            part.number, display_points))
+        print()
+
+    def get_selected_parts(self):
+        parts = []
+        for part in self.parts:
+            if self.selectedPartName is not None and self.selectedPartName != part.number:
+                continue
+            if self.mode == BASIC_MODE:
+                if part.is_basic():
+                    parts.append(part)
+            elif self.mode == AUTO_MODE:
+                if part.is_auto():
+                    parts.append(part)
+            elif self.mode == ALL_MODE:
+                parts.append(part)
+            else:
+                raise Exception("Invalid mode: {}".format(self.mode))
+        return parts
+
+    def grade(self):
+        parts = self.get_selected_parts()
+
+        result = {'mode': self.mode}
+
+        # Grade it!
+        if not self.params.summary and not self.fatalError:
+            print('========== START GRADING')
+            for part in parts:
+                self.grade_part(part)
+
+            # When students have it (not useSolution), only include basic tests.
+            active_parts = [part for part in parts if self.useSolution or part.basic]
+
+            total_points = sum(part.points for part in active_parts if not part.extra_credit)
+            extra_credit = sum(part.points for part in active_parts if part.extra_credit)
+            max_total_points = sum(part.max_points for part in active_parts if not part.extra_credit)
+            max_extra_credit = sum(part.max_points for part in active_parts if part.extra_credit)
+
+            print('========== END GRADING [%s/%s points + %s/%s extra credit]' %
+                  (total_points, max_total_points, extra_credit, max_extra_credit))
+
+        result_parts = []
+        leaderboard = []
+        for part in parts:
+            r = {'number': part.number, 'name': part.description}
+
+            if self.params.summary:
+                # Just print out specification of the part
+                r['description'] = part.description
+                r['max_seconds'] = part.max_seconds
+                r['max_points'] = part.max_points
+                r['extra_credit'] = part.extra_credit
+                r['basic'] = part.basic
+            else:
+                r['score'] = part.points
+                # Force max_score to be 0 for extra credits for displaying correct total points on Gradescope
+                r['max_score'] = 0 if (part.extra_credit and self.mode == AUTO_MODE) else part.max_points
+                r["visibility"] = "after_published" if part.is_hidden() else "visible"
+                r['seconds'] = part.seconds
+                if part.side is not None:
+                    r['side'] = part.side
+                r['output'] = "\n".join(part.messages)
+
+                if part.side is not None:
+                    for k in part.side:
+                        leaderboard.append({"name": k, "value": part.side[k]})
+            result_parts.append(r)
+        result['tests'] = result_parts
+        result['leaderboard'] = leaderboard
+
+        self.output(self.mode, result)
+
+        def display(name, select_extra_credit):
+            parts_to_display = [p for p in self.parts if p.extra_credit == select_extra_credit]
+            max_basic_points = sum(p.max_points for p in parts_to_display if p.is_basic())
+            max_hidden_points = sum(p.max_points for p in parts_to_display if p.is_hidden())
+            max_manual_points = sum(p.max_points for p in parts_to_display if p.is_manual())
+            max_total_points_found = max_basic_points + max_hidden_points + max_manual_points
+            print("Total %s (basic auto/coding + hidden auto/coding + manual/written): %d + %d + %d = %d" %
+                  (name, max_basic_points, max_hidden_points, max_manual_points, max_total_points_found))
+            if not select_extra_credit and max_total_points_found != 75:
+                print('WARNING: max_total_points = {} is not 75'.format(max_total_points_found))
+
+        if self.params.summary:
+            display('points', False)
+            display('extra credit', True)
+
+    def output(self, mode, result):
+        if self.params.json:
+            path = 'grader-{}.json'.format(mode)
+            with open(path, 'w') as out:
+                print(json.dumps(result), file=out)
+            print('Wrote to %s' % path)
+        if self.params.js:
+            path = 'grader-{}.js'.format(mode)
+            with open(path, 'w') as out:
+                print('var ' + mode + 'Result = ' + json.dumps(result) + ';', file=out)
+            print('Wrote to %s' % path)
+
+    # Called by the grader to modify state of the current part
+
+    def add_points(self, amt):
+        self.currentPart.points += amt
+
+    def assign_full_credit(self):
+        if not self.currentPart.failed:
+            self.currentPart.points = self.currentPart.max_points
+        return True
+
+    def assign_partial_credit(self, credit):
+        self.currentPart.points = credit
+        return True
+
+    def set_side(self, side):
+        self.currentPart.side = side
+
+    @staticmethod
+    def truncate_string(string, length=200):
+        if len(string) <= length:
+            return string
+        else:
+            return string[:length] + '...'
+
+    def require_is_numeric(self, answer):
+        if isinstance(answer, int) or isinstance(answer, float):
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected either int or float, but got '%s'" % self.truncate_string(answer))
+
+    def require_is_one_of(self, true_answers, pred_answer):
+        if pred_answer in true_answers:
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected one of %s, but got '%s'" % (
+                self.truncate_string(true_answers), self.truncate_string(pred_answer)))
+
+    def require_is_equal(self, true_answer, pred_answer, tolerance=TOLERANCE):
+        if is_equal(true_answer, pred_answer, tolerance):
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected '%s', but got '%s'" % (
+                self.truncate_string(str(true_answer)), self.truncate_string(str(pred_answer))))
+
+    def require_is_less_than(self, less_than_quantity, pred_answer):
+        if pred_answer < less_than_quantity:
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected to be < %f, but got %f" % (less_than_quantity, pred_answer))
+
+    def require_is_greater_than(self, greater_than_quantity, pred_answer):
+        if pred_answer > greater_than_quantity:
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected to be > %f, but got %f" %
+                             (greater_than_quantity, pred_answer))
+
+    def require_is_true(self, pred_answer):
+        if pred_answer:
+            return self.assign_full_credit()
+        else:
+            return self.fail("Expected to be true, but got false")
+
+    def fail(self, message):
+        print('FAIL:', message)
+        self.add_message(message)
+        if self.currentPart:
+            self.currentPart.points = 0
+            self.currentPart.fail()
+        return False
+
+    def print_exception(self):
+        tb = [item for item in traceback.extract_tb(sys.exc_info()[2]) if not is_traceback_item_grader(item)]
+        for item in traceback.format_list(tb):
+            self.fail('%s' % item)
+
+    def add_message(self, message):
+        if not self.useSolution:
+            print(message)
+        if self.currentPart:
+            self.currentPart.messages.append(message)
+        else:
+            self.messages.append(message)

hw2/ints/submission.py

@@ -0,0 +1,42 @@
+############################################################
+# Problem 4: Odd and even integers
+from typing import Tuple, List
+from logic import *
+
+
+# Return the following 6 laws. Be sure your formulas are exactly in the order specified.
+# 0. Each number $x$ has exactly one successor, which is not equal to $x$.
+# 1. Each number is either even or odd, but not both.
+# 2. The successor number of an even number is odd.
+# 3. The successor number of an odd number is even.
+# 4. For every number $x$, the successor of $x$ is larger than $x$.
+# 5. Larger is a transitive property: if $x$ is larger than $y$ and $y$ is
+#    larger than $z$, then $x$ is larger than $z$.
+# Query: For each number, there exists an even number larger than it.
+def ints() -> Tuple[List[Formula], Formula]:
+    def Even(x): return Atom('Even', x)  # whether x is even
+
+    def Odd(x): return Atom('Odd', x)  # whether x is odd
+
+    def Successor(x, y): return Atom('Successor', x, y)  # whether x's successor is y
+
+    def Larger(x, y): return Atom('Larger', x, y)  # whether x is larger than y
+
+    # Note: all objects are numbers, so we don't need to define Number as an
+    # explicit predicate.
+    #
+    # Note: pay attention to the order of arguments of Successor and Larger.
+    # Populate `formulas` with the 6 laws above.
+    #
+    # Hint: You might want to use the Equals predicate, defined in logic.py.  This
+    # predicate is used to assert that two objects are the same.
+    formulas = []
+    formulas.append(Forall('$x', Exists('$y', And(Successor('$x', '$y'), And(Not(Equals('$x', '$y')), Forall('$z', Implies(Not(Equals('$z', '$y')), Not(Successor('$x', '$z')))))))))
+    formulas.append(Forall('$x', Or(And(Even('$x'), Not(Odd('$x'))), And(Odd('$x'), Not(Even('$x'))))))
+    formulas.append(Forall('$x', Implies(Even('$x'), Exists('$y', Odd(Successor('$x', '$y'))))))
+    formulas.append(Forall('$x', Implies(Odd('$x'), Exists('$y', Even(Successor('$x', '$y'))))))
+    formulas.append(Forall('$x', Implies(Exists('$y', Successor('$x', '$y')), Larger('$y', '$x'))))
+    formulas.append(Forall('$x', Forall('$y', Forall('$z', Implies(And(Larger('$x', '$y'), Larger('$y', '$z')), Larger('$x', '$z'))))))
+
+    query = Forall('$x', Exists('$y', And(Even('$y'), Larger('$y', '$x'))))
+    return formulas, query

hw2/knights/logic.py

@@ -0,0 +1,260 @@
+class Sentence:
+
+    def evaluate(self, model):
+        """Evaluates the logical sentence."""
+        raise Exception("nothing to evaluate")
+
+    def formula(self):
+        """Returns string formula representing logical sentence."""
+        return ""
+
+    def symbols(self):
+        """Returns a set of all symbols in the logical sentence."""
+        return set()
+
+    @classmethod
+    def validate(cls, sentence):
+        if not isinstance(sentence, Sentence):
+            raise TypeError("must be a logical sentence")
+
+    @classmethod
+    def parenthesize(cls, s):
+        """Parenthesizes an expression if not already parenthesized."""
+        def balanced(s):
+            """Checks if a string has balanced parentheses."""
+            count = 0
+            for c in s:
+                if c == "(":
+                    count += 1
+                elif c == ")":
+                    if count <= 0:
+                        return False
+                    count -= 1
+            return count == 0
+        if not len(s) or s.isalpha() or (
+            s[0] == "(" and s[-1] == ")" and balanced(s[1:-1])
+        ):
+            return s
+        else:
+            return f"({s})"
+
+
+class Symbol(Sentence):
+
+    def __init__(self, name):
+        self.name = name
+
+    def __eq__(self, other):
+        return isinstance(other, Symbol) and self.name == other.name
+
+    def __hash__(self):
+        return hash(("symbol", self.name))
+
+    def __repr__(self):
+        return self.name
+
+    def evaluate(self, model):
+        try:
+            return bool(model[self.name])
+        except KeyError:
+            raise Exception(f"variable {self.name} not in model")
+
+    def formula(self):
+        return self.name
+
+    def symbols(self):
+        return {self.name}
+
+
+class Not(Sentence):
+    def __init__(self, operand):
+        Sentence.validate(operand)
+        self.operand = operand
+
+    def __eq__(self, other):
+        return isinstance(other, Not) and self.operand == other.operand
+
+    def __hash__(self):
+        return hash(("not", hash(self.operand)))
+
+    def __repr__(self):
+        return f"Not({self.operand})"
+
+    def evaluate(self, model):
+        return not self.operand.evaluate(model)
+
+    def formula(self):
+        return "¬" + Sentence.parenthesize(self.operand.formula())
+
+    def symbols(self):
+        return self.operand.symbols()
+
+
+class And(Sentence):
+    def __init__(self, *conjuncts):
+        for conjunct in conjuncts:
+            Sentence.validate(conjunct)
+        self.conjuncts = list(conjuncts)
+
+    def __eq__(self, other):
+        return isinstance(other, And) and self.conjuncts == other.conjuncts
+
+    def __hash__(self):
+        return hash(
+            ("and", tuple(hash(conjunct) for conjunct in self.conjuncts))
+        )
+
+    def __repr__(self):
+        conjunctions = ", ".join(
+            [str(conjunct) for conjunct in self.conjuncts]
+        )
+        return f"And({conjunctions})"
+
+    def add(self, conjunct):
+        Sentence.validate(conjunct)
+        self.conjuncts.append(conjunct)
+
+    def evaluate(self, model):
+        return all(conjunct.evaluate(model) for conjunct in self.conjuncts)
+
+    def formula(self):
+        if len(self.conjuncts) == 1:
+            return self.conjuncts[0].formula()
+        return " ∧ ".join([Sentence.parenthesize(conjunct.formula())
+                           for conjunct in self.conjuncts])
+
+    def symbols(self):
+        return set.union(*[conjunct.symbols() for conjunct in self.conjuncts])
+
+
+class Or(Sentence):
+    def __init__(self, *disjuncts):
+        for disjunct in disjuncts:
+            Sentence.validate(disjunct)
+        self.disjuncts = list(disjuncts)
+
+    def __eq__(self, other):
+        return isinstance(other, Or) and self.disjuncts == other.disjuncts
+
+    def __hash__(self):
+        return hash(
+            ("or", tuple(hash(disjunct) for disjunct in self.disjuncts))
+        )
+
+    def __repr__(self):
+        disjuncts = ", ".join([str(disjunct) for disjunct in self.disjuncts])
+        return f"Or({disjuncts})"
+
+    def evaluate(self, model):
+        return any(disjunct.evaluate(model) for disjunct in self.disjuncts)
+
+    def formula(self):
+        if len(self.disjuncts) == 1:
+            return self.disjuncts[0].formula()
+        return " ∨  ".join([Sentence.parenthesize(disjunct.formula())
+                            for disjunct in self.disjuncts])
+
+    def symbols(self):
+        return set.union(*[disjunct.symbols() for disjunct in self.disjuncts])
+
+
+class Implication(Sentence):
+    def __init__(self, antecedent, consequent):
+        Sentence.validate(antecedent)
+        Sentence.validate(consequent)
+        self.antecedent = antecedent
+        self.consequent = consequent
+
+    def __eq__(self, other):
+        return (isinstance(other, Implication)
+                and self.antecedent == other.antecedent
+                and self.consequent == other.consequent)
+
+    def __hash__(self):
+        return hash(("implies", hash(self.antecedent), hash(self.consequent)))
+
+    def __repr__(self):
+        return f"Implication({self.antecedent}, {self.consequent})"
+
+    def evaluate(self, model):
+        return ((not self.antecedent.evaluate(model))
+                or self.consequent.evaluate(model))
+
+    def formula(self):
+        antecedent = Sentence.parenthesize(self.antecedent.formula())
+        consequent = Sentence.parenthesize(self.consequent.formula())
+        return f"{antecedent} => {consequent}"
+
+    def symbols(self):
+        return set.union(self.antecedent.symbols(), self.consequent.symbols())
+
+
+class Biconditional(Sentence):
+    def __init__(self, left, right):
+        Sentence.validate(left)
+        Sentence.validate(right)
+        self.left = left
+        self.right = right
+
+    def __eq__(self, other):
+        return (isinstance(other, Biconditional)
+                and self.left == other.left
+                and self.right == other.right)
+
+    def __hash__(self):
+        return hash(("biconditional", hash(self.left), hash(self.right)))
+
+    def __repr__(self):
+        return f"Biconditional({self.left}, {self.right})"
+
+    def evaluate(self, model):
+        return ((self.left.evaluate(model)
+                 and self.right.evaluate(model))
+                or (not self.left.evaluate(model)
+                    and not self.right.evaluate(model)))
+
+    def formula(self):
+        left = Sentence.parenthesize(str(self.left))
+        right = Sentence.parenthesize(str(self.right))
+        return f"{left} <=> {right}"
+
+    def symbols(self):
+        return set.union(self.left.symbols(), self.right.symbols())
+
+
+def model_check(knowledge, query):
+    """Checks if knowledge base entails query."""
+
+    def check_all(knowledge, query, symbols, model):
+        """Checks if knowledge base entails query, given a particular model."""
+
+        # If model has an assignment for each symbol
+        if not symbols:
+
+            # If knowledge base is true in model, then query must also be true
+            if knowledge.evaluate(model):
+                return query.evaluate(model)
+            return True
+        else:
+
+            # Choose one of the remaining unused symbols
+            remaining = symbols.copy()
+            p = remaining.pop()
+
+            # Create a model where the symbol is true
+            model_true = model.copy()
+            model_true[p] = True
+
+            # Create a model where the symbol is false
+            model_false = model.copy()
+            model_false[p] = False
+
+            # Ensure entailment holds in both models
+            return (check_all(knowledge, query, remaining, model_true) and
+                    check_all(knowledge, query, remaining, model_false))
+
+    # Get all symbols in both knowledge and query
+    symbols = set.union(knowledge.symbols(), query.symbols())
+
+    # Check that knowledge entails query
+    return check_all(knowledge, query, symbols, dict())

hw2/knights/puzzle.py

@@ -0,0 +1,82 @@
+from logic import *
+
+AKnight = Symbol("A is a Knight")
+AKnave = Symbol("A is a Knave")
+
+BKnight = Symbol("B is a Knight")
+BKnave = Symbol("B is a Knave")
+
+CKnight = Symbol("C is a Knight")
+CKnave = Symbol("C is a Knave")
+
+# Puzzle 0
+# A says "I am both a knight and a knave."
+knowledge0 = And(
+    Or(AKnight, AKnave),  # A is either a knight or a knave
+    Not(And(AKnight, AKnave)),  # A cannot be both a knight and a knave
+    Biconditional(AKnight, And(AKnight, AKnave))  # If A is a knight, then the statement is true; if A is a knave, the statement is false
+)
+
+# Puzzle 1
+# A says "We are both knaves."
+# B says nothing.
+knowledge1 = And(
+    Or(AKnight, AKnave),  # A is either a knight or a knave
+    Or(BKnight, BKnave),  # B is either a knight or a knave
+    Not(And(AKnight, AKnave)),  # A cannot be both a knight and a knave
+    Not(And(BKnight, BKnave)),  # B cannot be both a knight and a knave
+    Biconditional(AKnight, And(AKnave, BKnave)),  # If A is a knight, then the statement is true; if A is a knave, the statement is false
+    Biconditional(AKnave, Not(And(AKnave, BKnave)))  # If A is a knave, then the opposite of the statement is true
+)
+
+# Puzzle 2
+# A says "We are the same kind."
+# B says "We are of different kinds."
+knowledge2 = And(
+    Or(AKnight, AKnave),  # A is either a knight or a knave
+    Or(BKnight, BKnave),  # B is either a knight or a knave
+    Not(And(AKnight, AKnave)),  # A cannot be both a knight and a knave
+    Not(And(BKnight, BKnave)),  # B cannot be both a knight and a knave
+    Biconditional(AKnight, Or(And(AKnight, BKnight), And(AKnave, BKnave))),  # If A is a knight, then A's statement is true; if A is a knave, then A's statement is false
+    Biconditional(BKnight, Or(And(AKnight, BKnave), And(AKnave, BKnight)))  # If B is a knight, then B's statement is true; if B is a knave, then B's statement is false
+)
+
+# Puzzle 3
+# A says either "I am a knight." or "I am a knave.", but you don't know which.
+# B says "A said 'I am a knave'."
+# B says "C is a knave."
+# C says "A is a knight."
+knowledge3 = And(
+    Or(AKnight, AKnave),
+    Or(BKnight, BKnave),
+    Or(CKnight, CKnave),
+    Biconditional(AKnight, Not(AKnave)),
+    Biconditional(BKnight, Not(BKnave)),
+    Biconditional(CKnight, Not(CKnave)),
+    Implication(BKnight, Not(AKnave)),
+    Implication(BKnave, And(AKnight, CKnight)),
+    Implication(AKnight, CKnight),
+    Implication(AKnight, Not(BKnight))
+)
+
+
+def main():
+    symbols = [AKnight, AKnave, BKnight, BKnave, CKnight, CKnave]
+    puzzles = [
+        ("Puzzle 0", knowledge0),
+        ("Puzzle 1", knowledge1),
+        ("Puzzle 2", knowledge2),
+        ("Puzzle 3", knowledge3)
+    ]
+    for puzzle, knowledge in puzzles:
+        print(puzzle)
+        if len(knowledge.conjuncts) == 0:
+            print("    Not yet implemented.")
+        else:
+            for symbol in symbols:
+                if model_check(knowledge, symbol):
+                    print(f"    {symbol}")
+
+
+if __name__ == "__main__":
+    main()

main.aux

@@ -10,4 +10,8 @@
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Grid City}{7}{}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Six Degrees}{8}{}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Tic Tac Toe}{8}{}\protected@file@percent }
-\gdef \@abspage@last{9}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Homework 2}{8}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Cake}{8}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Knights and Knaves}{10}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Odds and Evens}{10}{}\protected@file@percent }
+\gdef \@abspage@last{11}

main.fdb_latexmk

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main.fls

@@ -1,6 +1,6 @@
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+INPUT .\hw2\gameTree.png
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main.tex

@@ -261,4 +261,64 @@ Now consider UCS running on an arbitrary graph.
 
 \end{itemize}
 
+\section{Homework 2}
+
+    \subsection{Cake}
+
+    Alice and Bob are sharing a cake....
+
+    \begin{center}
+        \includegraphics[scale=0.3]{hw2/gameTree.png}
+    \end{center}
+
+    
+    Write down the utility Alice should expect to receive in each of the game states given the following knowlege of player strategies:
+
+    \begin{itemize}
+        \item [a.] Alice and Bob playing adversarially, each trying to maximize the cake they receive.
+            \begin{enumerate}
+                \item 1/2
+                \item 1/2
+                \item 1/2
+            \end{enumerate}
+        \item [b. ] Alice still trying to maximize, Bob now playing collaboratively and helping Alice.
+            \begin{enumerate}
+                \item 2/3
+                \item 1/2
+                \item 2/3
+            \end{enumerate}
+        \item [c. ] Random play.
+            \begin{enumerate}
+                \item Node 2 or 3
+                \item Doesn't matter because of constant utility
+                \item Node 3
+            \end{enumerate}
+        \item [d. ] Alpha Beta pruning
+            \begin{enumerate}
+                \item Leaf notes with utility 1/3, 1/3, 1/3, 1/3 on left, and right leaf node with utility 1/6
+            \end{enumerate}
+        \item [e. ] Alpha Beta pruning with tree elements swapped.
+            \begin{enumerate}
+                \item No nodes are pruned
+            \end{enumerate}
+    \end{itemize}
+
+    \begin{itemize}
+        \item [2. ] Logical Formulas
+        \begin{itemize}
+            \item [a. ] $(P \land \neg Q) \lor (\neg P \land Q)$
+            \item [b. ] $(\exists x \text{Course}(x) \land \text{Enrolled}(A, x) \land \text{Enrolled}(B,x))$
+            \item [c. ] $(\forall x \text{Course}(x) \land \text{Enrolled}(A, x) \rightarrow \text{Enrolled}(B,x))$
+            \item [d. ] $\forall x \forall y (\text{Enrolled}(x,y) \land \text{Course}(y) \rightarrow \text{Student}(x))$
+            \item [e. ] $\forall x (\text{Course}(x) \rightarrow \exists y (\text{Student}(y) \land \text{Enrolled}(y,x)))$
+        \end{itemize}
+    \end{itemize}
+
+    \subsection{Knights and Knaves}
+        See attached puzzle.py file
+
+    \subsection{Odds and Evens}
+        See attached submission.py file
+    
+
 \end{document}