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Midterm Review

Midterm Review. Python class code for Aristotle example – animal, cat, human, and knowledge classes class animal() : num_eyes = 2 num_teeth = 24 def __init__(self, e, t) : self.num_eyes = e self.num_teeth = t class cat(animal) : def __init__(self, c, l) :

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Midterm Review

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  1. Midterm Review

  2. Python class code for Aristotle example – animal, cat, human, and knowledge classes class animal() : num_eyes = 2 num_teeth = 24 def __init__(self, e, t) : self.num_eyes = e self.num_teeth = t class cat(animal) : def __init__(self, c, l) : self.fur_color = c self.len_tail = l a1 = animal(2, 30) print a1.num_eyes, a1.num_teeth my_cat = cat("yellow", 4) print my_cat.num_eyes, my_cat.num_teeth, my_cat.fur_color, my_cat.len_tail class human(animal) : IQ = 100 sports_played = "Football" knowledge = [] def __init__(self, s, i = 100) : self.IQ = i self.sports_played = s socrates = human(s="Golf") print socrates.num_eyes, socrates.num_teeth, socrates.IQ, socrates.sports_played class knowledge() : grammatical = '' math = '' human = [] def __init__(self, g, m) : self.grammatical = g self.math = m socrates_Knowledge = knowledge('Some Greek language knowledge', "Some math smarts") socrates.knowledge.append(socrates_Knowledge) socrates_Knowledge.human.append(socrates) print socrates.num_eyes, socrates.num_teeth, socrates.IQ, socrates.sports_played, socrates.knowledge[0].grammatical, socrates.knowledge[0].math print socrates.knowledge print socrates_Knowledge.grammatical, socrates_Knowledge.math, socrates_Knowledge.human[0].sports_played

  3. Code from September 17, 2013 Lecture class Person() : name = None parents = [] kids = [] has = None def __init__(self, name) : self.name = name p1 = Person("phil") p2 = Person("rita") p3 = Person("chris") p1.kids.append(p3) p3.parents.append(p1) print "My name is ", p1.name, "My first kids name is ", p1.kids[0].name class Job(): name = "" employees = [] def __init__(self, name) : self.name = name j1 = Job("professor") j1.employees = [] # This was added after class. p1.has = j1 j1.employees.append(p1) print p1.has.name, j1.employees[0].name

  4. Code from September 17, 2013 Lecture class Person(object): _registry = [] # _registry starts off as an empty list. name = "" amount = 0 def __init__(self, name, amount): self._registry.append(self) # Each instance of Person is added to _registry. self.name = name self.amount = amount def exchange(self, p, amnt) : # Behavior or Method self.amount -= amnt p.amount += amnt p1, p2, p3, p4 = Person('tom', 1000), Person('jerry', 2000), Person('phineas', 3000), Person('ferb', 4000) for p in Person._registry: print p.name + ", " + str(p.amount) , # The comma at the end of the print statement causes all to print on one line. def transfer(p1, p2, amnt) : p1.amount -= amnt # Fill in these 2 lines for Homework 1. Note, the “transfer” function p2.amount += amnt # requires no return statement. transfer(p1, p2, 50) transfer(p3, p4, 50) print for p in Person._registry: print p.name + ", " + str(p.amount) , # More on Next Page

  5. Code from September 17, 2013 Lecture p1.exchange(p2, 50) print for p in Person._registry: print p.name + ", " + str(p.amount) , p10 = Person("me", "you") print print p10._registry print print p1._registry class MeekPerson(Person) : def __init__(self, name, amount): self._registry.append(self) # Each instance of Person is added to _registry. self.name = name self.amount = amount def exchange(self, p, amnt) : self.amount -= 2*amnt p.amount += 2*amnt m1 = MeekPerson("snoopy", 10000) p6 = Person("charlie", 20000) m1.exchange(p6,50) # Dynamic Binding will be done here to choose the right method. print for p in Person._registry: print p.name + ", " + str(p.amount) ,

  6. def __str__(self): result = "'(" current = self.head for i in range(self.size+1): if current != None: result += str(current.element) if current.next != None : result += ", current = current.next else: result += ")" # Insert the closing ] in the string return result # Return an iterator for a linked list def __iter__(self): # To be discussed in Section 18.3 return LinkedListIterator(self.head) # The Node class class Node: def __init__(self, element): self.element = element self.next = None class LinkedListIterator: def __init__(self, head): self.current = head def next(self): if self.current == None: raise StopIteration else: element = self.current.element self.current = self.current.next return element class LinkedList() : head = None tail = None size = 0 def cons(self, val) : n = Node(val) self.size+=1 if self.head == None : self.head = n self.tail = n else : n.next = self.head self.head = n return self def car(self) : return self.head.element def cdr(self) : l = self if self.size > 0 : l.head = l.head.next l.size -= 1 else : l.head, l.tail = None, None return l

  7. Aristotle’s syllogistic logic If it’s raining outside, then the grass is wet. Its raining outside Therefore, the grass is wet. If it’s raining outside, then the grass is wet. The grass is wet. Therefore, its raining outside. Valid argument Fallacy Aristotle

  8. Euclid’s “The Elements” Five axioms (postulates) Euclid

  9. P QPQ False False True False True True True False False True True True P  P False True True False P QP && Q False False False False True False True False False True True True P QP || Q False False False False True True True False True True True True P QP<=>Q False False True False True False True False False True True True Propositional Logic Frege

  10. P Q False False False True True False True True (P  Q) (P) ((PQ)((P)Q)) ((P)Q) If prop is True when all variables are True: P, Q((PQ)((P)Q)) Some True: prop is Satisfiable* If they were all True: Valid / Tautology A Truth double turnstile All False: Contradiction (not satisfiable*) *Satisfiability was the first known NP-complete (see next slide) problem Reasoning with Truth Tables Proposition: ((P  Q)((P)Q)) False True False False True True True True True False True True True False True True Frege

  11. Reasoning with Truth Tables

  12. Tautological Proof using Propositional Logic It’s either summer or winter. If it’s summer, I’m happy. If it’s winter, I’m happy. Is there anything you can uncompress from this? The above statements can be written like this: ( (s  w) ^ (s -> h) ^ (w -> h) ) -> h This is a Haskell proof of this Tautology valid3 :: (Bool -> Bool -> Bool -> Bool) -> Boolvalid3 bf = and [ bf r s t| r <- [True,False],                            s <- [True,False],                            t <- [True,False]]LOGIC> valid3 (\ s w h -> ((s || w) && (s ==> h) && (w ==> h)) ==> h)True Another form of a un-compression (proof): ( (p  q) ^ (¬p  r) ^ (¬q  r) ) -> r( (p ^ ¬p)  (r ^ q) ^ (¬q  r) ) -> r(F  (q ^ ¬q)  r) -> rr -> r¬r  r.: T Frege

  13. Peano's Axioms 1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are themselves equal. 5. (induction axiom.) If a set S of numbers contains zero and also the successor of every number in S, then every number is in S. Peano's axioms are the basis for the version of number theory known as Peano arithmetic. Peano

  14. Peano's Arithmetic Peano

  15. Cantor Diagonalization Create a new number from the diagonal by adding 1 and changing 10 to 0. The above example would give .960143… Now try to find a place for this number in the table above, it can’t be the first line because 8 != 9, it can’t be the second line because 5 != 6, etc. to infinity. So this line isn’t in the table above and therefore was not counted.  The real numbers are not countable. Cantor

  16. Set Theory Paradoxes Suppose there is a town with just one barber, who is male. In this town, every man keeps himself clean-shaven, and he does so by doing exactly one of two things: shaving himself; or going to the barber. Another way to state this is that "The barber is a man in town who shaves all those, and only those, men in town who do not shave themselves." From this, asking the question "Who shaves the barber?" results in a paradox because according to the statement above, he can either shave himself, or go to the barber (which happens to be himself). However, neither of these possibilities is valid: they both result in the barber shaving himself, but he cannot do this because he only shaves those men "who do not shave themselves". Cantor and Russell

  17. Primitive Recursive Functions and Arithmetic (see “A Profile of Mathematical Logic” by Howard Delong – pages 152 – 160) A Sequence of Functions from definitions on DeLong,page 157: Skolem

  18. Gödel Numbering 1 = (0)’ = 211 x 31 x 513 x 73 Gödel

  19. Lambda Calculus Examples in python: print (lambda x : x) (lambda s : s) print (lambda s : (s) (s)) (lambda x : x) print (lambda func, arg : (func) (arg)) ((lambda x : x + 3), 4) Church

  20. Turing Machine Turing

  21. Combinator Logic A function is called primitive recursive if there is a finite sequence of functions ending with f such that each function is a successor, constant or identity function or is defined from preceding functions in the sequence by substitution or recursion. Combinators s f g x = f x (g x) k x y   = x b f g x = f (g x) c f g x = f x g y f     = f (y f) cond p f g x = if p x then f x else g x -- Some Primitive Recursive Functions on Natural Numbers addition x z = y (b (cond ((==) 0) (k z)) (b (s (b (+) (k 1))      ) (c b pred))) x multiplication x z = y (b (cond ((==) 0) (k 0)) (b (s (b (pradd1) (k z)) ) (c b pred))) x exponentiation x z = y (b (cond ((==) 0) (k 1)) (b (s (b (prmul1) (k x)) ) (c b pred))) z factorial x   = y (b (cond ((==) 0) (k 1)) (b (s (prmul1)           ) (c b pred))) x No halting problem here but not Turing complete either Implies recursion or bounded loops, if-then-else constructs and run-time stack. see the BlooP language in Haskell Currie

  22. John McCarthy’s Takeaways -- Primitive Recursive Functions on Lists are more interesting than Primitive Recursive Functions on Numbers length x    = y (b (cond ((==) []) (k 0))  (b (s (b (+) (k 1)) ) (c b cdr))) x sum x   = y (b (cond ((==) []) (k 0))  (b (s (b (+) (car)) ) (c b cdr))) x product x  = y (b (cond ((==) []) (k 1))  (b (s (b (*) (car)) ) (c b cdr))) x map f x = y (b (cond ((==) []) (k [])) (b (s (b (:) (f)  ) ) (c b cdr))) x   -- map (\ x -> (car x) + 2) [1,2,3] or                                                                                 -- map (\ x -> add (car x) 2) [1,2,3] -- A programming language should have first-class functions as (b p1 p2 . . . Pn), substitution, lists with car, cdr and cons operations and recursion. car (f:r) = f cdr (f:r) = r cons is : op John’s 1960 paper: “Recursive Functions of Symbolic Expressions and Their Computation by Machine”– see copy on class calendar. McCarthy

  23. Stack and Queue class Stack(LinkedList): def push(self, e): self.addFirst(e) def pop(self): return self.removeFirst() def peek(self): return self.car() class Queue(LinkedList): def enqueue(self, e): self.cons(e) def dequeue(self): return self.removeLast() print "Stack test"

  24. Stack Example def calc(expr): s1 =Stack() for s in expr: if s == ")": e = "" for i in range(s1.getSize()): v = s1.pop() if v == "(": break else: e += str(v) # print e, e[::-1], eval(e[::-1]) e = eval(e[::-1]) # Comment for no extra credit s1.push(str(e)[::-1]) # Comment for no extra credit # s1.push(eval(e)) # Uncomment for no extra credit # print s1 else: s1.push(s) # return s1.pop() # Uncomment for no extra credit return s1.pop()[::-1] # Comment for no extra credit print eval("(((12+33.3)*(1.4*701))/(2.2-1.1))") print calc("(((12+33.3)*(1.4*701))/(2.2-1.1))") print eval("(((2+3)*(4*7))*2)") print calc("(((2+3)*(4*7))*2)"

  25. Bubble Sort l = [i for i in range(10, 0, -1)] # or [i for i in range(10)][::-1] cnt = len(l) - 1 total = 0 while cnt > 0: swap = 0 i = 0 for e in l: if i + 1 < len(l) and l[i] > l[i+1]: l[i], l[i+1] = l[i+1], l[i] swap += 1 i += 1 total += swap cnt -= 1 print total

  26. Merge Sort

  27. Merge Sort # Merge two sorted lists */ def merge(list1, list2, temp): global swaps current1 = 0 # Current index in list1 current2 = 0 # Current index in list2 current3 = 0 # Current index in temp while current1 < len(list1) and current2 < len(list2): if list1[current1] < list2[current2]: temp[current3] = list1[current1] current1 += 1 current3 += 1 swaps += 1 else: temp[current3] = list2[current2] current2 += 1 current3 += 1 swaps += 1 while current1 < len(list1): temp[current3] = list1[current1] current1 += 1 current3 += 1 swaps += 1 while current2 < len(list2): temp[current3] = list2[current2] current2 += 1 current3 += 1 swaps += 1 global swaps swaps = 0 def mergeSort(list): if len(list) > 1: # Merge sort the first half # firstHalf = list[ : len(list) // 2] This is what the book does. firstHalf = [i for i in list[: len(list) // 2]] # This uses list comprehension. mergeSort(firstHalf) # Merge sort the second half # secondHalf = list[len(list) // 2 : ]This is what the book does. secondHalf = [i for i in list[len(list) // 2 :]] # This uses list comprehension. mergeSort(secondHalf) # Merge firstHalf with secondHalf into list merge(firstHalf, secondHalf, list)

  28. Bubble and Merge Sort Efficiency

  29. List Comprehension and Lambda Expressions for Propositional Logic It's Monday. If it's Monday, the next day is Tuesday. If the next day is Tuesday, then I will win a thousand dollars. # m stands for "it's Monday", t stands for "the next day is Tuesday", and d stands for "I will win a thousand dollars" print [(lambda (m, t, d) : not (m and (not m or t) and (not t or d)) or d) ((i, j, k)) for i in (False, True) for j in (False, True) for k in (False, True)]

  30. List Comprehension and Lambda Expressions and SQL emp = (('EMPNO', 'ENAME', 'JOB', 'MGR', 'HIREDATE', 'SAL', 'COMM', 'DEPTNO'), (7369, 'SMITH', 'CLERK', 7902, '1980-12-17 00:00:00', 800.0, 0.0, 20), (7499, 'ALLEN', 'SALESMAN', 7698, '1981-02-20 00:00:00', 1600.0, 300.0, 30), (7521, 'WARD', 'SALESMAN', 7698, '1981-02-22 00:00:00', 1250.0, 500.0, 30), (7566, 'JONES', 'MANAGER', 7839, '1981-04-02 00:00:00', 2975.0, 0.0, 20), (7654, 'MARTIN', 'SALESMAN', 7698, '1981-09-28 00:00:00', 1250.0, 1400.0, 30), (7698, 'BLAKE', 'MANAGER', 7839, '1981-05-01 00:00:00', 2850.0, 0.0, 30), (7782, 'CLARK', 'MANAGER', 7839, '1981-06-09 00:00:00', 2450.0, 0.0, 10), (7788, 'SCOTT', 'ANALYST', 7566, '1982-12-09 00:00:00', 3000.0, 0.0, 20), (7839, 'KING', 'PRESIDENT', 0, '1981-11-17 00:00:00', 5000.0, 0.0, 10), (7844, 'TURNER', 'SALESMAN', 7698, '1981-09-08 00:00:00', 1500.0, 0.0, 30), (7876, 'ADAMS', 'CLERK', 7788, '1983-01-12 00:00:00', 1100.0, 0.0, 20), (7900, 'JAMES', 'CLERK', 7698, '1981-12-03 00:00:00', 950.0, 0.0, 30), (7902, 'FORD', 'ANALYST', 7566, '1981-12-03 00:00:00', 3000.0, 0.0, 20), (7934, 'MILLER', 'CLERK', 7782, '1982-01-23 00:00:00', 1300.0, 0.0, 10)) dept = (('DEPTNO', 'DNAME', 'LOC'), (10, 'ACCOUNTING', 'NEW YORK'), (20, 'RESEARCH', 'DALLAS'), (30, 'SALES', 'CHICAGO'), (40, 'OPERATIONS', 'BOSTON')) print[ (i[1], j[1]) for i in emp for j in dept if i[7] == j[0] ] İs similar to “select ename, dname from emp join dept on( emp.deptno = dept.deptno)”in SQL

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