LING 408/508: Computational Techniques for Linguists

LING 408/508: Computational Techniques for Linguists Lecture 2 8/22/2012

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Outline • Running IDLE • Overview of computer programming • Programming languages and computer hardware • Python datatypes • Assignment operator and references • Short assignment #1

Programming involves: • Choosing a computational problem • Finding a solution in terms of abstract representations and operations • Implementation in a particular programming language

1. Formulate computational problem • Problem to be solved, with input and output • Example 1: multiplication • Input: two numbers x and y • Output: a number z, which is the result of multiplying x and y together • Example 2: weather prediction • Input: today’s temperature, today’s humidity, time of year, geographic location, etc. • Output: a temperature and quantity of precipitation predicted for tomorrow • Develop a simplified model for complex real-world problems

2. Abstract representations and operations • Decide on relevant objects / states / characteristics / actions of the problem • Formulate abstract representations of those objects / states • Formulate algorithms that operate upon those representations to produce some result • Complex problems can be modeled by breaking it down into small, interacting components

Example: chess game • What do we need to represent? • What operations are applied to those representations?

Example: chess game • What do we need to represent? • chess board • pieces • configuration of pieces (at a particular moment in time) • starting configuration • whose turn it is • end state: checkmate / draw • whether the current player is in check • etc. • What actions take place upon those representations? • Legal moves of pieces • pawn, rook, pawn becoming king, castling, check, etc. • Result of moving pieces • Whether the configuration of pieces is a an end state • etc.

3. Implementation in programming language • Choose a programming language • Write the program in terms of the constructs available in the language • Program = algorithm implemented in a particular programming language

Example: multiplication • Write the program in terms of the constructs available in the language • Multiply 3 by 5 in Python: 3 * 5 • It’s easy to write a program for this because the representations and operations correspond exactly to primitive constructs in Python: integers and the multiplication operator

Example: program to play chess • Not so straightforward… • For example, we want to represent a chess board. But the concept of a “chess board” is not directly available in the Python language (unlike integers). • Need compound data types • Begin with primitive data types, combine them to produce higher-level representations • Can produce arbitrarily complex models

Primitive data types in Python • Integers: • 3, 8, 0, -2, 100 • Floating-point numbers • 3.14159, 0.0001, -.101010101, 2.34e+18 • Booleans (binary-valued) • True, False • “None” • Value is None

Compound data types in Python • Strings • 'hello', "GOODBYE" • (note: in C, a string is an array of characters; Python doesn’t have characters; a single character is a 1-element string) • Lists • [1,2,3,4,5], ['how', 'are', 'you'] • Elements are indexed: element at index 0 of [1,2,3,4,5] is 1 • Tuples • (1, 2, 3, 'a', 'b')

Compound data types in Python • Sets • {1,2,3,4,5} {1,1,2,2,3,3,4,4} # these are same • Sets do not store duplicates, and set elements are notindexed • Dictionaries • {'a':1, 'b':2, 'c':3} • Map ‘a’ to 1, map ‘b’ to 2, map ‘c’ to 3 • Example application: represent the frequencies of letters in a text • Classes • Create your own data type

Operators • Operators are applied to data types to produce new results • Common integer operators: + addition - subtraction * multiplication // division / integer division % modulus ** exponentiation

Addition, subtraction, multiplication >>> 3 + 4 7 >>> 10 - 2 8 >>> 5 * 3 15 >>> 3 * (2 + 1) # parentheses for grouping 9

Exponentiation >>> 2**3 # 2 to third power = 2*2*2 = 8 8 >>> 2**4 # 2 to fourth power = 16 16 >>> 16**.5 # same as square root of 16 4

Integer division and remainder • In elementary school, you learned that: 7 / 2 = 3 r 1 • In Python: >>> 7 // 2 3 >>> 7 % 2 1

Floating-point division >>> 7 // 2 3 >>> 7 / 2 # result is a float 3.5

Complex arithmetic expressions • Apply operator to operands that may themselves be complex 2 3 2 / 3 1 + (2 / 3) 7 * (1 + (2 / 3)) 7 * (1 + (2 / 3)) – 18 ( 7 * (1 + (2 / 3)) – 18 ) % 4 (( 7 * (1 + (2 / 3)) – 18 ) % 4)**3

Assignment operator • Let’s say you want to calculate the result of 1 + (2 * (3 + ( 4 * ( 5 + 6 )))) • You want to re-use the result in subsequent computation • It will be cumbersome to repeatedly put this long expression in your code multiple times • Solution: assignment of value to variable >>> a = 1 + (2 * (3 + ( 4 * ( 5 + 6 )))) >>> a # value is retrieved from variable 95

Assignment operator • The assignment operator assigns a value to a variable >>> x = 3 >>> x 3 >>> y = 7 >>> x + y # look up values for x and y 10 >>> x * y 21 >>> x = x + 1 # modify value of variable >>> x 4

Variables are stored as references • What happens when we write x = 3 ? • Create an integer 3and store it in memory • Create a name x • xis associated with a reference to the memory location storing 3 • So, when we say that the value of xis 3, we mean that xnow refers to the integer 3 Type: Integer Data: 3 Variable name: x Variable name: x Ref: <address1> memory name list

Modification of immutabledatatypes(int, string, float, bool, tuple) • x = x + 1 • The reference of name x is looked up. • The value at that reference is retrieved. • Calculate 3+1, producing 4,which is assigned to a fresh memory location with a new reference. • The name x is changed to point to this new reference. • The old data 3 is garbage collected if no name refers to it. • Immutable: change what a variable refers to, rather than change its value Type: Integer Data: 3 Variable name: x Ref: <address1> Type: Integer Data: 4

Shortcut operators >>> a = 3 >>> a = a + 1 >>> a 4 >>> a += 1 # same as a = a + 1 >>> a 5 >>> a *= 3 # same as a = a * 3 >>> a 15

Swap values of variables >>> x = 3 >>> y = 4 • Want to swap values: want x to have value of 4, y to have value of 3 >>> x = y # this doesn’t work: >>> y = x # now x is 4, y is 4

Swap values of variables • Assign to a temporary variable: >>> x = 3 >>> y = 4 >>> temp = x # save value of x: temp is 3 >>> x = y # gets value of y: x is now 3 >>> y = temp # y gets value stored in temp • Alternatively, use multiple assignment: >>> x = 3 >>> y = 4 >>> x, y = y, x # now x is 4, y is 3 >>> (x, y) = (y, x) # parentheses are optional

Due by Friday 8/24 • Make 1,000 from eight 8’s, combined together in one arithmetic expression, through any combination of integer operators and parentheses • Example: (8888 – 888) / 8 = 1000 • Instructions: • Think of two more solutions to this problem • Create a python script file that, when executed, prints your formula, and evaluates and prints the result • Represent your formula as a string to print it: print('5+5') • Turn in a screenshot of script file and result in Python shell • Turn in at beginning of class, or place under my office door

Next class: functions

LING 408/508: Computational Techniques for Linguists