Functional Programming Charlie Li 6/4/2019 Content • Functional Programming • Haskell – Features • Haskell – Basic Types • Haskell – Classes • Haskell – Custom Types • Haskell – Infix Function • Haskell – Precedence and Associativity • Haskell – Partial Application Content • Haskell – Strict Type • Haskell – Syntax • Haskell – Pattern Matching • Haskell – Lists • Haskell – Folds • Haskell – Tuples • Haskell – Challenges • Haskell – More Functional Programing • Why functional programing? • Pros: • Less bug • Shorter and cleaner code • Focus on WHAT to calculate not HOW to calculate • Cons: • Looonger programming time and runtime • Compile errorsss Functional Programing • Pure function • A pure function is a function which gives the same result with the same input • No side effects • Outputting to screen is a side effect! Functional Programing • Which of the following functions are pure functions? void f1() { cout << "Hello World !" << endl; } int f2(int x) { return ++x; } int f3(int& x) { return ++x; } int f4(int x, int y) { return x + y; } Functional Programing • f1 is not a pure function! • It print the same string every time, isn’t it a constant function? • No, printing is a side effect, it changes your screen! • More precisely, it changes some part of the memory that does not belong to it Functional Programing • f2 is a pure function! • It has not side effects. • Although it changes the variable x, that x belongs to the function, not the outside world, so it is pure Functional Programing • f3 is not a pure function! • It has side effect. • Noted that x is passed by reference. • It changes the variable x which does not belong to itself Functional Programing • f4 is a pure function! • It has no side effects. • It returns the same output when the input is the same. Functional Programing • In a pure functional programing language, every function is a pure function • All variables are mathematically variables • It has Referential transparency, i.e. replacing the variable by its value does not change the behavior of the program • Global variables are essentially global constant • No input and output in the function • IO is troublesome and too difficult to be explained today Haskell - Features • Haskell is a pure functional programming language • Every function is a pure function • Haskell is statically typed • The type of variables are determined at compile time • Haskell supports type inference • The compile can detect the type of variables and functions even if it is not provided • Haskell supports lazy evaluation • The value of an expression is evaluated only if it is needed Haskell – Basic Types • Names of data types always starts with capital letter • Some basic types are: • Int • A 32-bit or 64-bit integer, depends on computer • Integer • Aka. Big integer • Double • Char • Bool • String Haskell – Basic Types • There are also two more kind of useful data types in Haskell • Lists • Every element are of the same type in a list (unlike Python) • There is no restriction on the length of lists • Yes, there are lists with infinite length • Tuples • Elements in a tuple may have different types • The largest tuple can have up to 62 entries Haskell – Basic Types • Lists • List are represented using brackets [] • [1, 2, 3] is a list of integer with length 3 • Its type maybe [Int] or [Double] or … • Tuples • Tuples are represented using parenthesis () • (1, ‘a’, [True, False]) is a tuple with three element • Its type maybe (Int, Char, [Bool]) or (Double, Char, [Bool]) or … Haskell Platform • Haskell Platform includes GHC (the Haskell compiler) and other useful tools • The latest version is 8.6.3, the installer for Windows can be downloaded here • You can find the download links for other OS at the bottom Haskell – Area • Let’s open ghci (winghci has better UI but cannot be used in this lab due to some permission issues) • Let’s first define a function to calculate the area of a rectangle • Type the following into ghci (let areaRect l w = l * w): • This is the definition of the function areaRect • What do you think will be the output of areaRect 2 3? Haskell – Area • Bingo • How about areaRect 2.5 3.5? Haskell – Area • Bingo • Next question, how about areaRect 2.5 3? Haskell – Area • Bingo • Next question, what do you think will be the type of areaRect? • Sometimes it takes two integers as input and return integer • Sometimes it takes two fractional numbers as input and return a fractional number Haskell – Area • In ghci, we can type :t name to check the type (aka. signature) of a function • The “::” tells that the following is the function type not a definition • The “Num a =>” part says that a is a type that belongs to the “Num” class • “Num” class contains all kinds of numbers, e.g. Int, Integer, Float, Double, … Haskell – Area • In ghci, we can type :t name to check the type (aka. signature) of a function • The “a -> a -> a” part is the type of the function • The last one is the type of the returned value • Others are the type of parameter • So area takes two parameter with the same type as input and return the same type • Also, this a must be some kind of number Haskell – Area • In ghci, we can type :t name to check the type (aka. signature) of a function • So this tells us that areaRect is a function that takes two numbers as input and return a number Haskell – Classes • Be careful, there is a bit difference between class and type • Haskell is a statically typed language • The existence of class is for safe function overload • There are similarity between class in Haskell and class in C++ • There are some inheritance relation • E.g. Integral a => Num a • But the class in Haskell is not the same as the class in C++ Haskell – Classes • There are many predefined classes in Haskell, the name are usually descriptive enough Haskell – Classes • Eq: All types that == and /= are defined • Ord: All types that <, >, <=, >= are defined • Num: All types of numbers • Real: All types of real numbers • Fractional: All types of numbers that are not necessarily integer • Integral: All types of integers • Foldable: All types that “foldr” is defined • Read: All types that “read” is defined • Show: All types that “show” is defined • … Haskell – Classes • So now do you know the type of [1, 2, 3] and (1, ‘a’, [True, False]) ? • How to check if you get the correct answer? • Just try to type :t [1, 2, 3] and :t (1, ‘a’, [True, False]) Haskell – Classes • Did you get it right? Haskell – Custom Type • In Haskell you can define your own type • Syntax like this: data Contact = Phone Integer | Email String data Maybe a = Just a | Nothing data Either a b = Left a | Right b data Ordering = LT | EQ | GT • Phone, Email, … are said to be the constructors of the corresponding type • Maybe, Either and Ordering are predefined in Haskell Haskell – Custom Type • You can use Notepad++ to write the code and save as “.hs” • Suppose your code is saved as “C:\Haskell\code\sample.hs” • You need to type the following to load the code into ghci :load C:\Haskell\code\sample.hs • You will see the “Prelude” become “Main” if it is loaded successfully Haskell – Custom Type • Phone and Email are constructors of Contact • They are also functions with the following type Haskell – Custom Type data Contact = Phone Integer | Email String data Maybe a = Just a | Nothing data Either a b = Left a | Right b data Ordering = LT | EQ | GT • Maybe, Either are kinds and NOT classes nor types • Contact, Maybe Int are types • Phone 98765432, Just 0, Nothing are values Haskell – Infix Function • A function with symbol only is assumed to be infix operator • Need to add a pair of brackets to make it like normal functions -- x + y == (+) x y • A function can become infix if it is wrapped by `` add x y = x + y -- add x y == x `add` y Haskell – Precedence and Associativity • Infix functions has lower precedence then normal functions • Normal functions are left associated • i.e. f a b == (f a) b • Associativity of infix functions depend on the function • Usually left associated • Some right associated functions: exponent, (.), ($) ($) :: (a -> b) -> a -> b -- trick: f $ g $ h x == f (g (h x)) /= ((f g) h) x == f g h x Haskell – Anonymous Function • In Haskell, it is able to define anonymous function using lambda expression. • Syntax: \var1 var2 … varn -> expression • The expression goes as far as possible • Remember to add parentheses • Example: \x -> x + 1 \x y -> x + y Haskell – Anonymous Function • Remember when will you use anonymous function in C++? sort(v.begin(), v.end(), [] (int x, int y) { return x > y; }); • You can also write something similar in Haskell • There is a sortBy function in Haskell (in the package Data.List) • To import Data.List into ghci, simply type import Data.List sort :: Ord a => [a] -> [a] sortBy :: (a -> a -> Ordering) -> [a] -> [a] Haskell – Anonymous Function sort [1, 4, 2, 3] -- [1, 2, 3, 4] sortBy (\x y -> negate x `compare` negate y) [1, 4, 2, 3] -- [4, 3, 2, 1] -- negate :: Num a => a -> a -- compare :: Ord a => a -> a -> Ordering -- *this is not the best way to define it, why? Haskell – Unary Functions • Actually all functions can be viewed as unary functions • How about (+) which takes two parameter? (+) :: Num a => a -> a -> a -- can be viewed as (+) :: Num a => a -> (a -> a) -- (+) x == \y -> x + y • (->) is right associative • (+) takes one input (number) and returns one output (function) Haskell – Partial Application • Consider add x y = x + y addTwo = add 2 • What is the type of addTwo? • This is called partial application. Haskell – Partial Application • Here comes some function that are often applied partially const :: a -> b -> a -- usually be viewed as const :: a -> (b -> a) flip :: (a -> b -> c) -> b -> a -> c -- usually be viewed as flip :: (a -> b -> c) -> (b -> a -> c) (.) :: (b -> c) -> (a -> b) -> a -> c -- usually be viewed as (.) :: (b -> c) -> (a -> b) -> (a -> c) -- aka.