Two (too?) big assumptions Recollecting Haskell, Part I (Based on - PowerPoint PPT Presentation

Two (too?) big assumptions Recollecting Haskell, Part I (Based on Chapters 1 and 2 of LYH ⋆ ) CIS 352: Programming Languages You can read LYH 1 You will read LYH. 2 January 15, 2019 ⋆ LYH = Learn You a Haskell for Great Good CIS 352 Recollecting Haskell, Part I January 15, 2019 1 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 2 / 24 The Blurb from wiki.haskell.org So why do we care about Haskell in this course? Haskell is great for prototyping. Haskell is an advanced purely-functional programming language. Forces you to think compositionally. ...it allows rapid development of robust, concise, correct software. Semi-automated testing: QuickCheck With strong support for Haskell can give you executable specifications. integration with other languages, Good for “model building” built-in concurrency and parallelism, e.g., direct implementations of operational semantics debuggers, profilers, . . . and beyond this course rich libraries and Many modern systems/applications languages an active community, (e.g., Swift and Rust) steal lots of ideas from Haskell and ML. Haskell makes it easier to produce flexible, maintainable, high-quality These ideas are a lot clearer in Haskell and ML software. than the munged versions in Swift, Rust, etc., CIS 352 Recollecting Haskell, Part I January 15, 2019 3 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 4 / 24

Set up A sample session: ghci as a calculator Go visit https://www.haskell.org/downloads#platform . [Post:~] jimroyer% ghci Download the appropriate version of the current Haskell Platform GHCi, version 8.6.3: http://www.haskell.org/ghc/ :? for help and install it. Loaded GHCi configuration from /Users/jimroyer/.ghci ghci> 2+3 !!! Do the above even if you have an old copy of the Haskell Platform 5 ghci> 2*3 from a previous year. 6 You want the latest version of the GHC compiler and libraries. ghci> 2-3 -1 !!! Use a reasonable editor. ghci> 2/3 0.6666666666666666 Using Notepad or Word is a waste of your time. ghci> :q See http://www.haskell.org/haskellwiki/Editors . Leaving GHCi. Emacs is my weapon of choice. [Post:~] jimroyer% Atom is a popular alternative, see: https://atom-haskell.github.io/extra-packages/ CIS 352 Recollecting Haskell, Part I January 15, 2019 5 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 6 / 24 Fussy bits Using functions ghci> succ 4 5 ✘ 5 * -3 ghci> succ 4 * 10 ✔ 5 * (-3) 50 baby.hs ghci> succ (4 * 10) ✘ 5 * 10 - 49 �≡ 5 * (10 - 49) doubleMe x = x + x 41 ✔ 5 * 10 - 49 ≡ (5 * 10) - 49 ghci> max 5 3 ghci> :load baby 5 ✘ 5 * True [1 of 1] Compiling Main ghci> 1 + max 5 3 ( baby.hs, interpreted ) ghci> 5 + True 6 Ok, modules loaded: Main. ghci> max 5 3 + 1 ghci> doubleMe 5 6 <interactive>:2:3: error: (What does all this mean?) 10 ghci> max 5 (3 + 1) No instance for (Num Bool) arising from a use of ‘+’ ghci> doubleMe 7.7 5 15.4 In the expression: 5 + True ghci> 10 ‘max‘ 23 In an equation for ‘it’: it = 5 + True 23 ghci> (+) 3 5 8 CIS 352 Recollecting Haskell, Part I January 15, 2019 7 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 8 / 24

Defining and using functions, continued Lists A list : a sequence of things of the same type . ✔ [2,3,5,7,11,13,17,19] ::[Int] ✔ [True,False,False,True] ::[Bool] baby.hs ✔ [’b’,’o’,’b’,’c’,’a’,’t’] ≡ "bobcat" ::[Char] doubleMe x = x + x ✔ [] ::[a] ✔ [[],[1],[2,3],[4,5,6]] ::[[Int]] doubleUs x y = 2*x+2*y ✘ [[1],[[2],[3]]] fuss doubleUs’ x y = doubleMe x + doubleMe y ✘ [2,True,"foo"] fuss If you want to bundle together things of different types, doubleSmallNumber x = if x > 100 then x else x * 2 use tuples (e.g., (2,True,"foo") ...explained later) . doubleSmallNumber’ x = (if x > 100 then x else x * 2)+1 conanO’Brien = "It’s a-me, Conan O’Brien!" Notation expression 1 ❀ expression 2 means expression 1 evaluates to expression 2 E.g.: 2+3 ❀ 5 CIS 352 Recollecting Haskell, Part I January 15, 2019 9 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 10 / 24 Lists: Building them up Lists: Tearing them down Write them down: [ item 1 , item 2 , ... , item n ] [2,3,5,7,11,13,17,19] , [] , etc. Concatenation: list 1 ++ list 2 [1,2,3,4]++[10,20,30] ❀ [1,2,3,4,10,20,30] "salt"++"potato" ❀ "saltpotato" []++[1,2,3] ❀ [1,2,3] [1,2,3]++[] ❀ [1,2,3] 1++[2,3] ❀ ERROR [1,2]++3 ❀ ERROR Cons: item : list 1:[2,3] ❀ [1,2,3] [1,2]:3 ❀ ERROR head [1,2,3] ❀ 1 last [1,2,3] ❀ 3 [1,2,3] is syntactic sugar for 1:2:3:[] ≡ 1:(2:(3:[])) tail [1,2,3] ❀ [2,3] init [1,2,3] ❀ [1,2] You can tell (:) is important head [] ❀ ERROR last [] ❀ ERROR because they gave it such a short name. (Actually, a design error.) tail [] ❀ ERROR init [] ❀ ERROR CIS 352 Recollecting Haskell, Part I January 15, 2019 11 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 12 / 24

Lists: More operations Ranges [m..n] ❀ [m,m+1,m+2,...,n] length :: [a] -> Int [1..5] ❀ [1,2,3,4,5] (!!) :: [a] -> Int -> a [5..1] ❀ [] null :: [a] -> Bool reverse :: [a] -> [a] [’a’..’k’] ❀ "abcdefghijk" drop, take :: Int -> [a] -> [a] [1..] ❀ [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, sum, product :: (Num a) => [a] -> a minumum, maximum :: (Ord a) => [a] -> a [m,p..n] ❀ [m, m+(p-m), m+2(m-p), ... ,n ∗ ] elem, notElem :: (Eq a) => a -> [a] -> Bool [3,5..10] ❀ [3,5,7,9] [5,4..1] ❀ [5,4,3,2,1] You can look up what these do on: [9,7..2] ❀ [9,7,5,3] Hoogle: https://www.haskell.org/hoogle/ Hayoo: http://hayoo.fh-wedel.de ∗ Or the “closest” number before n that is in the sequence. CIS 352 Recollecting Haskell, Part I January 15, 2019 13 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 14 / 24 List comprehensions Example: Squaring every element of a list squares.hs Set comprehensions in math (CIS 375 review) squares :: [Integer] -> [Integer] squares xs = [ x*x | x <- xs ] { x | x ∈ N , x = x 2 } = { 0, 1 } { x | x ∈ N , x > 0 } = the positive integers squares [1,2,3] { x 2 | x ∈ N } = squares { xs = [1,2,3] } = [ x*x | x <- [1,2,3] ] { ( x , y ) | x ∈ N , y ∈ N , x ≤ y } { x=1 } , { x=2 } , { x=3 } = Suppose we have lst = [5,10,13,4,10] [ 1*1 ] ++ [ 2*2 ] ++ [ 3*3 ] [2*n+1 | n <- lst] ❀ [11,21,27,9,21] = [1]++[4]++[9] [even n | n <- lst] ❀ [False,True,False,True,True] = [ 2*n+1 | n <- lst , even n , n>5 ] ❀ [21,21] � �� � � �� � � �� � ���� [1,4,9] generator transform filter filter Example lifted from Phil Wadler. CIS 352 Recollecting Haskell, Part I January 15, 2019 15 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 16 / 24

Example: Odd elements of a list Example: Sum of the squares of the odd elements, 1 odds.hs odds :: [Integer] -> [Integer] sumSqOdds.hs odds xs = [ x | x <- xs, odd x ] squares :: [Integer] -> [Integer] squares xs = [ x*x | x <- xs ] odds [1,2,3] odds :: [Integer] -> [Integer] { xs = [1,2,3] } = odds xs = [ x | x <- xs, odd x] [ x | x <- [1,2,3], odd x ] { x=1 } , { x=2 } , { x=3 } = f :: [Integer] -> Integer [ 1 | odd 1 ] ++ [ 2 | odd 2 ] ++ [ 3 | odd 3 ] f xs = sum (squares (odds xs)) = f’ :: [Integer] -> Integer [ 1 | True ] ++ [ 2 | False ] ++ [ 3 | True ] f’ xs = sum [ x*x | x <- xs, odd x ] = [1]++[]++[3] = Another example lifted from Phil Wadler. [1,3] Example lifted from Phil Wadler. CIS 352 Recollecting Haskell, Part I January 15, 2019 17 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 18 / 24 Example: Sum of the squares of the odd elements, 2 Example: Sum of the squares of the odd elements, 3 f’ xs = sum [ x*x | x <- xs, odd x] f xs = sum (squares (odds xs)) f’ [1,2,3] { xs = [1,2,3] } = f [1,2,3] sum [ x*x | x <- [1,2,3], odd x] = { xs = [1,2,3] } { x=1 } , { x=2 } , { x=3 } = sum (squares (odds [1,2,3])) sum ([ 1*1 | odd 1 ] ++ [ 2*2 | odd 2 ] ++ [ 3*3 | odd 3 ]) = = sum (squares [1,3]) sum ([ 1 | True ] ++ [ 4 | False ] ++ [ 9 | True]) = = sum [1,9] sum ([ 1 ] ++ [] ++ [ 9 ]) = = 10 sum [1,9] = 10 CIS 352 Recollecting Haskell, Part I January 15, 2019 19 / 24 CIS 352 Recollecting Haskell, Part I January 15, 2019 20 / 24