Haskell: A Functional Language for Aesthetics, Pragmatics and Performance
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We introduce Haskell. Why is it interesting. Where did it come from. What is it like. How to get started. We show a GHCi session. We introduce simple recursive function and data. And we demo QuickCheck for testing properties of automatically generated data.
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Haskell: A Functional Language for Aesthetics, Pragmatics and Performance
- 1. Haskell A Whirlwind Tour William Taysom 2011
- 2. Haskell
- 5. Why? Aesthetics
- 6. Why? Aesthetics “We provided DARPA with a copy of our prototype implemented in Haskell without explaining that it was a program, and based on preconceptions from their past experience, they had studied the program under the assumption that it was a mixture of requirements specification and top level design. They were convinced it was incomplete because it did not address issues such as data structure design and execution order.” — Paul Hudak
- 7. Why? Aesthetics “Take Lisp: you know it's the most beautiful language in the world. At least up until Haskell came along.” — Larry Wall
- 8. Why? Aesthetics “Reading Haskell is like reading poetry. Writing Haskell is like writing poetry.” — Oliver Steele
- 9. Why? Aesthetics “I also have interest in Haskell, but my brain just explodes every time I read a Haskell program bigger than ten lines.” — Matz
- 10. Why? Aesthetics “The biggest advantage of Haskell to me is that it helps me write better programs in other languages.” — Tenerife Skunkworks
- 11. Why? Aesthetics .NET LINQ Python List Comprehensions Java Generics JavaScript jQuery
- 12. Why? Pragmatics
- 13. Why? Pragmatics Platform Compiler Debugger Profiler Testing Libraries Network Graphics Hackage Community Books Documentation Hoogle
- 14. Why? Pragmatics Platform Compiler Debugger Profiler Testing Libraries Network Graphics Hackage Community Books Documentation Hoogle
- 15. Why? Pragmatics Hoogle
- 16. Why? Pragmatics Hoogle
- 17. Why? Pragmatics Platform Compiler Debugger Profiler Testing Libraries Network Graphics Hackage Community Books Documentation Hoogle
- 18. Why? Pragmatics Platform Compiler Debugger Profiler Testing Libraries Network Graphics Hackage Community Books Documentation Hoogle
- 19. How? GHC Documentation Libraries Cabal Hackage
- 20. Why? Pragmatics Platform Compiler Debugger Profiler Testing Libraries Network Graphics Hackage Community Books Documentation Hoogle
- 21. Why? Pragmatics
- 22. Why? Pragmatics
- 23. Why? Pragmatics “A programming language must be considered in the context of its community, and Haskell has an exemplary one. I have come to believe, however, that this polite exterior conceals a deep and consuming madness.” — Avdi Grimm
- 24. Why? Performance
- 25. Why? Performance The Computer Language Benchmarks Game
- 26. Why? Performance Web Server Pong benchmark, extra large instance, requests/second
- 27. Why? Performance Web Server Pong benchmark, extra large instance, requests/second
- 28. Why? Aesthetics Pragmatics Performance
- 29. Haskell Who? What? When? Where? Why? Aesthetics Pragmatics Performance How?
- 30. Haskell Who? What? When? Where? Why? Aesthetics Pragmatics Performance How?
- 31. Who? When? Where? September 1987
- 32. Who? When? Where? Portland, Oregon
- 33. Who? When? Where? Functional Programming Languages and Computer Architecture Conference
- 34. Who? When? Where? A Dozen Purely Functional Languages
- 35. Who? When? Where? All Similar
- 36. Who? When? Where? Committee Formed
- 37. Who? When? Where? Committee Formed
- 39. Provide faster communication of new ideas. Stable foundation for real application development. Vehicle through which others would be encouraged to use functional languages.
- 40. Who? When? Where? Haskell Report April 1st 1990 “You know, Haskell actually never liked the name Haskell.” — Mary Curry
- 41. Who? When? Where? 2002 Revised Haskell 98 Report
- 42. Who? When? Where? 2010 Haskell'
- 43. Haskell Who? Research Wadler Hudak Peyton-Jones What? When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How?
- 44. Haskell Who? Research Wadler Hudak Peyton-Jones What? When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How?
- 45. What? A non-strict, purely functional programming language with strong, static type inference.
- 46. What? A non-strict, purely functional programming language with strong, static type inference.
- 47. What? Programming Source Code Formal, Textural Syntax Static & Runtime Semantics Data, Variables, Lexical Scope Interpreter, Compiler
- 48. What? A non-strict, purely functional programming language with strong, static type inference.
- 49. What? A non-strict, purely functional programming language with strong, static type inference.
- 50. What? Functional (Not Imperative)
- 51. What? Functional Imperative Statements Executed Step-by-step
- 52. What? Functional Imperative Statements Executed Step-by-step Modifying State
- 53. What? Functional Imperative Statements Executed Step-by-step Modifying State Turing Machine
- 54. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture
- 55. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture Functional Expressions Recursively Simplified
- 56. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture Functional Expressions Recursively Simplified Reduced Value
- 57. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture Functional Expressions Recursively Simplified Reduced Value Lambda Calculus
- 58. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture Functional Expressions Recursively Simplified Reduced Value Lambda Calculus
- 59. What? Functional Imperative Statements Executed Step-by-step Modifying State Von Neumann Architecture Functional Expressions Recursively Simplified Reduced Value Lambda Calculus
- 60. What? A non-strict, purely functional programming language with strong, static type inference.
- 61. What? A non-strict, purely functional programming language with strong, static type inference.
- 62. What? Pure (No Side Effects)
- 63. What? Pure Immutable Only
- 65. What? Pure Functions always return the same value. If v = f x, then you can always replace f x with v.
- 66. What? Pure Functions always return the same value. If v equals f x, then you can always replace f x with v.
- 67. What? A non-strict, purely functional programming language with strong, static type inference.
- 68. What? A non-strict, purely functional programming language with strong, static type inference.
- 69. What? Non-strict Be lazy.
- 70. What? Non-strict Be lazy. Ignore evaluation order.
- 71. Wait...
- 72. if everything is immutable and there are no side effects and evaluation is lazy,
- 73. then how the hell do you do anything?
- 74. MONADS Bring your own Semicolon
- 75. What? Monads
- 76. What? Monads
- 77. What? Monads
- 78. What? Monads
- 79. What? Monads
- 80. What? Monads “Haskell is the world's finest imperative programming language.” — Simon Peyton-Jones
- 81. What? Monads “Haskell is the only language I know with first-class support for imperative programming.” — SamB
- 82. What? Monads “Haskell has no preferred imperative semantics, and the monad just lets you swap out the semantics according to your needs.” — Jared Updike
- 83. What? A non-strict, purely functional programming language with strong, static type inference.
- 84. What? A non-strict, purely functional programming language with strong, static type inference.
- 85. What? Types Strong Static Inference
- 86. What? Types Strong Static Inference
- 87. What? Strong Types Runtime values have types.
- 88. What? Strong Types Runtime values have types. like Java and Ruby unlike C and Assembly (Not Weak)
- 89. What? Types Strong Static Inference
- 90. What? Types Strong Static Inference
- 91. What? Static Types Source code expressions have types.
- 92. What? Static Types Source code expressions have types. like C and Java unlike Ruby and JavaScript (Not Dynamic)
- 93. What? Types Strong Static Inference
- 94. What? Types Strong Static Inference
- 95. What? Type Inference Automatically determines types of variables.
- 96. What? Type Inference Automatically determines types of variables. like C# and Go unlike C and Java (Not Manifest)
- 97. You don’t need to type the type!
- 98. SYNERGY Purity means types tell you a lot.
- 99. What? Type Purity No side effects mean,
- 100. What? Type Purity No side effects mean, argument and return types limit what a function can do.
- 101. What? Type Purity “Haskell is so strict about type safety that randomly generated snippets of code that successfully type check are likely to do something useful, even if you've no idea what that useful thing is.” — sigfpe
- 102. What? Type Purity “Since when does "it compiles" equate to "it will run (correctly)"? We're talking about C, after all, not Haskell.” — Sean Russell
- 103. What? Types Strong Static Inference
- 104. What? A non-strict, purely functional programming language with strong, static type inference.
- 105. What? A non-strict, purely functional programming language with strong, static type inference.
- 106. Haskell Who? Research Wadler Hudak Peyton-Jones What? Non-strict Purely Functional Static Types When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How?
- 107. Haskell Who? Research Wadler Hudak Peyton-Jones What? Non-strict Purely Functional Static Types When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How?
- 108. How? Just Download and Install the Platform
- 109. How? Just Download and Install the Platform
- 110. Glorious Glasgow Haskell Compilation System
- 111. GHC Compiler ghc Interactive ghci Scripts runghc
- 112. GHC Compiler ghc Interactive ghci Scripts runghc
- 113. Haskell Who? Research Wadler Hudak Peyton-Jones What? Non-strict Purely Functional Static Types When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How? Platform Hoogle Hackage
- 114. Haskell Who? Research Wadler Hudak Peyton-Jones What? Non-strict Purely Functional Static Types When? 1987 1990 2002 Now Where? Portland Glasgow Microsoft Why? Aesthetics Pragmatics Performance How? Platform Hoogle Hackage
- 115. Example
- 116. ┼ $ Example
- 117. $ ghci
- 118. $ ghci GHCi, version 7.0.2: http:// www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer-gmp ... linking ... done. Loading package base ... linking ... done. Loading package ffi-1.0 ... linking ... done. ghci>
- 119. $ ghci GHCi, version 7.0.2: http:// www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer-gmp ... linking ... done. Loading package base ... linking ... done. Loading package ffi-1.0 ... linking ... done. ghci> "hello, world"
- 120. $ ghci GHCi, version 7.0.2: http:// www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer-gmp ... linking ... done. Loading package base ... linking ... done. Loading package ffi-1.0 ... linking ... done. ghci> "hello, world" "hello, world" ghci>
- 121. "hello, world" ghci>
- 122. "hello, world" ghci> 6 * 9
- 123. "hello, world" ghci> 6 * 9 42 ghci>
- 124. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3]
- 125. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] ghci>
- 126. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] ghci> it
- 127. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] ghci> it [1,2,3] ghci>
- 128. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] application is so important in Haskell that “Function ghci> it it using the quietest possible syntax: we denote [1,2,3]at all.” nothing ghci> reverse it — Simon Peyton-Jones
- 129. “Function application is so important in Haskell that we denote it using the quietest possible syntax: nothing at all.” — Simon Peyton-Jones
- 130. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] application is so important in Haskell that “Function ghci> it it using the quietest possible syntax: we denote [1,2,3]at all.” nothing ghci> reverse it — Simon Peyton-Jones
- 131. "hello, world" ghci> 6 * 9 42 ghci> [1, 2, 3] [1,2,3] ghci> it [1,2,3] ghci> reverse it [3,2,1] ghci>
- 132. [3,2,1] ghci>
- 133. [3,2,1] ghci> let xs = [1..100]
- 134. [3,2,1] ghci> let xs = [1..100] ghci>
- 135. [3,2,1] ghci> let xs = [1..100] ghci> xs
- 136. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1 7,18,19,20,21,22,23,24,25,26,27,28,29,30, 31,32,33,34,35,36,37,38,39,40,41,42,43,44 ,45,46,47,48,49,50,51,52,53,54,55,56,57,5 8,59,60,61,62,63,64,65,66,67,68,69,70,71, 72,73,74,75,76,77,78,79,80,81,82,83,84,85 ,86,87,88,89,90,91,92,93,94,95,96,97,98,9 9,100] ghci>
- 137. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci>
- 138. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21]
- 139. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,24,25,26,27,28,29,30,31,32,33,34,3 5,36,37,38,39,40,41,42,43,44,45,46,47,48, 49,50,51,52,53,54,55,56,57,58,59,60,61,62 ,63,64,65,66,67,68,69,70,71,72,73,74,75,7 6,77,78,79,80,81,82,83,84,85,86,87,88,89, 90,91,92,93,94,95,96,97,98,99,100] ghci>
- 140. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] ghci>
- 141. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] ghci> filter (> 21) xs
- 142. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] ghci> filter (> 21) xs [22,23,⋯,99,100] ghci>
- 143. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] ghci> filter (> 21) xs [22,23,⋯,99,100] ghci> filter (x -> x > 21) xs
- 144. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] TMTOWTDI ghci> filter (> 21) xs [22,23,⋯,99,100] ghci> filter (x -> x > 21) xs [22,23,⋯,99,100] ghci>
- 145. TMTOWTDI
- 146. The Evolution of a Haskell Programmer 1. Freshman 13. Continuation-passing 2. Sophomore 14. Boy Scout 3. Junior (Peano) 15. Combinatory 4. Junior (Ban n+k) 16. List-encoding 5. Senior (Leans Right) 17. Interpretive 6. Senior (Leans Left) 18. Static 7. Senior (Leans Around) 19. Beginning Graduate 8. Memoizing 20. Origamist 9. Points-free 21. Cartesianally-inclined 10. Iterative 22. Ph.D. 11. Iterative one-liner 23. Post-doc 12. Accumulating 24. Tenured Professor
- 147. TMTOWTDI
- 148. [3,2,1] ghci> let xs = [1..100] ghci> xs [1,2,⋯,99,100] ghci> [x | x <- xs, x > 21] [22,23,⋯,99,100] TMTOWTDI ghci> filter (> 21) xs [22,23,⋯,99,100] ghci> filter (x -> x > 21) xs [22,23,⋯,99,100] ghci>
- 150. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0
- 151. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci>
- 152. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0
- 153. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci>
- 154. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12
- 155. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci>
- 156. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12
- 157. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12 True ghci>
- 158. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12 True ghci> let divisors x = [d | d <- [1..x], d `divides` x]
- 159. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12 True ghci> let divisors x = [d | d <- [1..x], d `divides` x] ghci>
- 160. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12 True ghci> let divisors x = [d | d <- [1..x], d `divides` x] ghci> divisors 100
- 161. [22,23,⋯,99,100] ghci> let divides = x y -> rem y x == 0 ghci> let divides x y = rem y x == 0 ghci> divides 3 12 True ghci> 3 `divides` 12 True Fundamentals ghci> let divisors x = [d | d <- [1..x], d `divides` x] ghci> divisors 100 [1,2,4,5,10,20,25,50,100] ghci>
- 162. Fundamentals
- 163. Data Declaration data Color = Red | Green | Blue
- 164. Variables red = Red -- Lower case for variable and upper case for constructor. nan = 0 / 0 -- Variables stand for values. They do not label locations. -- Don't need let because we aren't at GHCi. -- Declarations go at top-level, not expressions. (Like Java, unlike Ruby.)
- 165. Functions hue Red = 0 hue Green = 120 hue Blue = 240
- 166. Lambda & Case hue = c -> case c of Red -> 0 Green -> 120 Blue -> 240
- 167. Pattern Wildcard isRed Red = True isRed _ = False
- 168. Boolean Data data Bool = True | False
- 169. Boolean Functions otherwise = True not True = False not False = True
- 170. Boolean Operators True && x = x False && _ = False (||) True _ = True (||) False x = x -- Parenthesis let us use operators prefix.
- 171. Operator Precedence infixr 3 && infixr 2 || -- Ten precedence levels: 0 binds least tightly, 9 (default) binds most tightly. -- Three associativities: infixl (default), infixr, infix (non-associative).
- 172. Types “Types in Haskell express high-level design in the same way that UML diagrams do in Object Oriented languages.” — Simon Peyton-Jones
- 173. Types ghci> :l example “Types in Haskell express high-level design in the same way that UML diagrams do in Object Oriented languages.” — Simon Peyton-Jones
- 174. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci>
- 175. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci> :r
- 176. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci> :r Ok, modules loaded: Main. ghci>
- 177. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci> :r Ok, modules loaded: Main. ghci> :type red
- 178. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci> :r Ok, modules loaded: Main. ghci> :type red Red :: Color ghci>
- 179. ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, modules loaded: Main. ghci> :r Ok, modules loaded: Main. ghci> :type red Red :: Color ghci> :t isRed
- 180. Types ghci> :l example [1 of 1] Compiling Main ( example.hs, interpreted ) Ok, :: Color loaded: Main. red modules ghci> Double nan :: :r Ok, modules loaded: Main. ghci> Color -> Double hue :: :type red Red :: Color otherwise :: Bool ghci> :t isRed isRed Bool -> Bool Bool not :: :: Color -> ghci> (||) :: Bool -> Bool -> Bool (&&),
- 181. Types red :: Color nan :: Double hue :: Color -> Double otherwise :: Bool not :: Bool -> Bool (&&), (||) :: Bool -> Bool -> Bool
- 182. Recursive Data data Color = Red | Green | Blue | Mix Color Color
- 183. Recursive Data data Color = Red | Green | Blue | Mix Color Color mix :: Color -> Color -> Color mix = Mix -- Mix is a type constructor function.
- 184. Recursive Data yellow, cyan, magenta :: Color yellow = Mix Red Green Mix cyan magenta = Mix (Mix Green Blue) (Mix Red Blue) -- Constructor functions can be used for pattern matching, but variables bind.
- 185. Recursive Functions isRed :: Color -> Bool isRed Red = True isRed (Mix c c') = isRed c && isRed c' isRed _ = False
- 186. Recursive Functions hue :: Color -> Double hue Red =0 hue Green = 120 hue Blue = 240
- 187. Recursive Functions hue :: Color -> Double hue Red =0 hue Green = 120 hue Blue = 240 hue (Mix c c') = ???
- 188. hue (Mix c c') = ???
- 189. hue (Mix c c') = ??? h
- 190. hue (Mix c c') = let h = hue c ??? h
- 191. h' hue (Mix c c') = let h = hue c ??? h
- 192. h' hue (Mix c c') = let h = hue c h' = hue c' ??? h
- 193. h' m hue (Mix c c') = let h = hue c h' = hue c' ??? h
- 194. h' m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h ???
- 195. h' m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h average x y = abs (x + y) / 2 ???
- 196. h' m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h average x y = abs (x + y) / 2 in m
- 197. h' m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h average x y = abs (x + y) / 2 in ??!
- 198. m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h average x y = abs (x + y) / 2 in ??! h'
- 199. m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h average x y = abs (x + y) / 2 in ??! h' m'
- 200. m hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 average x y = abs (x + y) / 2 in ??! h' m'
- 201. m d hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 average x y = abs (x + y) / 2 in ??! h' m'
- 202. m d hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 d = distance h m average x y = abs (x + y) / 2 in ??! h' m'
- 203. m d hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 d = distance h m average x y = abs (x + y) / 2 distance x y = abs (x - y) h' m' in ??!
- 204. m d hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 d = distance h m average x y = abs (x + y) / 2 distance x y = abs (x - y) h' m' in case compare d 90 of LT -> m EQ -> ??! GT -> m'
- 205. m d hue (Mix c c') = let h = hue c h' = hue c' m = average h h' h m' = m + 180 d = distance h m average x y = abs (x + y) / 2 distance x y = abs (x - y) h' m' in case compare d 90 of LT -> m EQ -> nan GT -> m'
- 206. m d hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan h GT -> m' h = hue c h' = hue c' m = average h h' m' = m + 180 h' m' d = distance h m average x y = abs (x + y) / 2 distance x y = abs (x - y)
- 207. Testing test-framework organize tests HUnit what you’re used to QuickCheck test properties with automatically generated data
- 208. QuickCheck prop_hue_bounds c = let h = hue c in isNaN h || 0 <= h && h < 360
- 209. QuickCheck prop_hue_bounds c = let h = hue c in isNaN h || 0 <= h && h < 360 prop_hue_mix_reflexivity c = let h = hue c in isNaN h || hue (Mix c c) == h
- 210. QuickCheck prop_hue_bounds c = let h = hue c in isNaN h || 0 <= h && h < 360 prop_hue_mix_reflexivity c = let h = hue c in isNaN h || hue (Mix c c) == h prop_hue_mix_commutativity c c' = let h = hue (Mix c c') in isNaN h || hue (Mix c' c) == h
- 211. QuickCheck ghci> quickCheck prop_hue_mix_commutativi ty prop_hue_bounds c = let h = hue c in isNaN h || 0 <= h && h < 360 prop_hue_mix_reflexivity c = let h = hue c in isNaN h || hue (Mix c c) == h prop_hue_mix_commutativity c c' = let h = hue (Mix c c') in isNaN h || hue (Mix c' c) == h
- 212. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci>
- 213. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity
- 214. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity +++ OK, passed 100 tests. ghci>
- 215. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity +++ OK, passed 100 tests. ghci> quickCheck prop_hue_bounds
- 216. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity +++ OK, passed 100 tests. ghci> quickCheck prop_hue_bounds *** Failed! Falsifiable (after 3 tests): Mix (Mix Red Blue) (Mix Green Red) ghci>
- 217. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity +++ OK, passed 100 tests. ghci> quickCheck prop_hue_bounds *** Failed! Falsifiable (after 3 tests): Mix (Mix Red Blue) (Mix Green Red) ghci> hue (Mix magenta yellow)
- 218. ghci> quickCheck prop_hue_mix_commutativi ty +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_reflexivity +++ OK, passed 100 tests. ghci> quickCheck prop_hue_bounds *** Failed! Falsifiable (after 3 tests): Mix (Mix Red Blue) (Mix Green Red) ghci> hue (Mix magenta yellow) 360.0 ghci>
- 219. h' hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan m m' GT -> m' h = hue c h' = hue c' m = average h h' d h m' = m + 180 d = distance h m
- 220. h' hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan m m' GT -> m' h = hue c h' = hue c' m = average h h' d h m' = normalize (m + 180) d = distance h m
- 221. h' hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan m m' GT -> m' h = hue c h' = hue c' m = average h h' d h m' = normalize (m + 180) d = distance h m normalize h | h < 360 = h | otherwise = h - 360
- 222. h' hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan m m' GT -> m' h = hue c h' = hue c' m = average h h' d h m' = normalize (m + 180) d = distance h m normalize h | h < 360 = h | otherwise = normalize (h - 360)
- 223. ghci> h' hue (Mix c c') = r where r = case compare d 90 of LT -> m EQ -> nan m m' GT -> m' h = hue c h' = hue c' m = average h h' d h m' = normalize (m + 180) d = distance h m normalize h | h < 360 = h | otherwise = normalize (h - 360)
- 224. ghci> quickCheck prop_hue_bounds m'
- 225. ghci> quickCheck prop_hue_bounds +++ OK, passed 100 tests. ghci> m'
- 226. QuickCheck prop_hue_mix_nothing c c' = distance (hue c) (hue c') == 180 ==> isNaN (hue (Mix c c'))
- 227. QuickCheck ghci> quickCheck prop_hue_mix_nothing prop_hue_mix_nothing c c' = distance (hue c) (hue c') == 180 ==> isNaN (hue (Mix c c'))
- 228. QuickCheck ghci> quickCheck prop_hue_mix_nothing *** Gave up! Passed only 23 tests. ghci> prop_hue_mix_nothing c c' = distance (hue c) (hue c') == 180 ==> isNaN (hue (Mix c c'))
- 229. QuickCheck prop_hue_mix_nothing c c' = distance (hue c) (hue c') == 180 ==> isNaN (hue (Mix c c'))
- 230. QuickCheck prop_hue_mix_nothing c c' = distance (hue c) (hue c') == 180 ==> isNaN (hue (Mix c c')) -- Can we easily find the complement of a color?
- 231. complement Red = ??? complement Green = ??? complement Blue = ??? complement (Mix c c') = ???
- 232. complement Red = cyan complement Green = ??? complement Blue = ??? complement (Mix c c') = ???
- 233. complement Red = cyan complement Green = magenta complement Blue = ??? complement (Mix c c') = ???
- 234. complement Red = cyan complement Green = magenta complement Blue = yellow complement (Mix c c') = ???
- 235. complement Red = cyan complement Green = magenta complement Blue = yellow complement (Mix c c') = Mix ??? ???
- 236. complement Red = cyan complement Green = magenta complement Blue = yellow complement (Mix c c') = Mix (complement c ) (complement c' )
- 237. QuickCheck prop_complement c = let h = hue c in not (isNaN h) ==> distance h (hue (complement c)) == 180
- 238. QuickCheck prop_complement c = let h = hue c in not (isNaN h) ==> distance h (hue (complement c)) == 180 prop_hue_mix_complement c = isNaN (hue (Mix c (complement c)))
- 239. QuickCheck ghci> quickCheck prop_complement prop_complement c = let h = hue c in not (isNaN h) ==> distance h (hue (complement c)) == 180 prop_hue_mix_complement c = isNaN (hue (Mix c (complement c)))
- 240. ghci> quickCheck prop_complement +++ OK, passed 100 tests. ghci>
- 241. ghci> quickCheck prop_complement +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_complement
- 242. ghci> quickCheck prop_complement +++ OK, passed 100 tests. ghci> quickCheck prop_hue_mix_complement +++ OK, passed 100 tests. ghci>
- 243. To be continued...
- 244. Summary Haskell is functional. Haskell has types. QuickCheck is cool.
- 245. Preview: Infinite Lists primes = sieve [2..] where sieve (p:xs) = p : sieve [x | x <- xs, rem x p /= 0]
- 246. Preview: IO (echo.hs) import System.Environment (getArgs) import Data.List (intercalate) main = do args <- getArgs putStrLn (intercalate " " args)
- 247. Preview: Parsers
- 248. Preview: Parse JSON data Value = String String | Number Double | Object [(String, Value)] | Array [Value] | Bool Bool | Null
- 249. Preview: Parse JSON value = String <$>jsstring <|> Number <$>number <|> Object <$>commaGroup '{' pair '}' <|> Array <$>commaGroup '[' value ']' <|> Bool True <$ string "true" <|> Bool False <$ string "false" <|> Null <$ string "null"
- 250. Preview: Parse JSON pair :: Parser (String, Value) pair = do s <- jsstring sp_char_sp ':' v <- value spaces return (s, v)
- 251. To be continued...