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Functional Programming Lecture 5 - Tuples Packaging several values together Sometimes you need to package up several values into a single object – A function returns one value, but what if you have several values to return? – Several data values are used together; it is logical to treat the entire collection as one object. Tuples • (2,3) :: (Int,Int) – a pair or a 2-tuple • (2, “dog”) :: (Int, String) – a pair or a 2-tuple • (“Calder”,”Monday”,[9,11,14]) :: (String, String,[Int]) – a triple or a 3-tuple • (pi, times2) :: (Double, Int->Int) – where times2 x = x * 2 • ( ) :: ( ) – a 0-tuple (sometimes used as a dummy value) You can have n-tuples for any n. x1 :: T1 … xn :: Tn (x1,…,xn) :: (T1,…Tn) What is type of (2,3)? What is type of (2,”dog”)? Convention, (5,6) is a pair, (Int,Int) is a Pair. Tuples vs. Lists Similarities: Both package up several values into one. Both are type constructors. Differences: Tuple: fixed number of components, the components may have different types. (3,4) :: (Int,Int) (3,”hello”) :: (Int,[Char]) List: any number of elements, the elements must have the same type. [3,4] ::[Int] [3,”hello”] :: type error Example: Cross Product Represent sets A and B as lists. mathematics A B = {(x,y) | x A, y B} Haskell crossProd :: [a] -> [b] -> [(a,b)] crossProd xs ys = [(x,y) | x <- xs, y <- ys] crossProd “abc” [1..3] => [(‘a’,1), (‘a’,2), (‘a’,3), (‘b’,1), (‘b’,2), (‘b’,3), (‘c’,1), (‘c’,2), (‘c’,3)] Example: A Database A database holds information about employees. type Item = (String, String, String, Int, Int) -- (name, address, postcode, age, salary) type Database = [Item] ex1 = [(“Smith”, “Byres”, “G12 8QQ”, 30, 30000), ….. Database queries Make a mailing label for every employee under 30 who is making at least 30k per year, and who lives within the G1 postcode area. labels :: Database -> [String] labels db = [n ++ “\n” ++ a ++ “\n” | (n,a,p,o,s) <- db, o<30, s>=30000, take 3 p == “G1_”] (n,a,p,o,s) is called a pattern. Note difference between `\n’ and “\n” Returning several results Example: Quadratic Equation Quadratic equation ax2 + bx + c = 0 has two solutions (- b (b2 - 4ac)) / 2a. We would like a function that solves the equation properly, and returns both solutions Note - in some cases there are complex solutions - we will ignore these. Example: Quadratic Equation quadratic :: Double -> Double -> Double -> (Double,Double) 3 arguments and one result which is a pair quadratic a b c = (x1, x2) where x1 = (-b + d) / (2*a) x2 = (-b - d) / (2*a) d = sqrt (b^2 - 4*a*c) or quadratic a b c = let d = sqrt (b^2 - 4*a*c) x1 = (-b + d) / (2*a) x2 = (-b - d) / (2*a) in (x1, x2) A note about floating point It is not always exact 0.11 - 0.10 => 0.01 :: Double but 2.11 - 2.10 => 0.00999999 :: Double This is not an error. It is a property of floating point, not of Haskell. You must be careful with floating point, as in any programming language. Rounding • It is possible to round the numbers 0.00999999 => 0.01 • But rounded output DOES NOT affect the number actually represented, it gives only the illusion that the number is exactly correct. Comparison of floating point • It may be unsafe to use == to compare two floating point numbers – if 0.11-0.10 == 2.11-2.10 then should get this result else but you’ll get this result instead • It does not make any difference if the output is printed in rounded form the internal computation will be wrong. • This is true for all programming languages When should floating point be used? The input data already has some imprecision data measured in an experiment. You expect an approximate result, and you know what the “error tolerance” is. The result may be big (astronomical) or small (microscopic), and it would be written in scientific notation. Do not use floating point for money!