Programming Paradigms

1. Programming Paradigms CPSC 449 Week 3-1 Prepared by : Mona Hosseinkhani, ArashAfshar Winter 2014 Department of Computer Science, University of Calgary

2. Program Testing • Different type of tests: • Prove: expensive process • QuickCheck: to test properties of functions using randomly generated data (defining properties is not always clear) • Traditional test: manually specify inputs and expected output • The art of testing: • choose the inputs as comprehensive as possible • represent all the different ‘kinds’ of input to the function

3. Program testing approaches • Black box testing • Devise test data just by knowing specification of function not the function definition • White box testing • Devise test data according to the function definition • Example: • function that returns the maximum of three integers • maxThree:: Int -> Int -> Int -> Int

4. Program Testing – Black box test • Partition the inputs into different testing groups • e.g. positive and negative numbers • Make sure you choose at least one representative from each group • Pay attention to any special cases • i.e. boundaries of groups. e.g. zero

5. Program Testing – Black box test • Example: maxThree:: Integer -> Integer -> Integer -> Integer maxThree x y z |x >= y && x >= z = x |y >= z = y |otherwise = z • Testing groups: • all three values different • all three values the same • two items equal, the third different • two values equal to maximum, one other • one value equal to the maximum, two others • Set of test data • 641 • 666 • 266 • 226

6. Program Testing – Black box test • We can code this test in Hunit testing framework testMax1 = TestCase (assertEqual "for: maxThree 6 4 1" 6 (maxThree 6 4 1)) testMax2 = TestCase (assertEqual "for: maxThree 6 6 6" 6 (maxThree 6 6 6)) testMax3 = TestCase (assertEqual "for: maxThree 2 6 6" 6 (maxThree 2 6 6)) testMax4 = TestCase (assertEqual "for: maxThree 2 2 6" 6 (maxThree 2 2 6)) testsMax = TestList [testMax1, testMax2, testMax3, testMax4] -- run as -- runTestTTtestsMax

7. Program Testing – Black box test • Does this function calculate the maximum of three numbers? mysteryMax :: Integer -> Integer -> Integer -> Integer mysteryMax x y z | x > y && x > z = x | y > x && y > z = y | otherwise = z testMMax1 = TestCase (assertEqual "for: mysteryMax 6 4 1" 6 (mysteryMax 6 4 1)) testMMax2 = TestCase (assertEqual "for: mysteryMax 6 6 6" 6 (mysteryMax 6 6 6)) testMMax3 = TestCase (assertEqual "for: mysteryMax 2 6 6" 6 (mysteryMax 2 6 6)) testMMax4 = TestCase (assertEqual "for: mysteryMax 2 2 6" 6 (mysteryMax 2 2 6)) testMMax5 = TestCase (assertEqual "for: mysteryMax 6 6 2" 6 (mysteryMax 6 6 2)) testsMMax = TestList [testMMax1, testMMax2, testMMax3, testMMax4, testMMax5] Testing alone cannot assure us that a function is correct

8. Program testing – white box test • Same principles of black box testing applies here + • Use the form of program to choose test data • for functions containing guards, supply data for each case (also pay attention to boundary conditions) • e.g. in mysteryMax example, the first two inputs of 6 6 2 data are at the guards boundaries • guards: x>y && x>z y>x && y>z • for recursive functions, test zero case, the one case and the general case

9. Program testing – white box test • Example for general case test in recursive functions • function definition: • general property • We expect this property to be True whatever the input n • Test result: • Int is the fixed-size representation of Integers. When numbers become big enough, they wrap around into the negative fact :: Int -> Int fact n | n>1 = n * fact (n-1) | otherwise = 1 prop_fact n = fact n > 0 *Chapter4> quickCheckprop_fact *** Failed! Falsifiable (after 12 tests and 2 shrinks): 21

10. Tuples vs. Lists • Tuples • defined using ( ) • Can contain different types of data • Lists • Defined using [ ] • Can contain same type of data • Strings are lists

11. Naming Types • Give name to your types • Do it often to make the code more readable • type FName = String • type LName = String • type ID = (FName, LName) • identity :: ID • identity = (”Jack",”Smith") • Haskell treats them as synonyms

12. Tuple Operators • Pattern matching • f1 (a, b) = …function definition… • f1 (1, 2) would match “1” to “a” , “2” to “b” • In Pairs: fst & snd • f2 d = (fst d) + (snd d)

13. Examples • Define three different versions for Sum • Regular • sum a b = a + b • Pattern matching • sum (a, b) = a + b • Using pair operators • sum c = (fst c) + (snd c)

14. List Operators • Taking elements • head vs take • head [‘a’, ‘b’, ‘c’, ‘d’] = ‘a’ • take 2 [‘a’, ‘b’, ‘c’, ‘d’] = [‘a’, ‘b’] • last vs drop • last [‘a’, ‘b’, ‘c’, ‘d’] = ‘d’ • drop 3 [‘a’, ‘b’, ‘c’, ‘d’] = [‘d’]

15. List Operators (cont.) • tail vs init • tail ['a', 'b', 'c', 'd'] = ['b', 'c', 'd'] • init ['a', 'b', 'c', 'd'] = ['a', 'b', 'c'] • Taking only the n-th element • ['a', 'b', 'c', 'd'] !! 2 = ‘c’

16. List Operators (cont.) • Concatenation • Add a single element • 'a' : ['b', 'c', 'd'] = ['a', 'b', 'c', 'd'] • Add another list • ['a', 'b'] ++ ['c', 'd'] = ['a', 'b', 'c', 'd'] • Merge a 2D array into a simple list • concat [[‘a’],[‘b’, ‘c’],[‘d’]] = [‘a’, ‘b’, ‘c’, ‘d’]

17. List Operators (cont.) • Reversal • reverse ['a', 'b', 'c', 'd'] = ['d', 'c', 'b', 'a'] • Length • length ['a', 'b', 'c', 'd'] = 4 • Make copies • replicate 3 ['a', 'b', 'c', 'd'] = [['a','b','c','d'],['a','b','c','d'],['a','b','c','d']]

18. Question hossem@ucalgary.ca