CSCE 314 Programming Languages - TAMU Computer Science ...

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Why is Recursion Useful? Some functions, such as factorial, are simplerto define in terms of other functions. As we shall see, however, many functions cannaturally be defined in terms of themselves. Properties of functions defined using recursioncan be proved using the simple but powerfulmathematical technique of induction.38
Recursion on ListsLists have naturally a recursive structure. Consequently,recursion is used to define functions on lists.product :: [Int] → Intproduct [] = 1product (n:ns) = n * product nsproduct [2,3,4] = 2 * product [3,4]product maps theempty list to 1, and anynon-empty list to itshead multiplied by theproduct of its tail.====2 * (3 * product [4])2 * (3 * (4 * product []))2 * (3 * (4 * 1))2439
Page 1 and 2: CSCE 314Programming LanguagesHaskel
Page 3 and 4: Conditional ExpressionsAs in most p
Page 5 and 6: Guarded Equations (Cont.)Guards and
Page 7 and 8: Functions can often be defined in m
Page 9 and 10: List PatternsInternally, every non-
Page 11 and 12: Totality of Functions (Total) funct
Page 13 and 14: Why Are Lambda's Useful?1. Lambda e
Page 15 and 16: Case ExpressionsPattern matching ne
Page 17 and 18: Let vs. WhereThe let … in … is
Page 19 and 20: Why Are Sections Useful?Useful func
Page 21 and 22: (2)(3)Give three possible definitio
Page 23 and 24: List Comprehensions A convenient sy
Page 25 and 26: For example:> [(x,y) | y
Page 27 and 28: GuardsList comprehensions can use g
Page 29 and 30: The Zip FunctionA useful library fu
Page 31 and 32: Exercises(1)A triple (x,y,z) of pos
Page 33 and 34: (3)The scalar product of two lists
Page 35 and 36: A Function without RecursionMany fu
Page 37: Note: The base case factorial 0 = 1
Page 41 and 42: Using a similar pattern of recursio
Page 43 and 44: Laziness RevisitedLaziness interact
Page 45 and 46: QuicksortThe quicksort algorithm fo
Page 47 and 48: For example (abbreviating qsort as
Page 49 and 50: Produce a list with n identical ele
Page 51: (3) Define a recursive functionmsor

CSCE 314 Programming Languages - TAMU Computer Science ...

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