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Objectives Function Calls Example Recursions Lists References Basic Recursion Dr. Mattox Beckman University of Illinois at Urbana-Champaign Department of Computer Science Objectives Function Calls Example Recursions Lists References

  1. Objectives Function Calls Example Recursions Lists References Basic Recursion Dr. Mattox Beckman University of Illinois at Urbana-Champaign Department of Computer Science

  2. Objectives Function Calls Example Recursions Lists References Objectives ◮ Diagram the stack frames that result from a series of function calls. ◮ Use Haskell to write a recursive function on integers. ◮ Use Haskell to write a recursive function on lists.

  3. in aa + a let aa = a * a Objectives Function Calls Example Recursions Lists References Function Calls ◮ Remember the syntax of a function defjnition in Haskell . Function Syntax 1 foo a = 2 3 ◮ The above function has one paramater and one local. ◮ If we call it three times, what will happen in memory? 1 x = (foo 1) + (foo 2) + (foo 3)

  4. 1 let aa = a * a aa 1 a in aa + a Objectives Function Calls Example Recursions Lists References Function Calls ◮ Remember the syntax of a function defjnition in Haskell . Function Syntax 1 foo a = 2 3 ◮ The above function has one paramater and one local. ◮ If we call it three times, what will happen in memory? 1 x = (foo 1) + (foo 2) + (foo 3) First Call Second Call Third Call

  5. 4 let aa = a * a aa 2 a 1 aa 1 a in aa + a Objectives Function Calls Example Recursions Lists References Function Calls ◮ Remember the syntax of a function defjnition in Haskell . Function Syntax 1 foo a = 2 3 ◮ The above function has one paramater and one local. ◮ If we call it three times, what will happen in memory? 1 x = (foo 1) + (foo 2) + (foo 3) First Call Second Call Third Call

  6. 9 a aa 3 a 4 aa 2 a 1 let aa = a * a aa in aa + a 1 Objectives Function Calls Example Recursions Lists References Function Calls ◮ Remember the syntax of a function defjnition in Haskell . Function Syntax 1 foo a = 2 3 ◮ The above function has one paramater and one local. ◮ If we call it three times, what will happen in memory? 1 x = (foo 1) + (foo 2) + (foo 3) First Call Second Call Third Call

  7. Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  8. 1 x ret Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  9. ret x 2 y ret 1 Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  10. ret x 3 z ret 2 y ret 1 Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  11. 30 x ret 3 z ret 2 y ret 1 Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  12. 30 1 ret 3 z ret 30 2 y ret x Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  13. 30 1 ret 3 z 32 ret 30 2 y ret x Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  14. 30 32 ret 3 z 32 ret 30 2 y ret 1 x Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  15. 30 32 ret 3 z 32 ret 30 2 y 33 ret 1 x Objectives Function Calls Example Recursions Lists References Functions Calling Functions ◮ If one function calls another, both activation records exist simultaneously. 1 foo x = x + bar (x + 1) 2 bar y = y + baz (y + 1) 3 baz z = z * 10 ◮ What happens when we call foo 1 ?

  16. 1 24 ret 1 n 2 ret 1 2 n 6 ret 2 3 n ret 6 4 n Objectives Function Calls Example Recursions Lists References Factorial ◮ This works if the function calls itself. Factorial 1 fact 0 = 1 2 fact 1 = 1 3 fact n = n * fact (n - 1) ◮ fact 4 ...

  17. 1 : 2 : 3 : 4 : [] Objectives Function Calls Example Recursions Lists References Lists in Haskell ◮ Haskell has a built-in syntax for singly linked lists. ◮ The empty list is [] . ◮ You can use : to create a new list … 1 2 3 4 ◮ You can also write [1,2,3,4] .

  18. Objectives Function Calls Example Recursions Lists References Lists Because lists are recursive, functions that deal with lists tend to be recursive. Length 1 mylength :: [a] -> Int 2 mylength [] = 0 3 mylength (x : xs) = 1 + mylength xs 4 5 mylength s -- would return 3 ◮ The base case stops the computation. ◮ Your recursive case calls itself with a smaller argument than the original call.

  19. Objectives Function Calls Example Recursions Lists References Activity ◮ Write a function fib that computes the n th Fibonacci number F n . Let F 1 = 1 and F 2 = 1 . ◮ Write a function sumList that takes a list and sums its elements. ◮ Write a function incList that takes a list and increments its elements.

  20. Objectives Function Calls Example Recursions Lists References Solutions to fib and sumList 1 fib 1 = 1 2 fib 2 = 1 3 fib n = fib (n - 1) + fib (n - 2) 4 5 sumList [] = 0 6 sumList (x : xs) = x + sumList xs

  21. Objectives Function Calls Example Recursions Lists References Solution to incList ◮ Remember that you must create a new list! 1 incList [] = [] 2 incList (x : xs) = x + 1 : incList xs

  22. Objectives Function Calls Example Recursions Lists References History ◮ The fjrst programming language to implement recursion was Lisp in 1958. [McC79] References [McC79] John McCarthy. History of Lisp . Stanford University, 1979. URL: http://www-formal.stanford.edu/jmc/history/lisp/lisp.html .

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