1. Function Design in LISP

2. Program Files n LISP programs are plain text –DOS extensions vary; use.lsp for this course n (load “filename.lsp”) n Can use Unix-style paths –(load “c:/Work/Comp2043/A4/myFile.lsp”) –(load “A4/myFile.lsp”) –(load “A4\\myFile.lsp”) OK in Windows

3. Comments n For this course: –identify file as we did with Prolog programs –function comments similar to predicates –also say what gets returned ;; (fib N) ;; -- returns the Nth Fibonacci number, N > 0 ;; -- no error checking (infinite loop if N =< 0)

4. Comments n Many similar functions –conversion functions, for example n One comment for all ;; (print-no-X-warning N) ;; -- where X in {student, course, section} ;; -- print a warning message that there is no ;; object X corresponding to N ;; -- N is a student number, course number, etc.

5. Functional Cohesion n You should be able to describe what your function does in a simple sentence –how it’s doing it may require more explanation n If you need the word “and”, you’re probably doing too much! –see if you can split it into two functions… –…or move some functionality into another f n

6. Non-Cohesive Function ;; (squeeze-input) ;; -- rewrite output getting rid of excess spaces … ;; (punc L) ;; -- checks whether L is punctuation ;; and if it isn’t it prints a space ;; and continues “squeezing” input

7. Cohesive Function ;; (squeeze-input) ;; -- rewrite output getting rid of excess spaces … ;; (punc L) ;; -- says whether L is a punctuation character n Let (squeeze-input) worry about printing spaces and continuing squeezing input

8. Writing Functions in LISP n First (as usual): understand what’s required –what are you given? –what is the value to return? n Second: plan how to get result –break down into its conditions (if any) –identify easy cases –break harder cases down into parts

9. Functions and Lists n List argument generally needs to be broken into parts –(first L) – operate on this directly –(rest L) – recur on this n Mapped parts need to be re-combined –maybe some math function – atomic result –usually using CONS – list result

10. Implementing a Plan n Plan is in steps: –calculate this –use it to calculate that n All must be combined into one function call n Early calculations become arguments for later ones –will evaluate from the inside out

11. Plus-1 List: Imperative n Add one to each element of a list plus1List(L) if (L == nil) return nil; else var newFirst  first(L) + 1; var newRest  plus1List(rest(L)); return cons(newFirst, newRest); variables not necessary

12. Plus-1 List: Imperative n Add one to each element of a list plus1List(L) if (L == nil) return nil; else return cons(first(L) + 1, plus1List(rest(L))); plus1List(rest(L))); replace conditional command with conditional expression

13. Plus-1 List: Imperative n Add one to each element of a list plus1List(L) return(L == nil) ? nil: cons(first(L) + 1, plus1List(rest(L))); plus1List(rest(L))); now functional: rewrite to LISP

14. Plus-1 List: LISP n Add one to each element of a list (defun plus1List (L) (if (null L) nil (cons (+ (first L) 1) (plus1List (rest L))))) (plus1List (rest L))))) make more “idiomatic”

15. Plus-1 List: LISP n Add one to each element of a list (defun plus1List L (unless (null L) (cons (+ (first L) 1) (plus1List (rest L))))) (plus1List (rest L))))) (unless(null Arg) (cons(…(first Arg)…) (…(rest Arg)…))) programming idiom translating a list

16. Functional Abstraction n Complicated (or repeated) steps should get their own function definitions –apply same process again –understand what you want out of the function (don’t let the code control you) n Laziness is a virtue –leave it for later –but make sure you understand it, first

17. Example n Standard deviation (population) –square root of the average of the deviations –given a list of numbers, returns a number n Functional abstraction –square root is built in, average we can build –deviations??? Time to be lazy! (defun stdevp (L) (sqrt (average (deviations L))))

18. Sub-Problems n Average –given a list of numbers, return a number –add up the numbers, divide by the # of numbers –left as an exercise n Deviations –deviation = difference from average, squared –given a list of #s, return another list of #s

19. Deviations n Need the average of the list –use the average function: (average L) n Need to find the deviation for every element in the list – its difference from the average –time to be lazy again – another function –given a list & its average, return list of deviations –(deviation-list L (average L))

20. Deviation List n Need to process a list & return a list –break down list (using first & rest) –calculate deviation (separate function on first, recursion on rest) –reconstruct list (using cons) n Unless the list is empty, of course (unless (null L) (cons (…(first L)…) (…(rest L)…))) Calculation of deviation of first Calculation of deviations of rest

21. Calculating a Single Deviation n Given a number and the mean, return a number (its deviation) –their difference, squared –use expt for squaring (expt x 2) = x 2 (defun calculate-deviation (Value Mean) (expt (– Value Mean) 2))

22. List of Deviations (defun deviation-list (L M) (unless (null L) (cons (calculate-deviation (first L) M) (deviation-list (rest L) M) ))) (defun deviations (L) (deviation-list L (average L)))

23. Function Call n Calculate standard deviation (population) of the list (5 10 15) > (stdevp ‘(5 10 15)) (sqrt (average (deviations ‘(5 10 15)))) (average (deviations ‘(5 10 15))) (deviations ‘(5 10 15)) (deviation-list ‘(5 10 15) (average ‘(5 10 15))) = (deviation-list ‘(5 10 15) 10)

24. Function Call (cont.) (deviation-list ‘(5 10 15) 10) (unless (null ‘(5 10 15)) (…)) = (unless NIL (cons (…) (…))) (cons (calculate-deviation …) (…)) (calculate-deviation (first ‘(5 10 15)) 10) = (calculate-deviation 5 10) (expt (– 10 5) 2) = 25 = (cons 25 (deviation-list (rest ‘(5 10 15)) 10))

25. Function Call (cont.) (deviation-list ‘(10 15) 10) (unless (null ‘(10 15)) (…)) = (unless NIL (cons (…) (…))) (cons (calculate-deviation …) (…)) (calculate-deviation (first ‘(10 15)) 10) = (calculate-deviation 10 10) (expt (– 10 10) 2) = 0 = (cons 0 (deviation-list (rest ‘(10 15)) 10))

26. Function Call (cont.) (deviation-list ‘(15) 10) (unless (null ‘(15)) (…)) = (unless NIL (cons (…) (…))) (cons (calculate-deviation …) (…)) (calculate-deviation (first ‘(15)) 10) = (calculate-deviation 15 10) (expt (– 10 15) 2) = 25 = (cons 25 (deviation-list (rest ‘(15)) 10))

27. Function Call (cont.) (deviation-list ‘() 10) (unless (null ‘()) (…)) = (unless T (cons (…) (…))) = NIL =(cons 25 NIL) = (25) =(cons 0 ‘(25)) = (0 25) =(cons 25 ‘(0 25)) = (25 0 25) =(average ‘(25 0 25)) = 16.6667 =(sqrt 16.6667) = 4.0825

28. Tweaking the Code n Deviations just calls deviation-list with own argument plus another n Could be combined into one function –make the mean an optional argument –default value – average of the given list (defun deviations (L &optional (M (average L))) …) n Will call average if & only if no mean given

29. Combined Deviations Code (defun deviations (L &optional (M (average L))) (unless (null L) (cons (calculate-deviation (first L) M) (deviations (rest L) M) ))) n Note: important to pass M in recursive call –else calculates average of (10 15) = wrong

30. Optional Parameters n Use &optional in parameter list –everything before &optional is required –if not given use NIL – or default value (next) > (defun opt-args (a &optional b c) (list a b c)) OPT-ARGS > (list (opt-args 1) (opt-args 2 3) (opt-args 4 5 6)) ((1 NIL NIL) (2 3 NIL) (4 5 6))

31. Default Values n For optional arguments –list with parameter name & default value –default calculated at call time > (defun def-args (a &optional (b 5)) (list a b)) DEF-ARGS > (list (def-args 1) (def-args 2 3)) ((1 5) (2 3))

32. Correlation n Write a function to calculate the correlation between two lists –the two lists must be the same length n Understanding –given two lists (same length) –returns a number –formula to follow

33. Calculating a Correlation n Complicated formula requires: –length of lists (N) –sums of lists (Sx and Sy) –dot product of the two lists (Sxy) –sums of squares of lists (Sxx and Syy) n Result is (N*Sxy – Sx*Sy) sqrt((N*Sxx) – (Sx) 2 )*(N*Syy – (Sy) 2 ))

34. What Do We Need? n Functions that calculate: –length of a list –sum of a list –dot product of two lists –sum of squares of list

35. Assume We Have Them n Write the result calculation function n Write the main function –N = length of lists (must be same for both) –Sx = sum of list 1 st list, Sy = sum of second –Sxy = dot product of lists –Sxx = sums of squares of 1 st list, Syy = ditto 2 nd (N*Sxy – Sx*Sy) sqrt((N*Sxx) – (Sx) 2 )*(N*Syy – (Sy) 2 ))

36. Now for the Helpers n Already have the length function built in n Write the sum of a list function n Write the dot product function –(1 2 3) * (4 5 6) = (1*4)+(2*5)+(3*6) = 32 n Write the sum of squares function –note: can use dot product function

37. Final Result (defun correlation (Xs Ys) …) (defun correlation-calc (N Sx Sy Sxy Sxx Sxy) …) (defun sum-of-list (L) …) (defun dot-product (Xs Ys) …) (defun sum-of-squares (L) …) > (correlation ‘(5 10 15) ‘(3 6 12)) 0.989

38. Exercise n Write a function that calculates the correlation of a list of pairs –(correlate-pairs ‘((5 3) (10 6) (15 12))) => 0.989 –list of (X Y) pairs n Use the correlation function from last time –(correlation ‘(5 10 15) ‘(3 6 12)) => 0.989 –only difference is the form of the data –(write it in two lines! (hint: be lazy))

39. Exercise n Use the list translation programming idiom we discussed earlier to write the rest of the support functions for our new correlations function –translate list of XY pairs into a list of Xs –translate list of XY pairs into a list of Ys

40. Next Time n Control over lists –Chapter 6