Function Design in LISP Program Files n LISP

Function Design in LISP

Program Files n LISP programs are plain text – DOS extensions vary; use. lsp for this course (load “filename. lsp”) n Can use Unix-style paths n – (load “c: /Work/Comp 2043/A 4/my. File. lsp”) – (load “A 4\my. File. lsp”) OK in Windows

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)

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.

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 fn

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

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

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

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

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

Plus-1 List: Imperative n Add one to each element of a list plus 1 List(L) if (L == nil) variables not necessary return nil; else var new. First first(L) + 1; var new. Rest plus 1 List(rest(L)); return cons(new. First, new. Rest);

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

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

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

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

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

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))))

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

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))

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

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))

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)))

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)

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))

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))

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))

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

Tweaking the Code Deviations just calls deviation-list with own argument plus another n Could be combined into one function n – 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

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

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) (2 3 NIL) (4 5 6))

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))

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

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))

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

Assume We Have Them n Write the result calculation function (N*Sxy – Sx*Sy) sqrt((N*Sxx) – (Sx)2)*(N*Syy – (Sy)2)) 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

Now for the Helpers Already have the length function built in n Write the sum of a list function n Write the dot product function n – (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

Final Result (defun correlation (Xs Ys) …) (defun correlation-calc (N Sx Sy 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

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))

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

Next Time n Control over lists – Chapter 6