Associated code files to read, execute in Hugs, modify: Intro.lhs, Trans1.hs, IntroFuns.lhs, ListOps.hs, Tuples.lhs. 12/5/2003. Author: J. Nino.

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1 ! " # $ $ # Associated code files to read, execute in Hugs, modify: Intro.lhs, Trans1.hs, IntroFuns.lhs, istops.hs, Tuples.lhs % & ' ( ) * ++,( ' -. / 1,2 / ' ' 6 6,/ 5 +' / 5. ' 5 * : ; < =< >:? ' 1 ' A ' +. * ( ' 1 ' ( * ( B 2 / * C.,+1 ' 4 * / * A * 4 D ' / 5 EF 8 : H I ; < =J?,( ' 3 4,6 ' 4 K 2 / ( * 8 & * ' A K. ( * 2 - =M : ; N J ; O : ; -. / 1,2 / ( B,E* E -. / 1,2 / ( P D, D 1 ' ) * -. / 1,2 / ( ' ' 1 ' ' 4 * 1. 4 / -. / 1,2 / ( ' ( 4 * (. +1 ( F 8 Q. / 1,2 / ' (,1,2 / ' ( 6 ',/ 6 * ' / ( (,/ ' 6 (. (,/ 5 3 ' 4 1 ( 8 R S ' 6 3 +* +' / 5. ' 5 * ( 7 T U V W W Y Z [\ ] ^ _ ] Y Z ` Y a U ] b c % d 6 3 * 4 ' 1,A * +' / 5. ' 5 * ( e C K 2 / 1 4 ' ( 1 e * 6 3 D ' (,f * 7 8 g I >h i j: A ' 4,' C +* ( ' 1 ' ( * ( E 8 k J J l =?M 4 ' 1 D * 4 1 D ' / 4 *. 4 (,2 /,( * 6 3 D ' (,f E 8 m =; < > N J ; O : ; 4 ' 1 D * 4 1 D ' / D,5 D * 4 n 2 * 4 -. / 1,2 / ( E 8 R S ' 6 3 +* ( 7 o Y p a q r q s t Y u ] v U ] b Y s _ ] Y o w w Y x ] y ] Y u W \ be 12/5/23. Author: J. Nino. 1 12/5/23. Author: J. Nino. 2 z $ { # } ~ { % & ' ( ) * ++,( ' / W \ W v v [ ^ +' / 5. ' 5 * E ' 6,( ' / * S 3 4 * ( (,2 / E ƒ D * 6 * ' /,/ D * ' 6,( 1 D * A ' +. * 2-1 D * * S 3 4 * ( (,2 / ˆ Š Š 7 ( Œ. ' 4 * B F (. 6 Ž EE ( Œ. ' 4 * B B Š e ˆ F F ,( d / ' / 5 * B (. 6 B -,4 ( 1 Q ' 1 ˆ F F { # š œ ž Ÿ š Ÿ š ž ž œ ž ž œš š Ÿ ž ª «ž ž œ š ž š ž Ÿ ž œ œÿ š œ ± Ÿ œÿ œ ž ž ž Ÿ œ ž ž ž ² Ÿ ž š ± ž œ ž ž œ ž Ÿ š ³ Ÿ š ² œµ š µ ž Ÿ read-eval-print š š š œÿ œ ± ž ž š ž ž µ ž Ÿ Ÿ œš œÿ ž ž ž œ š ž œ ž ž ž Ÿ š œ ± ¹ ž ž œ ± š œ œš š Ÿ ž š ± Ÿ ¹ º œ œ œ œž Ÿ š š ž š œ ± š œ š ž š ž Ÿ Ÿ ž œÿ ž ± ± ž ¹ Ÿ ž Ÿ ž œ ž ž ž Ÿ œ š ž š ± ž ¹ º š ž š ž Ÿ š ž š ž ž ž ž µ ž Ÿ Ÿ œš» œ œ ± Ÿ ž š š ž š Ÿ œÿ Ÿ š ± œ œ ± Ÿ ž š ž œ œ œš Ÿ š ž ž Ÿ ¹ ž ž Ÿ ž œš Ÿ Ÿ ž š ± Ÿ ž Ÿ ž ž œ œ œš œ ž š œš š ž µ ž Ÿ Ÿ œš Ÿ ž Ÿ ž ž µ ž Ÿ Ÿ œš Ÿ Ÿ ž ž ž œ œ œš Ÿ š ž ž ž ž µ ž Ÿ Ÿ œš š ž ž ž ¼ ½ ¾ ½ À Á Ÿ ž ž Ÿ š º œ ž µ ž Ÿ Ÿ œš Ÿ ž ž ž š Ÿ ž ž Ÿ š ž Ÿ ž š š Ÿ œ ž Â ž ž Ÿ 12/5/23. Author: J. Nino. 3 12/5/23. Author: J. Nino. 4 1

2 ! š ± Á inchespermile = 12*3*176 drivingage :: Int drivingage = 17 e = ± Ÿ š š ± Main> :l Prog.hs Main> inchespermile 2736 Main> :t inchespermile inchespermile :: Integer Main> drivingage 17 Main> :t drivingage drivingage :: Int Main> :t e e :: Double Main> 12/5/23. Author: J. Nino. 5 Int, Integer, Float, Double Bool " # $% & ' : True, False ( ) * +, -. * / &&, :: Bool -> Bool -> Bool not :: Bool -> Bool Char +1 2 ( ) * +, -. * / ord :: Char -> Int, chr :: Int -> Char 12/5/23. Author: J. Nino. 6 E F H I J K J M N O K P Q FR K S T O F IQ U F K P R H R S FQ J Q V H J S W F S Q S square:: Int -> Int square val = val * val cube x = x * x * x fac x = if x == then 1 else x * fac (x - 1) fac :: Int -> Int fac n n == = 1 n > = n * fac (n-1) newfac = 1 newfac n = n * newfac (n-1) fac :: Int -> Int fac n n == = 1 n > = n * fac (n-1) otherwise = error n< f2 m n = (f m) / (g n) where f m = 2*m 3*m g m = n/5 f1 n m = let k1 = 2*n k2 = 3*m in k1 + k2 Y 2 Z - [ \ +] ^ _ ) 1 ) * 1 [ `, 1 ` [ Z 2 - [ * Z - a a ` ], 1 +- ] ) b. [ - ^ [ ) c c +] ^ d e - [ 1 2 Z * 1 - [ +] ^ - a ), - bbz, 1 +- ] - a f g h g i j k j g l m _ ) 1 ) n ) b` Z * d o Z * 1 ) [ * - c Z b+1 Z [ ) b b+* 1 n ) b` Z * / [] [2, 3, 5, 7, 9, 11, 17, 23] :: [Int] [4.5, 7.2, 6.666] :: [Float] [ a, r, m ] :: [Char] -- can also be written as arm [True, True, False, True, False] :: [Bool] [ [2,6], [3,7,9], [1,6,4,11] ] :: [[Int]] hello p q r st r u p v u w [ h, e, l, l, o ] 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 7 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 8 2

3 T O F IQ U F K P R H R S FQ J Q V H J S R K S Q O P Q F K W F S Q S ) * \ Z bb. [ - n +_ Z * ] ` c Z [ - ` * ( ` +b1 +] -. Z [ ) 1 +- ] * 1 2 ) 1 c ) ] +. ` b) 1 Z ) ] _ [ Z 1 ` [ ] b+* 1 * d Y 2 Z c - * 1 ( ) * +, - ] Z, [ Z ) 1 Z * ) ] Z b+* 1 ( ) +] ^ ) ] Z bz c Z ] Z a [ - ] 1 - a ) ] Z +* 1 +] ^ b+* 1 d Y 2 Z -. Z [ ) 1 +- ] +* [ +1 1 Z ] ) ] _. [ - ] - ` ], Z _ g k m 3:[2,5] p q r st r u p v u w [3,2,5] a :[ b, c, d ] p q r st r u p v u w [a, b, c, d ] hello : [ there ] p q r st r u p v u w [ hello, there ] 3:5:7:[] p q r st r u p v u w [3,5,7] 1 2 Z [ b+* 1 n ) b` Z * / [1..1] p q r st r u p v u w [1,2,3,4,5,6,7,8,9,1] [5,7..] -- this is an infinite list! 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 9 T O F IQ U F K P R H R S FQ J Q V H J S W F S Q R H J Q F R K S ) * \ Z bb. [ - n +_ Z * k l h j g l m -. Z [ ) 1 +- ] * - ] b+* 1 * d - c Z Z ) c. bz * / head :: [a] -> a head (x:_) = x last :: [a] -> a last [x] = x last (_:xs) = last xs tail :: [a] -> [a] tail (_:xs) = xs length :: [a] -> Int length [] = length (x:xs) = 1 + length(xs) (++) :: [a] -> [a] -> [a] [] ++ ys = ys (x:xs) ++ ys = x : (xs ++ ys) filter :: (a -> Bool) -> [a] -> [a] filter p [] = [] filter p (x:xs) = if p x then x: (filter p xs) else filter p xs map :: (a -> b) -> [a] -> [b] map f [] = [] map f (x:xs ) = f x : (map f xs) replicate :: Int -> a -> [a] replicate n x = take n (repeat x) Z Z Y 2 - c. * - ] *. ^ d 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 1 W F S Q R H J Q F R K S Q Q J K Q P F K ) 1 1 Z [ ] c ) 1, 2 +] ^ +* ^ Z ] Z [ ) bb ` * Z _ 1 - ),, Z * * *. Z, +a +, n ) b` Z * - a _ ) 1 ) * 1 [ `, 1 ` [ Z * ) c - ] ^ Z [ * d 1 *, - c c - ] b ` * Z _ +] 1 2 Z a - bb- +] ^ 1 -, ) * Z * / a ` ], 1 +- ] _ Z a +] ] d ] +1 +) b+ ) 1 +- ] - a ) n ) [ +) ( bz d - ` *. Z, +a ). ) 1 1 Z [ ] 2 +, 2 *. Z, +a +Z * ) n ) b` Z - [ n ) b` Z _ Z, - c. - * ] a - [ _ ) 1 ) * 1 [ `, 1 ` [ Z * ) ] ` [ +] ^ [ ` ] 1 +c Z +a 1 2 Z. ) 1 1 Z [ ] +* c ) 1, 2 Z _ 1 2 Z +] * 1 [ `, 1 +- ] * ) * * -, +) 1 Z _ ) [ Z Z Z, ` 1 Z _ d R R K I F S Q H Q Q J K S ) 1 1 Z [ ] c ) 1, 2 Z * Z c. 1 b+* 1 [] ) b+* ] Z Z bz c Z ] 1 [x] ) 1 - Z bz c Z ] 1 b+* 1 [x,y] ) b+* 1 x:xs +1 2 ) 1 bz ) * 1 - ] Z Z bz c Z ] 1 +bb, - ] 1 ) +] 1 2 Z n ) b` Z - a 1 2 Z a +[ * 1 Z bz c Z ] 1 * - a 1 2 Z 1 ) +b - a b+* 1 d ) b+* 1 x:y:xs +1 2 ) 1 bz ) * Z bz c Z ] 1 * +bb, - ] 1 ) +] 1 2 Z n ) b` Z - a 1 2 Z a +[ * 1 Z bz c Z ] 1 - a 1 2 Z * Z, - ] _ ) ] _ * - a 1 2 Z 1 ) +b - a b+* 1 d _ ` ] _ Z [ *, - [ Z c ) 1, 2 Z * ) ] 1 2 +] ^ d 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 11 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 12 3

4 R M M Q J J I J J K Q S R N K K Q sum list = if (length list) == then else (head list) + sum (tail list) sum list length list == = otherwise = (head list) + sum (tail list) sum list = case (length list) of -> _ -> (head list) + sum (tail list) sum [] = sum [x] = x sum (x:xs) = x + sum xs 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 13 T O F IQ U F K P R H R S FQ J Q V H J S O H I J S * Z _ a - [ 1 2 Z ^ [ - `. +] ^ - a n ) b` Z * - a. - * * +( b _ +a a Z [ Z ] 1 1. Z * d Y 2 +] \ * 1 [ `, 1 * +] [ Z, - [ _ * +] (8, 3) :: (Int, Int) ( a, 1) :: (Char, Int) ( John Doe, True, [ Mary, Joseph ]) :: (String, Bool,[String])! " # $ " # " % # fst $ " snd & ' $ (! # ( # ( % $ " % # % & ) * ( # $ " & 12/5/23. Author: J. Nino : ; <=>?@@ 5ABCD 14 = B C C A D E F B C H IE J $ ( # & ' # # % flip :: (Int, Int) -> (Int, Int) flip pair = (snd pair, fst pair) -- better below: flip (x,y) = (y, x) -- match equal:: (Int, Int) -> (Int, Int) -> Bool equal (x,y) (x1,y1) = x * y1 == x1 * y numberchildren :: (String, Bool, [String]) -> Int numberchildren (name, married, children) = length children 12/5/23. Author: J. Nino. +, + -./ :;< 15 = > K A K M N O P Q RS P T N O U S V O W RO T N S T U T W Y Z T U [\ ] ^ W W O Z W _ U [\ ` S U Z S R W a _ S Q RS P b N O \ RP _ [c c O W O \ Z O d [T N T N O U O [U T N S T e P _ O cs Y RT f S U g O RR U T W Y Z T U c [O R_ U _ \ T W O h Y [W O RS e O RU i M N O P Z S \ e O Y U O _ c W T N O _ O c [\ [T [ \ c Y U O W _ O c [\ O _ T P Q O U i type Date = (Int, Int, Int) -- (day, month, year) type Testrade = (String, Int, Char) --(id, score, grade) type Employee = (Date, String, Float) (begin, name, salary) M N O P Z S \ S RU e O Y U O _ T W O T Y W \ V W O T N S \ \ O j S RY O c W V c Y \ Z T [ \ U i type Author = String type AuthorPubs = (Author, Int) - (author, book pubscount) type AuthorDB = [AuthorPubs] pubscount :: AuthorDB -> Author -> AuthorPubs pubscount [] anauthor = ( NoSuch, ) pubscount ((author, pubs):authors) anauthor = if author == anauthor then (author, pubs) else (pubscount authors anauthor) 12/5/23. Author: J. Nino. +, + -./ :;< 16 4

5 A I E I E IK C K IK C F? D A H A E K I E ] N S W S Z T O W [U T [Z S RRP c Y \ _ [\ Y \ Z T [ \ S R Q W W S V V [\ RS \ Y S O U i a R[U T Z V Q W O N O \ U [ \ [U Y U O _ T _ O c [\ O T N O O RO V O \ T U c \ O d R[U T [\ T O W V U c O RO V O \ T U c S \ T N O W R[U T i M N O R[U T e O [\ Y U O _ [U Z S RRO _ T N O O \ O W S T W i evennumbers = [2*n n <- [1..4]] [2,4,6,8] shiftvalues = [n + 1 n <- [5,8,11,15] ] [6,9,12, 16] primes = [ isprime n n <- [2..2]] [2,3,5,7,11,13,17] shiftvalues = [n + 1 n <- [5,8,11,15], iseven n ] [9] shiftvalues = [n + 1 n <- [5,8,11,15], n < 1] [6,9] digitist = [ ch ch <- string, isdigit ch] # $ " pairsum =[ n + m (n,m) <- pairist] pairsum = [ n + m (n,m) <- pairist, m mod n == ] 12/5/23. Author: J. Nino. +, + -./ :;< 17 D I D B D # # ( * % # " % & ( % % "! $ $ & ' # & $ ( " " & % $ # % # % # % $ & # $ $ ( type String = [Char] ERROR "c:\unocourses\451\haskell\code\simplefuns.hs":27 - Ambiguous type constructor occurrence "String" *** Could refer to: Main.String Prelude.String! " # $ # % & ' " " ( " ) ' * *! % ' * $# +! *, ' --! " ' ( # -. /! " $! ' -/ /5/23. Author: J. Nino. +, + -./ :;< 18 H I J K M I N OP Q R S M J T I P Q U N V M U W T Q U YQ Z U U [ \ ] I ^ U I Q Q _U ` _a J K I J Q a b U c W c Q U U _a P I J K Z c T P U ^ P J W H I J K J Q ` I M I T P U ^ P J W Q J d J O_J Z _I U _O I \ e f I P S OQ I Q g h \i j h \k l h \m l h \in l o \p l o \m l o \i n l o \i i l q \r l q \p l q \q l q \R l q \i h l q \i k l q \i q l q \i R l q \r k 12/5/23. Author: J. Nino : ; < = >?@ABB 7CDEF 19 5

Framework for functional tree simulation applied to 'golden delicious' apple trees

Purdue University Purdue e-pubs Open Access Theses Theses and Dissertations Spring 2015 Framework for functional tree simulation applied to 'golden delicious' apple trees Marek Fiser Purdue University