程序代写代做代考 DNA algorithm Haskell (==) :: Integer -> Integer -> Bool

(==) :: Integer -> Integer -> Bool
(==) :: Char -> Char -> Bool
(==) :: Bool -> Bool -> Bool
— Similarly for (/=) the not-equal operator.
class ClassName typeVar where
methodName :: type sig containing typeVar — Optional: default implementations
== /= Eq
class Eq a where
(==), (/=) :: a -> a -> Bool
— default implementation for (==)
x == y = not (x /= y)
— default implementation for (/=)
x /= y = not (x == y)
— default implementations deliberately circular so you just have to
— implement one of them to break the cycle
a
instance Eq Bool where — (so a=Bool here)
Bool
False == False
True == True
_ == _
= True
= True
= False
— default implementation for (/=) takes hold
Bool
Eq
Eq
== <= + foo :: Eq -> Eq -> Bool
bar :: Eq a -> Eq a -> Bool
Table of Contents
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(==) :: Eq a => a -> a -> Bool
Eq a =>
Eq
a
Bool Eq
— Determine whether the 3 arguments are mutually equal. Needs the user-chosen
— type to be an instance of Eq (supports “==”) but otherwise polymorphic.
eq3 :: Eq a => a -> a -> a -> Bool
eq3 x y z = x==y && y==z
<= < Ord class Eq a => Ord a where
compare :: a -> a -> Ordering — data Ordering = LT | EQ | GT
(<), (<=), (>), (>=) :: a -> a -> Bool
max, min :: a -> a -> a
— there are default implementations; an instance just has to provide
— compare or <= Eq a => Ord
Ord
Ord Eq
— Sorting algorithms just need Ord but otherwise polymorphic.
insertionSort :: Ord a => [a] -> [a]
insertionSort [] = []
insertionSort (x:xt) = insert x (insertionSort xt)
where
insert e [] = [e]
insert e xs@(x:xt)
| e <= x = e : xs | otherwise = x : insert e xt Eq Eq Ord a Eq a -- De-duplicating sorting uses both (==) and (<). Type sig just needs Ord. uniqInsertionSort :: Ord a => [a] -> [a]
uniqInsertionSort [] = []
uniqInsertionSort (x:xt) = insert x (uniqInsertionSort xt)
where
insert e [] = [e]
insert e xs@(x:xt)
| e < x = e : xs | e == x = xs | otherwise = x : insert e xt Table of Contents ti etirw( tseB . .)edoc s'esle enoemos morf tropmi ro flesruoy fo ecnatsni na osla si ti taht erusne , fo ecnatsni na epyt a gnikam er'uoy fI .sessalcbus POO ot detalernu si siht taht eraweb tub ,” fo ssalcbus a si “ yas eW .deilpmi s'ti ,” “ yas ot deen t'nod uoy neht ,” “ yas uoy fi ,serutangis epyt nI :selgna owt morf dootsrednu fo ecnatsni na osla si fo ecnatsni nA :snaem tI .tnereffid tib a si ” “ sihT : dellac si ssalc ehT .cte , , :elpmaxe rehtonA sh.2sepyTlleksaH ni ,.g.e ,sdohtem eht gnisu snoitcnuf cihpromylop etirw uoy nehw sraeppa osla rekram sihT . fo ecnatsni na eb tsum fo eciohc s'resu tub cihpromylop :rof rekram si ” “ lanoitidda ehT :siht ekil kool sessalc edistuo sepyt dohteM . fo ”ssalcbus“ a ton si .”ssalcbus“ a ton si epyt A sh.2sepyTlleksaH ni data MyIntegerList = INil | ICons Integer MyIntegerList deriving Show data MyList a = Nil | Cons a (MyList a) deriving Show Eq == instance Eq MyIntegerList where INil == INil = True ICons x xs == ICons y ys = x==y && xs==ys _ == _ = False instance Eq a => Eq (MyList a) where
— The “Eq a =>” there means I need to use (==) on type a.
— Try omitting it to see what happens.
Nil == Nil
Cons x xs == Cons y ys
_ == _
Show Read
= True
= x==y && xs==ys
— “x==y” is when we need to assume Eq a.
= False
Bounded Enum
[1..n]
data MyType = … deriving (Eq, Ord, Bounded, Enum, Show, Read)
==
Num
Int Integer Rational Float
Complex a a Double Float
+ – * abs
Double
Table of Contents
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Integral
Fractional
div mod Int Integer
/ recip
Rational Float Double Complex a
let xs :: [Double]
xs = [1, 2, 3]
in sum xs / length xs
sum xs :: Double
length xs :: Int
(/)
sum xs / fromIntegral (length xs)
realToFrac
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
Rational Complex
epsilon :: (Ord a, Fractional a) => a
epsilon = last notTooSmall
where
halves = iterate (/ 2) 1
notTooSmall = takeWhile (\e -> 1 + e > 1) halves
epsilonDouble :: Double
epsilonDouble = epsilon
epsilonFloat :: Float
epsilonFloat = epsilon
Table of Contents
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length :: Foldable t => t a -> Int
length :: [a] -> Int
length :: [a] -> Int
sum :: Num a => [a] -> a
minimum :: Ord a => [a] -> a
— assumes non-empty list
foldr :: (a -> b -> b) -> b -> [a] -> b [a] [] a
Foldable t
Foldable (t a)
sum :: Num a => Vector a -> a
— Vector is an array, 0-based Int index. Third-party but popular library.
— https://hackage.haskell.org/package/vector/
sum :: Num a => Seq a -> a
— Seq is a middle ground between array and linked list,
— O(1) prepend and append, log time random access.
[] Integer [] Char [] String [] a
[] Integer Vector Integer Seq Integer t Integer
Table of Contents
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class Foldable t where
length :: t a -> Int — implicitly ∀a, similarly below sum :: Num a => t a -> a
minimum :: Ord a => t a -> a
foldr :: (a -> b -> b) -> b -> t a -> b
— and others
class Foldable (t a)
instance Foldable ([] a)
instance Foldable []
Ord <= -- implicitly ∀a,b template SLL insertionSort(SLL)
<= insertionSort Table of Contents :ecafretni na dnetxe ot sah elbairav epyt eht taht setats erutangis epyT .detpoda ton saw tub ,sessalc epyt s'lleksaH fo enil eht gnola ”tpecnoc“ dellac lasoporp a saw erehT .segassem rorre roop ,noitalipmoc etarapes staefed :smelborp sti lla dna gnilpuoc thgit tub ,skroW .ti stroppus epyt nesohc-resu eht kcehc nac , sesu ti ees nac ,)ereht thgir ti dnapxe ot( edoc etalpmet eht ot ssecca sah relipmoc ,etis llac tA .orcam ekil si ”etalpmet“ tuB ++C od segaugnal depyt-yllacitats rehto tahW .secafetni dna sessalc tcartsba POO ,.g.e ,noitcartsba yna fo eurT .od ot tahw dnim ruoy pu gnikam gnitanitsarcorp ,edoc lautca gnitirw gnitanitsarcorP .eman dohtem nommoC .cte ,tsuR ,alacS ,avaJ :epytotorp eht ot egnahc oN :naht tfieneb rehtruf on rof detaerC :ssalc epyt daB .smhtirogla eert hcraes yranib dna smhtirogla gnitros fo sisab eht era swal esehT .latot ,cirtemmys-itna ,evitisnart ,evixefler si : :elpmaxE .smhtirogla lareneg lufesu dliub ot desu eb nac erofereht ,snoitatcepxe ro swal lufesu yfsitas sdohteM ,” “ ekil og secnatsni ,esiwekiL .” .” “ ton “ ton si tI :tnatropmI .secnatsni elpitlum evah uoY :stiart eseht sah ssalc epyt doog A sessalc epyt dab dna sessalc epyt dooG > SLL insertionSort(SLL)
insertionSort
Sorter
(* Example in OCaml *)
module Sorter(Cmp : sig
type t
insertionSort
val leq : (t,t) -> bool
end)
= struct
let rec insertionSort xs = …
(* insertion sort code; use Cmp.leq to compare *)
end
Sorter
Sorter
(* Example in OCaml *)
module IntCmp = struct
type t = int
let leq (x,y) = x<=y end module IntSorter = Sorter(IntCmp) (* Now can use IntSorter.insertionSort for [int] *) Comparable Comparable Table of Contents .sredro evitanretla neve ,sepyt tnemele rehto rof ylralimiS . etaitnatsni ot ti esu ,srotarepo nosirapmoc tni sniatnoc taht eludom a etirw ,stni rof esu oT .rotarapmoc dna epyt tnemele sefiiceps taht eludom rehtona retemarap sa sekat ti tub— ti llac—eludom a otni tuP .sdohteM etalpmeT laeR .sretemarap sa seludom rehto ekat nac eludom A .” dnetxet'nseodepytnesohc-resu“yastsuJ:etisesutasegassemrorredooG .gis epyt daer ot sdeen ylno ,edoc lanretni troSnoitresni daer ot deen ton seod , sdnetxe epyt nesohc-resu taht skcehc relipmoC :etis esu gnilipmoc nehW .setis esu wonk ot deen ton seod ,sdohtem nosirapmoc esu ot dewolla si edoC : gnilipmoc nehW :noitalipmoc etarapes ot yldneirF :)oot sessalc epyt lleksaH( stfieneb sti lla dna gnilpuoc-ed dooG ).msihpromylop cirtemarap lleksaH morf ti thguorb ohw reldaW lihP morf emac scireneg avaJ ,tcaf nI( .POO ot detpada tub sessalc epyt lleksaH morf denraeL lmaCO ,lmaC ,LMS