Background Constructors (1A) Young Won Lim 6/30/18

Transcription

1 Background Constructors (1A)

2 Copyright (c) Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to youngwlim@hotmail.com. This document was produced by using OpenOffice.

3 Based on Haskell in 5 steps Constructors 3

4 Advantages of let f :: s -> (a,s) f x = y where y =... x... f :: State s a f = State $ \x -> y where y =... x... Using Control.Monad.State monad will not work, because where refers to the pattern matching f =, where no x is in scope. with let, there is no problem. f :: s -> (a,s) f x = let y =... x... in y f :: State s a f = State $ \x -> let y =... x... in y Constructors 4

5 Advantages of while Because "where" blocks are bound to a syntactic construct, they can be used to share bindings between parts of a function that are not syntactically expressions. f x f x f x = f x = cond1 x = a = let a = w x let a = w x let a = w x cond2 x = g a in case () of in select (f (h x a)) in if cond1 x otherwise = f (h x a) _ cond1 x -> a [(cond1 x, a), then a where cond2 x -> g a (cond2 x, g a)] else if cond2 x a = w x otherwise -> f (h x a) then g a else f (h x a) an expression style a functional equivalent: a series of if-thenelse expressions: These alternatives are arguably less readable and hide the structure of the function more than simply using where. Constructors 5

6 Lambda Lifting let or where can often be implemented using lambda lifting and let floating, incurring at least the cost of introducing a new name. f x cond1 x = a cond2 x = g a otherwise = f (h x a) where a = w x f x = f' (w x) x f' a x cond1 x = a cond2 x = g a otherwise = f (h x a) The auxiliary definition can either be a top-level binding, or included in f using let or where. Constructors 6

7 Problems with where (1) fib = (map fib' [0..]!!) where fib' 0 = 0 fib' 1 = 1 fib' n = fib (n - 1) + fib (n - 2) fib x = map fib' [0..]!! x where fib' 0 = 0 fib' 1 = 1 fib' n = fib (n - 1) + fib (n - 2) the second one runs considerably slower than the first. You may wonder why simply adding an explicit argument to fib (known as eta expansion) degrades performance so dramatically. Constructors 7

8 Problems with where (2) fib = let fib' 0 = 0 fib' 1 = 1 fib' n = fib (n - 1) + fib (n - 2) in (map fib' [0..]!!) fib x = let fib' 0 = 0 fib' 1 = 1 fib' n = fib (n - 1) + fib (n - 2) in map fib' [0..]!! x In the second case, fib' is redefined for every argument x The compiler cannot know whether you intended this while it increases time complexity it may reduce space complexity. Thus it will not float the definition out from under the binding of x. In contrast, in the first function, fib' can be moved to the top level by the compiler. The where clause hid this structure and made the application to x look like a plain eta expansion, which it is not. Constructors 8

9 Data Constructor data Color = Red Green Blue Type Constructor Data Constructors values Red Green Blue is a constructor that contains a value of the type Color. is a constructor that contains a value of the type Color. is a constructor that contains a value of the type Color. Constructors 9

10 Data Constructor with Parameters data Color = RGB Int Int Int Type Constructor type Data Constructors (a function returning a value) RGB is not a value but a function taking three Int s and returning a value RGB :: Int -> Int -> Int -> Color RGB is a data constructor that is a function taking three Int values as its arguments, and then uses them to construct a new value. Constructors 10

11 Type Constructor Consider a binary tree to store Strings data SBTree = Leaf String Branch String SBTree SBTree Type Constructor type Data Constructors (functions returning a value) a type SBTree Leaf Branch is a type is a data constructor (a function) is a data constructor (a function) Leaf :: String -> SBTree Branch :: String -> SBTree -> SBTree -> SBTree Constructors 11

12 Similar Type Constructors Consider a binary tree to store Strings data SBTree = Leaf String Branch String SBTree SBTree Consider a binary tree to store Bool data BBTree = Leaf Bool Branch Bool BBTree BBTree Consider a binary tree to store a parameter type data BTree a = Leaf a Branch a (BTree a) (BTree a) Constructors 12

13 Type Constructor with a Parameter Type constructors Both SBTree and BBTree are type constructors data SBTree = Leaf String Branch String SBTree SBTree data BBTree = Leaf Bool Branch Bool BBTree BBTree data BTree a = Leaf a Branch a (BTree a) (BTree a) Now we introduce a type variable a as a parameter to the type constructor. BTree has become a function. It takes a type as its argument and it returns a new type. Constructors 13

14 Type Constructors and Data Constructors A type constructor a "function" that takes 0 or more types gives you back a new type. type SBTree = BTree String type BBTree = BTree Bool Type constructors with parameters allows slight variations in types A data constructor a "function" that takes 0 or more values gives you back a new value. Data constructors with parameters allows slight variations in values RGB #0c5c1b RGB RGB RGB Constructors 14

15 ( ) ( ) is both a type and a value. ( ) is a special type, pronounced unit, has one value ( ), sometimes pronounced void the unit type has only one value which is called unit. ( ) :: ( ) Type :: Expression It is the same as the void type void in Java or C/C++. Constructors 15

16 Unit Type a unit type is a type that allows only one value (and thus can hold no information). It is the same as the void type void in Java or C/C++. :t Expression :: Type data Unit = Unit Prelude> :t Unit Unit :: Unit Prelude> :t () () :: () Constructors 16

17 Type Language and Expression Language data Tconst Tvar Tvar = Vconst_1 type type Vconst_n type type A new datatype declaration Tconst (Type Constructor) Vconst (Value Constructor) is added to the type language is added to the expression language and its pattern sublanguage must not appear in types argument types in (Tconst Tvar Tvar) can be used as argument types in Vconst type type Constructors 17

18 Datatype Declaration data TypeC Tpar Tpar = ValC type type ValC type type A new datatype declaration The keyword data introduces a new datatype declaration, what the new type is TypeC Tpar Tpar what its values are. ValC type type ValC type type datatype data type type = data Constructors 18

19 Datatype Declaration Examples data Tree a = Leaf Node (Tree a) (Tree a) data Type = Value Tree Leaf or Node (Type Constructor) (Value Constructor) data ( ) = ( ) ( ) (Type Constructor) ( ) (Value Constructor) the type (), often pronounced "Unit" the value (), sometimes pronounced "void" the type () containing only one value () Constructors 19

20 Type Synonyms type String = [Char] phonebook :: [(String,String)] type PhoneBook = [(String,String)] phonebook :: PhoneBook phonebook = [("betty"," "),("bonnie"," "),("patsy"," "),("lucille"," "),("wendy"," "),("penny"," ") ] type PhoneNumber = String type Name = String type PhoneBook = [(Name,PhoneNumber)] phonebook :: PhoneBook Constructors 20

21 Type Synonyms for Functions type Bag a = a -> Int data Gems = Sapphire Emerald Diamond deriving (Show) a -> Int a Int a Bag a Int type Bag a = a -> Int type Bag Int = Int -> Int type Bag Char = Char -> Int Constructors 21

22 Type Synonyms for Functions type Bag a = a -> Int data Gems = Sapphire Emerald Diamond deriving (Show) mybag :: Bag Gems a mybag Int emptybag :: Bag Gems a emptybag Int Constructors 22

23 Type Synonyms for Functions type Bag a = a -> Int data Gems = Sapphire Emerald Diamond deriving (Show) mybag :: Bag Gems a mybag Int mybag Sapphire = 3 mybag Diamond = 2 mybag Emerald = 0 Sapphire Diamond Emerald emptybag :: Bag Gems a emptybag Int emptybag Sapphire = 0 Sapphire 0 emptybag Diamond = 0 Diamond 0 emptybag Emerald = 0 Emerald 0 Constructors 23

24 Toward the Record Syntax data Person = Person String String Int Float String String deriving (Show) let guy = Person "Buddy" "Finklestein" " " "Chocolate" pattern matching functions firstname :: Person -> String firstname (Person firstname _) = firstname lastname :: Person -> String lastname (Person _ lastname ) = lastname age :: Person -> Int age (Person age _) = age height :: Person -> Float height (Person _ height ) = height phonenumber :: Person -> String phonenumber (Person number _) = number flavor :: Person -> String flavor (Person _ flavor) = flavor firstname guy Buddy lastname guy John age guy 43 height guy phonenumber guy flavor guy Chocolate Constructors 24

25 The Record Syntax data Person = Person { fname :: String, lname :: String, age :: Int, ht :: Float, ph :: String, flavor :: String } deriving (Show) let guy = Person { fname="buddy", lname="john", age=43, ht=184.2, ph= , flavor= Orange } accessor functions fname lname age ht ph flavor :: Person -> String :: Person -> String :: Person -> Int :: Person -> Float :: Person -> String :: Person -> String fname guy Buddy lname guy John age guy 43 ht guy ph guy flavor guy Orange Constructors 25

26 The Record Syntax Example data Car = Car String String Int deriving (Show) Car "Ford" "Mustang" 1967 data Car = Car {company :: String, model :: String, year :: Int} deriving (Show) Car {company = "Ford", model = "Mustang", year = 1967} Constructors 26

27 Record Syntax (named field) data Configuration = Configuration { username :: String, localhost :: String, currentdir :: String, homedir :: String, timeconnected :: Integer } username :: Configuration -> String localhost :: Configuration -> String -- etc. -- accessor function (automatic) changedir :: Configuration -> String -> Configuration -- update function changedir cfg newdir = if directoryexists newdir -- make sure the directory exists then cfg { currentdir = newdir } else error "Directory does not exist" Constructors 27

28 newtype and data data newtype data can only be replaced with newtype if the type has exactly one value constructor which can have exactly only one field It ensures that the trivial wrapping and unwrapping of the single field is eliminated by the compiler. (using newtype is faster) Constructors 28

29 data, type, and newtype data State s a = State { runstate :: s -> (s, a) } type State s a = State { runstate :: s -> (s, a) } newtype State s a = State { runstate :: s -> (s, a) } instance : data(o), type(x), newtype(o) overhead : data(o), type(x), newtype(x) Constructors 29

30 Single value constructor with a single field simple wrapper types such as State Monad are usually defined with newtype. type : type synonyms newtype State s a = State { runstate :: s -> (s, a) } A single value constructor : State { runstate :: s -> (s, a) } A single field : { runstate :: s -> (s, a) } Constructors 30

31 Single value constructor with a single field one constructor with one field means that the new type and the type of the field are in direct correspondence (isomorphic) state :: (s -> (a, s)) -> State s a runstate :: State s a -> (s -> (a, s)) (s -> (a, s)) State s a state State s a runstate (s -> (a, s)) after the type is checked at compile time, at run time the two types can be treated identically to declare different type class instances for a particular type, or want to make a type abstract, wrap it in a newtype then distinct to the type-checker but identical at runtime. Constructors 31

32 data, newtype, type data newtype type value constructors : number many only one none value constructors : evaluation lazy strict N/A value constructors : fields many only one none Compilation Time affected affected affected Run Time Overhead runtime overhead none none Created Type a distinct new type a distinct new type a new name Type Class Instances type class instances type class instances no instance Pattern Matching Evaluation at least WHNF no evaluation same as the original Usage a new data type higher level concept higher level concept Constructors 32

33 data data - creates new algebraic type with value constructors can have several value constructors value constructors are lazy values can have several fields affects both compilation and runtime, have runtime overhead created type is a distinct new type can have its own type class instances when pattern matching against value constructors, WILL be evaluated at least to weak head normal form (WHNF) * used to create new data type (example: Address { zip :: String, street :: String } ) Constructors 33

34 newtype newtype - creates new decorating type with value constructor can have only one value constructor value constructor is strict value can have only one field affects only compilation, no runtime overhead created type is a distinct new type can have its own type class instances when pattern matching against value constructor, CAN not be evaluated at all * used to create higher level concept based on existing type with distinct set of supported operations or that is not interchangeable with original type (example: Meter, Cm, Feet is Double) Constructors 34

35 type type - creates an alternative name (synonym) for a type (like typedef in C) no value constructors no fields affects only compilation, no runtime overhead no new type is created (only a new name for existing type) can NOT have its own type class instances when pattern matching against data constructor, behaves the same as original type used to create higher level concept based on existing type with the same set of supported operations (example: String is [Char]) Constructors 35

36 newtype examples newtype Fd = Fd CInt -- data Fd = Fd CInt would also be valid -- newtypes can have deriving clauses just like normal types newtype Identity a = Identity a deriving (Eq, Ord, Read, Show) -- record syntax is still allowed, but only for one field newtype State s a = State { runstate :: s -> (s, a) } -- this is *not* allowed: -- newtype Pair a b = Pair { pairfst :: a, pairsnd :: b } -- but this is: data Pair a b = Pair { pairfst :: a, pairsnd :: b } -- and so is this: newtype NPair a b = NPair (a, b) Constructors 36

37 References [1] ftp://ftp.geoinfo.tuwien.ac.at/navratil/haskelltutorial.pdf [2]