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I'm a beginner in haskell and I wonder about the right way to define a new type. Suppose I want to define a Point type. In an imperative language, it's usually the equivalent of:
data Point = Int Int
However in haskell I usually see definitions such as:
data Point = Point Int Int
What are the differences and when should each approach be used?
In OO languages you can define a class with something like this
class Point {
int x,y;
Point(int x, int y) {...
}
it's similar
data Point = ...
is the type definition (similar to class Point above , and
... = Point Int Int
is the constructor, you can also define the constructor with a different name, but you need a name regardless.
data Point = P Int Int
The data definitions are, ultimately, tagged unions. For example:
data Maybe a = Nothing | Just a
Now how would you write this type using your syntax?
Moreover it remains the fact that in Haskell you can pattern match over this values and see which constructor was used to build a value. The name of the constructor is needed for pattern matching, and if the type has just one constructor it often re-uses the same name as the type.
For example:
let x = someOperationReturningMaybe
in case x of
Nothing -> 0
Just y -> y+5
This is different from plain union type, such as C's union where you can say "this thing is etiher an int or a float" but you have no way to know which one it actually is (except by keeping track of the state by hand).
Writing the code above using a C union you have no way to use a case to perform different actions depending on the constructor used, and you have to keep track explicitly what type is contained in that x and use an if.
I'm a beginner in Haskell playing around with parsing and building an AST. I wonder how one would go about defining types like the following:
A Value can either be an Identifier or a Literal. Right now, I simply have a type Value with two constructors (taking the name of the identifier and the value of the string literal respectively):
data Value = Id String
| Lit String
However, then I wanted to create a type representing an assignment in an AST, so I need something like
data Assignment = Asgn Value Value
But clearly, I always want the first part of an Assignment to always be an Identifier! So I guess I should make Identifier and Literal separate types to better distinguish things:
data Identifier = Id String
data Literal = Lit String
But how do I define Value now? I thaught of something like this:
-- this doesn't actually work...
data Value = (Id String) -- How to make Value be either an Identifier
| (Lit String) -- or a Literal?
I know I can simply do
data Value = ValueId Identifier
| ValueLit Literal
but this struck me as sort of unelegant and got me wondering if there was a better solution?
I first tried to restructure my types so that I would be able to do it with GADTs, but in the end the simpler solution was to go leftroundabout's suggestion. I guess it's not that "unelegant" anyways.
I am learning Haskell from learnyouahaskell.com. I am having trouble understanding type constructors and data constructors. For example, I don't really understand the difference between this:
data Car = Car { company :: String
, model :: String
, year :: Int
} deriving (Show)
and this:
data Car a b c = Car { company :: a
, model :: b
, year :: c
} deriving (Show)
I understand that the first is simply using one constructor (Car) to built data of type Car. I don't really understand the second one.
Also, how do data types defined like this:
data Color = Blue | Green | Red
fit into all of this?
From what I understand, the third example (Color) is a type which can be in three states: Blue, Green or Red. But that conflicts with how I understand the first two examples: is it that the type Car can only be in one state, Car, which can take various parameters to build? If so, how does the second example fit in?
Essentially, I am looking for an explanation that unifies the above three code examples/constructs.
In a data declaration, a type constructor is the thing on the left hand side of the equals sign. The data constructor(s) are the things on the right hand side of the equals sign. You use type constructors where a type is expected, and you use data constructors where a value is expected.
Data constructors
To make things simple, we can start with an example of a type that represents a colour.
data Colour = Red | Green | Blue
Here, we have three data constructors. Colour is a type, and Green is a constructor that contains a value of type Colour. Similarly, Red and Blue are both constructors that construct values of type Colour. We could imagine spicing it up though!
data Colour = RGB Int Int Int
We still have just the type Colour, but RGB is not a value – it's a function taking three Ints and returning a value! RGB has the type
RGB :: Int -> Int -> Int -> Colour
RGB is a data constructor that is a function taking some values as its arguments, and then uses those to construct a new value. If you have done any object-oriented programming, you should recognise this. In OOP, constructors also take some values as arguments and return a new value!
In this case, if we apply RGB to three values, we get a colour value!
Prelude> RGB 12 92 27
#0c5c1b
We have constructed a value of type Colour by applying the data constructor. A data constructor either contains a value like a variable would, or takes other values as its argument and creates a new value. If you have done previous programming, this concept shouldn't be very strange to you.
Intermission
If you'd want to construct a binary tree to store Strings, you could imagine doing something like
data SBTree = Leaf String
| Branch String SBTree SBTree
What we see here is a type SBTree that contains two data constructors. In other words, there are two functions (namely Leaf and Branch) that will construct values of the SBTree type. If you're not familiar with how binary trees work, just hang in there. You don't actually need to know how binary trees work, only that this one stores Strings in some way.
We also see that both data constructors take a String argument – this is the String they are going to store in the tree.
But! What if we also wanted to be able to store Bool, we'd have to create a new binary tree. It could look something like this:
data BBTree = Leaf Bool
| Branch Bool BBTree BBTree
Type constructors
Both SBTree and BBTree are type constructors. But there's a glaring problem. Do you see how similar they are? That's a sign that you really want a parameter somewhere.
So we can do this:
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. In this declaration, BTree has become a function. It takes a type as its argument and it returns a new type.
It is important here to consider the difference between a concrete type (examples include Int, [Char] and Maybe Bool) which is a type that can be assigned to a value in your program, and a type constructor function which you need to feed a type to be able to be assigned to a value. A value can never be of type "list", because it needs to be a "list of something". In the same spirit, a value can never be of type "binary tree", because it needs to be a "binary tree storing something".
If we pass in, say, Bool as an argument to BTree, it returns the type BTree Bool, which is a binary tree that stores Bools. Replace every occurrence of the type variable a with the type Bool, and you can see for yourself how it's true.
If you want to, you can view BTree as a function with the kind
BTree :: * -> *
Kinds are somewhat like types – the * indicates a concrete type, so we say BTree is from a concrete type to a concrete type.
Wrapping up
Step back here a moment and take note of the similarities.
A data constructor is a "function" that takes 0 or more values and gives you back a new value.
A type constructor is a "function" that takes 0 or more types and gives you back a new type.
Data constructors with parameters are cool if we want slight variations in our values – we put those variations in parameters and let the guy who creates the value decide what arguments they are going to put in. In the same sense, type constructors with parameters are cool if we want slight variations in our types! We put those variations as parameters and let the guy who creates the type decide what arguments they are going to put in.
A case study
As the home stretch here, we can consider the Maybe a type. Its definition is
data Maybe a = Nothing
| Just a
Here, Maybe is a type constructor that returns a concrete type. Just is a data constructor that returns a value. Nothing is a data constructor that contains a value. If we look at the type of Just, we see that
Just :: a -> Maybe a
In other words, Just takes a value of type a and returns a value of type Maybe a. If we look at the kind of Maybe, we see that
Maybe :: * -> *
In other words, Maybe takes a concrete type and returns a concrete type.
Once again! The difference between a concrete type and a type constructor function. You cannot create a list of Maybes - if you try to execute
[] :: [Maybe]
you'll get an error. You can however create a list of Maybe Int, or Maybe a. That's because Maybe is a type constructor function, but a list needs to contain values of a concrete type. Maybe Int and Maybe a are concrete types (or if you want, calls to type constructor functions that return concrete types.)
Haskell has algebraic data types, which very few other languages have. This is perhaps what's confusing you.
In other languages, you can usually make a "record", "struct" or similar, which has a bunch of named fields that hold various different types of data. You can also sometimes make an "enumeration", which has a (small) set of fixed possible values (e.g., your Red, Green and Blue).
In Haskell, you can combine both of these at the same time. Weird, but true!
Why is it called "algebraic"? Well, the nerds talk about "sum types" and "product types". For example:
data Eg1 = One Int | Two String
An Eg1 value is basically either an integer or a string. So the set of all possible Eg1 values is the "sum" of the set of all possible integer values and all possible string values. Thus, nerds refer to Eg1 as a "sum type". On the other hand:
data Eg2 = Pair Int String
Every Eg2 value consists of both an integer and a string. So the set of all possible Eg2 values is the Cartesian product of the set of all integers and the set of all strings. The two sets are "multiplied" together, so this is a "product type".
Haskell's algebraic types are sum types of product types. You give a constructor multiple fields to make a product type, and you have multiple constructors to make a sum (of products).
As an example of why that might be useful, suppose you have something that outputs data as either XML or JSON, and it takes a configuration record - but obviously, the configuration settings for XML and for JSON are totally different. So you might do something like this:
data Config = XML_Config {...} | JSON_Config {...}
(With some suitable fields in there, obviously.) You can't do stuff like this in normal programming languages, which is why most people aren't used to it.
Start with the simplest case:
data Color = Blue | Green | Red
This defines a "type constructor" Color which takes no arguments - and it has three "data constructors", Blue, Green and Red. None of the data constructors takes any arguments. This means that there are three of type Color: Blue, Green and Red.
A data constructor is used when you need to create a value of some sort. Like:
myFavoriteColor :: Color
myFavoriteColor = Green
creates a value myFavoriteColor using the Green data constructor - and myFavoriteColor will be of type Color since that's the type of values produced by the data constructor.
A type constructor is used when you need to create a type of some sort. This is usually the case when writing signatures:
isFavoriteColor :: Color -> Bool
In this case, you are calling the Color type constructor (which takes no arguments).
Still with me?
Now, imagine you not only wanted to create red/green/blue values but you also wanted to specify an "intensity". Like, a value between 0 and 256. You could do that by adding an argument to each of the data constructors, so you end up with:
data Color = Blue Int | Green Int | Red Int
Now, each of the three data constructors takes an argument of type Int. The type constructor (Color) still doesn't take any arguments. So, my favorite color being a darkish green, I could write
myFavoriteColor :: Color
myFavoriteColor = Green 50
And again, it calls the Green data constructor and I get a value of type Color.
Imagine if you don't want to dictate how people express the intensity of a color. Some might want a numeric value like we just did. Others may be fine with just a boolean indicating "bright" or "not so bright". The solution to this is to not hardcode Int in the data constructors but rather use a type variable:
data Color a = Blue a | Green a | Red a
Now, our type constructor takes one argument (another type which we just call a!) and all of the data constructors will take one argument (a value!) of that type a. So you could have
myFavoriteColor :: Color Bool
myFavoriteColor = Green False
or
myFavoriteColor :: Color Int
myFavoriteColor = Green 50
Notice how we call the Color type constructor with an argument (another type) to get the "effective" type which will be returned by the data constructors. This touches the concept of kinds which you may want to read about over a cup of coffee or two.
Now we figured out what data constructors and type constructors are, and how data constructors can take other values as arguments and type constructors can take other types as arguments. HTH.
As others pointed out, polymorphism isn't that terrible useful here. Let's look at another example you're probably already familiar with:
Maybe a = Just a | Nothing
This type has two data constructors. Nothing is somewhat boring, it doesn't contain any useful data. On the other hand Just contains a value of a - whatever type a may have. Let's write a function which uses this type, e.g. getting the head of an Int list, if there is any (I hope you agree this is more useful than throwing an error):
maybeHead :: [Int] -> Maybe Int
maybeHead [] = Nothing
maybeHead (x:_) = Just x
> maybeHead [1,2,3] -- Just 1
> maybeHead [] -- None
So in this case a is an Int, but it would work as well for any other type. In fact you can make our function work for every type of list (even without changing the implementation):
maybeHead :: [t] -> Maybe t
maybeHead [] = Nothing
maybeHead (x:_) = Just x
On the other hand you can write functions which accept only a certain type of Maybe, e.g.
doubleMaybe :: Maybe Int -> Maybe Int
doubleMaybe Just x = Just (2*x)
doubleMaybe Nothing= Nothing
So long story short, with polymorphism you give your own type the flexibility to work with values of different other types.
In your example, you may decide at some point that String isn't sufficient to identify the company, but it needs to have its own type Company (which holds additional data like country, address, back accounts etc). Your first implementation of Car would need to change to use Company instead of String for its first value. Your second implementation is just fine, you use it as Car Company String Int and it would work as before (of course functions accessing company data need to be changed).
The second one has the notion of "polymorphism" in it.
The a b c can be of any type. For example, a can be a [String], b can be [Int]
and c can be [Char].
While the first one's type is fixed: company is a String, model is a String and year is Int.
The Car example might not show the significance of using polymorphism. But imagine your data is of the list type. A list can contain String, Char, Int ... In those situations, you will need the second way of defining your data.
As to the third way I don't think it needs to fit into the previous type. It's just one other way of defining data in Haskell.
This is my humble opinion as a beginner myself.
Btw: Make sure that you train your brain well and feel comfortable to this. It is the key to understand Monad later.
It's about types: In the first case, your set the types String (for company and model) and Int for year. In the second case, your are more generic. a, b, and c may be the very same types as in the first example, or something completely different. E.g., it may be useful to give the year as string instead of integer. And if you want, you may even use your Color type.
I just uncovered this confusion and would like a confirmation that it is what it is. Unless, of course, I am just missing something.
Say, I have these data declarations:
data VmInfo = VmInfo {name, index, id :: String} deriving (Show)
data HostInfo = HostInfo {name, index, id :: String} deriving (Show)
vm = VmInfo "vm1" "01" "74653"
host = HostInfo "host1" "02" "98732"
What I always thought and what seems to be so natural and logical is this:
vmName = vm.name
hostName = host.name
But this, obviously, does not work. I got this.
Questions
So my questions are.
When I create a data type with record syntax, do I have to make sure that all the fields have unique names? If yes - why?
Is there a clean way or something similar to a "scope resolution operator", like :: or ., etc., so that Haskell distinguishes which data type the name (or any other none unique fields) belongs to and returns the correct result?
What is the correct way to deal with this if I have several declarations with the same field names?
As a side note.
In general, I need to return data types similar to the above example.
First I returned them as tuples (seemed to me the correct way at the time). But tuples are hard to work with as it is impossible to extract individual parts of a complex type as easy as with the lists using "!!". So next thing I thought of the dictionaries/hashes.
When I tried using dictionaries I thought what is the point of having own data types then?
Playing/learning data types I encountered the fact that led me to the above question.
So it looks like it is easier for me to use dictionaries instead of own data types as I can use the same fields for different objects.
Can you please elaborate on this and tell me how it is done in real world?
Haskell record syntax is a bit of a hack, but the record name emerges as a function, and that function has to have a unique type. So you can share record-field names among constructors of a single datatype but not among distinct datatypes.
What is the correct way to deal with this if I have several declarations with the same field names?
You can't. You have to use distinct field names. If you want an overloaded name to select from a record, you can try using a type class. But basically, field names in Haskell don't work the way they do in say, C or Pascal. Calling it "record syntax" might have been a mistake.
But tuples are hard to work with as it is impossible to extract individual parts of a complex type
Actually, this can be quite easy using pattern matching. Example
smallId :: VmInfo -> Bool
smallId (VmInfo { vmId = n }) = n < 10
As to how this is done in the "real world", Haskell programmers tend to rely heavily on knowing what type each field is at compile time. If you want the type of a field to vary, a Haskell programmer introduces a type parameter to carry varying information. Example
data VmInfo a = VmInfo { vmId :: Int, vmName :: String, vmInfo :: a }
Now you can have VmInfo String, VmInfo Dictionary, VmInfo Node, or whatever you want.
Summary: each field name must belong to a unique type, and experienced Haskell programmers work with the static type system instead of trying to work around it. And you definitely want to learn about pattern matching.
There are more reasons why this doesn't work: lowercase typenames and data constructors, OO-language-style member access with .. In Haskell, those member access functions actually are free functions, i.e. vmName = name vm rather than vmName = vm.name, that's why they can't have same names in different data types.
If you really want functions that can operate on both VmInfo and HostInfo objects, you need a type class, such as
class MachineInfo m where
name :: m -> String
index :: m -> String -- why String anyway? Shouldn't this be an Int?
id :: m -> String
and make instances
instance MachineInfo VmInfo where
name (VmInfo vmName _ _) = vmName
index (VmInfo _ vmIndex _) = vmIndex
...
instance MachineInfo HostInfo where
...
Then name machine will work if machine is a VmInfo as well as if it's a HostInfo.
Currently, the named fields are top-level functions, so in one scope there can only be one function with that name. There are plans to create a new record system that would allow having fields of the same name in different record types in the same scope, but that's still in the design phase.
For the time being, you can make do with unique field names, or define each type in its own module and use the module-qualified name.
Lenses can help take some of the pain out of dealing with getting and setting data structure elements, especially when they get nested. They give you something that looks, if you squint, kind of like object-oriented accessors.
Learn more about the Lens family of types and functions here: http://lens.github.io/tutorial.html
As an example for what they look like, this is a snippet from the Pong example found at the above github page:
data Pong = Pong
{ _ballPos :: Point
, _ballSpeed :: Vector
, _paddle1 :: Float
, _paddle2 :: Float
, _score :: (Int, Int)
, _vectors :: [Vector]
-- Since gloss doesn't cover this, we store the set of pressed keys
, _keys :: Set Key
}
-- Some nice lenses to go with it
makeLenses ''Pong
That makes lenses to access the members without the underscores via some TemplateHaskell magic.
Later on, there's an example of using them:
-- Update the paddles
updatePaddles :: Float -> State Pong ()
updatePaddles time = do
p <- get
let paddleMovement = time * paddleSpeed
keyPressed key = p^.keys.contains (SpecialKey key)
-- Update the player's paddle based on keys
when (keyPressed KeyUp) $ paddle1 += paddleMovement
when (keyPressed KeyDown) $ paddle1 -= paddleMovement
-- Calculate the optimal position
let optimal = hitPos (p^.ballPos) (p^.ballSpeed)
acc = accuracy p
target = optimal * acc + (p^.ballPos._y) * (1 - acc)
dist = target - p^.paddle2
-- Move the CPU's paddle towards this optimal position as needed
when (abs dist > paddleHeight/3) $
case compare dist 0 of
GT -> paddle2 += paddleMovement
LT -> paddle2 -= paddleMovement
_ -> return ()
-- Make sure both paddles don't leave the playing area
paddle1 %= clamp (paddleHeight/2)
paddle2 %= clamp (paddleHeight/2)
I recommend checking out the whole program in its original location and looking through the rest of the lens material; it's very interesting even if you don't end up using them.
Yes, you cannot have two records in the same module with the same field names. The field names are added to the module's scope as functions, so you would use name vm rather than vm.name. You could have two records with the same field names in different modules and import one of the modules qualified as some name, but this is probably awkward to work with.
For a case like this, you should probably just use a normal algebraic data type:
data VMInfo = VMInfo String String String
(Note that the VMInfo has to be capitalized.)
Now you can access the fields of VMInfo by pattern matching:
myFunc (VMInfo name index id) = ... -- name, index and id are bound here
I'm aware of partial updates for records like :
data A a b = A { a :: a, b :: b }
x = A { a=1,b=2 :: Int }
y = x { b = toRational (a x) + 4.5 }
Are there any tricks for doing only partial initialization, creating a subrecord type, or doing (de)serialization on subrecord?
In particular, I found that the first of these lines works but the second does not :
read "A {a=1,b=()}" :: A Int ()
read "A {a=1}" :: A Int ()
You could always massage such input using a regular expression, but I'm curious what Haskell-like options exist.
Partial initialisation works fine: A {a=1} is a valid expression of type A Int (); the Read instance just doesn't bother parsing anything the Show instance doesn't output. The b field is initialised to error "...", where the string contains file/line information to help with debugging.
You generally shouldn't be using Read for any real-world parsing situations; it's there for toy programs that have really simple serialisation needs and debugging.
I'm not sure what you mean by "subrecord", but if you want serialisation/deserialisation that can cope with "upgrades" to the record format to contain more information while still being able to process old (now "partial") serialisations, then the safecopy library does just that.
You cannot leave some value in Haskell "uninitialized" (it would not be possible to "initialize" it later anyway, since Haskell is pure). If you want to provide "default" values for the fields, then you can make some "default" value for your record type, and then do a partial update on that default value, setting only the fields you care about. I don't know how you would implement read for this in a simple way, however.