Haskell Recursive Type - haskell

I am attempting to create a function in Haskell returning the Resp type illustrated below in a strange mix between BNF and Haskell types.
elem ::= String | (String, String, Resp)
Resp ::= [elem]
My question is (a) how to define this type in Haskell, and (b) if there is a way of doing so without being forced to use custom constructors, e.g., Node, rather using only tuples and arrays.

You said that "the variety of keywords (data, type, newtype) has been confusing for me". Here's a quick primer on the data construction keywords in Haskell.
Data
The canonical way to create a new type is with the data keyword. A general type in Haskell is a union of product types, each of which is tagged with a constructor. For example, an Employee might be a line worker (with a name and a salary) or a manager (with a name, salary and a list of reports).
We use the String type to represent an employee's name, and the Int type to represent a salaray. A list of reports is just a list of Employees.
data Employee = Worker String Int
| Manager String Int [Employee]
Type
The type keyword is used to create type synonyms, i.e. alternate names for the same type. This is typically used to make the source more immediately understandable. For example, we could declare a type Name for employee names (which is really just a String) and Salary for salaries (which are just Ints), and Reports for a list of reports.
type Name = String
type Salary = Int
type Reports = [Employee]
data Employee = Worker Name Salary
| Manager Name Salary Reports
Newtype
The newtype keyword is similar to the type keyword, but it adds an extra dash of type safety. One problem with the previous block of code is that, although a worker is a combination of a Name and a Salary, there is nothing to stop you using any old String in the Name field (for example, an address). The compiler doesn't distinguish between Names and plain old Strings, which introduces a class of potential bugs.
With the newtype keyword we can make the compiler enforce that the only Strings that can be used in a Name field are the ones explicitly tagged as Names
newtype Name = Name String
newtype Salary = Salary Int
newtype Reports = Reports [Employee]
data Employee = Worker Name Salary
| Manager Name Salary Reports
Now if we tried to enter a String in the Name field without explicitly tagging it, we get a type error
>>> let kate = Worker (Name "Kate") (Salary 50000) -- this is ok
>>> let fred = Worker "18 Tennyson Av." (Salary 40000) -- this will fail
<interactive>:10:19:
Couldn't match expected type `Name' with actual type `[Char]'
In the first argument of `Worker', namely `"18 Tennyson Av."'
In the expression: Worker "18 Tennyson Av." (Salary 40000)
In an equation for `fred':
fred = Worker "18 Tennyson Av." (Salary 40000)
What's great about this is that because the compiler knows that a Name is really just a String, it optimizes away the extra constructor, so this is just as efficient as using a type declaration -- the extra type safety comes "for free". This requires an important restriction -- a newtype has exactly one constructor with exactly one value. Otherwise the compiler wouldn't know which constructor or value was the correct synonym!
One disadvantage of using a newtype declaration is that now a Salary is no longer just an Int, you can't directly add them together. For example
>>> let kate'sSalary = Salary 50000
>>> let fred'sSalary = Salary 40000
>>> kate'sSalary + fred'sSalary
<interactive>:14:14:
No instance for (Num Salary)
arising from a use of `+'
Possible fix: add an instance declaration for (Num Salary)
In the expression: kate'sSalary + fred'sSalary
In an equation for `it': it = kate'sSalary + fred'sSalary
The somewhat complicated error message is telling you that a Salary isn't a numeric type, so you can't add them together (or at least, you haven't told the compiler how to add them together). One option would be to define a function that gets the underlying Int from the Salary
getSalary :: Salary -> Int
getSalary (Salary sal) = sal
but in fact Haskell will write these for you if you use record syntax when declaring your newtypes
data Salary = Salary { getSalary :: Int }
Now you can write
>>> getSalary kate'sSalary + getSalary fred'sSalary
90000

Part 1:
data Elem = El String | Node String String Resp
type Resp = [Elem]
Part 2: Well... kinda. The unsatisfying answer is: You shouldn't want to because doing so is less type safe. The more direct answer is Elem needs it's own constructor but Resp is easily defined as a type synonym as above. However, I would recommend
newtype Resp = Resp { getElems :: [Elem] }
so that you can't mix up some random list of Elems with a Resp. This also gives you the function getElems so you don't have to do as much pattern matching on a single constructor. The newtype basically let's Haskell know that it should get rid of the overhead of the constructor during runtime so there's no extra indirection which is nice.

Related

What do Haskell (data) constructors construct?

Haskell enables one to construct algebraic data types using type constructors and data constructors. For example,
data Circle = Circle Float Float Float
and we are told this data constructor (Circle on right) is a function that constructs a circle when give data, e.g. x, y, radius.
Circle :: Float -> Float -> Float -> Circle
My questions are:
What is actually constructed by this function, specifically?
Can we define the constructor function?
I've seen Smart Constructors but they just seem to be extra functions that eventually call the regular constructors.
Coming from an OO background, constructors, of course, have imperative specifications. In Haskell, they seem to be system-defined.
In Haskell, without considering the underlying implementation, a data constructor creates a value, essentially by fiat. “ ‘Let there be a Circle’, said the programmer, and there was a Circle.” Asking what Circle 1 2 3 creates is akin to asking what the literal 1 creates in Python or Java.
A nullary constructor is closer to what you usually think of as a literal. The Boolean type is literally defined as
data Boolean = True | False
where True and False are data constructors, not literals defined by Haskell grammar.
The data type is also the definition of the constructor; as there isn't really anything to a value beyond the constructor name and its arguments, simply stating it is the definition. You create a value of type Circle by calling the data constructor Circle with 3 arguments, and that's it.
A so-called "smart constructor" is just a function that calls a data constructor, with perhaps some other logic to restrict which instances can be created. For example, consider a simple wrapper around Integer:
newtype PosInteger = PosInt Integer
The constructor is PosInt; a smart constructor might look like
mkPosInt :: Integer -> PosInteger
mkPosInt n | n > 0 = PosInt n
| otherwise = error "Argument must be positive"
With mkPosInt, there is no way to create a PosInteger value with a non-positive argument, because only positive arguments actually call the data constructor. A smart constructor makes the most sense when it, and not the data constructor, is exported by a module, so that a typical user cannot create arbitrary instances (because the data constructor does not exist outside the module).
Good question. As you know, given the definition:
data Foo = A | B Int
this defines a type with a (nullary) type constructor Foo and two data constructors, A and B.
Each of these data constructors, when fully applied (to no arguments in the case of A and to a single Int argument in the case of B) constructs a value of type Foo. So, when I write:
a :: Foo
a = A
b :: Foo
b = B 10
the names a and b are bound to two values of type Foo.
So, data constructors for type Foo construct values of type Foo.
What are values of type Foo? Well, first of all, they are different from values of any other type. Second, they are wholly defined by their data constructors. There is a distinct value of type Foo, different from all other values of Foo, for each combination of a data constructor with a set of distinct arguments passed to that data constructor. That is, two values of type Foo are identical if and only if they were constructed with the same data constructor given identical sets of arguments. ("Identical" here means something different from "equality", which may not necessarily be defined for a given type Foo, but let's not get into that.)
That's also what makes data constructors different from functions in Haskell. If I have a function:
bar :: Int -> Bool
It's possible that bar 1 and bar 2 might be exactly the same value. For example, if bar is defined by:
bar n = n > 0
then it's obvious that bar 1 and bar 2 (and bar 3) are identically True. Whether the value of bar is the same for different values of its arguments will depend on the function definition.
In contrast, if Bar is a constructor:
data BarType = Bar Int
then it's never going to be the case that Bar 1 and Bar 2 are the same value. By definition, they will be different values (of type BarType).
By the way, the idea that constructors are just a special kind of function is a common viewpoint. I personally think this is inaccurate and causes confusion. While it's true that constructors can often be used as if they are functions (specifically that they behave very much like functions when used in expressions), I don't think this view stands up under much scrutiny -- constructors are represented differently in the surface syntax of the language (with capitalized identifiers), can be used in contexts (like pattern matching) where functions cannot be used, are represented differently in compiled code, etc.
So, when you ask "can we define the constructor function", the answer is "no", because there is no constructor function. Instead, a constructor like A or B or Bar or Circle is what it is -- something different from a function (that sometimes behaves like a function with some special additional properties) which is capable of constructing a value of whatever type the data constructor belongs to.
This makes Haskell constructors very different from OO constructors, but that's not surprising since Haskell values are very different from OO objects. In an OO language, you can typically provide a constructor function that does some processing in building the object, so in Python you might write:
class Bar:
def __init__(self, n):
self.value = n > 0
and then after:
bar1 = Bar(1)
bar2 = Bar(2)
we have two distinct objects bar1 and bar2 (which would satify bar1 != bar2) that have been configured with the same field values and are in some sense "equal". This is sort of halfway between the situation above with bar 1 and bar 2 creating two identical values (namely True) and the situation with Bar 1 and Bar 2 creating two distinct values that, by definition, can't possibly be the "same" in any sense.
You can never have this situation with Haskell constructors. Instead of thinking of a Haskell constructor as running some underlying function to "construct" an object which might involve some cool processing and deriving of field values, you should instead think of a Haskell constructor as a passive tag attached to a value (which may also contain zero or more other values, depending on the arity of the constructor).
So, in your example, Circle 10 20 5 doesn't "construct" an object of type Circle by running some function. It directly creates a tagged object that, in memory, will look something like:
<Circle tag>
<Float value 10>
<Float value 20>
<Float value 5>
(or you can at least pretend that's what it looks like in memory).
The closest you can come to OO constructors in Haskell is using smart constructors. As you note, eventually a smart constructor just calls a regular constructor, because that's the only way to create a value of a given type. No matter what kind of bizarre smart constructor you build to create a Circle, the value it constructs will need to look like:
<Circle tag>
<some Float value>
<another Float value>
<a final Float value>
which you'll need to construct with a plain old Circle constructor call. There's nothing else the smart constructor could return that would still be a Circle. That's just how Haskell works.
Does that help?
I’m going to answer this in a somewhat roundabout way, with an example that I hope illustrates my point, which is that Haskell decouples several distinct ideas that are coupled in OOP under the concept of a “class”. Understanding this will help you translate your experience from OOP into Haskell with less difficulty. The example in OOP pseudocode:
class Person {
private int id;
private String name;
public Person(int id, String name) {
if (id == 0)
throw new InvalidIdException();
if (name == "")
throw new InvalidNameException();
this.name = name;
this.id = id;
}
public int getId() { return this.id; }
public String getName() { return this.name; }
public void setName(String name) { this.name = name; }
}
In Haskell:
module Person
( Person
, mkPerson
, getId
, getName
, setName
) where
data Person = Person
{ personId :: Int
, personName :: String
}
mkPerson :: Int -> String -> Either String Person
mkPerson id name
| id == 0 = Left "invalid id"
| name == "" = Left "invalid name"
| otherwise = Right (Person id name)
getId :: Person -> Int
getId = personId
getName :: Person -> String
getName = personName
setName :: String -> Person -> Either String Person
setName name person = mkPerson (personId person) name
Notice:
The Person class has been translated to a module which happens to export a data type by the same name—types (for domain representation and invariants) are decoupled from modules (for namespacing and code organisation).
The fields id and name, which are specified as private in the class definition, are translated to ordinary (public) fields on the data definition, since in Haskell they’re made private by omitting them from the export list of the Person module—definitions and visibility are decoupled.
The constructor has been translated into two parts: one (the Person data constructor) that simply initialises the fields, and another (mkPerson) that performs validation—allocation & initialisation and validation are decoupled. Since the Person type is exported, but its constructor is not, this is the only way for clients to construct a Person—it’s an “abstract data type”.
The public interface has been translated to functions that are exported by the Person module, and the setName function that previously mutated the Person object has become a function that returns a new instance of the Person data type that happens to share the old ID. The OOP code has a bug: it should include a check in setName for the name != "" invariant; the Haskell code can avoid this by using the mkPerson smart constructor to ensure that all Person values are valid by construction. So state transitions and validation are also decoupled—you only need to check invariants when constructing a value, because it can’t change thereafter.
So as for your actual questions:
What is actually constructed by this function, specifically?
A constructor of a data type allocates space for the tag and fields of a value, sets the tag to which constructor was used to create the value, and initialises the fields to the arguments of the constructor. You can’t override it because the process is completely mechanical and there’s no reason (in normal safe code) to do so. It’s an internal detail of the language and runtime.
Can we define the constructor function?
No—if you want to perform additional validation to enforce invariants, you should use a “smart constructor” function which calls the lower-level data constructor. Because Haskell values are immutable by default, values can be made correct by construction; that is, when you don’t have mutation, you don’t need to enforce that all state transitions are correct, only that all states themselves are constructed correctly. And often you can arrange your types so that smart constructors aren’t even necessary.
The only thing you can change about the generated data constructor “function” is making its type signature more restrictive using GADTs, to help enforce more invariants at compile-time. And as a side note, GADTs also let you do existential quantification, which lets you carry around encapsulated/type-erased information at runtime, exactly like an OOP vtable—so this is another thing that’s decoupled in Haskell but coupled in typical OOP languages.
Long story short (too late), you can do all the same things, you just arrange them differently, because Haskell provides the various features of OOP classes under separate orthogonal language features.

Is "RGB Int Int Int | Transparent" a sum or product type?

Sum type
The Maybe Int type is a sum type.
data Maybe Int = Nothing | Just Int
From my understanding, this is due to the fact that the Nothing value constructor takes no arguments and the second value constructor called Just takes only one argument. Therefore, because no value constructor takes more than one argument, this type is a product type.
Product type
The type below is a product type since its data constructor takes two arguments and therefore is a product type.
data Colour = Person String Int
However, I am not sure how we would classify the following type in the context of the sum and product types. How should we refer to this?
data Shade = RGB Int Int Int | Transparent
All data types are "sums of products".
We sum over the number of constructors, and for each constructor we multiply over the number of arguments.
Sometimes the sum is trivial. When there is a single constructor, or none at all, we sum over a singleton or empty set. Summing over a single constructor makes the resulting type isomorphic to a product. Summing over no constructors makes the type to be empty (e.g. Data.Void.Void).
Sometimes, some of the products are trivial as well. When there is a single argument, or none at all, we multiply over a singleton or empty set. Multiplying over a single argument T simply produces T (after lifting). Multiplying over no arguments produces a type with only one value (e.g. ()).
Hence, sometimes our data is a non-trivial sum of trivial products, and we call it a "sum"; sometimes it is a trivial sum of non-trivial products, and we call it a "product". But, in the general case, it is always a "sum of products".
Note that algebraic types (up to isomorphism) form a commutative semiring, satisfying roughly the same laws of high school algebra for sums and products. In high school algebra, we can turn any expression involving nested sums and products into a polynomial, i.e. into a "sum of products". This also happens with types (up to isomorphism), hence the choice of making data types to be "sums of products" is rather expressive.
The Maybe Int type is a sum type because it has an alternation
data SumType = This | That
the fact that it has arguments on its constructors doesn't affect its "sum-ness." Sum types can also contain product constructors, such as:
type Username = String
type Email = String
-- User is a sum of three products
data User = NotLoggedIn -- nullary constructor
| Guest Username -- unary constructor
| RegisteredUser Username Email -- binary constructor

Path dependent types in Haskell

I am trying to design an API for some database system in Haskell, and I would like to model the columns of this database in a way such that interactions between columns of different tables cannot get mixed up.
More precisely, imagine that you have a type to represent a table in a database, associated to some type:
type Table a = ...
and that you can extract the columns of the table, along with the type of the column:
type Column col = ...
Finally, there are various extractors. For example, if your table contains descriptions of frogs, a function would let you extract the column containing the weight of the frog:
extractCol :: Table Frog -> Column Weight
Here is the question: I would like to distinguish the origin of the columns so that users cannot do operations between tables. For example:
bullfrogTable = undefined :: Table Frog
toadTable = undefined :: Table Frog
bullfrogWeights = extractCol bullfrogTable
toadWeights = extractCol toadTable
-- Or some other columns from the toad table
toadWeights' = extractCol toadTable
-- This should compile
addWeights toadWeights' toadWeights
-- This should trigger a type error
addWeights bullfrogWeights toadWeights
I know how to achieve this in Scala (using path-dependent types, see [1]), and I have been thinking of 3 options in Haskell:
not using types, and just doing a check at runtime (the current solution)
the TypeInType extension to add a phantom type on the Table type itself, and pass this extra type to the columns. I am not keen on it, because the construction of such a type would be very complicated (tables are generated through complex DAG operations) and probably slow to compile in this context.
wrapping the operations using a forall construct similar to the ST monad, but in my case, I would like the extra tagging type to actually escape the construction.
I am happy to have a very limited valid scoping for the construction of the same columns (i.e. columns from table and (id table) not being mixable), and I mostly care about the DSL feel of the API rather than the safety.
[1] What is meant by Scala's path-dependent types?
My current solution
Here is what I ended up doing, using RankNTypes.
I still want to give users the ability to use columns how they see fit without having some strong type checks, and opt in if they want some stronger type guarantees: this is a DSL for data scientist who will not know the power of the Haskell side
Tables are still tagged by their content:
type Table a = ...
and columns are now tagged with some extra reference types, on top of the type of the data they contain:
type Column ref col = ...
Projections from tables to columns are either tagged or untagged. In practice, this is hidden behind a lens-like DSL.
extractCol :: Table Frog -> Column Frog Weight
data TaggedTable ref a = TaggedTable { _ttTable :: Table a }
extractColTagged :: Table ref Frog -> Column ref Weight
withTag :: Table a -> (forall ref. TaggedTable ref a -> b) -> b
withTag tb f = f (TaggedTable tb)
Now I can write some code as following:
let doubleToadWeights = withTag toadTable $ \ttoadTable ->
let toadWeights = extractColTagged ttoadTable in
addWeights toadWeights toadWeights
and this will not compile, as desired:
let doubleToadWeights =
toadTable `withTag` \ttoads ->
bullfrogTable `withTag` \tbullfrogs ->
let toadWeights = extractColTagged ttoads
bullfrogWeights = extractColTagged tbullfrogs
in addWeights toadWeights bullfrogWeights -- Type error
From a DSL perspective, I believe it is not as straightforward as what one could achieve with Scala, but the type error message is understandable, which is paramount for me.
Haskell does not (as far as I know) have path dependent types, but you can get some of the way by using rank 2 types. For instance the ST monad has a dummy type parameter s that is used to prevent leakage between invocations of runST:
runST :: (forall s . ST s a) -> a
Within an ST action you can have an STRef:
newSTRef :: a -> ST s (STRef s a)
But the STRef you get carries the s type parameter, so it isn't allowed to escape from the runST.

Haskell record accessors shared by different constructors of the same data type

A basic question about Haskell records. If I define this datatype,
data Pet = Dog { name :: String } | Cat { name :: String } deriving (Show)
the following works:
main = do
let d = Dog { name = "Spot" }
c = Cat { name = "Morris" }
putStrLn $ name d
putStrLn $ name c
But if I do this,
data Pet = Dog { name :: String } | Cat { name :: Integer } deriving (Show)
I'll get this error: Multiple declarations of 'name'.
I think I understand intuitively why this should be the case, since the type of name in the first case is just Pet -> String regardless of the constructor that was used. But I don't recall seeing this rule about record accessor functions in any of the Haskell books I've read. Can someone give a slightly more in-depth explanation about the behavior I'm seeing above?
From the Haskell '98 Report:
A data declaration may use the same field label in multiple constructors as long as the typing of the field is the same in all cases after type synonym expansion. A label cannot be shared by more than one type in scope. Field names share the top level namespace with ordinary variables and class methods and must not conflict with other top level names in scope.
I don't think there's anything more in-depth to it. As you said, the resulting field accessor has the type Pet -> String anyway so the powers that be decided it convenient to allow you to re-use the same field name in different constructors.

Haskell: Confusion with own data types. Record syntax and unique fields

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

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