I have got an error: Not a data constructor: "%:":
data KV = forall a. Show a => (%:) Text a
Interestingly, but :% is fine as data constructor! %% is not fine again. But %% is fine to be infix function. Why is it treating as an error? What is the difference between these variants?
It's not a valid name for a data constructor. All infix operator data constructors must start with :. So (:%) would be fine.
This is just the operator equivalent of "constructors must start with capital letters", as a syntactic means to distinguish constructors from other names when pattern matching.
Related
I had previously asked where the Winery types are indexed. I noticed that in the serialization for the schema for Bool, which is [4,6], the 4 is the version number, and 6 is the index of SBool in SchemaP. I verified the hypothesis using other "primitive" types like Integer (serialization: 16), Double (18), Text (20). Also, [Bool] will be SVector SBool, serialized to [4,2,6], which makes sense: the 2 is for SVector, the 6 is for SBool.
But SchemaP also contains constructors that I don't intuitively see how are used: SFix, SVar, STag and SLet. What are they, and which type would I need to construct the schema for, to see them used? Why is SLet at the end, but SFix at the beginning?
SFix looks like a µ quantifier for a recursive type. The type µx. T is the type T where x refers to the whole type µx. T. For example, a list data List a = Nil | Cons a (List a) can be represented as L(a) = µr. 1 + a × r, where the recursive occurrence of the type is replaced with the variable r. You could probably see this with a recursive user-defined type like data BinTree a = Leaf | Branch a (BinTree a) (BinTree a).
This encoding doesn’t explicitly include a variable name, because the next constructor SVar specifies that “SVar n refers to the nth innermost fixpoint”, where n is an Int in the synonym type Schema = SchemaP Int. This is a De Bruijn index. If you had some nested recursive types like µx. µy. … = SFix (SFix …), then the inner variable would be referenced as SVar 0 and the outer one as SVar 1 within the body …. This “relative” notation means you can freely reorganise terms without worrying about having to rename variables for capture-avoiding substitution.
SLet is a let binding, and since it’s specified as SLet !(SchemaP a) !(SchemaP a), I presume that SLet e1 e2 is akin to let x = e1 in e2, where the variable is again implicit. So I suspect this may be a deficiency of the docs, and SVar can also refer to Let-bound variables. I don’t know how they use this constructor, but it could be used to make sharing explicit in the schema.
Finally, STag appears to be a way to attach extra “tag” metadata within the schema, in some way that’s specific to the library.
The ordering of these constructors might be maintained for compatibility with earlier versions, so adding new constructors at the end would avoid disturbing the encoding, and I figure the STag and SLet constructors at the end were simply added later.
Take a data type declaration like
data myType = Null | Container TypeA v
As I understand it, Haskell would read this as myType coming in two different flavors. One of them is Null which Haskell interprets just as some name of a ... I guess you'd call it an instance of the type? Or a subtype? Factor? Level? Anyway, if we changed Null to Nubb it would behave in basically the same way--Haskell doesn't really know anything about null values.
The other flavor is Container and I would expect Haskell to read this as saying that the Container flavor takes two fields, TypeA and v. I expect this is because, when making this type definition, the first word is always read as the name of the flavor and everything that follows is another field.
My question (besides: did I get any of that wrong?) is, how does Haskell know that TypeA is a specific named type rather than an un-typed variable? Am I wrong to assume that it reads v as an un-typed variable, and if that's right, is it because of the lower-case initial letter?
By un-typed I mean how the types appear in the following type-declaration for a function:
func :: a -> a
func a = a
First of all, terminology: "flavors" are called "cases" or "constructors". Your type has two cases - Null and Container.
Second, what you call "untyped" is not really "untyped". That's not the right way to think about it. The a in declaration func :: a -> a does not mean "untyped" the same way variables are "untyped" in JavaScript or Python (though even that is not really true), but rather "whoever calls this function chooses the type". So if I call func "abc", then I have chosen a to be String, and now the compiler knows that the result of this call must also be String, since that's what the func's signature says - "I take any type you choose, and I return the same type". The proper term for this is "generic".
The difference between "untyped" and "generic" is that "untyped" is free-for-all, the type will only be known at runtime, no guarantees whatsoever; whereas generic types, even though not precisely known yet, still have some sort of relationship between them. For example, your func says that it returns the same type it takes, and not something random. Or for another example:
mkList :: a -> [a]
mkList a = [a]
This function says "I take some type that you choose, and I will return a list of that same type - never a list of something else".
Finally, your myType declaration is actually illegal. In Haskell, concrete types have to be Capitalized, while values and type variables are javaCase. So first, you have to change the name of the type to satisfy this:
data MyType = Null | Container TypeA v
If you try to compile this now, you'll still get an error saying that "Type variable v is unknown". See, Haskell has decided that v must be a type variable, and not a concrete type, because it's lower case. That simple.
If you want to use a type variable, you have to declare it somewhere. In function declaration, type variables can just sort of "appear" out of nowhere, and the compiler will consider them "declared". But in a type declaration you have to declare your type variables explicitly, e.g.:
data MyType v = Null | Container TypeA v
This requirement exist to avoid confusion and ambiguity in cases where you have several type variables, or when type variables come from another context, such as a type class instance.
Declared this way, you'll have to specify something in place of v every time you use MyType, for example:
n :: MyType Int
n = Null
mkStringContainer :: TypeA -> String -> MyType String
mkStringContainer ta s = Container ta s
-- Or make the function generic
mkContainer :: TypeA -> a -> MyType a
mkContainer ta a = Container ta a
Haskell uses a critically important distinction between variables and constructors. Variables begin with a lower-case letter; constructors begin with an upper-case letter1.
So data myType = Null | Container TypeA v is actually incorrect; the first symbol after the data keyword is the name of the new type constructor you're introducing, so it must start with a capital letter.
Assuming you've fixed that to data MyType = Null | Container TypeA v, then each of the alternatives separated by | is required to consist of a data constructor name (here you've chosen Null and Container) followed by a type expression for each of the fields of that constructor.
The Null constructor has no fields. The Container constructor has two fields:
TypeA, which starts with a capital letter so it must be a type constructor; therefore the field is of that concrete type.
v, which starts with a lowercase letter and is therefore a type variable. Normally this variable would be defined as a type parameter on the MyType type being defined, like data MyType v = Null | Container TypeA v. You cannot normally use free variables, so this was another error in your original example.2
Your data declaration showed how the distinction between constructors and variables matters at the type level. This distinction between variables and constructors is also present at the value level. It's how the compiler can tell (when you're writing pattern matches) which terms are patterns it should be checking the data against, and which terms are variables that should be bound to whatever the data contains. For example:
lookAtMaybe :: Show a => Maybe a -> String
lookAtMaybe Nothing = "Nothing to see here"
lookAtMaybe (Just x) = "I found: " ++ show x
If Haskell didn't have the first-letter rule, then there would be two possible interpretations of the first clause of the function:
Nothing could be a reference to the externally-defined Nothing constructor, saying I want this function rule to apply when the argument matches that constructor. This is the interpretation the first-letter rule mandates.
Nothing could be a definition of an (unused) variable, representing the function's argument. This would be the equivalent of lookAtMaybe x = "Nothing to see here"
Both of those interpretations are valid Haskell code producing different behaviour (try changing the capital N to a lower case n and see what the function does). So Haskell needs a rule to choose between them. The designers chose the first-letter rule as a way of simply disambiguating constructors from variables (that is simple to both the compiler and to human readers) without requiring any additional syntactic noise.
1 The rule about the case of the first letter applies to alphanumeric names, which can only consist of letters, numbers, and underscores. Haskell also has symbolic names, which consists only of symbol characters like +, *, :, etc. For these, the rule is that names beginning with the : character are constructors, while names beginning with another character are variables. This is how the list constructor : is distinguished from a function name like +.
2 With the ExistentialQuantification extension turned on it is possible to write data MyType = Null | forall v. Container TypeA v, so that the the constructor has a field with a variable type and the variable does not appear as a parameter to the overall type. I'm not going to explain how this works here; it's generally considered an advanced feature, and isn't part of standard Haskell code (which is why it requires an extension)
From LYAH book, parameterizing type synonyms:
I would understand:
type MyName = String
But this example I don't get:
type IntMap v = Map Int v -- let alone it can be shortened
'Map' is a function, not a type, right? This got me in loops in the book constantly now. Next to that: Map would require a function and a list to work, correct? If so, and 'v' is the list, what is the 'Int'?
Map is the name of a type. It's an associative array and maps values of type T to values of type K. So IntMap is the type of a Map which has Int keys and v values. Maps are also known as dictionaries in some languages. They're implemented by hash tables, balanced trees or other more exotic data structures.
It's an unfortunate name collision that there's also the map function. They kind of do the same thing, only in different contexts. map transforms values in the input by applying a function to them, whereas Map transforms input keys to output values.
There is a type named Map (with a capital "M"). There is also a function named map (with a lowercase "M"). These are unrelated other than having kind-of similar names. Try not to confuse them. ;-)
I am currently working on a homework for a lecture in which I have to write a Interpreter for a language we defined in the lecture. Part of my homework is to write a function that will take an expression from my datatype and turn it into a string.
Here is my datatype so far:
datatype basicType = voidType | intType | boolType;
datatype etype = basicType
| tupelType of (etype * etype)
| functionType of etype -> basicType;
Note that I am not even sure that this datatype is correct.
I am allowed to use the SML functions String.concatWith and Int.toString.
Since this is a homework I should do I like to only get a start and tips and tricks. No full blown solutions please.
I am thankfull for any input from you girls/guys since I am about to lose my sanity from this lecture.
You need to implement a function that can print all variants of etype by recursing into each value. You also need a helper function for printing basicType values, bot it does not need to be recursive but instead act as the base case in your recursion.
Both of them need one function body for each variant of the respective datatype. The body handling the functionType would also need to apply the function.
You should also think about addnig some extra string output in each function body to make it possible for the reader to distinguish between the different types.
The tupelType could for example be printed something like this: (a, b) where a and b are recursive calls into each of the tuple elements.
I've declared a recursive data type with the following structure:
data Path = GET | POST | Slash Path String
I'd really like to rename that last value constructor to / so that I can infix it in cute expressions like GET /"controller"/"action". However, if I try to do so:
import Prelude hiding ((/))
infixr 5 /
data Path = GET | POST | Path / String
...then I get this:
Path.hs:4:30: parse error on input `/'
Those same three lines compile just fine if I replace / with :/ or any other special character sequence beginning with :.
So, is there any way I can name my value constructor /? I know that I can just name it Slash and then declare a separate function:
(/) :: Path -> String -> Path
(/) = Slash
...but that won't let me pattern match, as in:
request :: Path -> String
request path = case path of GET /"hello" -> "Hello!"
GET /"goodbye" -> "Goodbye!"
Short answer: No.
Long answer: Type classes, type names, and data constructors must begin with either a capital letter or a colon (some of this requires using a language extension). Everything else must begin with a lowercase letter or any other allowed symbol.
Note that type variables, which are normally lowercase identifiers, follow the same rules and do not begin with a colon.
See also the GHC user's guide for enabling type operators. Data constructors are always allowed, I think.
Personally, in your case I'd just use (:/). It doesn't look that bad, and after a while you get used to ignoring the colons. Some people like a trailing colon as well, especially if the data is "symmetric" in some sense.
No, you can't do this. In pure Haskell 98, user-defined type names and constructors must be alphanumeric and begin with an uppercase letter; this is in section 4.1.2 of the Haskell 98 Report. In GHC, just as user-defined constructors with alphanumeric names must begin with an uppercase letter, user-defined constructors which are operators must begin with a :.1 (The same is true for user-defined type names.) This is documented in section 7.4.2 of the GHC manual. I'd probably use :/, myself, with or without / as a synonym.
1: The reason for the "user-defined" qualification is that there are a few built-in exceptions: ->, [], (), and the tuple types (,), (,,), etc. as type names; and () and the tuple type constructors (,), (,,), etc., as type constructors
I think all constructor operators need to start with a colon, (but I may be wrong).
So you could do:
data Path = GET | POST | Path :/ String