I try to understand this line:
query : SelectionSet Response RootQuery
I understand this is a "Type Annotations" syntax, but I don't find documentation example or explanation about multiple "word" separated by whitespace.
I see these examples:
answer : Int
factorial : Int -> Int
distance : { x : Float, y : Float } -> Float
add : number -> number -> number (ref)
I found anywhere query: Int Int Int syntax, neither in Elm Syntax nor in Beginning Elm nor in Elm FAQ.
Do SelectionSet, Response, RootQuery are
functions arguments?
multi value function results?
Best regards,
Stéphane
Same question on Elm Discourse
A response in How do I read the type of a SelectionSet?
SelectionSet is a type with two type variables. Here's the definition:
type SelectionSet decodesTo scope
= SelectionSet (List RawField) (Decoder decodesTo)
In a type declaration like this, any lowercase name after the type is a type variable, which can be filled in by any type (except for a few special constrained type variables, number, appendable, comparable, and compappend). A simpler example would be Maybe, where you can have a Maybe Int or a Maybe String. Similarly, Dict takes two type variables (for the key and value) so you can have Dict String String or Dict Int MyCustomType (the key type of a Dict does need to be comparable).
So, in your scenario, Response corresponds to decodesTo and RootQuery corresponds to scope. The SelectionSet has a Decoder that decodes to a Response value, and it also carries around this scope type variable, which isn't used directly in the data that it holds. It's used as a piece of information at the type level, so that you (and the library) know that calling map (which has the type (a -> b) -> SelectionSet a scope -> SelectionSet b scope) will preserve that scope value; that is, it prevents mixing scopes.
The above is mostly general function syntax for functional languages such as Haskell, Elm, etc.
For example:
add : Int -> Int -> Int
add x y = x + y
The first line says that is function of two integer arguments with an integer return value. The second line implements the specification given in the first. One calls this function as follows:
> add 2 3
5
Note this example:
> inc = add 1
> inc 2
3
Here add 1 is a "partially applied function." It has type Int -> Int. In many languages, add 1 would not make sense. But since functions are first-class things in Elm, add 1 makes sense: it is a function. Partial application is also called "currying."
Related
I'm trying to write a version of Printf.printf that always appends a newline character after writing its formatted output. My first attempt was
# let say fmt = Printf.ksprintf print_endline fmt;;
val say : ('a, unit, string, unit) format4 -> 'a = <fun>
The type signature looks right and say works as expected. I noticed that fmt is listed twice, and thought that partial application could eliminate it. So I tried this instead:
# let say = Printf.ksprintf print_endline;;
val say : ('_weak1, unit, string, unit) format4 -> '_weak1 = <fun>
The function definition looks cleaner, but the type signature looks wrong and say no longer works as expected. For example, say doesn't type check if the format string needs a variable number of arguments: I get an error that say "is applied to too many arguments".
I can use the let say fmt = … implementation, but why doesn't partial application work?
OCaml's type-checker loses polymorphism during partial application. That is, when you partially apply a function, the resulting function is no longer polymorphic. That's why you see '_weak1 in the second type signature.
When you include the fmt argument, you help the type-checker recognize that polymorphism is still present.
This process is called "eta conversion." Removing your fmt argument is "eta reduction" and adding it back in is called "eta expansion." You may encounter that terminology when working with other functional programming languages.
This is the value restriction at work: https://ocaml.org/manual/polymorphism.html#s:weak-polymorphism . In brief, only syntactic values can be safely generalized in let-binding in presence of mutable variables in the language.
In particular,
let f = fun x -> g y x
is a syntactic value that can be generalized, whereas
let f = g y
is a computation that cannot (always) be generalized.
A example works quite well to illustrate the issue, consider:
let fake_pair x =
let store = ref None in
fun y ->
match !store with
| None ->
store := Some y;
x, y
| Some s ->
x, s
then the type of fake_pair is 'a -> 'b -> 'a * 'b.
However, once partially applied
let p = fake_pair 0
we have initialized the store mutable value, and it is important that all subsequent call to p share the same type (because they must match the stored value). Thus the type of p is '_weak1 -> int * '_weak1 where '_weak1 is a weak type variable, aka a temporary placeholder for a concrete type.
So for example:
var a = true
val test = if (a) -1 else -3.2
I was expecting the Type of the test should be the most closest intersection of the type-hierarchy i.e. for Int and Double is Number.
But looking at the IDE, it seems to have a type of {Comparable<{ Double & Int }> & Number}.
And the weird thing is, I cannot specify it like that (since {} is reserved for creating lambdas), I can only set it to a type of Number.
And another wierd thing is that if I try some function from Comparable interface, it throws some error:
// Warning at value 2
// The integer literal does not conform to the expected type {Double & Int}
test.compareTo(2)
3.compareTo(-1.1) // possible
2.3.compareTo(100) // possible
// But why not this is possible, while it has inferred type of Comparable?
test.compareTo(2)
Could somebody help in understanding the concept here? And few questions:
How does that type work all together, i.e. how could one variable hold two types at once?
How could one specify that type explicitly?
How do you use functions from Comparable interface, when test has implementaion of it?
& here means an intersection type (which isn't supported in the Kotlin language itself, but the compiler uses them internally). You can see it mentioned in the (incomplete) specification.
Intersection types are special non-denotable types used to express the fact that a value belongs to all of several types at the same time.
"Non-denotable" means exactly that you can't specify that type. I am not sure but I think the extra { } in types are supposed to indicate exactly this.
In particular, Comparable<Double & Int> means you can only compare test to something which is both Double and Int, but there are no such values. The compiler could probably simplify it to Comparable<Nothing>.
the most closest intersection of the type-hierarchy i.e. for Int and Double is Number.
It's least upper bound, which is closer to union, not intersection. The specification actually calls it "union types", but that's not the normal usage of that term.
This least upper bound is not Number because it also takes least upper bound of the Comparable interfaces which works out to Comparable<Double & Int> because Comparable is contravariant:
lub(Int, Double) =
Number & lub(Comparable<Int>, Comparable<Double>) =
Number & Comparable<Int & Double>
This calculation is described under type decaying:
All union types are subject to type decaying, when they are converted to a specific intersection type, representable within Kotlin type system.
The answer to question 1 is that the compiler is doing its best to infer the type, inventing new constraints to describe it as it goes.
The answer to question 2 is that you cannot.
The answer to question 3 is that you cannot, because Int is not comparable to Double and vice versa. So none of the methods from Comparable are actually usable, but the value definitely implements Comparable against something. This is not useful for Comparable, but could be for another interface. For example, imagine:
interface ZeroAndComparable<T> {
fun compareTo(t: T): Int
fun zero(): T
}
val foo : ZeroAndComparable<Int> = someZeroAndComparableInt()
val bar : ZeroAndComparable<Double> = someZeroAndComparableDouble()
val foobar = if (a) foo else bar
val zero : Any = foobar.zero() // should work
foobar.compareTo(something) // cannot work
In F#, I'd simply do:
> let x = Set.empty;;
val x : Set<'a> when 'a : comparison
> Set.add (2,3) x;;
val it : Set<int * int> = set [(2, 3)]
I understand that in OCaml, when using Base, I have to supply a module with comparison functions, e.g., if my element type was string
let x = Set.empty (module String);;
val x : (string, String.comparator_witness) Set.t = <abstr>
Set.add x "foo";;
- : (string, String.comparator_witness) Set.t = <abstr>
But I don't know how to construct a module that has comparison functions for the type int * int. How do I construct/obtain such a module?
To create an ordered data structure, like Map, Set, etc, you have to provide a comparator. In Base, a comparator is a first-class module (a module packed into a value) that provides a comparison function and a type index that witnesses this function. Wait, what? Later on that, let us first define a comparator. If you already have a module that has type
module type Comparator_parameter = sig
type t (* the carrier type *)
(* the comparison function *)
val compare : t -> t -> int
(* for introspection and debugging, use `sexp_of_opaque` if not needed *)
val sexp_of_t : t -> Sexp.t
end
then you can just provide to the Base.Comparator.Make functor and build the comparator
module Lexicographical_order = struct
include Pair
include Base.Comparator.Make(Pair)
end
where the Pair module provides the compare function,
module Pair = struct
type t = int * int [##deriving compare, sexp_of]
end
Now, we can use the comparator to create ordered structures, e.g.,
let empty = Set.empty (module Lexicographical_order)
If you do not want to create a separate module for the order (for example because you can't come out with a good name for it), then you can use anonymous modules, like this
let empty' = Set.empty (module struct
include Pair
include Base.Comparator.Make(Pair)
end)
Note, that the Pair module, passed to the Base.Comparator.Make functor has to be bound on the global scope, otherwise, the typechecker will complain. This is all about this witness value. So what this witness is about and what it witnesses.
The semantics of any ordered data structure, like Map or Set, depends on the order function. It is an error to compare two sets which was built with different orders, e.g., if you have two sets built from the same numbers, but one with the ascending order and another with the descending order they will be treated as different sets.
Ideally, such errors should be prevented by the type checker. For that we need to encode the order, used to build the set, in the set's type. And this is what Base is doing, let's look into the empty' type,
val empty' : (int * int, Comparator.Make(Pair).comparator_witness) Set.t
and the empty type
val empty : (Lexicographical_order.t, Lexicographical_order.comparator_witness) Set.t
Surprisingly, the compiler is able to see through the name differences (because modules have structural typing) and understand that Lexicographical_order.comparator_witness and Comparator.Make(Pair).comparator_witness are witnessing the same order, so we can even compare empty and empty',
# Set.equal empty empty';;
- : bool = true
To solidify our knowledge lets build a set of pairs in the reversed order,
module Reversed_lexicographical_order = struct
include Pair
include Base.Comparator.Make(Pair_reveresed_compare)
end
let empty_reveresed =
Set.empty (module Reversed_lexicographical_order)
(* the same, but with the anonyumous comparator *)
let empty_reveresed' = Set.empty (module struct
include Pair
include Base.Comparator.Make(Pair_reveresed_compare)
end)
As before, we can compare different variants of reversed sets,
# Set.equal empty_reversed empty_reveresed';;
- : bool = true
But comparing sets with different orders is prohibited by the type checker,
# Set.equal empty empty_reveresed;;
Characters 16-31:
Set.equal empty empty_reveresed;;
^^^^^^^^^^^^^^^
Error: This expression has type
(Reversed_lexicographical_order.t,
Reversed_lexicographical_order.comparator_witness) Set.t
but an expression was expected of type
(Lexicographical_order.t, Lexicographical_order.comparator_witness) Set.t
Type
Reversed_lexicographical_order.comparator_witness =
Comparator.Make(Pair_reveresed_compare).comparator_witness
is not compatible with type
Lexicographical_order.comparator_witness =
Comparator.Make(Pair).comparator_witness
This is what comparator witnesses are for, they prevent very nasty errors. And yes, it requires a little bit of more typing than in F# but is totally worthwhile as it provides more typing from the type checker that is now able to detect real problems.
A couple of final notes. The word "comparator" is an evolving concept in Janestreet libraries and previously it used to mean a different thing. The interfaces are also changing, like the example that #glennsl provides is a little bit outdated, and uses the Comparable.Make module instead of the new and more versatile Base.Comparator.Make.
Also, sometimes the compiler will not be able to see the equalities between comparators when types are abstracted, in that case, you will need to provide sharing constraints in your mli file. You can take the Bitvec_order library as an example. It showcases, how comparators could be used to define various orders of the same data structure and how sharing constraints could be used. The library documentation also explains various terminology and gives a history of the terminology.
And finally, if you're wondering how to enable the deriving preprocessors, then
for dune, add (preprocess (pps ppx_jane)) stanza to your library/executable spec
for ocamlbuild add -pkg ppx_jane option;
for topelevel (e.g., ocaml or utop) use #require "ppx_jane";; (if require is not available, then do #use "topfind;;", and then repeat).
There are examples in the documentation for Map showing exactly this.
If you use their PPXs you can just do:
module IntPair = struct
module T = struct
type t = int * int [##deriving sexp_of, compare]
end
include T
include Comparable.Make(T)
end
otherwise the full implementation is:
module IntPair = struct
module T = struct
type t = int * int
let compare x y = Tuple2.compare Int.compare Int.compare
let sexp_of_t = Tuple2.sexp_of_t Int.sexp_of_t Int.sexp_of_t
end
include T
include Comparable.Make(T)
end
Then you can create an empty set using this module:
let int_pair_set = Set.empty (module IntPair)
I need to use perl6 type variables. It seems that the definitive manual is here http://www.jnthn.net/papers/2008-yapc-eu-perl6types.pdf, which is concise and v. useful in so far as it goes.
Is there anything more comprehensive or authoritative that I can be pointed to?
What you're referring to is called "type capture" in perl6, here's two pages about them:
Type Captures in function/method signatures: https://docs.perl6.org/type/Signature#index-entry-Type_Capture_%28signature%29
Type Captures in Roles: https://docs.perl6.org/language/typesystem#index-entry-Type_Capture_%28role%29
Hope that helps!
The way I like to think of it is that Int is really short for ::Int.
So most of the time that you are talking about a type, you can add the :: to the front of it.
Indeed if you have a string and you want to use it to get the type with the same short name you use ::(…)
my $type-name = 'Int';
say 42 ~~ ::($type-name); # True
The thing is that using a type in a signature is already used to indicate that the parameter is of that type.
-> Int $_ {…}
Any unsigiled identifier in a signature is seen as the above, so the following throws an error if there isn't a foo type.
-> foo {…}
What you probably want in the situation above is for foo to be a sigiless variable. So you have to add a \ to the front. (Inside of the block you just use foo.)
-> \foo {…}
So if you wanted to add a feature where you capture the type, you have to do something different than just use an identifier. So obviously adding :: to the front was chosen.
-> ::foo { say foo }
If you call it with the number 42, it will print (Int).
You can combine these
-> Real ::Type \Value {…}
The above only accepts a real number (all numerics except Complex), aliases the type to Type, and aliases the number to Value
sub example ( Real ::Type \Value ) {
my Type $var = Value;
say Type;
say Value;
}
> example 42;
(Int)
42
> example ''
Type check failed in binding to parameter 'Value'; expected Real but got Str ("")
in block <unit> at <unknown file> line 1
> example 42e0
(Num)
42
This is also used in roles.
role Foo[ Real ::Type \Value ] {
has Type $.foo = Value; # constrained to the same type as Value
}
class Example does Foo[42] {}
say Example.new( :foo(128) ).foo; # 128
say Example.new().foo; # 42
say Example.new( :foo(1e0) ); # Type check error
You can of course leave off any part that you don't need.
role Foo[::Type] {…}
I'm curious to understand why this error happens and which is the best way to get around it.
I have a couple of files types.ml and types.mli which define a variant type value that can be of many different builtin OCaml types (float, int, list, map, set, etc..).
Since I have to use the std-lib over this variant type I needed to concretize the Set module through the functor to be able to use sets of value type by defining the ValueSet module.
The final .ml file is something like:
module rec I :
sig
type value =
Nil
| Int of int
| Float of float
| Complex of Complex.t
| String of string
| List of (value list) ref
| Array of value array
| Map of (value, value) Hashtbl.t
| Set of ValueSet.t ref
| Stack of value Stack.t
...
type t = value
val compare : t -> t -> int
end
= struct
(* same variant type *)
and string_value v =
match v with
(* other cases *)
| Set l -> sprintf "{%s} : set" (ValueSet.fold (fun i v -> v^(string_value i)^" ") !l "")
end
and OrderedValue :
sig
type t = I.value
val compare : t -> t -> int
end
= struct
type t = I.value
let compare = Pervasives.compare
end
and ValueSet : Set.S with type elt = I.value = Set.Make(I)
As you can see I had to define the ValueSet module from the functor to be able to use that datatype. The problem occurs when I want to use that module inside the declaration of I. So that I obtain the following error:
Error: Cannot safely evaluate the definition of the recursively-defined module I
Why does this happen? Which is a good way to solve it? And just to know, is my approach to what I'm trying to do correct? Apart from that it works as intended (I'm able to use the ValueSet type with my operations in other modules, but I have to comment the involved line in types.ml to pass compilation phase).
I tried to remove all the superfluous code and reduce the code to essential needed to investigate this error.. if it's not enought just ask :)
EDIT: according to OCaml reference we have that
Currently, the compiler requires that all dependency cycles between the recursively-defined module identifiers go through at least one “safe” module. A module is “safe” if all value definitions that it contains have function types typexpr1 -> typexpr2.
This is everything I found so far, but I don't get the exact meaning..
Thank in advance
After fixing the obvious errors, your example does compile (with OCaml 3.10, but I think this hasn't changed since recursive modules were introduced in 3.07). Hopefully my explanations below will help you find what, amongst the definitions you left out, caused your code to be rejected.
Here is some example code that is accepted:
module rec Value : sig
type t =
Nil
| Set of ValueSet.t
val compare : t -> t -> int
val nil : t
(*val f_empty : unit -> t*)
end
= struct
type t =
Nil
| Set of ValueSet.t
let compare = Pervasives.compare
let nil = Nil
(*let f_empty () = Set ValueSet.empty*)
end
and ValueSet : Set.S with type elt = Value.t = Set.Make(Value)
At the expression level, the module Value has no dependency on ValueSet. Therefore the compiler generates the code to initialize Value before the code to initialize Value, and all goes well.
Now try commenting out the definition of f_empty.
File "simple.ml", line 11, characters 2-200:
Cannot safely evaluate the definition of the recursively-defined module Value
Now Value does depend on ValueSet, and ValueSet always depends on Value because of the compare function. So they are mutually recursive, and the “safe module” condition must apply.
Currently, the compiler requires that all dependency cycles between the
recursively-defined module identifiers go through at least one "safe" module. A
module is "safe" if all value definitions that it contains have function types
typexpr_1 -> typexpr_2.
Here, ValueSet isn't safe because of ValueSet.empty, and Value isn't safe because of nil.
The reason to the “safe module” condition is the chosen implementation technique for recursive module:
Evaluation of a recursive module definition proceeds
by building initial values for the safe modules involved, binding all
(functional) values to fun _ -> raise Undefined_recursive_module. The defining
module expressions are then evaluated, and the initial values for the safe
modules are replaced by the values thus computed.
If you comment out the declaration of nil in the signature of Value, you can leave the definition and declaration of f_empty. That's because Value is now a safe module: it contains only functions. It's ok to leave the definition of nil in the implementation: the implementation of Value is not a safe module, but Value itself (which is its implementation coerced to a signature) is safe.
I'm really not sure what kind of syntax you're using in the signature that allows let ... I'm going to assume it was a mistake while reducing the code for us. You also don't need that OrderedType definition, possibly another fiddling error for us, since you don't use it in parameterisation of the Set module.
Aside from that, I have no problem running the following in the toplevel. Since this works pretty directly, I am unsure how you're getting that error.
module rec Value :
sig
type t =
| Nil
| Int of int
| Float of float
| String of string
| Set of ValueSet.t
val compare : t -> t -> int
val to_string : t -> string
end = struct
type t =
| Nil
| Int of int
| Float of float
| String of string
| Set of ValueSet.t
let compare = Pervasives.compare
let rec to_string = function
| Nil -> ""
| Int x -> string_of_int x
| Float x -> string_of_float x
| String x -> x
| Set l ->
Printf.sprintf "{%s} : set"
(ValueSet.fold (fun i v -> v^(to_string i)^" ") l "")
end
and ValueSet : Set.S with type elt = Value.t = Set.Make (Value)