Single-element parethesized expressions/tuples vs common use of parentheses - swift

Sorry if this is trivial - I am so new to swift, actually I have only looked at the language guide+reference for a few minutes.
As far as I understand a parenthesized expression like (2,3) is used to construct a tuple, and (2) is a single-element tuple of type (Int).
But then what happens with common use of parentheses like (2+4) in expression (2+4)*5? Is this still a tuple of type (Int) multiplied by an Int?

From Types in the Swift book:
If there is only one element inside the parentheses, the type is
simply the type of that element. For example, the type of (Int) is
Int, not (Int).
So the type of (2) or (2+4) is simply Int, and the * in (2+4)*5 is
just integer multiplication.

+, * etc are infix operators, and they have a semantic meaning that's different from the comma ,, so the compiler treats it in a different way.

Related

Spark Scala Why is it that I can make certain function calls with parenthesis and certain function calls without parenthesis [duplicate]

What are the precise rules for when you can omit (omit) parentheses, dots, braces, = (functions), etc.?
For example,
(service.findAllPresentations.get.first.votes.size) must be equalTo(2).
service is my object
def findAllPresentations: Option[List[Presentation]]
votes returns List[Vote]
must and be are both functions of specs
Why can't I go:
(service findAllPresentations get first votes size) must be equalTo(2)
?
The compiler error is:
"RestServicesSpecTest.this.service.findAllPresentations
of type
Option[List[com.sharca.Presentation]]
does not take parameters"
Why does it think I'm trying to pass in a parameter? Why must I use dots for every method call?
Why must (service.findAllPresentations get first votes size) be equalTo(2) result in:
"not found: value first"
Yet, the "must be equalTo 2" of
(service.findAllPresentations.get.first.votes.size) must be equalTo 2, that is, method chaining works fine? - object chain chain chain param.
I've looked through the Scala book and website and can't really find a comprehensive explanation.
Is it in fact, as Rob H explains in Stack Overflow question Which characters can I omit in Scala?, that the only valid use-case for omitting the '.' is for "operand operator operand" style operations, and not for method chaining?
You seem to have stumbled upon the answer. Anyway, I'll try to make it clear.
You can omit dot when using the prefix, infix and postfix notations -- the so called operator notation. While using the operator notation, and only then, you can omit the parenthesis if there is less than two parameters passed to the method.
Now, the operator notation is a notation for method-call, which means it can't be used in the absence of the object which is being called.
I'll briefly detail the notations.
Prefix:
Only ~, !, + and - can be used in prefix notation. This is the notation you are using when you write !flag or val liability = -debt.
Infix:
That's the notation where the method appears between an object and it's parameters. The arithmetic operators all fit here.
Postfix (also suffix):
That notation is used when the method follows an object and receives no parameters. For example, you can write list tail, and that's postfix notation.
You can chain infix notation calls without problem, as long as no method is curried. For example, I like to use the following style:
(list
filter (...)
map (...)
mkString ", "
)
That's the same thing as:
list filter (...) map (...) mkString ", "
Now, why am I using parenthesis here, if filter and map take a single parameter? It's because I'm passing anonymous functions to them. I can't mix anonymous functions definitions with infix style because I need a boundary for the end of my anonymous function. Also, the parameter definition of the anonymous function might be interpreted as the last parameter to the infix method.
You can use infix with multiple parameters:
string substring (start, end) map (_ toInt) mkString ("<", ", ", ">")
Curried functions are hard to use with infix notation. The folding functions are a clear example of that:
(0 /: list) ((cnt, string) => cnt + string.size)
(list foldLeft 0) ((cnt, string) => cnt + string.size)
You need to use parenthesis outside the infix call. I'm not sure the exact rules at play here.
Now, let's talk about postfix. Postfix can be hard to use, because it can never be used anywhere except the end of an expression. For example, you can't do the following:
list tail map (...)
Because tail does not appear at the end of the expression. You can't do this either:
list tail length
You could use infix notation by using parenthesis to mark end of expressions:
(list tail) map (...)
(list tail) length
Note that postfix notation is discouraged because it may be unsafe.
I hope this has cleared all the doubts. If not, just drop a comment and I'll see what I can do to improve it.
Class definitions:
val or var can be omitted from class parameters which will make the parameter private.
Adding var or val will cause it to be public (that is, method accessors and mutators are generated).
{} can be omitted if the class has no body, that is,
class EmptyClass
Class instantiation:
Generic parameters can be omitted if they can be inferred by the compiler. However note, if your types don't match, then the type parameter is always infered so that it matches. So without specifying the type, you may not get what you expect - that is, given
class D[T](val x:T, val y:T);
This will give you a type error (Int found, expected String)
var zz = new D[String]("Hi1", 1) // type error
Whereas this works fine:
var z = new D("Hi1", 1)
== D{def x: Any; def y: Any}
Because the type parameter, T, is inferred as the least common supertype of the two - Any.
Function definitions:
= can be dropped if the function returns Unit (nothing).
{} for the function body can be dropped if the function is a single statement, but only if the statement returns a value (you need the = sign), that is,
def returnAString = "Hi!"
but this doesn't work:
def returnAString "Hi!" // Compile error - '=' expected but string literal found."
The return type of the function can be omitted if it can be inferred (a recursive method must have its return type specified).
() can be dropped if the function doesn't take any arguments, that is,
def endOfString {
return "myDog".substring(2,1)
}
which by convention is reserved for methods which have no side effects - more on that later.
() isn't actually dropped per se when defining a pass by name paramenter, but it is actually a quite semantically different notation, that is,
def myOp(passByNameString: => String)
Says myOp takes a pass-by-name parameter, which results in a String (that is, it can be a code block which returns a string) as opposed to function parameters,
def myOp(functionParam: () => String)
which says myOp takes a function which has zero parameters and returns a String.
(Mind you, pass-by-name parameters get compiled into functions; it just makes the syntax nicer.)
() can be dropped in the function parameter definition if the function only takes one argument, for example:
def myOp2(passByNameString:(Int) => String) { .. } // - You can drop the ()
def myOp2(passByNameString:Int => String) { .. }
But if it takes more than one argument, you must include the ():
def myOp2(passByNameString:(Int, String) => String) { .. }
Statements:
. can be dropped to use operator notation, which can only be used for infix operators (operators of methods that take arguments). See Daniel's answer for more information.
. can also be dropped for postfix functions
list tail
() can be dropped for postfix operators
list.tail
() cannot be used with methods defined as:
def aMethod = "hi!" // Missing () on method definition
aMethod // Works
aMethod() // Compile error when calling method
Because this notation is reserved by convention for methods that have no side effects, like List#tail (that is, the invocation of a function with no side effects means that the function has no observable effect, except for its return value).
() can be dropped for operator notation when passing in a single argument
() may be required to use postfix operators which aren't at the end of a statement
() may be required to designate nested statements, ends of anonymous functions or for operators which take more than one parameter
When calling a function which takes a function, you cannot omit the () from the inner function definition, for example:
def myOp3(paramFunc0:() => String) {
println(paramFunc0)
}
myOp3(() => "myop3") // Works
myOp3(=> "myop3") // Doesn't work
When calling a function that takes a by-name parameter, you cannot specify the argument as a parameter-less anonymous function. For example, given:
def myOp2(passByNameString:Int => String) {
println(passByNameString)
}
You must call it as:
myOp("myop3")
or
myOp({
val source = sourceProvider.source
val p = myObject.findNameFromSource(source)
p
})
but not:
myOp(() => "myop3") // Doesn't work
IMO, overuse of dropping return types can be harmful for code to be re-used. Just look at specification for a good example of reduced readability due to lack of explicit information in the code. The number of levels of indirection to actually figure out what the type of a variable is can be nuts. Hopefully better tools can avert this problem and keep our code concise.
(OK, in the quest to compile a more complete, concise answer (if I've missed anything, or gotten something wrong/inaccurate please comment), I have added to the beginning of the answer. Please note this isn't a language specification, so I'm not trying to make it exactly academically correct - just more like a reference card.)
A collection of quotes giving insight into the various conditions...
Personally, I thought there'd be more in the specification. I'm sure there must be, I'm just not searching for the right words...
There are a couple of sources however, and I've collected them together, but nothing really complete / comprehensive / understandable / that explains the above problems to me...:
"If a method body has more than one
expression, you must surround it with
curly braces {…}. You can omit the
braces if the method body has just one
expression."
From chapter 2, "Type Less, Do More", of Programming Scala:
"The body of the upper method comes
after the equals sign ‘=’. Why an
equals sign? Why not just curly braces
{…}, like in Java? Because semicolons,
function return types, method
arguments lists, and even the curly
braces are sometimes omitted, using an
equals sign prevents several possible
parsing ambiguities. Using an equals
sign also reminds us that even
functions are values in Scala, which
is consistent with Scala’s support of
functional programming, described in
more detail in Chapter 8, Functional
Programming in Scala."
From chapter 1, "Zero to Sixty: Introducing Scala", of Programming Scala:
"A function with no parameters can be
declared without parentheses, in which
case it must be called with no
parentheses. This provides support for
the Uniform Access Principle, such
that the caller does not know if the
symbol is a variable or a function
with no parameters.
The function body is preceded by "="
if it returns a value (i.e. the return
type is something other than Unit),
but the return type and the "=" can be
omitted when the type is Unit (i.e. it
looks like a procedure as opposed to a
function).
Braces around the body are not
required (if the body is a single
expression); more precisely, the body
of a function is just an expression,
and any expression with multiple parts
must be enclosed in braces (an
expression with one part may
optionally be enclosed in braces)."
"Functions with zero or one argument
can be called without the dot and
parentheses. But any expression can
have parentheses around it, so you can
omit the dot and still use
parentheses.
And since you can use braces anywhere
you can use parentheses, you can omit
the dot and put in braces, which can
contain multiple statements.
Functions with no arguments can be
called without the parentheses. For
example, the length() function on
String can be invoked as "abc".length
rather than "abc".length(). If the
function is a Scala function defined
without parentheses, then the function
must be called without parentheses.
By convention, functions with no
arguments that have side effects, such
as println, are called with
parentheses; those without side
effects are called without
parentheses."
From blog post Scala Syntax Primer:
"A procedure definition is a function
definition where the result type and
the equals sign are omitted; its
defining expression must be a block.
E.g., def f (ps) {stats} is
equivalent to def f (ps): Unit =
{stats}.
Example 4.6.3 Here is a declaration
and a de?nition of a procedure named
write:
trait Writer {
def write(str: String)
}
object Terminal extends Writer {
def write(str: String) { System.out.println(str) }
}
The code above is implicitly completed
to the following code:
trait Writer {
def write(str: String): Unit
}
object Terminal extends Writer {
def write(str: String): Unit = { System.out.println(str) }
}"
From the language specification:
"With methods which only take a single
parameter, Scala allows the developer
to replace the . with a space and omit
the parentheses, enabling the operator
syntax shown in our insertion operator
example. This syntax is used in other
places in the Scala API, such as
constructing Range instances:
val firstTen:Range = 0 to 9
Here again, to(Int) is a vanilla
method declared inside a class
(there’s actually some more implicit
type conversions here, but you get the
drift)."
From Scala for Java Refugees Part 6: Getting Over Java:
"Now, when you try "m 0", Scala
discards it being a unary operator, on
the grounds of not being a valid one
(~, !, - and +). It finds that "m" is
a valid object -- it is a function,
not a method, and all functions are
objects.
As "0" is not a valid Scala
identifier, it cannot be neither an
infix nor a postfix operator.
Therefore, Scala complains that it
expected ";" -- which would separate
two (almost) valid expressions: "m"
and "0". If you inserted it, then it
would complain that m requires either
an argument, or, failing that, a "_"
to turn it into a partially applied
function."
"I believe the operator syntax style
works only when you've got an explicit
object on the left-hand side. The
syntax is intended to let you express
"operand operator operand" style
operations in a natural way."
Which characters can I omit in Scala?
But what also confuses me is this quote:
"There needs to be an object to
receive a method call. For instance,
you cannot do “println “Hello World!”"
as the println needs an object
recipient. You can do “Console
println “Hello World!”" which
satisfies the need."
Because as far as I can see, there is an object to receive the call...
I find it easier to follow this rule of thumb: in expressions spaces alternate between methods and parameters. In your example, (service.findAllPresentations.get.first.votes.size) must be equalTo(2) parses as (service.findAllPresentations.get.first.votes.size).must(be)(equalTo(2)). Note that the parentheses around the 2 have a higher associativity than the spaces. Dots also have higher associativity, so (service.findAllPresentations.get.first.votes.size) must be.equalTo(2)would parse as (service.findAllPresentations.get.first.votes.size).must(be.equalTo(2)).
service findAllPresentations get first votes size must be equalTo 2 parses as service.findAllPresentations(get).first(votes).size(must).be(equalTo).2.
Actually, on second reading, maybe this is the key:
With methods which only take a single
parameter, Scala allows the developer
to replace the . with a space and omit
the parentheses
As mentioned on the blog post: http://www.codecommit.com/blog/scala/scala-for-java-refugees-part-6 .
So perhaps this is actually a very strict "syntax sugar" which only works where you are effectively calling a method, on an object, which takes one parameter. e.g.
1 + 2
1.+(2)
And nothing else.
This would explain my examples in the question.
But as I said, if someone could point out to be exactly where in the language spec this is specified, would be great appreciated.
Ok, some nice fellow (paulp_ from #scala) has pointed out where in the language spec this information is:
6.12.3:
Precedence and associativity of
operators determine the grouping of
parts of an expression as follows.
If there are several infix operations in an expression, then
operators with higher precedence bind
more closely than operators with lower
precedence.
If there are consecutive infix operations e0 op1 e1 op2 . . .opn en
with operators op1, . . . , opn of the
same precedence, then all these
operators must have the same
associativity. If all operators are
left-associative, the sequence is
interpreted as (. . . (e0 op1 e1) op2
. . .) opn en. Otherwise, if all
operators are rightassociative, the
sequence is interpreted as e0 op1 (e1
op2 (. . .opn en) . . .).
Postfix operators always have lower precedence than infix operators. E.g.
e1 op1 e2 op2 is always equivalent to
(e1 op1 e2) op2.
The right-hand operand of a
left-associative operator may consist
of several arguments enclosed in
parentheses, e.g. e op (e1, . . .
,en). This expression is then
interpreted as e.op(e1, . . . ,en).
A left-associative binary operation e1
op e2 is interpreted as e1.op(e2). If
op is rightassociative, the same
operation is interpreted as { val
x=e1; e2.op(x ) }, where x is a fresh
name.
Hmm - to me it doesn't mesh with what I'm seeing or I just don't understand it ;)
There aren't any. You will likely receive advice around whether or not the function has side-effects. This is bogus. The correction is to not use side-effects to the reasonable extent permitted by Scala. To the extent that it cannot, then all bets are off. All bets. Using parentheses is an element of the set "all" and is superfluous. It does not provide any value once all bets are off.
This advice is essentially an attempt at an effect system that fails (not to be confused with: is less useful than other effect systems).
Try not to side-effect. After that, accept that all bets are off. Hiding behind a de facto syntactic notation for an effect system can and does, only cause harm.

Can type constructors be considered as types in functional programming languages?

I am approaching the Haskell programming language, and I have a background of Scala and Java developer.
I was reading the theory behind type constructors, but I cannot understand if they can be considered types. I mean, in Scala, you use the keywords class or trait to define type constructors. Think about List[T], or Option[T]. Also in Haskell, you use the same keyword data, that is used for defining new types.
So, are type constructors also types?
Let's look at an analogy: functions. In some branches of mathematics, functions are called value constructors, because that's what they do: you put one or more values in, and they construct a new value out of those.
Type constructors are exactly the same thing, except on the type level: you put one or more types in, and they construct a new type out of those. They are, in some sense, functions on the type level.
Now, to our analogy: what is the analog of the question you are asking? Well, it is this: "Can value constructors (i.e. functions) be considered as values in functional programming languages?"
And the answer is: it depends on the programming language. Now, for functional programming languages, the answer is "Yes" for almost all (if not all) of them. It depends on your definition of what a "functional programming language" is. Some people define a functional programming language as a programming language which has functions as values, so the answer will be trivially "Yes" by definition. But, some people define a functional programming language as a programming language which does not allow side-effects, and in such a language, it is not necessarily true that functions are values.
The most famous example may be John Backus' FP, from his seminal paper Can Programming Be Liberated from the von Neumann Style? – a functional style and its algebra of programs. In FP, there is a hierarchy of "function-like" things. Functions can only deal with values, and functions themselves are not values. However, there is a concept of "functionals" which are "function constructors", i.e. they can take functions (and also values) as input and/or produce functions as output, but they cannot take functionals as input and/or produce them as output.
So, FP is arguably a functional programming language, but it does not have functions as values.
Note: functions as values is also called "first-class functions" and functions that take functions as input or return them as output are called "higher-order functions".
If we look at some types:
1 :: Int
[1] :: List Int
add :: Int → Int
map :: (a → b, List a) → b
You can see that we can easily say: any value whose type has an arrow in it, is a function. Any value whose type has more than one arrow in it, is a higher-order function.
Again, the same applies to type constructors, since they are really the same thing except on the type level. In some languages, type constructors can be types, in some they can't. For example, in Java and C♯, type constructors are not types. You cannot have a List<List> in C♯, for example. You can write down the type List<List> in Java, but that is misleading, since the two Lists mean different things: the first List is the type constructor, the second List is the raw type, so this is in fact not using a type constructor as a type.
What is the equivalent to our types example above?
Int :: Type
List :: Type ⇒ Type
→ :: (Type, Type) ⇒ Type
Functor :: (Type ⇒ Type) ⇒ Type
(Note, how we always have Type? Indeed, we are only dealing with types, so we normally don't write Type but instead simply write *, pronounced "Type"):
Int :: *
List :: * ⇒ *
→ :: (*, *) ⇒ *
Functor :: (* ⇒ *) ⇒ *
So, Int is a proper type, List is a type constructor that takes one type and produces a type, → (the function type constructor) takes two types and returns a type (assuming only unary functions, e.g. using currying or passing tuples), and Functor is a type constructor, which itself takes a type constructor and returns a type.
Theses "type-types" are called kinds. Like with functions, anything with an arrow is a type constructor, and anything with more than one arrow is a higher-kinded type constructor.
And like with functions, some languages allow higher-kinded type constructors and some don't. The two languages you mention in your question, Scala and Haskell do, but as mentioned above, Java and C♯ don't.
However, there is a complication when we look at your question:
So, are type constructors also types?
Not really, no. At least not in any language I know about. See, while you can have higher-kinded type constructors that take type constructors as input and/or return them as output, you cannot have an expression or a value or a variable or a parameter which has a type constructor as its type. You cannot have a function that takes a List or returns a List. You cannot have a variable of type Monad. But, you can have a variable of type Int.
So, clearly, there is a difference between types and type constructors.
Well, types and type constructors have a calculus of their own and they each have kinds. If you use :k (Maybe Int) in ghci for example, you'll get *, now this is a proper type and it (usually) has inhabitants. In this case Nothing, Just 42, etc. * now has a more descriptive alias Type.
Now you can look at the kind of the constructor that is Maybe, and :k Maybe will give you * -> *. With the alias, this is Type -> Type which is what you expect. It takes a Type and constructs a Type. Now if you see types as set of values, one good question is what set of values do Maybe has? Well, none because it is not really a type. You might attempt something like Just but that has type a -> Maybe a with kind Type, rather than Maybe with kind Type -> Type.
At least in Haskell, there is a hierarchy that can roughly be described as follows.
Terms are things that exist at run-time, values like 1, 'a', and (+), for example.
Each term has a type, like Int or Char or Int -> Int -> Int.
Each type has a kind, and all types have the same kind, namely *.
A type constructor like [], though, has kind * -> *, so it is not a type. Instead, it is a mapping from a type to a type.
There are other kinds as well, including (in addition to * and * -> *, with an example of each):
* -> * -> * (Either)
(* -> *) -> * -> * (ReaderT, a monad transformer)
Constraint (Num Int)
* -> Constraint (Num; this is the kind of a type class)

Scala implicit type casting

I'm just beginning Scala, coming from Java.
So I know that in Scala, all things are objects, and Scala matches the longest token (source: http://www.scala-lang.org/docu/files/ScalaTutorial.pdf), so if i understand correctly:
var b = 1.+(2)
then b is a Double, plus and Int, which in Java would be a Double.
But when I check its type via println(b.isInstanceOf[Int]) I see that it is an Int. Why is it not a Double like in Java?
According to the specification:
1. is not a valid floating point literal because the mandatory digit after the . is missing.
I believe it's done like that, exactly because expressions like 1.+(2) should be parsed as an integer 1, method call ., method name + and method argument (2).
The compiler would treat 1 and 2 as Ints by default. You could force either one of these to be a Double using 1.toDouble And the result (b) would be a double.
Btw - did you mean to write 1.0+2 - in which case b would be a double?

What is type of 123_456_789?

I see in Swift examples values like 123_456_789, numbers with underscores. What type do these values have by default?
Does it depend on the type of the variable I assign them to? They look quite funny and new to me, so I wonder, how are they treated if they are thrown just like they are, without defining a type?
From the documentation
(The Swift Programming Language -> Language Guide -> The Basics
-> Numeric Literals):
Numeric literals can contain extra formatting to make them easier to
read. Both integers and floats can be padded with extra zeros and can
contain underscores to help with readability. Neither type of
formatting affects the underlying value of the literal:
let paddedDouble = 000123.456
let oneMillion = 1_000_000
let justOverOneMillion = 1_000_000.000_000_1
So your 123_456_789 is a integer literal, and identical to 123456789.
You can insert the underscores wherever you want, not only as a
"thousands separator", such as 1_2_3_4_5_6_7_8_9 or 1_23_4567_89, if you like to write obfuscated code.
123_456_789 is an "integer literal" just like 123456789. "integer literal" is a type separate from Int or Int32 or Int8 or whatever. An "integer literal" can be assigned to any integer type (unlike for example an Int value which can only be assigned to an Int).
If you ask "can I treat them as integers", that doesn't make sense. It's a different type. For every type there are rules how it can be used. The rules for Int and "integer literal" are different.

What is a "kind" in the context of Type Systems?

I have already read the Wikipedia article and searched for obvious places but I'm stuck. Can someone simple tell me what exactly is a Kind ? What is it used for ?
Scala examples are most appreciated
In short: a kind is to types what a type is to values.
What is a value? 1, 2, 3 are values. So are "Hello" and "World", true and false, and so forth.
Values belong to types. Types describe a set of values. 1, 2 and 3 belong to the type Nat, "Hello" and "World" to the type Text, true and false to the type Boolean.
Functions take one or more values as arguments and produce one or more values as results. In order to meaningfully do something with the arguments, the function needs to make some assumptions about them, this is done by constraining their types. So, function parameters and return values typically also have types.
Now, a function also has a type, which is described by the types of its inputs and outputs. For example, the abs function which computes the absolute value of a number has the type
Number -> NonNegativeNumber
The function add which adds two numbers has the type
(Number, Number) -> Number
The function divmod has the type
(Number, Number) -> (Number, Number)
Okay, but if functions take values as arguments and produce values as results, and functions are values, then functions can also take functions as arguments and return functions as results, right? What's the type of such a function?
Let's say we have a function findCrossing which finds the point where some other function (of numbers) crosses the y-axis. It takes as an argument the function and produces as a result a number:
(Number -> Number) -> Number
Or a function makeAdder which produces a function which takes a number and adds a specific number to it:
Number -> (Number -> Number)
And a function which computes the derivative of another function:
(Number -> Number) -> (Number -> Number)
Let's look at the level of abstraction here: a value is something very concrete. It only means one thing. If we were to order our levels of abstraction here, we could say that a value has the order 0.
A function, OTOH is more abstract: a single function can produce many different values. So, it has order 1.
A function which returns or accepts a function is even more abstract: it can produce many different functions which can produce many different values. It has order 2.
Generally, we call everything with an order > 1 "higher order".
Okay, but what about kinds? Well, we said above that 1, 2, "Hello", false etc. have types. But what is the type of Number? Or Text? Or Boolean?
Well, its type is Type, of course! This "type of a type" is called a kind.
And just like we can have functions which construct values out of values, we can have functions which construct types out of types. These functions are called type constructors.
And just like functions have types, type constructors have kinds. For example, the List type constructor, which takes an element type and produces a list type for that element has kind
Type -> Type
The Map type constructor, which takes a key type and a value type and produces a map type has kind
(Type, Type) -> Type
Now, continuing the analogy, if we can have functions which take functions as arguments, can we also have type constructors which take type constructors as arguments? Of course!
An example is the Functor type constructor. It takes a type constructor and produces a type:
(Type -> Type) -> Type
Notice how we always write Type here? Above, we had many different types like Number, Text, Boolean etc. Here, we always have only kind of type, namely Type. That gets tedious to (warning, bad pun ahead) type, so instead of writing Type everywhere, we just write *. I.e. Functor has the kind
(* -> *) -> *
and Number has the kind
*
Continuing the analogy, Number, Text and all others of kind * have order 0, List and all others of kind * -> * or more generally (*, …) -> (*, …) have order 1, Functor and all of kind (* -> *) -> * or * -> (* -> *) (and so forth) have order 2. Except in this case we sometimes also call it rank instead of order.
Everything above order/rank 1 is called higher-order, higher-rank or higher-kinded.
I hope the analogy is clear now: types describe sets of values; kinds describe sets of types.
Aside: I completely ignored currying. Basically, currying means that you can transform any function which takes two values into a function which takes one value and returns a function which takes the other value, similarly for three, four, five, … arguments. This means that you only ever need to deal with functions with exactly one parameter, which makes languages much simpler.
However, this also means that technically speaking, add is a higher-order function (because it returns a function) which is muddying the definitions.
The most eloquent explanation for kinds/higher-kinds I've seen so far and also in the context of Scala is Daniel Spiewak's High Wizardry in the Land of Scala. There are many versions, he gave this talk a few times, here I've chosen the longest one, but you can quickly google and find others.
The most important message from this talk is exactly the answer given by #Jörg W Mittag:
"kind is to types what a type is to values"
Another place for a more theoretical view on the subject is the paper Generics of a Higher Kind, also in the context of Scala.